JointsForTekla Ver January

Transcription

1 Ing. Giovanni Conticello Ing. Sebastiano Floridia With the important help of Ing. Giovanni Trigili JointsForTekla Ver January Design of joints of steel structures in environment TeklaStructures 19.0 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 1 of 354

2 JointsForTekla 1 INTRODUCTION 1.1 All you necessarily need know before starting - The software JointForTekla designs the following kind of joints: 141, 142, 143, 144, 42, 77, 14,11, 124, 128, 40, 1014, 1052; - TeklaStructures has got infinity potentialities of joints modeling so it s impossible that a controller can consider every estimated possibility. - JointForTekla has been positively tested about structures with real joints but it hasn t got tested about joints torn off by real design. 2 DIRECTIONS 2.1 Characteristics of the Software JointForTekla (JFT) is a software to design steel structures with steel joints in according with Eurocode 3 in environment TeklaStructures This software is closely linked with TeklaStructures. Without it the software cannot work and it works using every tridimensional modeling potentiality, get up every information about joints by Teklastructures and can use them for joint numerical code selected in according with EC3 and following report results. Among the most important JointForTekla potentialities we note: Immediate data input, by TeklaStructures data ; Possibility to get up by data file exterior the values of infinity loading combinations; Possibility to get up the data by structural MidasGen model; 2.2 Minimum qualification hardware and software Any for working with TeklaStructures; Framework 4.0 The Windows Panel control with International format, must be plan out so that the system know it: the point like decimal separator; the colon like thousands separator. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 2 of 354

3 2.3 Conventions The units are: for length the centimetre; for loadings: the KiloNewton (KN), corresponding to kg for forces; for loadings: the KiloNewton (KN*m), for static moment; for model get up from MidasGen the units will be N and mm; 2.4 Activation License At first start the window of dialog management license will appear. The software in demo version will work all through 30 days in whole formalities. Every customer will have an ID license and a password. To active the license there are 3 modalities: 1) Activation on line, without calling the assistance (faster and recommended); 2) By it is necessary have two codes for releasing the brake ; 3) By another pc, if your pc isn t collected in internet. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 3 of 354

4 2.5 Off License When you want to install your license in another pc, you can use the command removing license. So you can active your license in another pc and viceversa, whenever you want. 2.6 Start up Application The application must be started following the TeklaStructures start up. When TeklaStructures is working you can start up this software. 2.7 Software s Language This software uses TeklaStructures language. The languages are: Italian, English, French, German, Spanish, for the remaining languages the software graphic interface is in English and the reports will be in English and Italian language. 2.8 Software s interface graphic The software has been done using the new object oriented programming style in according with Microsoft NET Framework 4.0. It has got a toolbar that you can always see, you can put it when you want in your work area. The same toolbar commands are in the menu situated in tray icon notification. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 4 of 354

5 View Toolbar always in the foreground Command in tray bar The controls are: - Union selection: This command allowed to active the procedure of selection of every single joint (green little cone). After the selection the procedure of joint checking will start; - Open dialogue: this command allowed to get up the software s window without to select every single joint. It is in useful to have the list of connections, choose them for kinds and go on to multiple selection of selected joints; - Stress drop down menu: by it you can select the source where you can take the stress for joint design. You can choose by 4 options: o Stress by Tekla: for design the single joint it use the values that are in the window properties of TeklaStructures connection; o Stress by datasheet: for design the single joint it use the values entered in the data grid, the individual fields manually entering or by setting up an external excel file from which to copy 6 columns x n rows; o For restored resistance: for design single joint it use plastic members value that formed the joint; o Stress by Midas: for design single joint it use the value coming from modeling with MidasGen software (for detailed list see following paragraph); - Taking data by MidasGen: this command allowed to select data file coming from MidasGen, containing all stresses of whole model (for detailed list see following paragraph); U s e r M a n u a l V e r s i o n J a n u a r y P a g e 5 of 354

6 - Manual: From this command you can enter in Pdf manual; - Information from this window it is possible to enter in the software general information U s e r M a n u a l V e r s i o n J a n u a r y P a g e 6 of 354

7 - General planning out: From this window it is possible to enter in the software s general planning out: o Normative: You can choose between EC3 and DM2008 for the definition of general partial factor value M1; o Concrete type(cls): you can define the concrete with which did the foundation (it is necessary for design joints 1014 and 1052); o Concrete edge distance: the value of distance between anchor bolts and external foundation edge is in mm (it is necessary for anchor bolts design joints 1014 e 1052); o The software has got a connection at the server so you can always have the up to date software. The procedure can be done manually and outside from software, by special icon in operative system in the joint group or automatically at each software startup, if there is an active internet connection; o Radius zoom in the joint: This value allowed to adjust zoom factor in the click of joints in the model; o Zoom at treeview joint: this value allowed qualifying or not qualifying the possibility to take place the zoom over the joint in the model; o Default Value (if the materiali is unknow). In this pane are inserted the resistance values of the materials in case the material set is not present in the database of JointsForTekla; o Default Value (if the Botls are unknow). In this pane are inserted the resistance values of the bolts, in the case where the class of bolts set is not present in the database of JointsForTekla. - Esc: This command allowed exit the application. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 7 of 354

8 2.9 Stress made by Midas: Beam Force For design each joint it use the value made from modeling that we have made with MidasGen software. The procedure want that you choose the file Nomefilestruttura.mgt (created previously in Midas) and automatically it try to open the file Name filestructura.xls executed in MidasGen environment like stress export for each one single beam, but only in ends of the beams. Elem Load Part Axial (N) Shear-y (N) Shear-z (N) Torsion (N*mm) Moment-y (N*mm) Moment-z (N*mm) 10 Test I[19] Test J[20] Test I[23] Test J[17] Test I[17] Test J[19] Test I[19] sas J[21] U s e r M a n u a l V e r s i o n J a n u a r y P a g e 8 of 354

9 3 CONNECTIONS THEORY AND METHOD 3.1 Joint 141 (Supporting beam Supported beam) (Supported beam on the flange or on the web column) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 9 of 354

10 3.1.1 Angles The angles can be located on both surfaces or only one surface of the secondary profile axis They can have different thickness, but it not allowed to use different size angular The angular connection on the profiles can be either bolted that welded, like is represented in the following figure: If the connection (Joint) is both bolted and welded in the verifications we will not consider the weld, so we assume the connection only like bolted. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 10 of 354

11 3.1.2 Forces On the secondary profile we can apply the following forces: N axial force (positive if tensile) V, x V, y horizontal plane shear force vertical plane shear force The forces may be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore strength. If the stresses from Tekla Structures are zero, the forces will have minimum value according with EC3 1-8 point (13) N V N pl, y V pl where the plastic resistances are referred at the secondary profile. The joint is schematized as hinged joint, because it is generally used as end joint. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 11 of 354

12 3.1.3 Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint according with EC3 1-8, with following table 3.3 and figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 12 of 354

13 3.1.4 Design resistance of single bolt and single weld In this section we recall the common criteria for verification of single bolts and single weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 13 of 354

14 Design resistance at bolt s tension force Single bolt tension resistance is: F t, where 0.9 f ub M 2 A s A s is the tensile stressed area f ub is the last tensile bolt strength Bolt shear force resistance design For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear force design (for a single resistant section) is: F v,, v f ub M 2 A If the shear force plane is through the threated bolt portion: - for classes 4.6, 5.6 and 8.8 v for classes 4.8, 5.8 and 10.9 v 0.5 If the shear force plane is through not threaded bolt portion: v 0.6 While A is bolt area f ub is the last bolt tension Design resistance of weld Fillet weld design resistance is: F w, Where fvw. d a l f vwd. is the welding shear design resistance. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 14 of 354

15 a is throat weld height. l is cordon weld length. The welding shear resistance calculation is: f vwd. f u / 3 w M 2 where: f u is the nominal resistance breaking of weaker joint; w is the appropriate correlation factor shown in table Annotations In the verifications the sizes regarding supported beam will have the wb pedice and regarding supporting beam the pedice wc Verifications made Verifications made on the joint are the following: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 15 of 354

16 - Bolt s shear force on the supported beam F v, Fv, - Weld on the supported and supporting beam F w, Fw, - Shear and tension force bolt on the supporting beam Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In case of only shear In case of only tension In case of shear and tension - Net and gross sections profile and angular verification on supported and supporting beam due to stress tensile and shear force N N N pl, u, V V V pl, u, - Verification for profiles and angles Block Tearing on the supported and supporting beam, due to tensile and shear force N N eff V V eff - Verification bearing resistance on two directions, horizontal and vertical profiles and angular on supported an supporting beam F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 16 of 354

17 3.1.7 Shear force bolt verification (supported beam) The verification is made considering together normal stress and shear force acting on supported beam. If we consider a reference system x-y on the supported beam plan, with x coincident with beam axis,, y orthogonal to the beam axis and the origin coincident with bolt barycenter, for equilibrium to the translation and rotation relative the supporting beam axis, the loads in the barycenter of group bolts on the bracket are : Vx N Vy V T V Where, y y e e is the distance between the barycenter of the group bolts and the supporting axis beam, while T is the parasite torsion due to eccentricity. The single bolt shear actions, for single bolt shear plan are : V V V V x, y, x, y, With J b n b n v Vx ( Vx ) nv nb Vy ( Vy ) nv nb T ( T ) nv J b T ( T ) n J 2 v b y i x i 2 ( n x n y ) bolt s polar moment i bv bh total number bolts number shear resistant bolt sections n bh number bolts for line n bv number bolts for row U s e r M a n u a l V e r s i o n J a n u a r y P a g e 17 of 354

18 x i y i single bolt distance from the barycenter of the group bolts, in the verification we consider x max single bolt distance from the barycenter of the group bolts, in the verification we consider y max The resultant of the forces on single bolt for single bolt shear plan is: F 2 2 v, ( Vx, ( Vx ) Vx, ( T )) ( Vy, ( Vy ) Vy, ( T )) Must satisfy: F v, Fv, Weld verification (supported beam) Verification is done considering together orthogonal force supported beam. and shear acting on the If we consider a reference system x-y on supported beam plan, with x coincident with beam axis, y orthogonal beam axis and the origin in vertical cordon barycenter, for equilibrium to vertical translation and rotation relative to supporting beam axis, for each angle must be two horizontal welding (one superior and one inferior) and one vertical welding on supported beam. The forces on the bracket are : V V T y x N V V Where, y y e e is the distance between vertical welding barycenter and supporting beam axis, while T is the parasite torsion due to eccentricity. The horizontal and vertical actions on welds are : U s e r M a n u a l V e r s i o n J a n u a r y P a g e 18 of 354

19 V V V x, y, x, with ( V ( V ( T x y Vx ) 2 ) Vy T ) h hangles h hangles angle height Force resultant on horizontal welding is : F ( Vx, ( Vx ) Vx, ( T w, x, Force resultant on vertical welding is: F V ( V w, y, y, y ) ) Must satisfy: F w, Fw, with Fw, fvw. d a l one angle Fw, fvw. d a l 2 two angles where l is single cordon length a is throat height Shear and tension force bolt verification (supporting beam) The verification is made considering together normal stress and shear acting on supported beam. If we consider a reference system x-y on supporting beam s plan, with axis x coincident with beam s axis, axis y orthogonal to beam s axis and origin in the bolt s U s e r M a n u a l V e r s i o n J a n u a r y P a g e 19 of 354

20 barycenter that are on one angular, for vertical translation and rotation equilibrium relative to the supported beam axis, shear force solicitations in the group bolt s barycenter on single bracket are: V V T x y V V V, x, y y / 2 e / 2 If on supporting beam is only one angular the stresses on the group bolts barycenter on bracket are: V V T x y V V V, x, y y e Where e is the distance between the barycenter of group bolts of single angular and supported beam s axis, while T is the parasite torsion due to eccentricity. The force shear of single bolt for single bolt shear plan are: V V V V x, y, x, y, With J b n b n v Vx ( Vx ) nv nb Vy ( Vy ) nv nb T ( T ) nv J b T ( T ) n J 2 v b y i x i 2 ( n x n y ) bolts polar moment i bv bh bolts total number bolt number sections shear resistant n bh bolts number per horizontal row n bv bolts number per vertical row U s e r M a n u a l V e r s i o n J a n u a r y P a g e 20 of 354

21 x i y i single bolt distance from barycenter of group bolts, in verification we consider x max single bolt distance from barycenter of group bolts, in verification we consider y max The forces resultant on single bolt for single bolt shear plan is: F 2 2 v, ( Vx, ( Vx ) Vx, ( T )) ( Vy, ( Vy ) Vy, ( T )) The tension force on single bolt belonging to the group of bolts of a bracket is: F N / n t, b That must satisfy: Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In case of only shear In case of only tension In case of shear and tension Weld verification (supporting beam) The verification is made considering together axial force and shear force acting in two directions vertical and horizontal on supporting beam. If we consider a reference system x-y on supporting beam s plan, with axis x coincident with beam s axis, axis y orthogonal to beam s axis and origin in barycenter of vertical axis welding, for vertical translation and rotation equilibrium relative to the supporting beam axis, must be for each angular two horizontal welding ( one superior and one inferior) and one vertical weld on supporting beam. Stresses on single bracket are: N N z, Vx V V y V T V, x, y y / 2 / 2 / 2 e U s e r M a n u a l V e r s i o n J a n u a r y P a g e 21 of 354

22 If on the supporting beam there is only one angular the forces on the bracket are: N N z Vx V V y V T V,, x, y y e Where e is the distance between the vertical welding barycenter and supporting beam axis, while T is the parasite torsion had to eccentricity. The forces on single horizontal and vertical welding are: N V V V x, y, x, ( N) N / 2 Vx ( Vx ) 2 ( V y ) V y T ( T ) h hangles With h hangles angular height The forces resultant on horizontal welding is: Fw, x, ( Vx, ( Vx ) Vx, ( T ) N ( N) The forces resultant on vertical welding is: F V ( V w, y, y, y ) 2 That must satisfy: F w, Fw, With Fw, fvw. d a l one angle Fw, fvw. d a l 2 two angles Where U s e r M a n u a l V e r s i o n J a n u a r y P a g e 22 of 354

23 l a is single weld length is throat weld height Verification of net and gross sections (supported beam) The verification is made both for normal tension forces and shear forces Tension force The verification made both for the profile and angles should be satisfied if: N N t, 1 Where N, is the design resistance force at tension force of section cross, equal to t lower of: a) Plastic design resistance of gross section N pl, Af y M 0 b) Ultimate design resistance of net section in holes for devices connection N u, 0. 9 A net f M 2 y The axis is the profile resistant section, with the height equal to angular height in according with EC3. The angular resistant part is the sum of two angles cross section areas, if there are both, that is a single angular Shear force The verification is made both for profile and angles should be satisfied if: V V c, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 23 of 354

24 Where V, is the shear resistance design force of cross section, equal to lower of: c a) Plastic design resistance of gross section V pl, A( f y / M 0 3) b) Ultimate resistance design section of net section in hole for connection devices V u, A net ( f u / M 2 3) The axis is the profile resistant part, It will be eventually blunted. The angular resistant part is the sum of two angles cross section, if there are both, that is a single angular Verification net and gross section (supporting beam) The verification is made both for normal forces and shear forces Tension force Verification made both for profile and angles should be satisfied if: N N t, 1 Where N, is the design tension force at tension force of cross section, equal to lower t of: a) Plastic design resistance of gross section N pl, Af y M 0 b) Ultimate net design resistance section in holes for connection devices U s e r M a n u a l V e r s i o n J a n u a r y P a g e 24 of 354

25 N u, 0. 9 A net f M 2 y The tension force action is equal to horizontal shear force acting on supporting beam. The axis is the profile resistant part, it has an height equal to angular height in according with EC3. The verification is made for single angular Shear force The verification is made both for profile and angles should be satisfied : V V c, 1 Where V, is the shear design resistance force of cross section, equal to lower of: c a) Plastic design resistance of gross section V pl, A( f y / M 0 3) b) Ultimate design resistance of net section in holes for joining devices V u, A net ( f u / M 2 3) The axis is the profile resistant part The angles resistant part is the sum each single part Resistance design for Block Tearing The shear force resistance with collapse mechanism of block Tearing (EC3 1.8 point ), is characterized by two possible crisis mode: - Tensile force breaking along line holes and shear force section yield on gross section; - Shear force breaking on net section. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 25 of 354

26 For a group of bolts stressed by a symmetric force, tear resistance, V eff 1, V, is: eff,1, f u A nt M 2 f y 3 M 0 A nv where: A nt is net area with tensile force; A nv is net area with shear force. For a group of bolts stressed by eccentric shear force action, V eff,2, fu A 0.5 nt M 2 f y 3 M 0 A nv V eff 2,, is: The verification is made separately both for perpendicular action action, both for profile and angles. and shear force U s e r M a n u a l V e r s i o n J a n u a r y P a g e 26 of 354

27 Must be: N N eff V V eff Single bolt bearing resistance force The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where b is dt For external (outer) bolts b f min( f ub u e1 ; 3d For inner bolts is b f min( f ub while k 1 is u p ; 3d 0 0 ;1) 1 1 ;1) 4 for external (outer) bolts e2 k 1 min( ;2.5) d For innner bolts p2 k 1 min( ;2.5) d Where 0 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection d 0 is hole diameter For the other sizes definition see figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 27 of 354

28 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 28 of 354

29 3.2 Joint 142 (Supporting beam Supported beam) (Supporting beam on the flange or on the column web) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 29 of 354

30 3.2.1 Plates The connection plate can be single or multiple Actions On the secondary profile we can apply the following forces: N normal force (positive if tensile) V, x V, y M, x horizontal shear force vertical plane shear force bending moment around x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas,, by x text file or we can calculate the structure to restore strength. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 30 of 354

31 If the stresses from Tekla Structures are zero, the forces will have minimum value according with EC3 1-8 point (13) N V N pl, y M V pl M pl where the plastic design resistances are referred at the secondary profile Generally the joint can be schematized as hinged joint that is as a constrained joint. This type of connection, is generally used to ensure the continuity of supported beam, beam continuous beam ( constrained joint on both secondary profiles), or simulate some hinges on one of two secondary profiles and a joint on the other profile, that is like an hinge on both the secondary profiles. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 31 of 354

32 3.2.3 Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint according with EC3 1-8, with following table 3.3 and figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 32 of 354

33 Design resistance of the single bolt and the single weld In this section we recall the common criterions for verification of single bolts and single weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 33 of 354

34 Tension design resistance of the bolt Single bolt tension resistance is: F t, 0.9 f ub M 2 A s Where A s is the tensile stressed area f ub is the last tensile bolt strength Design resistance of the bolt to shear For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear force design (for only one resistant section) is: F v,, v f ub M 2 A If the shear force plane is through the threated bolt portion: - for classes 4.6, 5.6 and 8.8 v for classes 4.8, 5.8 and 10.9 v 0.5 If the shear force plane is through not threaded bolt portion: v 0.6 While A is bolt area f ub is the last bolt tension Design resistance of the Weld Fillet weld design resistance is: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 34 of 354

35 F w, fvw. d a l Where f vwd. is the welding shear design resistance. a is weld throat height. l is weld throat height. The welding shear resistance calculation f vw. d is: f vwd. f u / 3 w M 2 Where : f u is the nominal resistance breaking of weaker joint; w is the appropriate correlation factor shown in table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 35 of 354

36 Annotations In the verifications the sizes regarding supported beam will have the pedice wb and regarding supporting beam the pedice wc Verifications made - Verifications made on the joint are the following: - Weld on the supported beam F w, Fw, - Shear and tension force bolt on the supporting beam Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In case of only shear In case of only tension In case of shear and tension - Net and gross sections verification of profile and plates on supported beam, due to stress tensile and shear force N V N N V V pl, u, pl, u, - BlockTearing verification profiles and plates on the supported beam, due to tensile and shear force N N eff V V eff - Bearing resistance verification on two directions, horizontal and vertical of profiles and plate on supported beam U s e r M a n u a l V e r s i o n J a n u a r y P a g e 36 of 354

37 - F b, Fb, Verification of weld (supported beam) Verification is done considering together perpendicular force and shear acting on the supported beam. If we consider a reference system x-y on supported beam plan, with x coincident with beam axis, y orthogonal beam axis and the origin in vertical cordon barycenter, for equilibrium to vertical translation and rotation relative to supporting beam axis, we consider as that vertical cordon on supported beam is for the whole height plate. The forces on plate are: V V T y x N V V Where, y y e e is the distance between vertical welding barycenter and supporting beam axis, while T is the parasite torsion had to eccentricity, if the main supporting beam torsional stiffness isn t negligible, the connection is assumed as a constraint joint and T Vy e M, x. The horizontal and vertical actions on single weld are: V V V x, y, x, ( V ( V ( T x y Vx ) 2 Vy ) 2 ) T Force resultant on horizontal welding is F ( Vx, ( Vx ) Vx, ( T ) Vy, ( V w, x, y ) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 37 of 354

