Autodesk Robot Structural Analysis Professional 2014 Design of fixed beam-to-column connection EN :2005/AC:2009
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1 Autodesk Robot Structural Analysis Professional 2014 Design of fixed beam-to-column connection EN :2005/AC:2009 Ratio 0,44 GENERAL Connection no.: 24 Connection name: Ligação 2 Structure node: 34 Structure bars: 23, 43
2 GEOMETRY COLUMN Section: W 200x200x59 Bar no.: 23-90,0 [Deg Inclination angle h c 210,0 [mm Height of column section b fc 205,0 [mm Width of column section t wc 9,1 [mm Thickness of the web of column section t fc 14,2 [mm Thickness of the flange of column section r c 10,0 [mm Radius of column section fillet A c 75,50 [cm 2 Cross-sectional area of a column I xc 6113,00 [cm 4 Moment of inertia of the column section Material: A36 f yc 250,00 [MPa Resistance BEAM Section: W 200x135x26.6 Bar no.: 43-0,0 [Deg Inclination angle h b 207,0 [mm Height of beam section b f 133,0 [mm Width of beam section t wb 5,8 [mm Thickness of the web of beam section t fb 8,4 [mm Thickness of the flange of beam section r b 8,0 [mm Radius of beam section fillet r b 8,0 [mm Radius of beam section fillet A b 33,90 [cm 2 Cross-sectional area of a beam I xb 2587,00 [cm 4 Moment of inertia of the beam section Material: A36 f yb 250,00 [MPa Resistance BOLTS The shear plane passes through the THREADED portion of the bolt. d 20,0 [mm Bolt diameter Class 8.8 Bolt class F trd 141,12 [kn Tensile resistance of a bolt n h 2 Number of bolt columns n v 3 Number of bolt rows h 1 85,0 [mm Distance between first bolt and upper edge of front plate Horizontal spacing e i 95,0 [mm Vertical spacing p i 135,0;95,0 [mm PLATE h p 387,0 [mm Plate height b p 170,0 [mm Plate width t p 12,0 [mm Plate thickness Material: A36 f yp 250,00 [MPa Resistance UPPER STIFFENER h u 150,0 [mm Stiffener height
3 UPPER STIFFENER h u 150,0 [mm Stiffener height t wu 16,0 [mm Thickness of vertical stiffener l u 150,0 [mm Length of vertical stiffener Material: A36 f yu 250,00 [MPa Resistance FILLET WELDS a w 4,0 [mm Web weld a f 4,0 [mm Flange weld MATERIAL FACTORS M0 1,00 Partial safety factor [2.2 M1 1,00 Partial safety factor [2.2 M2 1,25 Partial safety factor [2.2 M3 1,25 Partial safety factor [2.2 LOADS Ultimate limit state Case: 10: ELU Q (1+2)*2.00 M b1,ed -3,45 [kn*m Bending moment in the right beam V b1,ed 2,62 [kn Shear force in the right beam N b1,ed -1,25 [kn Axial force in the right beam M c1,ed 0,93 [kn*m Bending moment in the lower column V c1,ed 0,43 [kn Shear force in the lower column N c1,ed -635,11 [kn Axial force in the lower column M c2,ed -10,19 [kn*m Bending moment in the upper column V c2,ed -174,90 [kn Shear force in the upper column N c2,ed -630,50 [kn Axial force in the upper column RESULTS BEAM RESISTANCES COMPRESSION A b 33,90 [cm 2 Area EN :[6.2.4 N cb,rd A b f yb / M0 N cb,rd 847,50 [kn Design compressive resistance of the section EN :[6.2.4 SHEAR A vb 37,39 [cm 2 Shear area EN :[6.2.6.(3) V cb,rd A vb (f yb / 3) / M0 V cb,rd 539,64 [kn Design sectional resistance for shear EN :[6.2.6.(2) V b1,ed / V cb,rd 1,0 0,00 < 1,00 verified (0,00) BENDING - PLASTIC MOMENT (WITHOUT BRACKETS) W plb 279,80 [cm 3 Plastic section modulus EN :[6.2.5.(2) M b,pl,rd W plb f yb / M0 M b,pl,rd 69,9 [kn* Plastic resistance of the section for bending (without 5 m stiffeners) EN :[6.2.5.(2) BENDING ON THE CONTACT SURFACE WITH PLATE OR CONNECTED ELEMENT W pl 279,80 [cm 3 Plastic section modulus EN :[6.2.5 M cb,rd W pl f yb / M0