38 must satisfy: F w, Fw, Where l is single cordon length a is throat height Shear and tension verification of the bolt (supporting beam) The verification is made considering together normal stress bending and shear force acting on supported beam, as the sum of the forces transmitted by the supported beam. If we consider a reference system x-y on supporting beam s plan, with axis x coincident with beam s axis, axis y orthogonal to beam s axis and origin in the bolt s barycenter that are on one angular, for vertical translation and rotation equilibrium relative to the supported beam axis, shear force solicitations in the group bolt s barycenter on single bracket are: V V T x y V V V, x, y y / 2 e / 2 If on supporting beam is only one angular the stresses on the group bolts barycenter on bracket are: V V T x y V V V, x, y y e Where e is the distance between the group bolts barycenter of single angular and supported beam s axis, while T is the parasite torsion had to eccentricity. The shear forces on the single bolt for single bolt shear plan are: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 38 of 354

39 V V V V x, y, x, y, Vx ( Vx ) nv nb Vy ( Vy ) nv nb T ( T ) nv J b T ( T ) n J v b y i x i With 2 2 J ( n x n y ) bolts polar moment b n b n v i bv bh bolts total number bolt sections number shear resistant n bh bolts number per horizontal row n bv bolts number per vertical row x i single bolt distance from barycenter of group bolts, in verification we consider x max y i single bolt distance from barycenter of group bolts, in verification we consider y max The forces resultant on single bolt for single bolt shear plan is: F 2 2 v, ( Vx, ( Vx ) Vx, ( T )) ( Vy, ( Vy ) Vy, ( T )) The tension force on single bolt belonging to the group of bolts of a bracket is: F N / n t, b If the constraint of the supported beam is similar to a joint, the bending force resulting from supported beam is tensile stressed and the tensile force on single bolt belonging to the group of bolts of a side of plate is: F n b M M / nb I, x t, N nb 2 nbh y yi N / i bolts total number, x n bh bolts total number for horizontal row b y i U s e r M a n u a l V e r s i o n J a n u a r y P a g e 39 of 354

40 y i distance of single bolts row from compression center (the compression center coincides with the lower edge of the bracket), in the verifications we consider the y max. must satisfy Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In presenzadi solo taglio In presenzadi sola trazione In presenzadi taglio e trazione Net and gross sections verification (supported beam) The verification is made both for normal tension forces and shear forces Tension force The verification made both for the profile and plates should satisfy if: N N t, 1 Where N, is the design resistance force at tension force of section cross, t equal to lower of: c) Plastic design resistance of gross section N pl, Af y M 0 d) Ultimate design resistance of net section in holes for devices connection N u, 0. 9 A net f M 2 y U s e r M a n u a l V e r s i o n J a n u a r y P a g e 40 of 354

41 The tensile force is equal to horizontal shear force acting on supporting beam. The axis is the profile resistant part, with height equal to plate height in according with EC3. The verification is made for single side plate Shear force The verification is made both for profile and plates should verify : V V c, 1 Where V, is the shear design resistance force of cross section, equal to lower of: c c) Plastic design resistance of gross section V pl, A( f y / M 0 3) d) Ultimate resistance design section of net section in hole for connection devices V u, A net ( f u / M 2 3) The axis is the profile resistant part. The plate resistant part is the sum of single cross area Resistance for Block Tearing - The shear force resistance with collapse mechanism block Tearing (EC3 1.8 point ), is characterized by two possible crisis mode: - Tensile force breaking along line holes and shear force section yield on gross section; - Shear force breaking on net section U s e r M a n u a l V e r s i o n J a n u a r y P a g e 41 of 354

42 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 42 of 354

43 For a group of bolts stressed by a symmetric force, the tear resistance, V eff 1, V, is: eff,1, f u A nt M 2 f y 3 M 0 A nv where: A nt is net area with tensile force; A nv is net area with shear force. V, For a group of bolts stressed by an eccentric shear force, eff, 2 is given by V eff,2, fu A 0.5 nt M 2 f y 3 M 0 A nv U s e r M a n u a l V e r s i o n J a n u a r y P a g e 43 of 354

44 The verification is made separately both for perpendicular action action, both for profile and angles. and shear force Must be: N N eff V V eff Single bolt bearing resistance force The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where b is dt For external bolts b f min( f ub u e1 ; 3d For inner bolts is b f min( f ub u While k 1 is p ; 3d 0 0 ;1) 1 for external bolts 1 ;1) 4 e2 k 1 min( ;2.5) d For internal bolts p2 k 1 min( ;2.5) d Where 0 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection U s e r M a n u a l V e r s i o n J a n u a r y P a g e 44 of 354

45 d 0 is hole diameter For the other sizes definition see figure 3.1 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 45 of 354

46 3.3 Joint 143 (Supporting beam Supported beam) (Supporting beam on web flange or column) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 46 of 354

47 3.3.1 Angles The angles can be both or on only one web side of the secondary profile Beyond the contemporary of four angles, they can have variable disposition on the profiles They can have different thickness, but it not allowed use angles of different sizes The angles connection on the profiles can be either bolted that welded, like is represented in the following figure: If the connection is either bolted that welded U s e r M a n u a l V e r s i o n J a n u a r y P a g e 47 of 354

48 In the verification we don t consider the welding, but we consider the connection like only bolted Forces On the secondary profiles we can apply the following forces: N axial force (positive if tension force) V, x V, y M, x horizontal shear vertical shear bending moment all round x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N V N pl, y M V pl M pl where the plastic resistances are referred to the secondary profile. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 48 of 354

49 The joint can be generally schematized as hinged joint that is considered like joint node. This type of connection, is generally used to ensure the supported beam continuity, beam continuous beam (constraint joint on both secondary profile), or simulate hinges on one of the two secondary profiles and a constrained on the other, that is hinge on both secondary profiles Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint, in according with l EC3 1-8 with the following table 3.3 and figure 3.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 49 of 354

50 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 50 of 354

51 3.3.4 Design resistance of single bolt and single weld In this section we recall the common criteria for verification of single bolts and single welds. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 51 of 354

52 Design resistance tensile of the bolt Tensile strength of single bolt is: F t, Where 0.9 f ub M 2 A A s is tensile stressed area s f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for classes 4.6, 5.6 e 8.8 v for classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v while 0.6 A is the bolt area f ub is the last bolt tensile stress Design resistance of the weld Design resistance of fillet weld is: F w, fvw. d a l U s e r M a n u a l V e r s i o n J a n u a r y P a g e 52 of 354

53 where f vwd. is weld shear design resistance. a is height throat weld. l is length cordon weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table Annotations In the verification the sizes regarding the supported beam will have the pedice wb,regarding supported beam will have the pedice wc. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 53 of 354

54 3.3.6 Verifications made The verifications made on the joint are the following: - Shear bolt on the supported beam F v, Fv, - Welding on the supported and supporting beam F w, Fw, - Bolt shear and tension force on the supporting beam Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In presenzadi solo taglio In presenzadi sola trazione In presenzadi taglio e trazione - Verification of net and gross section of profiles and angles on the supported and supporting beam, due tensile and shear action. N N N pl, u, V V V pl, u, - Profiles and angles verification for Block Tearing on the supported and supporting - beam, due tensile and shear action. N N eff V V eff - Bearing stress verification on the two profile and angle directions, horizontal and vertical on the supported and supporting beam F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 54 of 354

55 3.3.7 Shear bolt verification (supported beam) The verification is made considering together normal stress and shear acting on the single supported beam. If we consider a reference system x-y on the supported plan beam, with x axis coincident with beam axis, y axis orthogonal to beam axis and the origin coincident with bolts barycenter, for the equilibrium to the vertical translation and rotation relative beam axis of supporting beam, stresses in the group bolts barycenter on the bracket of single supported beam are: V V T y x N V V Where, y y e e is the distance between the group bolts barycenter and supporting beam axis, while T is the parasite torsion had to the eccentricity, if we consider the joint as constrained T Vy e M, x. The shear forces on the single bolt, for single bolt shear plan are: V V V V x, y, x, y, With Vx ( Vx ) nv nb Vy ( Vy ) nv nb T ( T ) nv J b T ( T ) n J v b y i x i J b n b n v 2 2 ( n x n y ) bolts polar moment i bv bh bolts total number shear resistant section number U s e r M a n u a l V e r s i o n J a n u a r y P a g e 55 of 354

56 n bh bolts number for each horizontal row n bv bolts number for each vertical row x i single bolt distance from group bolts barycenter, in the verification we consider the x max y i single bolt distance from group bolts barycenter, in the verification we consider the y max The force resultant on single bolt for single bolt shear plan is: F 2 2 v, ( Vx, ( Vx ) Vx, ( T )) ( Vy, ( Vy ) Vy, ( T )) Must satisfy: F v, Fv, Verification of the Welding (supported beam) The verification is made considering together perpendicular stress and shear force acting on the supported beam. If we consider a reference system x-y on the supported plan beam, with x axis coincident with beam axis, y axis orthogonal to beam axis and the origin coincident with vertical welding barycenter, for the equilibrium to the vertical translation and rotation relative beam axis of supporting beam, must be for each angle two horizontal welding ( one superior and one inferior) and one vertical weld on the supported beam. The stresses on the bracket are: V V T y x N V V Where, y y e e is the distance between the vertical weld barycenter and supporting beam axis, while T is the parasite torsion due to the eccentricity, if we consider the joint as constrained T Vy e M, x. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 56 of 354

57 The horizontal and vertical forces on the welding are: V V V x, y, x, With ( V ( V ( T x y Vx ) 2 ) Vy T ) h hangles h hangles angle height The forces resultant on the horizontal welding is: F ( Vx, ( Vx ) Vx, ( T w, x, The forces resultant on the vertical welding is: F V ( V w, y, y, y ) ) must satisfy: F w, Fw, With Fw, fvw. d a l one angle Fw, fvw. d a l 2 two angles Where l is the single cordon length a is the throat height. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 57 of 354

58 3.3.9 Shear and tensile force verification (supporting beam) The verification is made considering together perpendicular stress and shear force acting on the supported beam, as the sum of the supported beams forces. If we consider a reference system x-y on the supporting plan beam, with x axis coincident with beam axis, y axis orthogonal to beam axis and the origin coincident with bolts barycenter that are on one angle, for the equilibrium to the vertical translation and rotation relative beam axis of supported beam, stresses in the group bolts barycenter on the bracket of single supported beam are: V V T x y V V V, x, y y / 2 e / 2 If on the supporting beam there is only one angular the stresses on the group bolts barycenter on bracket are: V V T x y V V V, x, y y e where e is the distance between the group bolts barycenter of single angular and supported beam s axis, while T is the parasite torsion due to the eccentricity. The shear forces of single bolt for single bolt shear plan are: V V V V x, y, x, y, Vx ( Vx ) nv nb Vy ( Vy ) nv nb T ( T ) nv J b T ( T ) n J v b y i x i U s e r M a n u a l V e r s i o n J a n u a r y P a g e 58 of 354

59 with 2 2 J ( n x n y ) bolts polar moment b n b n v i bv bh bolts total number bolts section numbers shear resistant n bh bolts number per horizontal row n bv bolts number per vertical row x i single bolt distance from barycenter of group bolts, in verification we consider x max y i single bolt distance from barycenter of group bolts, in verification we consider y max The forces resultant on single bolt for single bolt shear plan is: F 2 2 v, ( Vx, ( Vx ) Vx, ( T )) ( Vy, ( Vy ) Vy, ( T )) The tension force on single bolt belonging to the group of bolts of a bracket is : F N / n t, b If we assume the supported beam connection like a constrained joint, the bending force coming from supported beam is stressed to tension and the tension force on the single bolt belonging to the group of bolts of a bracket is: F n b M M / nb I, x t, N nb 2 nbh y yi N / i bolts total number, x n bh bolts total number per horizontal row y i b y i single row bolts from the compression center (the center of compression coincides with the lower edge of the bracket), in the verification we consider y max. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 59 of 354

60 must satisfy: Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In presenzadi solo taglio In presenzadi sola trazione In presenzadi taglio e trazione Verification of the weld (supporting beam) The verification is made considering together axial force, bending and shear force acting, in two directions vertical and horizontal on supporting beam. If we consider a reference system x-y on supporting beam s plan, with axis x coincident with beam s axis, axis y orthogonal to beam s axis and origin in barycenter of vertical axis welding, for vertical translation and rotation equilibrium relative to the supporting beam axis, must be for each angler two horizontal welding ( one superior and one inferior) and one vertical weld on supporting beam. Stresses on single bracket are: N N z, / 2 Vx V, x / 2 V y V, y / 2 M M x, x / 2 T V y e If on supporting beam there is only one angle the forces on the bracket are: N N z, Vx V, x V y V, y M M x, x T V y e U s e r M a n u a l V e r s i o n J a n u a r y P a g e 60 of 354

61 where e is the distance between the vertical welding barycenter and supporting beam axis, while T is the parasite torsion had to eccentricity. The forces on single horizontal and vertical welding are: N V V V x, y, x, M ( N) N / 2 h Vx ( Vx ) 2 ( V y ) V y T ( T ) h hangles x hangles with h hangles angular height The forces resultant on horizontal welding is: Fw, x, ( Vx, ( Vx ) Vx, ( T ) N ( N) The forces resultant on vertical welding is: F V ( V w, y, y, y ) 2 must satisfy: F w, Fw, with Fw, fvw. d a l one angle Fw, fvw. d a l 2 two angles where l is the length of single weld a is throat weld height. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 61 of 354

62 Verification net and gross sections (supported beam) The verification is made both for normal tension forcer and shear force Tension force The verification made both for the profile and angles is verified if: N N t, 1 where N, is the design resistance force at tension force, equal to lower of: t e) Plastic design resistance of gross section N pl, Af y M 0 f) Ultimate design resistance of net section in holes for connection devices N u, 0. 9 A net f M 2 y The axis is the profile resistant part, with height equal to angular height in according with EC3. The angular resistant part is the sum of two angles cross section areas, if there are both, that is a single angular Shear force The verification is made both for profile and angles is verified if: V V c, 1 where V, is the shear resistance design force of cross section, equal to lower of : c e) Plastic design resistance of gross section U s e r M a n u a l V e r s i o n J a n u a r y P a g e 62 of 354

63 V pl, A( f y / M 0 3) Ultimate resistance design section of net section in holes for connection devices V u, A net ( f u / M 2 3) The axis is the profile resistant part, it will be eventually blunted. The angular resistant part is the sum of two angles cross section, if there are both, that is a single angular Verification net and gross section (supporting beam) The verification is made both for normal and shear forces Tension force Verification made both for profile and angles is verified if: N N t, 1 Where is the design tension force at tension force of cross section, equal to lower of: c) Plastic design resistance of gross section N pl, Af y M 0 d) Ultimate net design resistance section in holes for connection devices N u, 0. 9 A net f M 2 y The tension force action is equal at horizontal shear force acting on supporting beam. The axis is the profile resistant part, it has an height equal to angular height in according with EC3. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 63 of 354

64 The verification is made for single angular Shear force The verification made both for profile and angles is verified if : V V c, 1 Where V, is the shear design resistance force of cross section, equal to lower of: c c) Plastic design resistance of gross section V pl, A( f y / M 0 3) d) Ultimate design resistance of net section in holes for joining devices V u, A net ( f u / M 2 3) The axis is the profile resistant part The angles resistant part is the sum each single cross area Resistance for Block Tearing The shear force resistance with collapse mechanism block Tearing (EC3 1.8 point ), is characterized by two possible crisis mode: -Tensile force breaking along line holes and shear force section yield on gross section; -shear force breaking on net section. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 64 of 354

65 For a group of bolts stressed by a symmetric force, tear resistance, V eff,1, f u A nt M 2 f y 3 M 0 A nv V eff 1,, is: where: A nt is net area with tensile force; A nv is net area with shear force. For a group of bolts stressed by eccentric shear force action, V eff,2, fu A 0.5 nt M 2 f y 3 M 0 A nv V eff 2,, is: The verification is made separately both for perpendicular action action, both for profile and angles. and shear force U s e r M a n u a l V e r s i o n J a n u a r y P a g e 65 of 354

66 Must be: N N eff V V eff Single bolt bearing resistance force The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where b is dt For external bolts b f min( f ub u e1 ; 3d 0 ;1) For internal bolts is b f min( f ub u While k 1 is p ; 3d 1 For external bolts 0 1 ;1) 4 e2 k 1 min( ;2.5) d For internal bolts p2 k 1 min( ;2.5) d Where 0 0 f u is the ultimate tensile strength of lower resistant plate f ub is the ultimate tensile strength of the bolt t is minimum thickness of plates connection d 0 is the diameter of hole For the other sizes definition see figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 66 of 354

67 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 67 of 354

68 3.4 Joint (Supporting beam Supported beam) (Supporting beam on flange or on the column axis) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 68 of 354

69 3.4.1 Plates The connection plate can be single or multiple Forces On the secondary profile we can apply the following forces: N axial force (positive if tensile) V, x V, y M, x horizontal plane shear force vertical plane shear force bending moment around x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas,, by x text file or we can calculate the structure to restore strength. If the stresses from Tekla Structures are zero, the forces will have minimum value according with EC3 1-8 point (13) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 69 of 354

70 N V N pl, y V pl where the plastic resistances are referred to the secondary profile. Generally the joint can be schematized as hinged joint, if the supporting beam torsional stiffness is negligible, or as constrained joint if the torsional stiffness of the main supporting beam is not negligible. This joint generally is used for end connections Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint according with EC3 1-8, with following table 3.3 and figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 70 of 354

71 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 71 of 354

72 3.4.4 Design resistance of single bolt and single weld In this section we recall the common criteria for verification of single bolts and single weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 72 of 354

73 Design resistance at bolt s tension force Single bolt tension resistance is: F t, where 0.9 f ub M 2 A s A s is the stressed area to tensile force f ub is the last tensile bolt strength Bolt shear force resistance design For a shear connection (see class A EC3 1-8 point 3.4.1) the design resistance of single bolt for shear force (for a single resistant section) is: F v,, v f ub M 2 A If the shear force plane is through the threated bolt portion: - for classes 4.6, 5.6 and 8.8 v for classes 4.8, 5.8 and 10.9 v 0.5 If the shear force plane is through not threaded bolt portion: v 0.6 While A is bolt area f ub is the last bolt tension design resistance of the weld Fillet weld design resistance is: F w, Where fvw. d a l U s e r M a n u a l V e r s i o n J a n u a r y P a g e 73 of 354

74 f vwd. is the welding shear design resistance. a is throat weld height. l is cordon weld length. The welding shear resistance calculation f vw. d is: f vwd. f u / 3 w M 2 where: f u is the nominal resistance breaking of weaker joint; w is the appropriate correlation factor shown in table Annotations In the verifications the sizes regarding supported beam will have the pedice wb and regarding supporting beam the pedice wc. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 74 of 354

75 3.4.6 Verifications made - Verifications made on the joint are the following Weld on the supported beam F w, Fw, - Shear and tension force bolt on the supporting beam Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In presenzadi solo taglio In presenzadi sola trazione In presenzadi taglio e trazione - Net and gross sections verification of profile and plates on supported beam, due to stress tensile and shear force - N N N pl, u, V V V pl, u, - BlockTearing verification profiles and plates on the supported beam, due to tensile and shear force N N - eff V V eff - Bearing resistance verification on two directions, horizontal and vertical profiles and plate on supported beam F b, Fb, Weld verification (supported beam) Verification is done considering together perpendicular force and shear acting on the supported beam. If we consider a reference system x-y on supported beam plan, with x coincident with beam axis, y orthogonal beam axis and the origin in vertical cordon barycenter, for U s e r M a n u a l V e r s i o n J a n u a r y P a g e 75 of 354

76 equilibrium to vertical translation and rotation relative to supporting beam axis, we consider as that vertical cordon on supported beam is for the whole height plate. The forces on plate are: V V T y x N V V Where, y y e e is the distance between vertical welding barycenter and supporting beam axis, while T is the parasite torsion due to eccentricity, if the main supporting beam torsional stiffness is not negligible, the connection is assumed as a constraint joint and T Vy e M, x. The horizontal and vertical actions on single weld is: V V V x, y, x, ( V ( V ( T x y Vx ) 2 Vy ) 2 ) T Force resultant on horizontal welding is: F ( Vx, ( Vx ) Vx, ( T ) Vy, ( V w, x, y ) must satisfy: F w, Fw, Where l is the length of single cordon a is throat height. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 76 of 354

77 3.4.8 Shear and tension force bolt verification (supporting beam) The verification is made considering together normal stress bending and shear force acting on supported beam. If we consider a reference system x-y on supporting beam s plan, with axis x coincident with beam s axis, axis y orthogonal to beam s axis and origin in the bolt s barycenter that are on one angular, for vertical translation and rotation equilibrium relative to the supported beam axis, shear force solicitations in the group bolt s barycenter on single bracket are: V V T x y V V V, x, y y / 2 e / 2 If on supporting beam is only one angular the stresses on the group bolts barycenter on bracket are: V V T x y V V V, x, y y e Where e is the distance between the group bolts barycenter of single angular and supported beam s axis, while T is the parasite torsion due to eccentricity. The shear forces of single bolt for single bolt shear plan are: V V V V x, y, x, y, With Vx ( Vx ) nv nb Vy ( Vy ) nv nb T ( T ) nv J b T ( T ) n J v b y i x i U s e r M a n u a l V e r s i o n J a n u a r y P a g e 77 of 354

78 J b n b n v 2 2 ( n x n y ) bolts polar moment i bv bh bolts total number bolt sections number shear resistant n bh bolts number per horizontal row n bv bolts number per vertical row x i single bolt distance from barycenter of group bolts, in verification we consider x max y i single bolt distance from barycenter of group bolts, in verification we consider y max The forces resultant on single bolt for single bolt shear plan is: F 2 2 v, ( Vx, ( Vx ) Vx, ( T )) ( Vy, ( Vy ) Vy, ( T )) The tension force on single bolt belonging to the group of bolts of a bracket is: F N / n t, b if the main supporting beam torsional stiffness is not negligible the bolts for bending force resulting from supported beam are tensile stressed and the tensile on single bolt belonging to the group of bolts of a bracket is: F n b M M / nb I, x t, N nb 2 nbh y yi N / i bolts total number, x n bh bolts total number for horizontal rows y i b y i is the distance of the single bolt from the center of compression (the center of compression coincides with the lower edge of the bracket), in the verification we have considered the y max. Must satisfy Fv, Ft, Fv, F F / F v, t, v, F t, /1.4F t, In case of only shear In case of only tension In case of shear and tension U s e r M a n u a l V e r s i o n J a n u a r y P a g e 78 of 354

79 3.4.9 Net and gross sections verification (supported beam) The verification is made both for normal tension forces and shear forces Tension force The verification made both for the profile and plates is verified if: N N t, 1 Where N, is the design resistance force at tension force of section cross, equal to t lower of: g) Plastic design resistance of gross section N pl, Af y M 0 h) Ultimate design resistance of net section in holes for devices connection N u, 0. 9 A net f M 2 y The tensile force is equal to horizontal shear force acting on supporting beam. The axis is the profile resistant part, with height equal to angular height in according with EC3. The verification is made for single angle Shear force The verification is made both for profile and angles is verified if: V V c, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 79 of 354

80 Where V, is the shear resistance design force of cross section, equal to lower of: c f) Plastic design resistance of gross section V pl, A( f y / M 0 3) g) Ultimate resistance design section of net section in hole for connection devices V u, A net ( f u / M 2 3) The axis is the profile resistant part. The angular resistant part is the sum of single cross area Resistance for Block Tearing - The shear force resistance with collapse mechanism block Tearing (EC3 1.8 point ), is characterized by two possible crisis mode: - Tensile force breaking along line holes and shear force section yield on gross section; - Shear force breaking on net section U s e r M a n u a l V e r s i o n J a n u a r y P a g e 80 of 354

81 For a group of bolts stressed by a symmetric force, tear resistance, V eff 1, V, is given by: eff,1, f u A nt M 2 f y 3 M 0 A nv where: A nt is net area with tensile force; A nv is net area with shear force. For a group of bolts stressed by an eccentric shear force action, V eff,2, fu A 0.5 nt M 2 f y 3 M 0 A nv V eff 2,, is: The verification is made separately both for perpendicular action action, both for profile and angles. and shear force U s e r M a n u a l V e r s i o n J a n u a r y P a g e 81 of 354

82 Must be: N N eff V V eff Single bolt bearing resistance force The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where b is dt For external bolts b f min( f ub u e1 ; 3d For inner bolts is 0 ;1) b f min( f ub u While k 1 is p ; 3d 1 for external bolts 0 1 ;1) 4 e2 k 1 min( ;2.5) d For internal bolts p2 k 1 min( ;2.5) d Where 0 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection d 0 is the hole diameter U s e r M a n u a l V e r s i o n J a n u a r y P a g e 82 of 354

83 For the other sizes definition see figure 3.1 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 83 of 354

84 3.5 Joint 42 (Beam Web beam) Forces On the single profiles can be applied the following forces: N normal force (positive if tension force) V, y M, x vertical shear force bending moment all round x axis The forces can be inserted by Tekla Structures, by modeler Midas, by text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N N pl U s e r M a n u a l V e r s i o n J a n u a r y P a g e 84 of 354

85 V, y M V pl M pl where the plastic resistances are referred to lowest value of two profile resistance. The connection is schematized as joint node. This type of connection, is generally used to ensure the continuity of the interrupted columns for reasons of the length of columns that are in commerce, or for design, the joint also transmits moment, and it can be assumed as joint node Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint, in according with l EC3 1-8 and the following table 3.3 and figure 3.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 85 of 354

86 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 86 of 354

87 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 87 of 354

88 3.5.2 Design resistance of single bolt In this paragraph we speak about the common criteria for verification of single bolts Design resistance at Bolt tensile force The tension resistance of single bolt is: F t, Where 0.9 f ub M 2 A A s is stressed tensile area s f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for the classes 4.6, 5.6 e 8.8 v for the classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v 0.6 While A is the bolt area f ub is the last bolt tensile stress U s e r M a n u a l V e r s i o n J a n u a r y P a g e 88 of 354

89 3.5.3 Annotations In the verifications the sizes regarding beam wing will have the pedice fb beam the pedice wb. for web Verification made The verifications made on the joint are the following: - Shear bolt on the plate and web beam F v, Fv, - Net and gross sections verification of profiles and angles on supported and supporting beam, due to stress tensile and shear force - N N N pl, u, V V V pl, u, - Bearing resistance verification on two directions, horizontal and vertical, of profiles and angles on supported and supporting beam F b, Fb, Flange design resistance due to axial and bending force It is assumed that the joint cover on the profile wing resist only at the applied design moment M, the axial force together the axial design resistance, N j, applied on j the single joint cover is: M F H t j, j, copr N 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 89 of 354

90 Where H is the width of the beam t copr is the thickness of the joint cover The shear forces on single bolt of single joint cover are: F v, fb, F n bolt The set of bolts will be stressed by a shear force: V j, nblot Fv,, fb, The total shear resistance of the bolts is: V fb, nbolt Fv, fb, Must be: V j, V fb, On the joint cover anyway should be made the bearing verification. The bearing verification for the single section must respect the following: F b,, fb, V n j, fb, bolt F b,, k1 b f u M 2 dt Joint design resistance due to the shear force on the web V, is the shear force, the stresses on joint cover are : j M V fc, wb, M V j, j, I I anima totale Taglio Torsione The shear forces on the single bolt are: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 90 of 354

91 F Fv, Where v, V, wc, H, wc, V n M wc, wc, 2 yi bolt y i Azione vertivale Azioneorizzontal e y i is the barycenter distance of single bolt from center of compression assumed on the bolts barycenter. The stressed force resultant is F 2 2 v,, wc, Fv,, V, wc, Fv,, H, wc, The set of bolts will be stressed by a shear force: V j, wc, nblot Fv,, wc, The total shear resistance of the bolts is: V wc, nbolt Fv, wc, Must be : V j, wc, Vwc, On the joint cover anyway should be made the bearing verification. The bearing verification for the single section must respect the following: F b,, wc, V n j, wc, bolt F b,, k1 b f u M 2 dt Verification of Net and gross sections The verification is made both for normal tension forces and shear forces Tension force The verification made both for the profile that for joint cover should satisfy if: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 91 of 354

92 N N t, 1 Where N, is the design resistance force at tension force of section cross, equal to t lower of: i) The plastic design resistance of gross section N pl, Af y M 0 j) The ultimate design resistance of net section in holes for devices connection N u, 0. 9 A net f M 2 y The resistant section of the profile is given from the web panel, with a width equal to the effective angle width in according with European standard. The resistant section of the angles is given by the sum of transversal areas of two angles if there are both, that is only one angle Shear force The verification is made both for profiles and cover joint should satisfy: V V c, 1 Where V, is the shear design resistance of cross section, equal to lower of: c h) Plastic design resistance of gross section V pl, A( f y / M 0 3) i) Ultimate resistance design section of net section in hole for connection devices V u, A net ( f u / M 2 3) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 92 of 354

93 The resistant section of cover joints is given by the sum of two transversal cover joints if there are both, that is only one, that is only one cover joint. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 93 of 354

94 3.6 Jonts 77 (Beam Web beam) Forces On the single profiles can be applied the following forces: N normal force (positive if tension force) V, y M, x vertical shear force bending moment all round x axis The forces can be inserted by Tekla Structures, by modeler Midas, by text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N N pl U s e r M a n u a l V e r s i o n J a n u a r y P a g e 94 of 354

95 V, y M V pl M pl where the plastic resistances are referred to lowest value of two profile resistance. The connection is schematized as joint node. This type of connection, is generally used to ensure the continuity of the interrupted columns for reasons of the length of columns that are in commerce, or for design, the joint also transmits moment, and it can be assumed as joint node. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 95 of 354

96 3.6.2 Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint, in according with l EC3 1-8 and the following table 3.3 and figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 96 of 354

97 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 97 of 354

98 3.6.3 Design resistance of single bolt In this section we recall the common criteria for verification of single bolts Design resistance at Bolt tensile force The tension resistance of single bolt is: F t, Where 0.9 f ub M 2 A s A s is stressed tensile area f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for the classes 4.6, 5.6 e 8.8 v for the classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v 0.6 While A is the bolt area f ub is the last bolt tensile stress U s e r M a n u a l V e r s i o n J a n u a r y P a g e 98 of 354

99 3.6.4 Annotations In the verifications the sizes regarding beam wing will have the pedice fb beam the pedice wb. for web Verifications made The verifications made on the joint are the following: Shear bolt on the plate and web beam F v, Fv, - Net and gross sections verification of profiles and angles on supported and supporting beam, due to stress tensile and shear force N N N pl, u, V V V pl, u, - Bearing resistance verification on two directions, horizontal and vertical, of profiles and angles on supported and supporting beam F b, Fb, Flange design resistance due to axial and bending force It is assumed that the joint cover on the profile wing resist only at the applied design moment M, the axial force together the axial design resistance, N j, applied on j the single joint cover is: M F H t j, j, copr N 2 Where H is the width of the beam U s e r M a n u a l V e r s i o n J a n u a r y P a g e 99 of 354

100 t copr is the thickness of the joint cover The shear forces on single bolt of single joint cover are: F v, fb, F n bolt The set of bolts will be stressed by a shear force: V j, nblot Fv,, fb, The total shear resistance of the bolts is: V fb, nbolt Fv, fb, Must be: V j, V fb, On the joint cover anyway should be made the bearing verification. The bearing verification for the single section must respect the following: F b,, fb, V n j, fb, bolt F b,, k1 b f u M 2 dt Joint design resistance due to the shear force on the web V, is the shear force, the stresses on joint cover are: j V M wb, fc, V M j, j, I I web total Shear Torsion The shear forces on the single bolt are: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 100 of 354

101 Fv Fv, Where, V, wc, H, wc, V nbolt M y wc, wc, 2 i y i vertical force horizontal force y i is the barycenter distance of single bolt from center of compression assumed on the bolts barycenter. The stressed force resultant is F 2 2 v,, wc, Fv,, V, wc, Fv,, H, wc, The set of bolts will be stressed by a shear force: V j, wc, nblot Fv,, wc, The total shear resistance of the bolts is: V wc, nbolt Fv, wc, Must be: V j, wc, Vwc, On the joint cover anyway should be made the bearing verification. The bearing verification for the single section must respect the following: F b,, wc, V n j, wc, bolt F b,, k1 b f u M 2 dt Verification of Net and gross sections The verification is made both for normal tension forces and shear forces Tension force The verification made both for the profile that for joint cover should satisfy if: N N t, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 101 of 354

102 Where N, is the design resistance force at tension force of section cross, equal to t lower of: k) The plastic design resistance of gross section N pl, Af y M 0 l) The ultimate design resistance of net section in holes for devices connection N u, 0. 9 A net f M 2 y The resistant section of the profile is given from the web panel, with a width equal to the effective angle width in according with European standard. The resistant section of the angles is given by the sum of transversal areas of two angles if there are both, that is only one angle Shear force The verification is made both for profiles and cover joint should satisfy: V V c, 1 Where V, is the shear design resistance of cross section, equal to lower of: c j) Plastic design resistance of gross section V pl, A( f y / M 0 3) k) Ultimate resistance design section of net section in hole for connection devices V u, A net ( f u / M 2 3) The resistant section of the joint cover is given by the sum of transversal areas of two joint covers if there are both, that is only one joint cover. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 102 of 354

103 3.7 Joint 14 (Beam Flange bolted beam) (Column Flange column web bolted) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 103 of 354

104 3.7.1 Stiffeners on the beam Forces On the profiles can be applied the following forces: N normal force (positive if tension force) V, x V, y M, x horizontal shear vertical shear bending moment all round x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 104 of 354

105 If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N V N pl, y V pl where the plastic resistances are referred to the column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 105 of 354

106 3.7.3 Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint, in according with l EC3 1-8 and the following table 3.3 and figure 3.1. The verification is made only for e 1 and e 2, and not for p 1 e p 2 because the local buckling resistance of the plate is always prevented by the stiffeners and by the same column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 106 of 354

107 3.7.4 Design resistance of single bolt and single weld In this paragraph we speak about the common criteria for verification of single bolts and single weld Design resistance at Bolt tensile force The tension resistance of single bolt is: F t, Dove 0.9 f ub M 2 A A s is stressed tensile area s f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for the classes 4.6, 5.6 e 8.8 v for the classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v 0.6 While A is the bolt area U s e r M a n u a l V e r s i o n J a n u a r y P a g e 107 of 354

108 f ub is the last bolt tensile stress Design resistance of the weld Design resistance of fillet weld is: F w, Where fvw. d a l f vwd. is weld shear design resistance. a is height throat weld. l is cordon weld length. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 108 of 354

109 3.7.5 Verifications made The verifications made on the joint are the following: - Flange and beam web in compression F c, fb, Fc, fb, - Bearing resistance verification on two horizontal directions on the connection plate F b, Fb, - Verification of beam web panel in shear V wp, Vwp, - Verification of beam web in compression F c, wc, Fc, wc, - Verification axial force resistance without moment resistance applied N N j, j, 1 - Verification for shear force V V j, j, 1 - Verification in bending without axial force applied M M j, j, 1 - Verification for buckling M M j, j, N N j, j, 1 If the axial force N does not exceed the 5% of the plastic axial force N pl,, is neglected the coexistence of the axial force and the rule becomes M M j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 109 of 354

110 3.7.6 Single bolt bearing resistance The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where is b dt For outer bolts b f min( f ub u e1 ; 3d For inner bolts is b f min( f ub u While k 1 is p ; 3d For outer bolts 0 0 ;1) 1 1 ;1) 4 e2 k 1 min( ;2.5) d 0 For inner bolts p2 k 1 min( ;2.5) d Where 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection d 0 is hole diameter For the other sizes definition see figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 110 of 354

111 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 111 of 354

112 3.7.7 Plate Connection in bending Verification made in according with EC3 1-8 point The design resistance and failure mode of a plate in bending, together with the associated bolts in tension, should be taken as similar to those of an equivalent T-stub (EC3 1-8 point 6.2.4), the design resistance for both: - each individual bolt-row required to resist tension; - each group of bolt-rows required to resist tension. The group of bolt rows, both the reinforced sides connecting to the end plate should be considered as an equivalent T-stub. In an extended end-plate, considered as the part of the plate extended on the beam (extended end - plate), the bolt-row in the extended part is considered as a separated T-stub equivalent, see Figure The design resistance and failure mode should be determined separately for each T-stub equivalent. The size portion e min (EC3 1-8 point 6.2.4) should be taken from Figure 6.8 for the beam that is between the superior and inferior beam flange. For the end-plate extension e min should be taken as e x, see Figure The effective length l eff equivalent T-stub of plate should be determined in according with EC3 1-8 point using the values for each row bolts represented in the table 6.6. Figure The values of m and m x to use for the Table 6.6 should be determined from U s e r M a n u a l V e r s i o n J a n u a r y P a g e 112 of 354

113 To note as for the bolt rows between the superior and inferior beam flange the l eff is a vertical size so as the case of l eff column flange While for the extended end plate l eff is an horizontal size. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 113 of 354

114 The extended end plate is calculated separately Generally for the plate we consider a different value of l eff an equivalent T- stub for bolt-rows of beam end-plate, they are subject to the stiffener given by web panel beam and so it has design resistance and stiffener superior than end bolt-row plate. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 114 of 354

115 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 115 of 354

116 3.7.8 Plate and web beam in compression Verification made in according with EC3 1-8 point U s e r M a n u a l V e r s i o n J a n u a r y P a g e 116 of 354

117 Beam not reinforced Beam web and flange in compression and references The resultant of the design compression resistance of beam flange and the adjacent compression zone of the beam web, may be assumed to act at the level of the center of compression, the design compression resistance of combined beam flange and web is given by the following expression: F c, fb, M h t c, fb where: h is the depth (height) of beam; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point For a reinforced beam M, may be calculated neglecting the c intermediate flange. t fb is the flange thickness of the connected beam. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 117 of 354

118 Center of compression If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. For the c reduced moment M, calculation with shear force, see EC3-1-1 point 6.2.8, we use U s e r M a n u a l V e r s i o n J a n u a r y P a g e 118 of 354

119 M y, V, W pl, y M 0 2 w A 4t w f y Where 2V V pl, Beam web in tension Beam web and flange in tension and references The design resistance of the web beam is given as follows : F t, wb, b t eff, t, wb wb f y, wb M 0 The effective width b eff t, wb, is taken as equal to the effective length of an equivalent T- stub represented from the end plate in bending, for bolt-rows between two beam plates, considering the individual bolt-rows and the bolt-groups. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 119 of 354

120 Welding Design resistance of fillet weld is: F w, Where fvw. d a l f vwd. is weld shear design resistance. a is height throat weld. l is length cordon weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. The weld verification should be satisfied if: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 120 of 354

121 F w, Fw, where: F w, is the force design value acting all over cordon weld; F w, is the design resistance of all over weld cordon. Below are summaries the action of calculation should be considered for the welds verification Welds beam connection plate to the column The plate generally should be bending moment resistant and normal force, welding on the plate should be checked when: F M N b, b, t, ep, Fw, fvwd. Where z 2 a b b r is the length cordon weld on the tension or compressed beam area r The web beam generally should be shear resisting, the welding on the web should be checked when: F t, ep, V Fw, fvwd. Where a h h r is length cordon weld on the web column r Joint design resistance due to axial force Verification made in according with EC3 1-8 point The design resistance for pure normal stress N j, is calculated as the less value of single design resistance calculated for the joint ( first considered), if is compression force or tension force. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 121 of 354

122 Resistance of design Compression The compression design resistance N j, is the smallest of following values: - Column Web panel in transverse compression 2 F c, wc, - Plate and beam web in compression N pl, b ( plastic normal stress of the beam) Design resistance in tension The normal stress tension N, of connection beam-column of a bolted joint with a j plate should be determined by: N j, nrowftr, where: F, is the effective design resistance of tension of the bolt-row r ; tr n row is the number of bolt-rows. The effective design tension resistance tr F, for each row-bolt r, taken as single boltrows, is the smaller design tension resistance for a single bolt-row of the following basic components: F, - Column Web in transverse tension t, wc F,, - the column flange in transverse bending t, fc F,, - Connection end plate in bending t, ep F,, - Web beam in tension t, wb - Flange and web beam in tension N pl, b Shear resistance Verification made in according EC3 1-8 point The shear force is totally transferred to the bolts, so the design shear resistance is connected to the shear resistance. For a shear connection of class A (EC3 1-8 point 3.4.1) the single bolt shear resistance should be obtained: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 122 of 354

123 F v,, v f ub M 2 A If the shear plane is through the thread bolt portion: - for classes 4.6, 5.6 e 8.8 v for classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through the not thread bolt portion: v 0.6 For the bolts of connection stressed in tension (see bolts in tension in the case of bending) their resistance should be reduced by 0.4/1. 4, so: F F v,, v,, tr, Where F v,, tr, M v fub A is the shear bolt resistance stressed to tension too. The shear resistance V, of connection beam-column of a bolted joint with plate j should be determined by: n bolt V j F, 1 v, The bearing verification for single bolt is: F b,, Where k1 b f u M 2 dt For outer bolts b f min( f ub e1 ; 3d For inner bolts u 0 ;1) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 123 of 354