4 M cb,rd 69,95 [kn*m Design resistance of the section for bending EN :[6.2.5 FLANGE AND WEB - COMPRESSION M cb,rd 69,95 [kn*m Design resistance of the section for bending EN :[6.2.5 h f 198,6 [mm Distance between the centroids of flanges [ (1) F c,fb,rd M cb,rd / h f F c,fb,rd 352,22 [kn Resistance of the compressed flange and web [ (1) COLUMN RESISTANCES WEB PANEL - SHEAR M b1,ed -3,45 [kn*m Bending moment (right beam) [5.3.(3) M b2,ed 0,00 [kn*m Bending moment (left beam) [5.3.(3) V c1,ed 0,43 [kn Shear force (lower column) [5.3.(3) V c2,ed -174,90 [kn Shear force (upper column) [5.3.(3) z 98,3 [mm Lever arm [6.2.5 V wp,ed (M b1,ed - M b2,ed ) / z - (V c1,ed - V c2,ed ) / 2 V wp,ed -122,81 [kn Shear force acting on the web panel [5.3.(3) A vs 21,41 [cm 2 Shear area of the column web EN :[6.2.6.(3) A vc 21,41 [cm 2 Shear area EN :[6.2.6.(3) V wp,rd 0.9*( f y,wc *A vc +f y,wp *A vp +f ys *A vd ) / ( 3 M0 ) V wp,rd 278,15 [kn Resistance of the column web panel for shear [ V wp,ed / V wp,rd 1,0 0,44 < 1,00 verified (0,44) WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE Bearing: t wc 9,1 [mm Effective thickness of the column web [ (6) b eff,c,wc 162, [mm Effective width of the web for compression 1 [ (1) A vc 21,4 EN [cm2 Shear area 1:[6.2.6.(3) 0,79 Reduction factor for interaction with shear [ (1) com,ed 96,9 8 k wc 1,00 [MPa Maximum compressive stress in web [ (2) Reduction factor conditioned by compressive stresses [ (2) F c,wc,rd1 k wc b eff,c,wbc t wc f yc / M0 F c,wc,rd1 289,96 [kn Column web resistance [ (1) Buckling: d wc 161,6 [mm Height of compressed web [ (1) p 0,57 Plate slenderness of an element [ (1) 1,00 Reduction factor for element buckling [ (1) F c,wb,rd2 k wc b eff,c,wc t wc f yc / M1 F c,wc,rd2 289,96 [kn Column web resistance [ (1) Final resistance: F c,wc,rd,low Min (F c,wc,rd1, F c,wc,rd2 ) F c,wc,rd 289,96 [kn Column web resistance [ (1) WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM TOP FLANGE Bearing: t wc 9,1 [mm Effective thickness of the column web [ (6) b eff,c,wc 162, [mm Effective width of the web for compression 1 [ (1) A vc 21,4 EN [cm2 Shear area 1:[6.2.6.(3) 0,79 Reduction factor for interaction with shear [ (1)
5 t wc 9,1 [mm Effective thickness of the column web [ (6) com,ed 96,9 [MPa Maximum compressive stress in web [ (2) 8 Reduction factor conditioned by compressive k wc 1,00 [ (2) stresses F c,wc,rd1 k wc b eff,c,wbc t wc f yc / M0 F c,wc,rd1 289,96 [kn Column web resistance [ (1) Buckling: d wc 161,6 [mm Height of compressed web [ (1) p 0,57 Plate slenderness of an element [ (1) 1,00 Reduction factor for element buckling [ (1) F c,wb,rd2 k wc b eff,c,wc t wc f yc / M1 F c,wc,rd2 289,96 [kn Column web resistance [ (1) Final resistance: F c,wc,rd,upp Min (F c,wc,rd1, F c,wc,rd2 ) F c,wc,rd,upp 289,96 [kn Column web resistance [ (1) GEOMETRICAL PARAMETERS OF A CONNECTION EFFECTIVE LENGTHS AND PARAMETERS - COLUMN FLANGE Nr m m x e e x p l eff,cp l eff,nc l eff,1 l eff,2 l eff,cp,g