124 b f min( f ub u p ; 3d For outer bolts ;1) 4 e2 k 1 min( ;2.5) d 0 For inner bolts p2 k 1 min( ;2.5) d 0 Without shear force however should be considered a shear force equal to 2,5% of the normal force of weaker section Bending force resistance Verification made in according with EC3 1-8 point The design moment resistance in bending of a bolted joint with an end plate connection that has an individual bolt-row in tension (or if is considered only a bolt-row in tension) should be calculated as shown in Figure 6.15 (c). The design moment resistance of a bolted joint with a plate with more than tension bolt-rows should be determined as shown in For compression center see Figure U s e r M a n u a l V e r s i o n J a n u a r y P a g e 124 of 354

125 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 125 of 354

126 The moment of calculation should be taken as not less than a moment equal to 25% of plastic moment of the weaker section, if the action is less. The design moment resistance M, f bolted joint beam- to-column with an end- j plate may be determined from: r M j, hr Ftr, where: F, is the effective design resistance of tension calculation of bolt-row r; tr h r is the distance from bolt-row r from center of compression; r is the bolt-row number. NOTE: The bolt-rows are numerated from farther bolt-row from center of compression. The center of compression should be assumed to be in line with the center of the compression flange of the connected member. The effective design tension resistance F, for each bolt-row should be determined tr in sequence, from bolt-rows number 1, that is from farther bolt-row from center of compression, then proceeding to row 2, ecc. When determining the effective design tension resistance F tr, of bolt-row r the effective design tension resistance of all other bolt-rows closer to the center of compression should be ignored. The effective design tension resistance F, of each bolt-row r taken as an individual tr bolt-row, should be taken as the smallest value of the design tension resistance F tr, for an individual bolt-row of the following basic components: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 126 of 354

127 F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, - The end-plate in bending t, ep, F, - The beam web in tension t, wb, The effective design tension resistance F tr,, of bolt-row r, should,if necessary, be reduced below the value of tr F, to ensure that all bolt-rows up to and including boltrow r, the following conditions are satisfied: - The total resistance design Vwp, Ftr, ; - The total design resistance F tr, does not exceed the smaller of: F,, ; - The design resistance of the column web in compression c wc, F,,. - The design resistance of the beam web in compression c fb, The effective design tension resistance F tr,, of bolt-row r, should,if necessary, be reduced below the value of F tr,, to ensure that the sum of the design resistances taken for the bolt-rows up and including bolt-row r that form part of the same group of bolt-rows, does not exceed the design resistance of that group as a whole. This should be checked for the following basic components: F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, - The end-plate in bending t, ep, F, t, wb, - The beam web in tension U s e r M a n u a l V e r s i o n J a n u a r y P a g e 127 of 354

128 Resistance to buckling and tension-bending Verification made in according EC3 1-8 point If the axial force N on the beam exceed the 5% of the design resistance N pl,, the conservative domain should be used is: M M j, j, N N j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 128 of 354

129 3.8 Joint 124 (Connection beam circular section beam) Forces On the profiles can be applied the following forces: N normal force (positive if tension force) V, x V, y M, x horizontal shear vertical shear bending moment all round x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 129 of 354

130 N V N pl, y V pl where the plastic resistances are referred to the column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 130 of 354

131 3.8.2 Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint, in according with l EC3 1-8 and the following table 3.3 and figure 3.1. The verification is made only for e 1 and e 2, and not for p 1 e p 2 because the local buckling resistance of the plate is always prevented by the stiffeners and by the same column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 131 of 354

132 3.8.3 Design resistance of single bolt and single weld In this paragraph we recall the common criteria for verification of single bolts and single weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 132 of 354

133 Design resistance at Bolt tensile force The tension resistance of single bolt is: F t, Where 0.9 f ub M 2 A A s is stressed tensile area s f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for the classes 4.6, 5.6 e 8.8 v for the classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v 0.6 While A è is the bolt area f ub is the last bolt tensile stress Design resistance of the weld Design resistance of fillet weld is: F w, Where fvw. d a l f vwd. is weld shear design resistance. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 133 of 354

134 a is height throat weld. l is cordon weld length. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 134 of 354

135 3.8.4 Verifications made The verifications made on the joint are the following: - Flange and beam web in compression F c, fb, Fc, fb, Bearing resistance verification on two horizontal directions on the connection F b, Fb, - Verification beam web panel in shear V wp, Vwp, - Verification of web beam in compression F c, wc, Fc, wc, - Verification axial force resistance without moment resistance applied N N j, j, 1 - Verification for shear force V V j, j, 1 Verification in bending without axial force applied M M j, j, 1 - Verification in buckling M M j, j, N N j, j, 1 If the axial force N does not exceed the 5% of the plastic axial force N pl,, is neglected the coexistence of the axial force and the rule becomes M M j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 135 of 354

136 3.8.5 Bearing resistance of single bolt The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where b is dt For outer bolts b f min( f ub u e1 ; 3d For inner bolts is b f min( f ub u While k 1 is p ; 3d For outer bolts 0 0 ;1) 1 1 ;1) 4 e2 k 1 min( ;2.5) d For inner bolts is p2 k 1 min( ;2.5) d Where 0 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection d 0 is hole diameter For the other sizes definition see figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 136 of 354

137 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 137 of 354

138 3.8.6 Plate Connection in bending Verification made in according with EC3 1-8 point The design resistance and failure mode of a plate in bending, together with the associated bolts in tension, should be taken as similar to those of an equivalent T-stub (EC3 1-8 point 6.2.4), the design resistance for both: - each individual bolt-row required to resist tension; - each group of bolt-rows required to resist tension. The group of bolt rows, both the reinforced sides connecting to the end plate should be considered as an equivalent T-stub. In an extended end-plate, considered as the part of the plate extended on the beam (extended end - plate), the bolt-row in the extended part is considered as a separated T-stub equivalent, see Figure The design resistance and failure mode should be determined separately for each T-stub equivalent. The size portion e min (EC3 1-8 point 6.2.4) should be taken from Figure 6.8 for the beam that is between the superior and inferior beam flange. For the end-plate extension e min should be taken as e x, see Figure The effective length l eff equivalent T-stub of plate should be determined in according with EC3 1-8 point using the values for each row bolts represented in the table 6.6. Figure The values of m and m x to use for the Table 6.6 should be determined from U s e r M a n u a l V e r s i o n J a n u a r y P a g e 138 of 354

139 To note as for the bolt rows between the superior and inferior beam flange the l eff is a vertical size so as the case of l eff column flange While for the extended end plate l eff is an horizontal size. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 139 of 354

140 The extended end plate is calculated separately Generally for the plate we consider a different value of l eff of an equivalent T-stub for bolt-rows of beam end-plate, they are subject to the stiffener given by web panel beam and so it has design resistance and stiffener superior than end bolt-row plate.. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 140 of 354

141 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 141 of 354

142 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 142 of 354

143 3.8.7 Plate and web beam in compression Verification made in according with EC3 1-8 point Beam not reinforced Beam web and flange in compression and references The resultant of the design compression resistance of beam flange and the adjacent compression zone of the beam web, may be assumed to act at the level of the center of compression, the design compression resistance of combined beam flange and web is given by the following expression: F c, fb, M h t c, fb where: h is the depth (height) of beam; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point For a reinforced beam M, may be calculated neglecting the c intermediate flange. t fb is the flange thickness of the connected beam. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 143 of 354

144 Center of compression If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. For the M, calculation with shear force, see EC3-1-1 point 6.2.8, we use c reduced moment M y, V, W pl, y M 0 2 w A 4t w f y U s e r M a n u a l V e r s i o n J a n u a r y P a g e 144 of 354

145 Where 2V V pl, Beam web in tension Verification made in according with EC3 1-8 point Beam web and flange in tension and references The design resistance of the web beam is given as follows : F t, wb, b t eff, t, wb wb f y, wb M 0 The effective width b eff t, wb, is taken as equal to the effective length of an equivalent T- stub represented from the end plate in bending, for bolt-rows between two beam plates, considering the individual bolt-rows and the bolt-groups. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 145 of 354

146 3.8.9 Welding Design resistance of fillet weld Where is: F w, fvw. d a l f vwd. is weld shear design resistance. a is height throat weld. l is length cordon weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. The weld verification should be satisfied if: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 146 of 354

147 F w, Fw, where: F w, is the force design value acting all over cordon weld; F w, is the design resistance of all over weld cordon. Below are summaries the action of calculation should be considered for the welds verification Welds beam connection plate to the column The plate generally should be bending moment resistant and normal force, welding on the plate should be checked when: F M N b, b, t, ep, Fw, fvwd. Where z 2 a b b r is the length cordon weld on the tension or compressed beam area r The web beam generally should be shear resisting, the welding on the web should be checked when: F t, ep, V Fw, fvwd. Where a h h r is length cordon weld on the web column r Joint design resistance due to axial force Verification made in according with EC3 1-8 point The design resistance for pure normal stress N j, is calculated as the less value of single design resistance calculated for the joint ( first considered), if is compression force or tension force. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 147 of 354

148 Resistance of design compression The compression design resistance N j, is the smallest of following values: - Column Web panel in transverse compression 2 F c, wc, - Plate and beam web in compression N pl, b ( plastic normal stress of the beam) Design resistance in tension The normal stress tension N, of connection beam-column of a bolted joint with a j plate should be determined by: N j, nrowftr, where: F, is the effective design resistance of tension of the bolt-row r; tr n row is the number of bolt-rows. The effective design tension resistance tr F, for each row-bolt r, taken as single boltrows, is the smaller design tension resistance for a single bolt-row of the following basic components: F, - Column Web in transverse tension t, wc F,, - the column flange in transverse bending t, fc F,, - Connection end plate in bending t, ep F,, - Web beam in tension t, wb - Flange and web beam in tension N pl, b Shear resistance Verification made in according EC3 1-8 point The shear force is totally transferred to the bolts, so the design shear resistance is connected to the shear resistance. For a shear connection of class A (EC3 1-8 point 3.4.1) the single bolt shear resistance should be obtained: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 148 of 354

149 F v,, v f ub M 2 A If the shear plane is through the thread bolt portion: - for the classes 4.6, 5.6 e 8.8 v for the classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through the not thread bolt portion: v 0.6 For the bolts of connection stressed in tension (see bolts in tension in the case of bending) their resistance should be reduced by 0.4/1. 4, so: F F v,, v,, tr, Where F v,, tr, M v fub A is the shear bolt resistance stressed to tension too. The shear resistance V, of connection beam-column of a bolted joint with plate j should be determined by: n bolt V j F, 1 v, The bearing verification for single bolt is: F b,, Where k1 b f u M 2 dt For outer bolts b f min( f ub u e1 ; 3d for inner bolts 0 ;1) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 149 of 354

150 b f min( f ub u p ; 3d for outer bolts ;1) 4 e2 k 1 min( ;2.5) d 0 for inner bolts p2 k 1 min( ;2.5) d 0 Without shear force however should be considered a shear force equal to 2,5% of the normal force of weaker section Bending force resistance The design moment resistance in bending of a bolted joint with an end plate connection that has an individual bolt-row in tension (or if is considered only a bolt-row in tension) should be calculated as shown in Figure 6.15 (c). The design moment resistance of a bolted joint with a plate with more than tension bolt-rows should be determined as shown in For compression center see Figure U s e r M a n u a l V e r s i o n J a n u a r y P a g e 150 of 354

151 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 151 of 354

152 The moment of calculation should be taken as not less than a moment equal to 25% of plastic moment of the weaker section, if the action is less. The design moment resistance M, f bolted joint beam- to-column with an end- j plate may be determined from: r M j, hr Ftr, where: F, is the effective design resistance of tension calculation of bolt-row r; tr h r is the distance from bolt-row r from center of compression; r is the bolt-row number. NOTE: The bolt-rows are numerated from farther bolt-row from center of compression. The center of compression should be assumed to be in line with the center of the compression flange of the connected member. The effective design tension resistance F, for each bolt-row should be determined tr in sequence, from bolt-rows number 1, that is from farther bolt-row from center of compression, then proceeding to row 2, ecc. When determining the effective design tension resistance F tr, of bolt-row r the effective design tension resistance of all other bolt-rows closer to the center of compression should be ignored. The effective design tension resistance F, of each bolt-row r taken as an individual tr bolt-row, should be taken as the smallest value of the design tension resistance F tr, for an individual bolt-row of the following basic components: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 152 of 354

153 F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, - The end-plate in bending t, ep, F, - The beam web in tension t, wb, The effective design tension resistance F tr,, of bolt-row r, should,if necessary, be reduced below the value of tr F, to ensure that all bolt-rows up to and including boltrow r, the following conditions are satisfied: - The total design resistance Vwp, Ftr, ; - The total design resistance F tr, does not exceed the smaller of: F,, ; - The design resistance of the column web in compression c wc, F,,. - The design resistance of the beam web in compression c fb, The effective design tension resistance F tr,, of bolt-row r, should,if necessary, be reduced below the value of F tr,, to ensure that the sum of the design resistances taken for the bolt-rows up and including bolt-row r that form part of the same group of bolt-rows, does not exceed the design resistance of that group as a whole. This should be checked for the following basic components: F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, - The end-plate in bending t, ep, F, t, wb, - The beam web in tension U s e r M a n u a l V e r s i o n J a n u a r y P a g e 153 of 354

154 Resistance to buckling and tension-bending Verification made in according EC3 1-8 point If the axial force N on the beam exceed the 5% of the design resistance N pl,, the conservative domain should be used is: M M j, j, N N j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 154 of 354

155 3.9 Joint 128 (Beam web Column plate welded) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 155 of 354

156 3.9.1 Stiffeners of the column On the column web can located transverse and diagonal stiffeners. the following stiffeners: supplementary plates, The supplementary plates may be applied on a single-sided or a double sided column web panel. The transverse stiffeners can be aligned with the corresponding superior and inferior web beam plate Forces On the profile can be applied the following forces: N axial force (positive if tension force) V, x V, y M, x shear force parallel to column flange shear force parallel to column axis bending moment all round x axis U s e r M a n u a l V e r s i o n J a n u a r y P a g e 156 of 354

157 The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N V N pl, y V pl where the plastic resistances are referred to the column Design resistance of single bolt and single weld In this paragraph we speak about the common criteria for verification of each bolts and each weld Design resistance at Bolt tensile force Tensile strength of single bolt is: F t, Where 0.9 f ub M 2 A s A s is the stressed tensile area f ub is the last tensile force of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 157 of 354

158 - for the classes 4.6, 5.6 e 8.8 v for the classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through the not threaded bolt portion: v 0.6 While A is the bolt area f ub is the last bolt tensile stress Design resistance of the weld Design resistance of fillet weld is: F w, Dove fvw. d a l f vwd. is weld shear design resistance. a is the height throat of the weld. l is the length cordon of the weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 158 of 354

159 3.9.4 Verifications made The verifications made on the joint are the following: - Shear verification on the column web panel V wp, Vwp, - Bearing resistance verification on the column web panel F c, wc, Fc, wc, - Flange and column web to compressive force F c, fb, Fc, fb, - Bearing resistance verification on two horizontal directions on the connection plate F b, Fb, - Shear verification on the web beam V wp, Vwp, - Compression verification on the web beam V wp, Vwp, F c, wc, Fc, wc, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 159 of 354

160 - Verification of axial force without moment resistance applied N N j, j, 1 - Shear force verification V V j, j, 1 - Bending force verification without axial force M M j, j, 1 - Buckling verififcation M M j, j, N N j, j, 1 If the axial force N does not exceed the 5% of the plastic axial force N pl,, is neglected the coexistence of the axial force and the rule becomes M M j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 160 of 354

161 3.9.5 Design resistance of column web panel in shear Verification made according with EC3 1-8 point Shear action in the column web and references The design resistance calculation of column web in shear, is valid provided the column web slenderness satisfies the condition d / t w 69 Where d ( h 2t f ) 2r height web 235 coefficient that considers the material f y Unstiffened web panel column For a single sided joint (single-sided-joint), or for a double-sided joint (double-sidedjoint) joint which the depths are similar the design plastic shear resistance V wp, of an unstiffened column web panel, subject to a design shear force V wp,, should be obtained using: V wp, 09f y, wc A 3 M 0 vc U s e r M a n u a l V e r s i o n J a n u a r y P a g e 161 of 354

162 Where: A A 2bt ( t 2r) t is the shear area of the column, see EN v f w f 2 A 2bt ( h 2t ) t (4 ) r 2bt ( h 2t ) t r is the cross section area. f f w f f w 2 Single-sided-joint and double-sided-joint Design shear force V, is given by: wp V wp, M b1, M z b2, V c1, V 2 c2, In JFT the value according to the above expression, is calculated only if the data derived from a software calculation that allows the determination of the forces all over the joint (see Midas or from text file). If the stresses are recorded by Tekla the shear force considered is: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 162 of 354

163 V wp, M z Where z is the lever arm that is z h b t f, b The forces that contribute to the shear calculation V, are shown in the following wp figure, Stiffened column web panel The design shear resistance on the column web may be increased by the use of horizontal or transverse stiffeners or supplementary web plates. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 163 of 354

164 . When transverse web stiffeners are used in both the compression zone and the tension zone, the design plastic shear resistance of the column web panel V, increases, so wp the design plastic shear resistance of the column web panel may be increased by: V wp, add, 4M pl, fc, but should be d s V wp, add, That should be taken the smaller between the two Where: 2M pl, fc, 2M d d s is the distance between the centerlines of the stiffeners; M pl fc, s pl, st,, is the design plastic moment resistance of a column flange M pl st,, is the design plastic moment resistance of a stiffener. Example of transverse stiffener on the web column NOTE: The joint 128 is a welded joint, the transverse stiffeners should be aligned with the corresponding beam flange(ec3 1-8 point ). When diagonal web stiffeners are used, the design plastic shear resistance of a column web should be determined according to EN Due to the diagonal geometry, the plastic normal stress of single plate is: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 164 of 354

165 N pl, diag A diag f y, diag 0 That should be greater than the force transmitted from the beam plate N pl, diag Where M z / cos M is the design moment transmitted from a single beam h b arctan is the angle that the diagonal forms with the axis parallel to the beam hc flange h b e h c are respectively the beam width and the length column The design shear resistance of column web panel V N wp, add, pl, diag cos V, may be increased by: wp Example of diagonal stiffener on the web column If the column web is reinforced by adding a supplementary web plate, see Figure 6.5, the shear area A vcw may be increased by di b s t wc. If a further supplementary web plate is added on the other side of the web column, no further increase of the shear area should be made. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 165 of 354

166 NOTE: The Weldability at the corner should be taken into account for a correct modeling of reinforcement with supplementary web plate. The supplementary web plate on the column web increase the rotational stiffness of a joint, increasing the stiffness column web in shear, in compression or in tension (EC (1). The supplementary web plate should comply the following mechanical and geometrical in according with EC3: - The steel grade of the supplementary web plate should be equal to that of the column; - The width b s should be such that the supplementary web plate extends at least to the toe of the root radius with of plate column or of the weld (fig. 6.5); - The length l s should be such that the supplementary web plate extends throughout the effective width of the web in tension and compression, see Figure 6.5; The thickness t s of the supplementary web plate should be not less than the column web thickness t wc. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 166 of 354

167 The welds between the supplementary web plate and profile should be designed to resist the applied design forces V,. wp The width b s of a supplementary web plate should be less than Discontinuous welds may be used in not corrosive environments. The increase of the resistances on the web are cumulative. 40 t. s The local verification should be satisfied if: V wp, Vwp, Resistance of column web in transverse compression Verification made in according with EC3 1-8 point Web column subject to compression and references Unstiffened column web panel The design resistance of an unstiffened column web subject to transverse compression should be determined from: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 167 of 354

168 F c, wc, kwcbeff, c. wctwc f y, wc but M 0 F c, wc, k wc b eff, c. wc wc M1 t f y, wc It is considered as resistance of column web subject to transverse compression the less of two values.. The first expression represents the web resistance for crushing (in the figure is represented with the letter l, column web crushing), the second expression represents the resistance for column web buckling (in the figure is represented with the letter m, column web buckling). Where: is a reduction factor to allow the possible effects of interaction with shear in the column web panel according to Table 6.3; b eff c, wc, is the effective width of column web in compression that for welded end-plate connection is: b eff, c, wc t fb 2 2ab 5( t fc s) a c, r c and a b are as indicated Figure 6.6. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 168 of 354

169 - For a rolled I or H section column : s rc - For a welded I or H section column : s 2ac Definition of b eff, c, wc is the reduction factor for column web buckling: - If 0. 72: 1. 0 p - If 0. 72: p p p p is the plate slenderness (web column): p b d eff, c, wc wc 2 Etwc f y, wc - For a rolled I or H section column I o H : d h ( t r ) wc c 2 fc c - For a welded I or H section column I o H : d h ( t 2a ) wc c 2 fc c U s e r M a n u a l V e r s i o n J a n u a r y P a g e 169 of 354

170 k wc is a reduction factor, that considers the maximum longitudinal compressive stress due to axial force and bending moment in the column exceeds 0.7 f y, wc in the com, web (adjacent to the root radius for a rolled section or the toe of the weld for a welded section), its value as a function of com, is: - When com, 0. 7 f y, wc : k 1. 0 wc - When com, 0. 7 f y, wc : k wc 1.7 f com, y, wc The compressive stress is: F c, wc, com, beff twc While the force on the compression web beam is: F c, wc, M z b, N b, 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 170 of 354

171 Stiffened Column web panel If the minimum design resistance of an unstiffened column web, subjected to a column sway buckling mode illustrated in Figure 6,7, is due to its buckling, should normally be prevented by appropriate constructional stiffeners. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 171 of 354

172 To increase the design resistance of the column web in transverse compression, in order may be used: supplementary web plates, transverse stiffeners, diagonal stiffeners. Increase of design resistance due to transverse and diagonal stiffeners When there are transverse stiffeners on the column web in compression zone, increases the design resistance in compression that should be taken as similar to shear added resistance on the web column V wp,, in this case the compression design resistance on the web column is increased (similarly the shear resistance in the column web) with: V wp, add, 4M pl, fc, but should be V d s wp, add, 2M pl, fc, 2M d s pl, st, For the meaning of the values see the shear verification of column web. When we use transverse stiffeners, the design resistance in compression of column web should be determined in according with EN Given the geometry of the diagonal stiffeners, the design plastic normal stress of single plate is: A N pl, diag diag f y, diag 0 That should be greater than the force transmitted by beam flange N pl, diag M z / cos U s e r M a n u a l V e r s i o n J a n u a r y P a g e 172 of 354

173 Where M is the calculation moment transmitted by a single beam h b arctan is the angle that the diagonal forms with the axis parallel to the hc beam flange h b e h c are respectively the beam width and the length column The design shear resistance of column web panel V N wp, add, pl, diag cos The calculation resistance with stiffeners is V, may be increased by: wp F c, wc, Fc, wc, Vwp, add, NOTE: The joint 128 is a welded joint, the transverse stiffeners should be aligned with the corresponding beam flange (EC3 1-8 point ). When the web column is reinforced by adding the supplementary web plate, should be respected the following mechanical and geometrical sizes: - The steel grade of the supplementary web plate should be equal to that of the column; - The width b s should be such that the supplementary web plate extends at least to the toe of the root radius with of plate column or of the weld (fig. 6.5); - The length l s should be such that the supplementary web plate extends throughout the effective width of the web in tension and compression, see Figure 6.5; - The thickness t s of the supplementary web plate should be not less than the column web thickness t wc. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 173 of 354

174 When there is the supplementary web plate, the effective web thickness to use for, calculation is 1.5t wc, if is added a single supplementary web plate, 2.0twc if the F c wc, supplementary web plates are placed on the double-sided web. The shear web area resistant A vc for the calculation of should be increased by b s t wc The web resistance increased are cumulative. The local verification should be satisfied if: F c, wc, Fc, wc, Resistance of web Column in transverse tension Verification made in according with EC3 1-8 point Column web in tension and references Unstiffened column web panel The design resistance of an unstiffened column web subject to transverse tension should be determined from: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 174 of 354

175 F t, wc, b t eff, t, wc wc M 0 f y, wc where: is a reduction factor to allow the possible effects of interaction with shear in the column web panel according to table 6.3. b eff t, wc b, is the effective width of column web in tension that for end-plate connection is: t 2 2a 5( t ) (6.16) eff, t, wc fb b fc s where: - For a rolled I or H section column : s rc - For a welded I or H section column : s 2ac where: a c e r c are as indicated Figure 6.8 e a b is as indicated Figure 6.6. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 175 of 354

176 The reduction factor to allow for the possible effects of interaction with shear in the column web panel should be determined from table 6.3, using the value of b eff, t, wc determined for the connection considered Stiffened column web panel To increase the design resistance of the column web in transverse tension, in order may be used: supplementary web plates, transverse stiffeners, diagonal stiffeners. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 176 of 354

177 NOTE: The joint 128 is a welded joint, the transverse stiffeners should be aligned with the corresponding beam flange (EC3 1-8 point ). The welds of a diagonal stiffener that connect the column flange should be all over the length of the reinforcement, with throat section similar to the thickness reinforcements. When the web column is reinforced by adding the supplementary web plate, should be respected the following mechanical and geometrical sizes: - the steel grade of the supplementary web plate should be equal to that of the column; - the width b s should be such that the supplementary web plate extends at least to the toe of the root radius with of plate column or of the weld (fig. 6.5); - the length l s should be such that the supplementary web plate extends throughout the effective width of the web in tension and compression, see Figure 6.5; - the thickness t s of the supplementary web plate should be not less than the column web thickness t wc. The design tension resistance for one supplementary web plate depends on the throat thickness of the longitudinal welds connecting the supplementary web plates. The effective thickness of the web t w, ef should be taken as follows: - When the longitudinal welds are full penetration butt welds with a throat thickness a t s then: - For one supplementary web plate: tw, eff 1. 5t wc - For supplementary web plates both sides: tw, eff 2. 0t wc - When the longitudinal welds are fillet welds with a throat thickness either one or two supplementary web plates: - For steel grades S 235, S 275 e S 355: tw, eff 1. 4t wc t a s then for 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 177 of 354

178 - For steel grades S 420 e S 460: tw, eff 1. 3t wc The resistant shear area should be increased of di A vc of a column web in calculating the reduction factor di b s t wc. The local verification should be satisfied if: F t, wc, Ft, wc, Resistance of column flange in transverse bending Verification made in according with EC3 1-8 point Column flange in bending and references The design resistance F, of an unstiffened column flange in transverse bending, due fc to a tension or a bending of the beam flange, is: F fc, where: b eff b, fc b t eff, b. fc fb M 0 f y, fb, is the effective width b eff (see EC3 1-8 point 4.10), considering the beam flange as a plate. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 178 of 354

179 The effective width b eff is b t 2s 7kt eff w where: f k t / t )( f / f ) but should be k 1 y f ( f p y, f y, p f, is the yield strength of the flange of the I or H section; f, is the yield strength of the plate welded to the I or H section. y p The dimension s should be obtained from: - For a rolled I or H section : s r - For a welded I or H section : s 2a For an unstiffened flange of an I or H section, the following criterion should be satisfied: b ) b eff where: y p ( f y, p / f y, u p f, the ultimate strength of the plate welded to the I or H section; b p is the width of the plate welded to the I or H section. Otherwise the joint should be stiffened Plate and web beam in compression Verification made in according with EC3 1-8 point U s e r M a n u a l V e r s i o n J a n u a r y P a g e 179 of 354

180 Beam Not reinforced Beam web and flange in compression and references The resultant of the design compression resistance of beam flange and the adjacent compression zone of the beam web, may be assumed to act at the level of the center of compression, the design compression resistance of combined beam flange and web is given by the following expression: F c, fb, M h t c, fb where: h is the depth (height) of beam; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point For a reinforced beam M, may be calculated neglecting the c intermediate flange. t fb is the flange thickness of the connected beam. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 180 of 354

181 Center of compression If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. For the M, calculation with shear force, see EC3-1-1 point 6.2.8, we use c reduced moment M y, V, W pl, y M 0 2 w A 4t w f y Where 2V V pl, 1 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 181 of 354

182 Reinforced Beam Reinforced beam. Beam web and flange in compression and references Such as in the case of not reinforced beam the design resistance in compression of the flange and web corresponding to connection beam-column is given as follows: F c, fb, where: M h t c, fb h is the total height, including the depth of the beam and the maximum height of the reinforcement; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point 6.2.8, may be calculated neglecting the intermediate flange (inferior flange of the beam). t fb is the flange thickness of the connected beam. If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. For the reinforced beam should be determined using the following rules, that we use in the modeling connection - the steel grade of the reinforcement should be equal to that the beam; - The size and web thickness reinforcement should be less than of the beam; - The angle of plate reinforcement respect to the beam should not be higher than 45 ; U s e r M a n u a l V e r s i o n J a n u a r y P a g e 182 of 354

183 For a reinforced beam, the web beam is subject to compression force, its design resistance is calculated in according EC3 1-8 point (see resistance of column web in transverse compression) Weldings Design resistance of fillet weld is: F w, Where fvw. d a l f vwd. is weld shear design resistance. a is height throat weld. l is length cordon weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 183 of 354

184 The weld verification should be satisfied if: F w, Fw, Where: F w, is the force design value acting all over cordon weld; F w, is the design resistance of all over weld cordon. Below are summaries the action of calculation should be considered for the welds verification. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 184 of 354

185 Welds on the supplementary web plates The shear force on the web plate is transmitted to the supplementary plate by the welding, the verification should be satisfied if: F w, Vwp. Fw, fvw. d a bs and F w, Vwp, Fw, fvw. d a ls Welds on the stiffened column plates U s e r M a n u a l V e r s i o n J a n u a r y P a g e 185 of 354

186 F - Horizontal stiffener - Welding on the web panel column, the verification should be satisfy if: w, Vwp. Fw, fvwd. Where a n b b r is the base of the reinforce (parallel to the web column) r n is the cordon welds number (no more than two, when the cordon weld is on both the plate side) F - Welding on the plate column,, the verification should be satisfy if: w, Vwp. Fw, fvwd. Where a n h h r is the height of reinforce (orthogonal to the web column) r n is the cordon welds number (no more than two, when the cordon weld is on both the plate side) - Diagonal stiffener F M a 2 b z w, / cos Fw, fvwd. Where b r is the base of reinforce (connection to flange column) r Welds beam connection plate to the column The plate generally should be bending moment resistant and normal force, welding on the plate should be checked when: F M N b, b, t, ep, Fw, fvwd. Where z 2 a b b r is the length cordon weld on the tension or compressed beam area r U s e r M a n u a l V e r s i o n J a n u a r y P a g e 186 of 354

187 The web beam generally should be shear resisting, the welding on the web should be checked when: F t, ep, V Fw, fvwd. Where a h h r is length cordon weld on the web column r Joint design resistance due to axial force The design resistance for only normal stress N j, is calculated as the less value of single design resistance calculated for the joint ( first considered), if is compression force or tension force Compression design resistance The compression design resistance N j, is the smallest of following values: - Column Web panel in transverse compression 2 F c, wc, - Plate and beam web in compression N pl, b ( plastic normal stress of the beam) Tension design resistance The normal stress tension N, of connection beam-column of a welded joint is the j smallest of following values: - Web Beam welded with column plate F w, F, - Column Web in transverse tension t, wc F,, - Web beam in tension t, wb - Flange and web beam in tension N pl, b Shear resistance The shear force is totally transferred to the weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 187 of 354

188 The shear resistance V, of connection beam-column of a welded joint with plate j should be determined by: V j, Fw, fvwd. Where a h r h r is length cordon weld on the web column Resistance to bending force The design moment resistance in bending of a welded joint should be calculated as shown in Figure 6.15 (a). U s e r M a n u a l V e r s i o n J a n u a r y P a g e 188 of 354

189 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 189 of 354

190 The moment of calculation should be taken as not less than a moment equal to 25% of plastic moment of the weaker section, if the action is less. The design moment resistance M, of welded joint beam- to-column may be j determined from: M j, where: tr Ftr, z F, is the effective design resistance of tension calculation of the member; z r is the distance from the compression center; The center of compression should be assumed to be in line with compression flange of the connected member. the center of the The effective design tension resistance F, should be taken as the smallest value of tr the design tension resistance for a single basic component: - Web Beam welded with column plate F w, F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, t, wb, - The beam web in tension The effective design tension resistance F tr,, should be reduced below the value of F, to ensure that: tr - The total design resistance Vwp, Ftr, ; - The total design resistance F tr, does not exceed the following smaller values: F,, ; - The design resistance of the column web in compression c wc, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 190 of 354

191 F,,. - The design resistance of the plate and beam web in compression c fb, Resistance to buckling and tension-bending If the axial force N on the beam exceed the 5% of the design resistance N pl,, the conservative domain should be used is : M M j, j, N N j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 191 of 354

192 3.10 Joint 40 (Beam plate column bolted, reinforced) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 192 of 354

193 Stiffeners on the column On the column web can be located the following stiffeners: supplementary, transverse and diagonal reinforcements. The additional plates can be applied on single sided or for a double-sided web column. The supplementary plate can be only welded to the web column, is not permitted the bolting. The hole number must be set to 0. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 193 of 354

194 The transverse reinforcements can be placed corresponding : superior web beam plate, inferior web beam plate or end base reinforcement. The stiffener cross geometry considers the reinforcement on the beam Stiffeners on the beam U s e r M a n u a l V e r s i o n J a n u a r y P a g e 194 of 354

195 Forces On the profiles can be applied the following forces: N normal force (positive if tension force) V, x V, y M, x horizontal shear vertical shear bending moment all round x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N V N pl, y V pl where the plastic resistances are referred to the column Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint, in according with l EC3 1-8 and the following table 3.3 and figure 3.1. The verification is made only for e 1 and e 2, and not for p 1 e p 2 because the local buckling resistance of the plate is always prevented by the stiffeners (fasteners) and by the same column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 195 of 354

196 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 196 of 354

197 Design resistance of single bolt and single weld In this paragraph we recall the common criteria for verification of single bolts and single weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 197 of 354

198 Design resistance at Bolt tensile force Tensile strength of single bolt is: F t, Where 0.9 f ub M 2 A A s is stressed tensile area s f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point3.4.1) the single bolt shear strength design (for a single resistant section) is : F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for classes 4.6, 5.6 e 8.8 v for classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v while 0.6 A is the bolt area f ub is the last bolt tensile stress Design resistance of the weld Design resistance of fillet weld is: F w, Where fvw. d a l U s e r M a n u a l V e r s i o n J a n u a r y P a g e 198 of 354

199 f vwd. is weld shear design resistance. a is height throat weld. l is cordon weld length. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 199 of 354

200 Verifications made The verifications made on the joint are the following: - Verification column web panel in shear V wp, Vwp, - Verification column web in compression F c, wc, Fc, wc, - Plate and beam web in compression F c, fb, Fc, fb, - Bearing resistance verification on two horizontal directions on the connection plate F b, Fb, - Verification beam web panel in shear V wp, Vwp, - Verification beam web in compression F c, wc, Fc, wc, - Axial force resistance without moment resistance applied - Verification axial force resistance without moment resistance applied N N j, j, 1 - Verification for shear force V V j, j, 1 - Bending force resistance without axial force M M j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 200 of 354

201 - Verification in buckling M M j, j, N N j, j, 1 If the axial force N does not exceed the 5% of the plastic axial force N pl,, is neglected the coexistence of the axial force and the rule becomes M M j, j, Design resistance of column web panel in shear Verification made according with EC3 1-8 point Shear action in the column web and references The design resistance calculation of column web in shear, is valid provided the column web slenderness satisfies the condition d / t w 69 Where d ( h 2t f ) 2r height web 235 coefficient that considers the material f y U s e r M a n u a l V e r s i o n J a n u a r y P a g e 201 of 354

202 Unstiffened web panel column For a single sided joint, in or for a double-sided joint which the depths are similar the design plastic shear resistance design shear force V wp, Where: v 09f y, wc A 3 f M 0 vc w V wp, of an unstiffened column web panel, subject to a V wp,, should be obtained using: A A 2bt ( t 2r) t is the shear area of the column, see EN f 2 A 2bt ( h 2t ) t (4 ) r 2bt ( h 2t ) t r is the cross section area. f f w f f w 2 Single-sided-joint and double-sided-joint U s e r M a n u a l V e r s i o n J a n u a r y P a g e 202 of 354

203 Design shear force V, is given by: wp V wp, M b1, M z b2, V c1, V 2 c2, In JFT the value according to the above expression, is calculated only if the data derived from a software calculation that allows the determination of the forces all over the joint (see Midas or from text file). If the stresses are recorded by Tekla the shear force considered is: V wp, M z Where: z is the lever arm that is z h b t f, b U s e r M a n u a l V e r s i o n J a n u a r y P a g e 203 of 354

204 The forces that contribute to the shear calculation V, are shown in the following wp figure, Stiffened column web panel The design shear resistance on the column web may be increased by the use of horizontal or transverse stiffeners or supplementary web plates. Where transverse web stiffeners are used in both the compression zone and the tension zone, the design plastic shear resistance of the column web panel V, may be wp increased, by: V wp, add, 4M pl, fc, but should be d s V wp, add, That should be taken the smaller between the two 2M pl, fc, 2M d s pl, st, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 204 of 354

205 where: d s is the distance between the centerlines of the stiffeners; M pl fc,, is the design plastic moment resistance of a column flange M pl st,, is the design plastic moment resistance of a stiffener. Example of transverse stiffener on the web column When diagonal web stiffeners are used, the design plastic shear resistance of a column web should be determined according to EN Due to the diagonal geometry, the plastic normal stress of single plate is: A N pl, diag diag f y, diag 0 That should be greater than the force transmitted from the beam plate N pl, diag Where M z / cos M is the design moment transmitted from a single beam h b arctan is the angle that the diagonal forms with the axis parallel to the beam hc flange h b e h c are respectively the beam width and the length column U s e r M a n u a l V e r s i o n J a n u a r y P a g e 205 of 354

206 The design shear resistance of column web panel V, may be increased by: wp V N wp, add, pl, diag cos Example of diagonal stiffener on the web column If the column web is reinforced by adding a supplementary web plate, see figure 6.5, the shear area A vcw may be increased by b s t wc. If a further supplementary web plate is added on the other side of the web column, no further increase of the shear area should be made. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 206 of 354

207 NOTE: Weldability at the corner should be taken into account for a correct modeling of reinforcement with supplementary web plate. The supplementary web plate on the column web increase the rotational stiffness of a joint, increasing the stiffness column web in shear, in compression or in tension (EC (1). The supplementary web plate should comply the following mechanical and geometrical in according with EC3: - The steel grade of the supplementary web plate should be equal to that of the column; - The width b s should be such that the supplementary web plate extends at least to the toe of the root radius with of plate column or of the weld (fig. 6.5); - The length l s should be such that the supplementary web plate extends throughout the effective width of the web in tension and compression, see Figure 6.5; - The thickness t s of the supplementary web plate should be not less than the column web thickness t wc. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 207 of 354

208 The welds between the supplementary web plate and profile should be designed to resist the applied design forces V,. wp The width b s of a supplementary web plate should be less than Discontinuous welds may be used in not corrosive environments. The increase of the resistances on the web are cumulative. 40 t. s The local verification should be satisfied if: V wp, Vwp, Resistance of column web in transverse compression Verification made in according with EC3 1-8 point Web column subject to compression and references Unstiffened column web panel The design resistance of an unstiffened column web subject to transverse compression should be determined from: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 208 of 354

209 F c, wc, kwcbeff, c. wctwc f y, wc but M 0 F c, wc, k wc b eff, c. wc wc M1 t f y, wc We consider as resistance of column web subject to transverse compression the less of two values. The first expression represents the web resistance for crushing (in the figure is represented with the letter l, column web crushing), the second expression represents the resistance for column web buckling (in the figure is represented with the letter m, column web buckling). Where: is a reduction factor to allow the possible effects of interaction with shear in the column web panel according to Table 6.3; b eff c, wc, is the effective width of column web in compression that for bolted end-plate connection is: b eff, c, wc t 2 2a 5( t s) s fb p fc p where : U s e r M a n u a l V e r s i o n J a n u a r y P a g e 209 of 354

210 s p is the length obtained by dispersion at 45 through the end- plate with the column flange (at least t p provided that the length of end-plate below the flange is sufficient up to 2 t p ). - For a rolled I o H section column : s rc - For a welded I o H section column : s 2ac Sizes are indicated in Figure 6.6. Definition of b eff, c, wc is the reduction factor for column web buckling: - If 0. 72: 1. 0 p - If 0. 72: p p p p is the plate slenderness (web column): U s e r M a n u a l V e r s i o n J a n u a r y P a g e 210 of 354

211 p b d eff, c, wc wc 2 Etwc f y, wc - For a rolled I o H section column I o H : d h ( t r ) wc c 2 fc c - For a welded I o H section column : d h ( t 2a ) wc c 2 fc c k wc is a reduction factor, that considers the maximum longitudinal compressive stress due to axial force and bending moment in the column exceeds 0.7 f y, wc in the com, web (adjacent to the root radius for a rolled section or the toe of the weld for a welded section), its value as a function of com, is: - When com, 0. 7 f y, wc : k 1. 0 wc - When com, 0. 7 f y, wc : k wc 1.7 f com, y, wc U s e r M a n u a l V e r s i o n J a n u a r y P a g e 211 of 354

212 The compressive stress is: F c, wc, com, beff twc While the force on the compression web beam is: F c, wc, M z b, N b, 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 212 of 354

213 Stiffened Column web panel If the minimum design resistance of an unstiffened column web, subjected to a column sway buckling mode illustrated in Figure 6,7, is due to its buckling, should normally be prevented by appropriate constructional stiffeners. To increase the design resistance of the column web in transverse compression, in order may be used: supplementary web plates, transverse stiffeners, diagonal stiffeners. Increase of design resistance due to transverse and diagonal stiffeners When there are transverse stiffeners on the column web in compression zone, increases the design resistance in compression that should be taken as similar to shear added resistance on the web column V wp,, in this case the compression design resistance on the web column is increased (similarly the shear resistance in the column web) with: V wp, add, 4M pl, fc, but should be V d s wp, add, 2M pl, fc, 2M d s pl, st, For the meaning of the values see the shear verification of column web. When we use transverse stiffeners, the design resistance in compression of U s e r M a n u a l V e r s i o n J a n u a r y P a g e 213 of 354

214 column web should be determined in according with EN Given the geometry of the diagonal stiffeners, the design plastic normal stress of single plate is: A N pl, diag diag f y, diag 0 That should be greater than the force transmitted by beam flange N pl, diag Where M z / cos M is the calculation moment transmitted by a single beam h b arctan is the angle that the diagonal forms with the axis parallel to the hc beam flange h b e h c are respectively the beam width and the length column The design shear resistance of column web panel V N wp, add, pl, diag cos The calculation resistance with stiffeners is V, may be increased by wp F c, wc, Fc, wc, Vwp, add, When the web column is reinforced by adding the supplementary web plate, should be respected the following mechanical and geometrical sizes: - The steel grade of the supplementary web plate should be equal to that of the column; - The width b s should be such that the supplementary web plate extends at least to the toe of the root radius with of plate column or of the weld (fig. 6.5); - The length l s should be such that the supplementary web plate extends throughout the effective width of the web in tension and compression, see Figure 6.5; U s e r M a n u a l V e r s i o n J a n u a r y P a g e 214 of 354

215 - The thickness t s of the supplementary web plate should be not less than the column web thickness t wc. When there is the supplementary web plate, the effective web thickness to use for, calculation is 1.5t wc, if is added a single supplementary web plate, 2.0twc if the F c wc, supplementary web plates are placed on the double-sided web. The shear web area resistant A vc for the calculation of should be increased by b s t wc The web resistance increased are cumulative. The local verification should be satisfied if: F c, wc, Fc, wc, Single bolt bearing resistance The bearing verification for single bolt resistance section is: F b,, k1 b f u M 2 Where b is dt For outer bolts b f min( f ub u e1 ; 3d For inner bolts is b f min( f ub u While k 1 is p ; 3d For outer bolts 0 0 ;1) 1 1 ;1) 4 e2 k 1 min( ;2.5) d For inner bolts 0 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 215 of 354

216 p2 k 1 min( ;2.5) d Where 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection d 0 is hole diameter For the other sizes definition see figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 216 of 354

217 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be satisfied: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 217 of 354

218 Resistance of web Column in transverse tension Verification made in according with EC3 1-8 point Column web in tension and references Unstiffened column web panel The design resistance of an unstiffened column web subject to transverse tension should be determined from: F t, wc, b t eff, t, wc wc M 0 f y, wc where: is a reduction factor to allow the possible effects of interaction with shear in the column web panel according to table 6.3. The effective width b eff t, wc, of web column in tension is similar to the effective length of an equivalent T-stub represented by column flange in unstiffened transverse bending. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 218 of 354

219 b eff, t, wc l eff For the calculation should be taken the smallest value of the l eff, generally we have the maximum value of the tension force in the end bolt, we should be considered the end bolt row (End bolt-row) tab. 6.4, should be considered as single bolt not as a group of bolts. The reduction factor to allow for the possible effects of interaction with shear in the column web panel should be determined from table 6.3, using the value of b eff, t, wc determined for the connection considered. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 219 of 354

220 Stiffened column web panel The effective width b eff t, wc, of web column in tension is similar to the effective length of an equivalent T-stub represented by column flange in stiffened transverse bending. b eff, t, wc l eff For the calculation should be taken the smallest value of the l eff, generally we have the maximum value of the tension force in the end bolt (End bolt-row adjacent to a stiffener) tab. 6.5 should be considered as single bolt not as a group of bolts. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 220 of 354

221 To increase the design resistance of the column web in transverse tension, in order may be used: supplementary web plates, transverse stiffeners, diagonal stiffeners. The welds of a diagonal stiffener that connect the column flange should be all over the length of the reinforcement, with throat section similar to the thickness reinforcements. When the web column is reinforced by adding the supplementary web plate, should be respected the following mechanical and geometrical sizes: - the steel grade of the supplementary web plate should be equal to that of the column; - the width b s should be such that the supplementary web plate extends at least to the toe of the root radius with of plate column or of the weld (fig. 6.5); - the length l s should be such that the supplementary web plate extends throughout the effective width of the web in tension and compression, see Figure 6.5; - the thickness t s of the supplementary web plate should be not less than the column web thickness t wc. The design tension resistance for one supplementary web plate depends on the throat thickness of the longitudinal welds connecting the supplementary web plates. The effective thickness of the web t w, ef should be taken as follows: - When the longitudinal welds are full penetration butt welds with a throat thickness a t s then: - For one supplementary web plate: tw, eff 1. 5t wc - For supplementary web plates both sides: tw, eff 2. 0t wc U s e r M a n u a l V e r s i o n J a n u a r y P a g e 221 of 354

222 - When the longitudinal welds are fillet welds with a throat thickness either one or two supplementary web plates: - For steel grades S 235, S 275 e S 355: tw, eff 1. 4t wc t a s then for 2 - For steel grades S 420 e S 460: tw, eff 1. 3t wc The resistant shear area should be increased of A vc of a column web,in calculating the reduction factor di b s t wc. The local verification should be satisfied if : F t, wc, Ft, wc, Resistance of column flange in transverse bending Verification made in according with EC3 1-8 point Column flange in bending and references Unstiffened column flange The design resistance and failure mode of an unstiffened column flange in transverse bending, together with the associated bolts in tension, should be taken as similar to those of an equivalent T-stub (EC3 1-8 point 6.2.4), the design resistance for both: - each individual bolt-row required to resist tension; U s e r M a n u a l V e r s i o n J a n u a r y P a g e 222 of 354

223 - each group of bolt-rows required to resist tension. The dimensions e min and m to use for verification in according with EC3 1-8 point 6.2.4, should be determined from Figure 6.8. The effective length of equivalent T-stub flange should be determined the individual bolt-rows and bolt-group (in accordance with EC3 1-8 point ) from the values given for each group of bolt-rows in Table 6.4. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 223 of 354

224 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 224 of 354

225 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 225 of 354

226 Example of failure mechanism unstiffened column flange, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 226 of 354

227 The size e 1 is the end distance from the edge plate (see figure) For the meaning of the effective length see the following figure U s e r M a n u a l V e r s i o n J a n u a r y P a g e 227 of 354

228 Stiffened column flange To increase the design resistance of column flange in transverse bending, we use transverse stiffeners and/or diagonal reinforcements. The design resistance and the collapse mode of an unstiffened column flange in transverse bending, is calculated considering also the bolts in tension, considered as a T-stub (EC3 1-8 point 6.2.4), the design resistance is calculated for: - Each individual bolt-row necessary to endure the tension; - Each group of bolt row necessary to endure the tension. The group of bolt rows, both the reinforced side is modeling as an equivalent T-stub for the flange, see Figure 6.9. The design resistance and the collapse mode is calculated separately for each equivalent T-stub. For the size e min e m see Figure 6.8. The effective length l eff an equivalent T-stub flange is determined in according with EC3 1-8 point , using the values for each row bolts represented in the table 6.5. The value of should be determined from the Figure U s e r M a n u a l V e r s i o n J a n u a r y P a g e 228 of 354

229 The stiffeners should be satisfied the requirements specified for shear verification of web column (EC3 1-8 point ) Plate Connection in bending Verification made in according with EC3 1-8 point The design resistance and failure mode of a plate in bending, together with the associated bolts in tension, should be taken as similar to those of an equivalent T-stub (EC3 1-8 point 6.2.4), the design resistance for both: - each individual bolt-row required to resist tension; - each group of bolt-rows required to resist tension. The group of bolt rows, both the reinforced sides connecting to the end plate should be considered as an equivalent T-stub. In an extended end-plate, considered as the part of the plate extended on the beam (extended end - plate), the bolt-row in the extended part is considered as a separated T-stub equivalent, see Figure The design resistance and failure mode should be determined separately for each T-stub equivalent. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 229 of 354

230 The size portion e min (EC3 1-8 point 6.2.4) should be taken from Figure 6.8 for the beam that is between the superior and inferior beam flange. For the end-plate extension e min should be taken as e x, see Figure The effective length l eff equivalent T-stub of plate should be determined in according with EC3 1-8 point using the values for each row bolts represented in the table 6.6. The values of m and m x to use for the Table 6.6 should be determined from Figure U s e r M a n u a l V e r s i o n J a n u a r y P a g e 230 of 354

231 To note as for the bolt rows between the superior and inferior beam flange the l eff is a vertical size so as the case of l eff column flange While for the extended end plate l eff is an horizontal size U s e r M a n u a l V e r s i o n J a n u a r y P a g e 231 of 354

232 The extended end plate is calculated separately Generally for the plate we consider a different value of l eff an equivalent T- stub for bolt-rows of beam end-plate, they are subject to the stiffener given by web panel beam and so it has design resistance and stiffener superior than end bolt-row plate U s e r M a n u a l V e r s i o n J a n u a r y P a g e 232 of 354

233 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 233 of 354

234 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 234 of 354

235 Plate and web beam in compression Beam not reinforced Verification made in according with EC3 1-8 point Beam web and flange in compression and references The resultant of the design compression resistance of beam flange and the adjacent compression zone of the beam web, may be assumed to act at the level of the center of compression, the design compression resistance of combined beam flange and web is given by the following expression: F c, fb, M h t c, fb where: h is the depth (height) of beam; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point For a reinforced beam M, may be calculated neglecting the c intermediate flange. t fb is the flange thickness of the connected beam. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 235 of 354

236 Center of compression If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. For the M, calculation with shear force, see EC3-1-1 point 6.2.8, we use c reduced moment M y, V, W pl, y M 0 2 w A 4t w f y U s e r M a n u a l V e r s i o n J a n u a r y P a g e 236 of 354

237 Where 2V V pl, Reinforced Beam Reinforced beam. Beam web and flange in compression and references Such as in the case of not reinforced beam the design resistance in compression of the flange and web corresponding to connection beam-column is given as follows: F c, fb, where: M h t c, fb h is the total height, including the depth of the beam and the maximum height of the reinforcement; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point 6.2.8, may be calculated neglecting the intermediate flange (inferior flange of the beam). t fb is the flange thickness of the connected beam. If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 237 of 354

238 Reinforced beam should be determined using the following rules, that we use in the modeling connection : - the steel grade of the reinforcement should be equal to that the beam; - The size and web thickness reinforcement should be less than of the beam; - The angle of plate reinforcement respect to the beam should not be higher than 45 ; For a reinforced beam, the web beam is subject to compression force, its design resistance is calculated in according EC3 1-8 point (see resistance of column web in transverse compression) Beam web in tension Beam web and flange in tension and references The design resistance of the web beam is given as follows : F t, wb, b t eff, t, wb wb f y, wb M 0 The effective width b eff t, wb, is taken as equal to the effective length of an equivalent T- stub represented from the end plate in bending, for bolt-rows between two beam plates, considering the individual bolt-rows and the bolt-groups Weldings Design resistance of fillet weld is: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 238 of 354

239 F w, fvw. d a l where f vwd. is weld shear design resistance. a is height throat weld. l is length cordon weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. The weld verification should be satisfied if: F w, Fw, where: F w, is the force design value acting all over cordon weld; U s e r M a n u a l V e r s i o n J a n u a r y P a g e 239 of 354

240 F w, is the design resistance of all over weld cordon. Below are summaries the action of calculation should be considered for the welds verification Welds on the supplementary web plates The shear force on the web plate is transmitted to the supplementary plate by the welding, the verification should be satisfied if: F w, Vwp. Fw, fvw. d a bs and F w, Vwp, Fw, fvw. d a ls U s e r M a n u a l V e r s i o n J a n u a r y P a g e 240 of 354

241 Welds on the stiffened column plates F a) Horizontal stiffener - Welding on the web panel column, the verification should be satisfy if: w, Vwp. Fw, fvwd. where a n b b r is the base of the reinforce (parallel to the web column) r n is the cordon welds number (no more than two, when the cordon weld is on both the plate side) F - Welding on the plate column,, the verification should be satisfy if: w, Vwp. Fw, fvwd. Where a n h h r is the height of reinforce (orthogonal to the web column) r n is the cordon welds number (no more than two, when the cordon weld is on both the plate side) F a) diagonal stiffener M a 2 b z w, / cos Fw, fvwd. r U s e r M a n u a l V e r s i o n J a n u a r y P a g e 241 of 354

242 Where b r is the base of reinforce (connection to flange column) Welds beam connection plate to the column The plate generally should be bending moment resistant and normal force, welding on the plate should be checked when: F M N b, b, t, ep, Fw, fvwd. Where z 2 a b b r is the length cordon weld on the tension or compressed beam area r The web beam generally should be shear resisting, the welding on the web should be checked when: F t, ep, V Fw, fvwd. where a h h r is length cordon weld on the web column r Joint design resistance due to axial force Verification made in according with EC3 1-8 point The design resistance for pure normal stress N j, is calculated as the less value of single design resistance calculated for the joint ( first considered), if is compression force or tension force Compression design resistance The compression design resistance N j, is the smallest of following values: - Column Web panel in transverse compression 2 F c, wc, - Plate and beam web in compression N pl, b ( plastic normal stress of the beam). U s e r M a n u a l V e r s i o n J a n u a r y P a g e 242 of 354

243 Tension design resistance The normal stress tension N, of connection beam-column of a bolted joint with a j plate should be determined by: N j, nrowftr, where: F, is the effective design resistance of tension of the bolt-row r; tr n row is the number of bolt-rows. The effective design tension resistance tr F, for each row-bolt r, taken as single boltrows, is the smaller design tension resistance for a single bolt-row of the following basic components: F, - Column Web in transverse tension t, wc F,, - the column flange in transverse bending t, fc F,, - Connection end plate in bending t, ep F,, - Web beam in tension t, wb - Flange and web beam in tension N pl, b Shear resistance Verification made in according EC3 1-8 point The shear force is totally transferred to the bolts, so the design shear resistance is connected to the shear resistance. For a shear connection of class A (EC3 1-8 point 3.4.1) the single bolt shear resistance should be obtained: F v,, v f ub M 2 A If the shear plane is through the thread bolt portion: - for classes 4.6, 5.6 e 8.8 v 0.6 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 243 of 354

244 - for classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through the not thread bolt portion: v 0.6 For the bolts of connection stressed in tension (see bolts in tension in the case of bending) their resistance should be reduced by 0.4/1. 4, so: F F v,, v,, tr, Where F v,, tr, M v fub A is the shear bolt resistance stressed to tension too. The shear resistance V, of connection beam-column of a bolted joint with plate j should be determined by: n bolt V j F, 1 v, The bearing verification for single bolt is: F b,, Where k1 b f u M 2 For end bolts b f min( f ub u dt e1 ; 3d For inner bolts b f min( f ub u For end bolts p ; 3d 0 0 ;1) 1 1 ;1) 4 e2 k 1 min( ;2.5) d 0 For inner bolt U s e r M a n u a l V e r s i o n J a n u a r y P a g e 244 of 354

245 p2 k 1 min( ;2.5) d 0 Without shear force however should be considered a shear force equal to 2,5% of the normal force of weaker section Bending force Resistance Verification made in according with EC3 1-8 point The design moment resistance in bending of a bolted joint with an end plate connection that has an individual bolt-row in tension (or if is considered only a bolt-row in tension) should be calculated as shown in Figure 6.15 (c). The design moment resistance of a bolted joint with a plate with more than tension bolt-rows should be determined as shown in For compression center see Figure U s e r M a n u a l V e r s i o n J a n u a r y P a g e 245 of 354

246 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 246 of 354

247 The moment of calculation should be taken as not less than a moment equal to 25% of plastic moment of the weaker section, if the action is less. The design moment resistance M, of bolted joint beam- to-column with an end- j plate may be determined from: r M j, hr Ftr, where: F, is the effective design resistance of tension calculation of bolt-row r; tr h r is the distance from bolt-row r from center of compression; r is the bolt-row number NOTE: The bolt-rows are numerated from farther bolt-row from center of compression. The center of compression should be assumed to be in line with the center of the compression flange of the connected member. The effective design tension resistance F, for each bolt-row should be determined tr in sequence, from bolt-rows number 1, that is from farther bolt-row from center of compression, then proceeding to row 2, ecc. When determining the effective design tension resistance F tr, of bolt-row r the effective design tension resistance of all other bolt-rows closer to the center of compression should be ignored. The effective design tension resistance F, of each bolt-row r,taken as an individual tr bolt-row, should be taken as the smallest value of the design tension resistance F tr, for an individual bolt-row of the following basic components: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 247 of 354

248 F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, - The end-plate in bending t, ep, F, - The beam web in tension t, wb, The effective design tension resistance F tr,, of bolt-row r, should,if necessary, be reduced below the value of tr F, to ensure that all bolt-rows up, to and including boltrow r, the following conditions are satisfied : - The total design resistance Vwp, Ftr, ; - The total design resistance F tr, does not exceed the smaller of : F,, ; - The design resistance of the column web in compression c wc, F,,. - The design resistance of the beam web in compression c fb, The effective design tension resistance F tr,, of bolt-row r, should,if necessary, be reduced below the value of F tr,, to ensure that the sum of the design resistances taken for the bolt-rows up and including bolt-row r that form part of the same group of bolt-rows, does not exceed the design resistance of that group as a whole. This should be checked for the following basic components: F, - The column web in transverse tension t, wc F,, - The column flange in transverse bending t, fc F, - The end-plate in bending t, ep, F, t, wb, - The beam web in tension U s e r M a n u a l V e r s i o n J a n u a r y P a g e 248 of 354

249 Resistance to buckling and tension-bending Verification made in according with EC3 1-8 point If the axial force N on the beam exceed the 5% of the design resistance N pl,, the conservative domain should be used is: M M j, j, N N j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 249 of 354

250 3.11 Connection 1014 (rectangular base plate connection) (Connection with beam or column in r.c.) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 250 of 354

251 Stiffeners The stiffeners can be placed in two directions Shear Key The shear key must have a section contrasting the shear force U s e r M a n u a l V e r s i o n J a n u a r y P a g e 251 of 354

252 Anchor steel bars The steel bar can be anchored with bolts or bars with stiffeners anchorage Bolts Straight bar L bar Hook bar Anchor with washer plate Anchor hammer U s e r M a n u a l V e r s i o n J a n u a r y P a g e 252 of 354

253 Forces On the profile we can apply the following forces: N axial force (positive if tension force) V, x V, y M, x shear force parallel to column flange shear force parallel to column axis bending moment all round x axis The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N V N pl, y V pl where the plastic resistances are referred to the column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 253 of 354

254 Geometrical verification The procedure provides to verify the construction requirements for drilling bolted joint, in according to l EC3 1-8 with the following table 3.3 and figure 3.1. The verification is made only for e 1 and e 2, and not for p 1 e p 2 because the local buckling resistance of the plate is always prevented by the stiffeners (fasteners) and by the same column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 254 of 354

255 Design resistance of single bolt and single weld In this paragraph we recall the common criteria for verification of single bolts and single welding. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 255 of 354

256 Design resistance at Bolt tensile force Tensile strength of single bolt is: F t, Where 0.9 f ub M 2 A s A s is the stressed tensile area f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is: F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for classes 4.6, 5.6 e 8.8 v for classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v 0.6 While A is the area of the bolt f ub is the last bolt tensile stress Design resistance of the weld Design resistance of fillet weld is: F w, Where fvw. d a l U s e r M a n u a l V e r s i o n J a n u a r y P a g e 256 of 354

257 f vwd. is weld shear design resistance. a is the height throat of the weld. l is the length cordon of the weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 Where f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 257 of 354

258 Verifications made - The verifications made on the joint are the following: - Shear verification of the connection F v, Fv, F w, Fw, V V j, j, 1 - Bearing resistance verification on two horizontal directions on the connection plate F b, Fb, - Compressive force verification F C, FC, - Weld column-base plate for bending force F w, Fw, - Flange and column web to compressive force F c, fb, Fc, fb, - Anchor resistance - F t, Ft, - Axial force resistance without moment resistance applied N N j, j, 1 - Bending force resistance without axial force M M j, j, 1 - Buckling, we consider the following resistance rule M M j, j, N N j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 258 of 354

259 If the axial force N does not exceed the 5% of the plastic axial force N pl,, is neglected the coexistence of the axial force and the rule becomes M M j, j, Verification of shear force The shear force verification are made with according EC3 1-8 point Without shear key In base plates, if no special elements for resisting shear are provided, such as shear key, the connection shear resistance is the friction resistance between base plate and grout layer (with compressive force) and anchor bolts resistance. If in a column there is a compressive force, the design friction resistance between base plate grout layer F f, C f, d Nc, where: f d F, is: f C, is the coefficient of friction between base plate and grout layer. For sand-cement mortar C f, d N, is the design value of the normal compressive force in the column. c NOTE: If the column is loaded by a tensile normal force, F 0. f, In a column base the design shear resistance of an anchor bolt F vb, should be taken as the smaller of F, vb, F, 1 and 2, vb where: - F, vb, 1 is the design shear resistance of the anchor bolt - F 2, vb, b f ub Mb A s where: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 259 of 354

260 b f yb f yb is the yield strength of the anchor bolt, with 2 235N / mm f 640N / mm yb 2 The design shear resistance of the joint F, is v F v, Ff, nfvb, where: n is the number of anchor bolts in the base plate. With Shear key if special elements for resisting shear are provided, such as shear key, the connection shear resistance is completely entrusted to the contact surface between the shear key and the concrete subject to compression. The design compression resistance F, is: C F C, f jd bh where: b is the effective contact area width with shear key and concrete h is the effective contact area length with shear key and concrete f jd is the design bearing strength of shear key with concrete It is assumed that the forces are uniformly distributed to the concrete. The pressure on the contact surface between the shear key and the foundation must not be superior the design bearing strength resistance f jd. The design bearing strength f jd is: f jd j F bh where: j u is the foundation material coefficient, which may be taken as 2 / 3. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 260 of 354

261 F is the compression design resistance force given in EN 1992, where A c0 is to be u taken as (bh). EXTRACT by EC2 6.7 localized forces (1) In the case of localized forces, we must note the local breaking (see below) and the cross tensile strength (see point 6.5). (2) When we have a load uniformly distributed on Ac0 area (see figure 6.29) the last compression force can be determined as follow: F u A A c1 c0 fcd 3 fcd Ac0 Ac0 (6.63) where: A c0 is loaded area; A c1 is the load maximum diffusion area used for the calculation and which has an homothetic shape to A c0. (3) It is recommended that the diffusion area A c1 wanted by ultimate compression force F u should be satisfied the following conditions: - the load height diffusion in load direction must be taken as is indicated in figure 6.29; - the area diffusion center A c1 must be on the line of action crossing through the loading area center A c0 ; - if on concrete area act more compression strength, it is recommended that the diffusion areas aren t overlapping. F It is recommended that the u value is reduced if the load is not uniformly distributed on area A c0 or if there are shear force significant. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 261 of 354

262 (4) It is recommended to provide adequate reinforcements to balance traction cross forces due to the load effect. In JFT it considers the minimum value F u so: 3 fcd Ac0 jfu j 3 fcdbeff leff f jd j 3 f b l b l eff eff eff eff cd The verification should be satisfied if F v, FC, Weld verification The verification is made considering acting only shear force, is made separately for connection column-base plate and for connection key shear block base plate. It should satisfy: F w, Fw, With U s e r M a n u a l V e r s i o n J a n u a r y P a g e 262 of 354

263 F w, fvw. d a l Where l is total cordon length a is throat height Resistance to bearing of single bolt The bearing verification for single bolt resistance section is : F b,, Where k1 b f u M 2 b is dt For outer bolts b f min( f ub u e1 ; 3d For inner bolts is b f min( f ub u While k 1 is p ; 3d for outer bolts 0 0 ;1) 1 1 ;1) 4 e2 k 1 min( ;2.5) d 0 For inner bolts p2 k 1 min( ;2.5) d Where 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of connected plates d 0 is the hole diameter U s e r M a n u a l V e r s i o n J a n u a r y P a g e 263 of 354

264 For the other sizes definition see figure 3.1 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 264 of 354

265 Base plate in compression For this resistance we use the equivalent T-stub in tension. The design compression resistance F, is: C F C, f jd b eff l eff where: b eff is the effective width of the T-stub plate l eff is the effective length of the T-stub plate f jd is the design bearing strength of the joint The forces transferred through a T-stub should be assumed to spread uniformly as shown in Figure 6.4 (a) e (b). The pressure on the resulting bearing area should not exceed the design bearing f jd and the additional bearing width c,should not exceed: c t f y 3 f jd M 0 where: t is the thickness of the flange; f y is the yield strength of the flange. If the projection of the physical length of the basic column plate is less than c, the effective area should be taken as indicated Figure 6.4 (a). If the projection of the physical length of the basic column plate exceeds of c,on any side, the part of the additional projection beyond the width c should be neglected, see Figure 6.4 (b). U s e r M a n u a l V e r s i o n J a n u a r y P a g e 265 of 354

266 The reinforcements web plates may also be used to increase identically the contact surface, with not overlapping diffusion. The common design bearing strength f jd is: f jd j F b l eff u eff where: j is the foundation material coefficient, which may be taken as 2 / 3 provided that the characteristic strength of the grout is not less than 0,2 times the characteristic strength of the concrete foundation and the thickness of the grout is not greater than 0,2 times the smallest width of the steel base plate. In cases where the thickness of the grout is more than 50 mm, the characteristic strength of the grout should be at least the same as that of the concrete foundation. F is the compression design resistance force given in EN 1992, where A c0 is to be u taken as b ). ( eff leff U s e r M a n u a l V e r s i o n J a n u a r y P a g e 266 of 354

267 6.7 EXTRACT by EC2 6.7 localized forces (1) In the case of localized forces, we should be noted the local breaking (see below) and the cross tensile strength (see point 6.5). (2) When we have a load uniformly distributed on Ac0 area (see figure 6.29) the last compression force can be determined as follow: F u A A c1 c0 fcd 3 fcd Ac0 Ac0 (6.63) where: A c0 is loaded area; A c1 is the load maximum diffusion area used for the calculation and which has an homothetic shape to A c0. (3) It is recommended that the diffusion area A c1 wanted by ultimate compression force F u should be satisfied the following conditions: - the load height diffusion in load direction must be taken as is indicated in figure 6.29; - the area diffusion center A c1 must be on the line of action crossing through the loading area center A c0 ; - if on concrete area act more compression strength, it is recommended that the diffusion areas aren t overlapping. It is recommended that the F value is reduced if the load is not uniformly distributed on area A c0 or if there are shear force significant. u U s e r M a n u a l V e r s i o n J a n u a r y P a g e 267 of 354

268 (4) It is recommended to provide adequate reinforcements to balance traction cross forces due to the load effect. In JFT it considers the minimum value F u so: 3 fcd Ac0 jfu j 3 fcdbeff leff f jd j 3 f b l b l eff eff eff eff cd Verification The compression force is transmitted by column flange and is: F C, M c, ( h t c fc Nc, ) 2 so: F C, FC, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 268 of 354

269 Base plate in bending under tension The design resistance and collapse mode of a bending base plate, is calculated considering the design tension resistance of the bolts too, it is considered similar as T- stub (EC3 1-8 point 6.2.4), the design resistance is calculated for: - the design resistance of an individual bolt row; - the contribution of each bolt row to design resistance. The group of bolt rows, on both the reinforced side connected to the end plate should be considered as separated as an equivalent T-stub. In extended plate, considered as the extended plate over the beam (extended end - plate), the bolt rows in extended plate is considered as an equivalent T-stub separated, see Figure The design resistance and the collapse mode is calculated separately for each equivalent T- stub. The dimension e min (EC3 1-8 point 6.2.4) is taken by Figure 6.8 regarding that part of plate that is between upper plate and the lower beam. For the extended part of plate e min is assumed as e x, see Figure The effective length l eff an equivalent T-stub flange is determined in according with EC3 1-8 point using the values for each row bolts represented in the table 6.6. The values of m and Figure m x to be used for the Table 6.6 should be determined from the U s e r M a n u a l V e r s i o n J a n u a r y P a g e 269 of 354

270 We note for the bolt rows between superior and inferior beam flange the l eff is a vertical size as in the case of l eff column flange While the extension of the end plate l eff is an horizontal size. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 270 of 354

271 The extension part of the end plate is calculated separately Generally for the plate we have different value of equivalent member l eff to T- stub equivalent for the bolt rows between the beam plate, these are influenced of stiffness given by web beam and so it has resistance and stiffness higher than the extended part of the plate. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 271 of 354

272 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 272 of 354

273 Weld verification The verification is made considering acting only bending force. Should satisfy: F w, Fw, With F w, fvw. d a l U s e r M a n u a l V e r s i o n J a n u a r y P a g e 273 of 354

274 Where l is the total cordon length a is the cordon throat height Column flange and web in compression Beam not reinforced Beam web and flange in compression and references The resultant of the design compression resistance of beam flange and the adjacent compression zone of the beam web, may be assumed to act at the level of the center of compression, the design compression resistance of combined beam flange and web is given by the following expression: F c, fb, M h t c, fb where: h is the depth (height) of beam; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point For a reinforced beam M, may be calculated neglecting the c intermediate flange. t fb is the flange thickness of the connected beam. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 274 of 354

275 Center of compression If the depth (height) of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. For the M, calculation with shear force, see EC3-1-1 point 6.2.8, we use c reduced moment M y, V, W pl, y M 0 2 w A 4t w f y U s e r M a n u a l V e r s i o n J a n u a r y P a g e 275 of 354

276 Where 2V V pl, Tension of beam web Beam web and flange in tension and references The beam web tension resistance is given from following expression: F t, wb, b t eff, t, wb wb f y, wb M 0 the effective width b eff t, wb, is taken as equal to the effective length of the equivalent T- stub representing the end-plate in bending, for bolt row located between two beam flanges, considering an individual bolt-row and the bolt-groups Tension of anchor bolts Anchor bolts should be designed to resist the effects of the design loads, due both for normal forces that bending. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 276 of 354

277 The lever arm due to bending should be taken as the distance between the barycenter (centroid) of compression area and the centroid (barycenter) of the bolt group on the tension side. The design resistance of the anchor bolts should be taken as the smallest value between resistance to tension and anchor bolts resistance with concrete. Single bolt tension resistance is: F t, Where 0.9 f ub M 2 A s A s is the tensile stressed area f ub is the last tensile bolt strength The design bond resistance of the concrete and anchor bolts is taken in according with EN One of the following methods should be used to secure anchor bolts, into foundation: - A hook (figure 6.14 (a)), - A washer plate (figure 6.14 (b)), - Some other appropriate load distributing member embedded in the concrete, - Some other fixing which has been adequately tested and approved. When the bolts are provided with a hook, the anchorage length should be such as to prevent yielding of the bolt. The anchorage length should be calculated in accordance with EN This type of anchorage should not be used for bolts with a yield strength f yb higher than 2 300N / mm. When the anchor bolts are provided with a washer plate or other load distributing member, the design bond resistance of the concrete and steel is not considered. The whole of the force should be transferred through the load distributing device. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 277 of 354

278 Recalled EC2 for anchor bars 8.4 Longitudinal reinforcement anchorage General (1) Steel bars, wire or mesh must be anchored so as to be transferred frictional forces to the concrete to avoid the longitudinal cracking and detachment concrete. If required, should be used transversal reinforcements. (2) We can see the fixing methods in figure 8.1 [see also point 8.8 (3)]. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 278 of 354

279 (3) Bends and hook don t give any contribute to anchor in compression. (4) It is recommended to prevent the concrete breakage inside the bends in according with the point 8.3 (3). (5) Where we use mechanical anchor, It is recommended that test requirements are in according with European Technical Approval. (6) To transmit the pre stressed forces to concrete see point Ultimate friction (adherence) tension (1) The ultimate friction (adherence) tension should be sufficient to prevent the loss of adhesion. (2) The design tension value of the ultimate adhesion, f bd assumed as: fbd f ctd where:, for ribbed bars should be (8.2) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 279 of 354

280 f ctd is the design value of resistance to concrete tension for point (2)P. Due to the increasing fragility of the concrete of higher strength, it is recommended that the value of fctk 0,05 is limited, for this case, to the relative value of class C60/75, unless it can verify that the average adhesion resistance exceed; 1 is a ratio related to the quality of adhesion condition and at the bar location during concreting (see figure 8.2): 1 1 with condition of good adhesion in all other cases and for structural elements made with slipform, unless we can demonstrate that exist good conditions of adhesion; 2 it is referred to bar diameter: 2 for 32mm (132 ) /100 for 32mm The length of anchor base (1)P The calculation of anchor length should be calculated considering the type of steel and the adhesion properties of the bars. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 280 of 354

281 (2) The anchor length necessary with base l b, rqd, to anchor the force As sd applied to a bar in assumption of uniform adhesion tension equal to fbd is: l ( / 4)( / f ) (8.3) b, rqd sd bd with anchor. sd the design tension corresponding to the point from which is measured the The values of f bd are in point (3) The anchor base length, l b, and the design length, l bd of bars should be measured along the bar axis (see figure 8.1a) Design anchor length (1) the design anchor length, l bd, is: l bd l l (8.4) b, rqd b,min with α 1 α2 α3 α4 α5 the ratios given in table 8.2: α 1 takes into account the shape of the bars assumed that the concrete cover is adequate (see figure 8.1); α 2 takes into account the effect of the coating minimum concrete (see figure 8.3); α 3 takes into account the edge effect due to transverse reinforcement; α 4 takes into account the influence of one or more welding transverse bars ( 0. 6 along the design anchor length l bd (see also point 8.6); t ) α 5 takes into account the transverse force effect to the plan of breaking along the design anchor length. The product ( α 5 l b, rqd is obtained (8.3); 2α3α 0.7 ): (8.5) l b,min is the minimum anchor length if there are not other limitations: - for tension anchor : l max0.3 l ;10 ; mm (8.6) b, min b, min for anchor in compression : l max0.6 l ;10 ; mm (8.7) b, min b, min 100 (2) For semplicity, alternatively at point (1), the tension anchor of some shape U s e r M a n u a l V e r s i o n J a n u a r y P a g e 281 of 354

282 shown in figure 8.1 can be considered as the equivalent anchor length, l beq. l beq it is defined in the same figure and can be assumed: for the shape that we can see in the figure from 8.1b to 8.1d (for the values of - 1 l b, rqd 1 see the table 8.2); for the shapes that we can see in the figure 8.1e (for the values of 4 see the - 4 l b, rqd table 8.2); U s e r M a n u a l V e r s i o n J a n u a r y P a g e 282 of 354

283 Design resistance of column bases with base plates General Column bases should be of sufficient size stiffness order to resist the axial force, bending moments and shear forces in columns to their foundations or other supports without exceeding the load carrying capacity of these supports. The design bearing strength between the base plate and its support may be determined on the basis of an uniform distribution of compressive force over the bearing area. For concrete foundations the bearing area stress should not exceed the design bearing strength, f jd. For a column base subject combined axial force and bending, the forces between the base plate and its support can take one of the following distribution depending on the relative magnitude of the applied axial force and bending moment: - In the case of a dominant compressive axial force, full compression may develop under both column flanges as shown in Figure 6.18 (a). - In the case of a dominant tensile force, full tension may develop under both flanges as shown in Figure 6.18 (b). - In the case of dominant bending moment compression may develop under one column flange and tension under the other as shown in Figure 6.18 (c) and Figure 6.18 (d). Base plates should be designed using the appropriate methods, only normal stress or of buckling. One of the following methods should be used to resist the shear force between the base plate and its support: - Frictional design resistance at the joint between the base plate and its support. - The design shear resistance of the anchor bolts. - The design shear resistance of the surrounding part of the foundation. If anchor bolts are used to resist the shear forces between the base plate and its support, the rupture of the concrete in bearing should also be checked, according with EN U s e r M a n u a l V e r s i o n J a n u a r y P a g e 283 of 354

284 Where the above methods are inadequate, should be used special elements such as blocks or bar shear connectors to transfer the shear forces between the base plate and its support. To know if the base is subject more compression then bending, it is necessary design the tension diagram U s e r M a n u a l V e r s i o n J a n u a r y P a g e 284 of 354

285 Column bases subjected to axial force (1) The design resistance, N j,, of a symmetric column base plate subject to an axial compressive force together the individual design resistance applied concentrically may be determined by adding F, of the three T-stubs shown in Figure 6.19 (two T-stubs under the column flanges and one T-stub under the column web.) The three T-stubs should not overlapping, see Figure The design resistance of each of these T-stubs should be calculated using the method given in point of EC C Column bases subject to axial forces and bending moments (1) The design moment resistance M j, of a column base subject to combined axial force and moment should be determined using the method given in table 6.7, where the contribution of the concrete portion just under the column web (T-stub 2 di Figure 6.19) to the compressive capacity is omitted. The following parameters are used in this method: - F T l, - F T r, - F C l, - F C r,, is the design tension resistance of the left hand side of the joint, is the design tension resistance of the right hand side of the joint, is the design compressive resistance of the left hand side of the joint, is the design compressive resistance of the right hand side of the joint The design tension resistance F T l,,, of the left side of the joint should be taken as the smallest values of the design resistance of following basic components: F,, ; - the column web in tension under the left column flange t wc F, - the base plate in bending under the left column flange t, pl U s e r M a n u a l V e r s i o n J a n u a r y P a g e 285 of 354

286 The design tension resistance taken as the smallest values components: F T r,,, of the right side of the joint should be of the design resistance of following basic F, - the column web in tension under the right column flange t, wc F, - the base plate in bending under the right column flange t, pl The design compressive resistance F C l,, of the left side of the joint should be taken as the smallest values of the design resistance of following basic component: F,, ; - the concrete in compression under the left column flange c pl F,,. - the left column flange and web in compression c fc (5) ) The design compressive resistance C, r of the right side of the joint should be taken as the smallest values of the design resistance of following basic components: F, F,, ; - the concrete in compression under the right column flange c pl F,,. - the concrete in compression under the right column flange c fc For the calculation of z,, T l z,, C l z T, r, C r z, see fig U s e r M a n u a l V e r s i o n J a n u a r y P a g e 286 of 354

287 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 287 of 354

288 3.12 Joint 1052 (connection circular base plate) (Connection with beam or column in r.c) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 288 of 354

289 Stiffeners The stiffeners can be placed along the profile contour Anchor bolts The bar can be anchored with bolts or bars with stiffeners anchorage Bolts Straight bar L bar U s e r M a n u a l V e r s i o n J a n u a r y P a g e 289 of 354

290 Hook bar Anchor with washer plate Forces On the profile we can apply the following forces: N axial force (positive if tension force) V shear force M, bending moment U s e r M a n u a l V e r s i o n J a n u a r y P a g e 290 of 354

291 The forces can be inserted by Tekla Structures (except V, ), by modeler Midas, by x text file or we can calculate the structure to restore resistance. If the stresses from Tekla Structures are zero, the actions will have minimum value in according with EC3 1-8 point (13) N V N pl V pl Where the plastic resistances are referred to the column Geometrical verification The procedure provides to verify the construction requirements for drilling bolted joint, in according to l EC3 1-8 with the following table 3.3 and figure 3.1. The verification is made only for e 1 and e 2, and not for p 1 e p 2 because the local buckling resistance of the plate is always prevented by the stiffeners and by the same column. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 291 of 354

292 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 292 of 354

293 Design resistance of single bolt and single weld In this paragraph we recall the common criteria for verification of single bolts and single weld. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 293 of 354

294 Design resistance at Bolt tensile force Tensile strength of single bolt is: F t, Where 0.9 f ub M 2 A A s is stressed tensile area s f ub is the last tensile of bolt Bolt shear design resistance For a shear connection (see class A EC3 1-8 point 3.4.1) the single bolt shear strength design (for a single resistant section) is : F v,, v f ub M 2 A If the shear plane is through the threaded bolt portion: - for classes 4.6, 5.6 e 8.8 v for classes 4.8, 5.8 e 10.9 v 0.5 If the shear plane is through not threaded bolt portion: v while 0.6 A is the bolt area f ub is the last bolt tensile stress Design resistance of Weld Design resistance of fillet weld is: F w, Where fvw. d a l U s e r M a n u a l V e r s i o n J a n u a r y P a g e 294 of 354

295 f vwd. is weld shear design resistance. a is height throat weld. l is length cordon weld. The welding shear calculation resistance f vw. d is: f vwd. f u / 3 w M 2 Where: f u is nominal breaking resistance of the weakest node; w is the appropriate correlation factor shown in Table 4.1. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 295 of 354

296 Verifications made - The verifications made on the joint are the following: - Shear verification of the connection - F v, Fv, F w, Fw, V V j, j, 1 - Bearing resistance verification on two horizontal directions on the connection plate F b, Fb, - Verification for compressive force F C, FC, - Weld column-base plate for bending force F w, Fw, - Column section in compression F c, fb, Fc, fb, - Design resistance of anchor F t, Ft, - Axial force resistance without moment resistance applied N N j, j, 1 - Bending force resistance without axial force M M j, j, 1 - Buckling, we consider the following resistance rule M M j, j, N N j, j, 1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 296 of 354

297 If the axial force N does not exceed the 5% of the plastic axial force N pl,, is neglected the coexistence of the axial force and the rule becomes M M j, j, Verification of shear force The shear force verification are made with according EC3 1-8 point In base plates, if no special elements for resisting shear are provided, such as shear key, the connection shear resistance is the friction resistance between base plate and grout layer (with compressive forces) and anchor bolts resistance. If in a column there is a compressive force, the design friction resistance between base plate grout layer F f, C f, d Nc, F, is: f where: is the coefficient of friction between base plate and grout layer. For sand-cement mortar C f, d N, is the design value of the normal compressive force in the column. c NOTE: If the column is loaded by a tensile normal force, F 0. f, In a column base the design shear resistance of an anchor bolt F vb, should be taken as the smaller of F, vb, F, 1 and 2, vb where: - F, vb, 1 is the design shear resistance of the anchor bolt - F 2, vb, b f ub Mb A s where: f b yb f yb is the yield strength of the anchor bolt, with 2 235N / mm f 640N / mm yb 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 297 of 354

298 The design shear resistance of the joint F, is v F v, Ff, nfvb, where: n is the number of anchor bolts in the base plate. Verification of the weld The verification is made considering acting only shear force, is made separately for connection column-base plate and for connection shear key base plate. must satisfy: F w, Fw, with F w, fvw. d a l Where l is total cordon length a is throat height Bearing resistance for the single bolt The bearing verification for single bolt resistance section is : F b,, Where k1 b f u M 2 b is dt For outer bolts b f min( f ub u e1 ; 3d 0 ;1) For inner bolts is b f min( f ub u p ; 3d ;1) 4 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 298 of 354

299 While k 1 is for outer bolts e2 k 1 min( ;2.5) d 0 For inner bolts p2 k 1 min( ;2.5) d Where 0 f u is the ultimate tensile strength of lower resistant plate f ub is the bolt ultimate tensile strength t is minimum thickness of plates connection d 0 is hole diameter For the other sizes definition see figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 299 of 354

300 The bearing verification is made separately on two horizontal and vertical directions both profile and supported and supporting beam angles. In the verification vertical and horizontal shear forces acting on local reference system, are combined. Must be: F b, Fb, U s e r M a n u a l V e r s i o n J a n u a r y P a g e 300 of 354

301 Base in compression For this resistance we use the equivalent T-stub in compression in according with EC3 1-8 point The design compression resistance F, is: C F C, f jd b eff l eff where: b eff is the effective width of the T-stub flange l eff is the effective length of the T-stub flange f jd is the design bearing strength of the joint The forces transferred through a T-stub should be assumed to spread uniformly as shown in Figure 6.4 (a) e (b). The pressure on the resulting bearing area should not exceed the design bearing f jd and the additional bearing width c,should not exceed: c t f y 3 f jd M 0 where: t is the thickness of the flange; f y is the yield strength of the flange. If the projection of the physical length of the basic column is less than c, the effective area should be taken as indicated Figure 6.4 (a). If the projection of the physical length of the basic column exceeds of c,on any side, the part of the additional projection beyond the width c should be neglected, see Figure 6.4 (b). U s e r M a n u a l V e r s i o n J a n u a r y P a g e 301 of 354

302 The reinforcements web plates may also be used to increase identically the contact surface, with not overlapping diffusion. The common design bearing strength f jd is: f jd j F b l eff u eff dove: j is the foundation material coefficient, which may be taken as 2 / 3 provided that the characteristic strength of the grout is not less than 0,2 times the characteristic strength of the concrete foundation and the thickness of the grout is not greater than 0,2 times the smallest width of the steel base plate. In cases where the thickness of the grout is more than 50 mm, the characteristic strength of the grout should be at least the same as that of the concrete foundation. F is the compression design resistance force given in EN 1992, where A c0 is to be u taken as b ). ( eff leff U s e r M a n u a l V e r s i o n J a n u a r y P a g e 302 of 354

303 EXTRACT by EC2 6.7 localized forces (1) In the case of localized forces, we should be noted the local breaking (see below) and the cross tensile strength (see point 6.5). (2) When we have a load uniformly distributed on A c0 (see figure 6.29) the last compression force can be determined as follow: F u A A c1 c0 fcd 3 fcd Ac0 Ac0 (6.63) dove: A c0 is loaded area; A c1 is the load maximum diffusion area used for the calculation and which has an homothetic shape to A c0. (3) It is recommended that the diffusion area A c1 wanted by ultimate compression force F u should be satisfied the following conditions: - the load height diffusion in load direction must be taken as is indicated in figure 6.29; - the area diffusion center A c1 must be on the line of action crossing through the loading area center A c0 ; - if on concrete area act more compression strength, it is recommended that the diffusion areas aren t overlapping. It is recommended that the F u value is reduced if the load is not uniformly distributed on area A c0 or if there are shear force significant. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 303 of 354

304 (4) It is recommended to provide adequate reinforcements to balance traction cross forces due to the load effect. In JFT it considers the minimum value F u So: 3 fcd Ac0 jfu j 3 fcdbeff leff f jd j 3 f b l b l eff eff eff eff cd Verification The compression force is transmitted by column flange and is: F C, So: M c, ( h t c F C, FC, fc Nc, ) 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 304 of 354

305 Connection base plate in bending EC3 1-8 point The design resistance and collapse mode of a bending base plate, is calculated considering the design tension resistance of the bolts too, it is considered similar as T- stub (EC3 1-8 point 6.2.4), the design resistance is calculated for: - the design resistance of an individual bolt row; - the contribution of each bolt row to design resistance. The group of bolt rows, both the reinforced side connected to the end plate should be considered as a separated equivalent T-stub. In extended plate, considered as the extended plate on the beam (extended end - plate), the bolt rows in extended plate is considered as an equivalent T-stub separated, see Figure The design resistance and the collapse mode is calculated separately for each equivalent T-stub. The size e min (EC3 1-8 point 6.2.4) is taken by Figure 6.8 regarding that part that is between upper plate and the lower beam. For the extended part plate as e x, see Figure e min is assumed The effective length l eff an equivalent T-stub flange is determined in according with EC3 1-8 point using the values for each row bolts represented in the table 6.6. The values of m and Figure m x to be used for the Table 6.6 should be determined from the U s e r M a n u a l V e r s i o n J a n u a r y P a g e 305 of 354

306 We note that for the bolt rows between superior and inferior beam flange the l eff is a vertical size as in the case of l eff column flange While the extension of the end plate l eff is an horizontal size. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 306 of 354

307 The extension part of the end plate is considered separately Generally for the plate we consider different value of equivalent member l eff to T-stub equivalent for the rows between the beam plate, these are influenced of stiffness given by web beam and so it has resistance and stiffness higher than the extended part of the plate. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 307 of 354

308 Verification of the weld The verification is made considering acting only bending force. Should satisfy: F w, Fw, With F w, fvw. d a l Where l is the total cordon length a is the cordon throat height U s e r M a n u a l V e r s i o n J a n u a r y P a g e 308 of 354

309 Section of column in compression Beam not reinforced EC3 1-8 point Beam web and flange in compression and references The resultant of the design compression resistance of beam flange and the adjacent compression zone of the beam web, may be assumed to act at the level of the center of compression, the design compression resistance of combined beam flange and web is given by the following expression: F c, fb, M h t c, fb where: h is the depth (height) of beam; M, is the design moment resistance of the beam, reduced to allow for shear, see c EC3-1-1 point For a reinforced beam M, may be calculated neglecting the c intermediate flange. t fb is the flange thickness of the connected beam. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 309 of 354

310 Center of compression If the depth of the beam is more than 600 mm, the design resistance compression beam contribution should be limited to 20%. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 310 of 354

311 For the M, calculation with shear force, see EC3-1-1 point 6.2.8, we use c reduced moment M y, V, W pl, y M 0 2 w A 4t w f y Where 2V V pl, Column section in tension EC3 1-8 point Beam web and flange in tension and references The beam web tension resistance is given from following expression: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 311 of 354

312 F t, wb, b t eff, t, wb wb f y, wb M 0 the effective width b eff t, wb, is taken as equal to the effective length of the equivalent T- stub representing the end-plate in bending, for bolt row located between two beam flanges, considering an individual bolt-row and the bolt-groups Anchor bolt in tension EC3 1-8 point Anchor bolts should be designed to resist the effects of the design loads, due both for normal forces that bending. The lever arm due to bending should be taken as the distance between the barycenter (centroid) of compression area and the centroid (barycenter) of the bolt group on the tension side. The design resistance of the anchor bolts should be taken as the smallest value between resistance to tension and anchor bolts resistance with concrete. Single bolt tension resistance is: F t, Where 0.9 f ub M 2 A s A s is the tensile stressed area f ub is the last tensile bolt strength The design bond resistance of the concrete and anchor bolts is taken in according with EN One of the following methods should be used to secure anchor bolts, into foundation: - A hook (figure 6.14 (a)), - A washer plate (figure 6.14 (b)), - Some other appropriate load distributing member embedded in the concrete U s e r M a n u a l V e r s i o n J a n u a r y P a g e 312 of 354

313 - Some other fixing which has been adequately tested and approved. When the bolts are provided with a hook, the anchorage length should be such as to prevent yielding of the bolt. The anchorage length should be calculated in accordance with EN This type of anchorage should not be used for bolts with a yield strength f yb higher than 2 300N / mm. When the anchor bolts are provided with a washer plate or other load distributing member, the design bond resistance of the concrete and steel is not considered. The whole of the force should be transferred through the load distributing device. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 313 of 354

314 Recalled EC2 for anchor bars 8.4 Longitudinal reinforcement anchorage General (1) Steel bars, wire or mesh must be anchored so as to be transferred frictional forces to the concrete to avoid the longitudinal cracking and detachment concrete. If required, should be used transversal reinforcements. (2) We can see the fixing methods in figure 8.1 [see also point 8.8 (3)]. (3) Bends and hook don t give any contribute to anchor in compression. (4) It is recommended to prevent the concrete breakage inside the bends in according with the point 8.3 (3). (5) Where we use mechanical anchor, It is recommended that test requirements are in according with European Technical Approval. (6) To transmit the pre stress forces to concrete see point U s e r M a n u a l V e r s i o n J a n u a r y P a g e 314 of 354

315 8.4.2 Ultimate friction (adherence) tension (1) The ultimate friction (adherence) tension should be sufficient to prevent the loss of adhesion. (2) The design tension value of the ultimate adhesion, f bd assumed as: fbd f ctd where:, for ribbed bars should be (8.2) f ctd is the design value of resistance to concrete tension for point (2)P. Due to the increasing fragility of the concrete of higher strength, it is recommended that the value of fctk 0,05 is limited, for this case, to the relative value of class C60/75, unless it can verify that the average adhesion resistance exceed; 1 is a ratio related to the quality of adhesion condition and at the bar location during concreting (see figure 8.2): 1 1 with condition of good adhesion in all other cases and for structural elements made with slipform, unless we can demonstrate that exist good conditions of adhesion; 2 it is referred to bar diameter: 2 for 32mm (132 ) /100 for 32mm 2 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 315 of 354

316 8.4.3 length of anchor base (1)P The calculation of anchor length should be calculated considering the type of steel and the adhesion properties of the bars. (2) The anchor length necessary with base l b, rqd, to anchor the force As sd applied to a bar in assumption of uniform adhesion tension equal to fbd is: l ( / 4)( / f ) (8.3) b, rqd sd bd With anchor. sd the design tension corresponding to the point from which is measured the The values of f bd are in point (3) The anchor base length, l b, and the design length, l bd of bars should be measured along the bar axis (see figure 8.1a) Design anchor length (1) the design anchor length, l bd, is: l bd l l (8.4) b, rqd b,min with α 1 α2 α3 α4 α5 the ratios given in table 8.2: α 1 takes into account the shape of the bars assumed that the concrete cover is U s e r M a n u a l V e r s i o n J a n u a r y P a g e 316 of 354

317 adequate (see figure 8.1); α 2 takes into account the effect of the coating minimum concrete (see figure 8.3); α 3 takes into account the edge effect due to transverse reinforcement; α 4 takes into account the influence of one or more welding transverse bars ( 0. 6 along the design anchor length l bd (see also point 8.6); t ) α 5 takes into account the transverse force effect to the plan of breaking along the design anchor length. The product ( α 5 l b, rqd is obtained from(8.3); 2α3α 0.7 ): (8.5) l b,min is the minimum anchor length if there are not other limitations: - for tension anchor: l max0.3 l ;10 ; mm (8.6) b, min b, min for compression anchor: l max0.6 l ;10 ; mm (8.7) b, min b, min 100 (2) For semplicity, alternatively at point (1), the tension anchor of some shape shown in figure 8.1 can be considered as the equivalent anchor length, l beq. l beq it is defined in the same figure and can be assumed: for the shape that we can see in the figure from 8.1b to 8.1d (for the values of - 1 l b, rqd 1 see the table 8.2); for the shapes that we can see in the figure 8.1e (for the values of 4 see the - 4 l b, rqd table 8.2); U s e r M a n u a l V e r s i o n J a n u a r y P a g e 317 of 354

318 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 318 of 354

319 Design resistance of column bases with base plates EC3 1-8 point General Column bases should be of sufficient size stiffness order to resist the axial force, bending moments and shear forces in columns to their foundations or other supports, without exceeding the load carrying capacity of these supports. The design bearing strength between the base plate and its support may be determined on the basis of an uniform distribution of compressive force over the bearing area. For concrete foundations the bearing area stress should not exceed the design bearing strength, f jd. For a column base subject combined axial force and bending, the forces between the base plate and its support can take one of the following distribution depending on the relative magnitude of the applied axial force and bending moment: - In the case of a dominant compressive axial force, full compression may develop under both column flanges as shown in Figure 6.18 (a). - In the case of a dominant tensile force, full tension may develop under both flanges as shown in Figure 6.18 (b). - In the case of dominant bending moment compression may develop under one column flange and tension under the other as shown in Figure 6.18 (c) and Figure 6.18 (d). Base plates should be designed using the appropriate methods, only normal stress or of buckling. One of the following methods should be used to resist the shear force between the base plate and its support: - Frictional design resistance at the joint between the base plate and its support. - The design shear resistance of the anchor bolts. - The design shear resistance of the surrounding part of the foundation. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 319 of 354

320 If anchor bolts are used to resist the shear forces between the base plate and its support, the rupture of the concrete in bearing should also be checked, according with EN Where the above methods are inadequate, should be used special elements such as blocks or bar shear connectors to transfer the shear forces between the base plate and its support. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 320 of 354

321 To know if the base plate is subject more compression then bending, it is necessary design the tension diagram Column base subjected to axial force (1) The design resistance, N j,, of a symmetric column base plate subject to an axial compressive force together the individual design resistance applied concentrically may be determined by adding F, of the three T-stubs shown in Figure 6.19 (two T-stubs under the column flanges and one T-stub under the column web.) The three T-stubs should not overlapping, see Figure The design resistance of each of these T-stubs should be calculated using the method given in point of EC C Column bases subject to axial forces and bending moments U s e r M a n u a l V e r s i o n J a n u a r y P a g e 321 of 354

322 (1) The design moment resistance M j, of a column base subject to combined axial force and moment should be determined using the method given in table 6.7, where the contribution of the concrete portion just under the column web (T-stub 2 di Figure 6.19) to the compressive capacity is omitted. The following parameters are used in this method: - F T l, - F T r, - F C l, - F C r,, is the design tension resistance of the left hand side of the joint, is the design tension resistance of the right hand side of the joint, is the design compressive resistance of the left hand side of the joint, is the design compressive resistance of the right hand side of the joint The design tension resistance F T l,,, of the left side of the joint should be taken as the smallest values of the design resistance of following basic components: F,, ; - the column web in tension under the left column flange t wc F, - the base plate in bending under the left column flange t, pl The design tension resistance taken as the smallest values components: F T r,,, of the right side of the joint should be of the design resistance of following basic F, - the column web in tension under the right column flange t, wc F, - the base plate in bending under the right column flange t, pl The design compressive resistance F C l,, of the left side of the joint should be taken as the smallest values of the design resistance of following basic component: F,, ; - the concrete in compression under the left column flange c pl F,,. - the left column flange and web in compression c fc (5) ) The design compressive resistance C, r of the right side of the joint should be taken as the smallest values of the design resistance of following basic components: F, F,, ; - the concrete in compression under the right column flange c pl U s e r M a n u a l V e r s i o n J a n u a r y P a g e 322 of 354

323 F,,. - the concrete in compression under the right column flange c fc For the calculation of z,, T l z,, C l z T, r, C r z, see fig U s e r M a n u a l V e r s i o n J a n u a r y P a g e 323 of 354

324 3.13 Joint 11 (Secondary bolted beam and welded plate on the main beam) (Secondary bolted beam and bolted plate on the main beam) U s e r M a n u a l V e r s i o n J a n u a r y P a g e 324 of 354

325 Principal and secondary beam For the secondary beams is allowed to use the following sections: L, U or double T (type IPE, HE). The profiles section L or U can be single or coupled, the section profile L must have a side parallel to the plate, while the section U profiles must have the web side parallel to the plate Plate The plate is always bolted on the secondary profiles. The bolts distance from the edge of the plate e 1, plate (parallel to the secondary web section) must be set by macro according with the following figure: The bolts distance from the edge of the plate orthogonal to the secondary web section must be set by macro for the first profile e 2, plate, 1 and for the subsequent i-esimi profiles e, plate, i 2, must be set by macro according with the following figure: U s e r M a n u a l V e r s i o n J a n u a r y P a g e 325 of 354

326 Connections on the principal beam The plate can be connected schemes : to the principal profile according with the following 11) Welded plate 10) Welded plate 12) Plate connected with a single angular 7) Plate connected with a double angular 8) Plate connected with a sigle angular 9) 6) Plate connected with a lateral plate 4) Plate connected with a lateral plate 5) 3) Plate connected with a head plate 1) Welded plate U s e r M a n u a l V e r s i o n J a n u a r y P a g e 326 of 354

327 Double T shaped principal beam If the main beam profile is the type H shape (ex. IPE o HE),the connection with the plate can be welded or bolted, it is very important to note that the forces transmitted by the beam on the plate are transmitted only to the main profile, we don t consider eventually beams that aren t in the list of the 11 joint, also if we can see them graphically in Tekla Structures. The forces can be transmitted between the plate and the main profile with weld or with a group of bolts, in succession there is a summary about the type of connections. Welding joint: - Connection type 1), 2), 9): the plate is welded to the main profile with two angular cordons along the contact height between the plate and the main profile; - Connection type 6), 7): a plate placed on one of two side of the plate is connected to the main profile with welding, the force resistant is that of welded plate and not that of welded plate on the main profile. U s e r M a n u a l V e r s i o n J a n u a r y P a g e 327 of 354

328 The plate or the lateral plate is welded on the main profile, the cordon height is the plate height, for the plate we consider two cordons on both the sides, while for the side plate we consider only one cordon, the force on the welding is the force resultant according EC3 1-8 point (1); - Connection type 3), 4), 5) (welded or bolted angular) One or two angular connect the plate with the main profile, the connection between the plate and the main profile can be welded or bolted. The force on the welding or on the bolts,is the force resultant according EC3 1-8 point (1); U s e r M a n u a l V e r s i o n J a n u a r y P a g e 328 of 354

329 - Connection type 8) (head plate welded or bolted) The plate is welded or bolted to the main profile with a plate Actions On the secondary profile we can apply the following forces: N normal force (positive if tensile) V, y M, z vertical plane shear force bending moment around z axis U s e r M a n u a l V e r s i o n J a n u a r y P a g e 329 of 354

330 The forces can be inserted by Tekla Structures, by modeler Midas, by text file or we can calculate the structure to restore strength. If the stresses from Tekla Structures are zero, the forces will have minimum value according with EC3 1-8 point (13) N N pl the plastic design resistances are referred at the secondary profile Geometric verification The procedure provides to verify the construction requirements for drilling bolted joint according with EC3 1-8, with following table 3.3 and figure 3.1 U s e r M a n u a l V e r s i o n J a n u a r y P a g e 330 of 354