l eff,nc,g l eff,1,g l eff,2,g 1 35,0-55,0-95,0 219,6 176,3 176,3 176,3 204,8 119,5 119,5 119,5 2 35,0-55,0-115,0 219,6 208,6 208,6 208,6 190,0 95,0 95,0 95,0 3 35,0-55,0-135,0 219,6 176,3 176,3 176,3 244,8 139,5 139,5 139,5 EFFECTIVE LENGTHS AND PARAMETERS - FRONT PLATE Nr m m x e e x p l eff,cp l eff,nc l eff,1 l eff,2 l eff,cp,g l eff,nc,g l eff,1,g l eff,2,g 1 40,1-37,5-95,0 251,8 221,8 221,8 221,8 220,9 165,8 165,8 165,8 2 40,1-37,5-95,0 251,8 207,2 207,2 207,2 220,9 151,1 151,1 151,1 3 35,0-37,5-168,4 219,8 190,1 190,1 190,1 278,3 180,9 180,9 180,9 m Bolt distance from the web m x Bolt distance from the beam flange e Bolt distance from the outer edge e x Bolt distance from the horizontal outer edge p Distance between bolts l eff,cp Effective length for a single bolt in the circular failure mode l eff,nc Effective length for a single bolt in the non-circular failure mode l eff,1 Effective length for a single bolt for mode 1 l eff,2 Effective length for a single bolt for mode 2 l eff,cp,g Effective length for a group of bolts in the circular failure mode l eff,nc,g Effective length for a group of bolts in the non-circular failure mode l eff,1,g Effective length for a group of bolts for mode 1 l eff,2,g Effective length for a group of bolts for mode 2 CONNECTION RESISTANCE FOR COMPRESSION N j,rd Min ( N cb,rd, 2 F c,wc,rd,low, 2 F c,wc,rd,upp ) N j,rd 579,92 [kn Connection resistance for compression [6.2 N b1,ed / N j,rd 1,0 0,00 < 1,00 verified (0,00) CONNECTION RESISTANCE FOR BENDING F t,rd 141,12 [kn Bolt resistance for tension [Table 3.4 B p,rd 217,15 [kn Punching shear resistance of a bolt [Table 3.4 F t,fc,rd column flange resistance due to bending
6 F t,fc,rd column flange resistance due to bending F t,wc,rd column web resistance due to tension F t,ep,rd resistance of the front plate due to bending F t,wb,rd resistance of the web in tension F t,fc,rd Min (F T,1,fc,Rd, F T,2,fc,Rd, F T,3,fc,Rd ) [ , [Tab.6.2 F t,wc,rd b eff,t,wc t wc f yc / M0 [ (1) F t,ep,rd Min (F T,1,ep,Rd, F T,2,ep,Rd, F T,3,ep,Rd ) [ , [Tab.6.2 F t,wb,rd b eff,t,wb t wb f yb / M0 [ (1) RESISTANCE OF THE BOLT ROW NO. 1 F t1,rd,comp - Formula F t1,rd,comp Component F t1,rd Min (F t1,rd,comp ) 187,91 Bolt row resistance F t,fc,rd(1) 207,41 207,41 Column flange - tension F t,wc,rd(1) 304,93 304,93 Column web - tension F t,ep,rd(1) 187,91 187,91 Front plate - tension F t,wb,rd(1) 321,68 321,68 Beam web - tension B p,rd 434,29 434,29 Bolts due to shear punching V wp,rd / 278,15 278,15 Web panel - shear F c,wc,rd 289,96 289,96 Column web - compression F c,fb,rd 352,22 352,22 Beam flange - compression RESISTANCE OF THE BOLT ROW NO. 2 F t2,rd,comp - Formula F t2,rd,comp Component F t2,rd Min (F t2,rd,comp ) 90,24 Bolt row resistance F t,fc,rd(2) 218,64 218,64 Column flange - tension F t,wc,rd(2) 333,72 333,72 Column web - tension F t,ep,rd(2) 184,51 184,51 Front plate - tension F t,wb,rd(2) 300,40 300,40 Beam web - tension B p,rd 434,29 434,29 Bolts due to shear punching V wp,rd / F ti,rd 278,15-187,91 90,24 Web panel - shear F c,wc,rd F tj,rd 289,96-187,91 102,05 Column web - compression F c,fb,rd F tj,rd 352,22-187,91 164,30 Beam flange - compression F t,fc,rd(2 + 1) F tj,rd 309,38-187,91 121,47 Column flange - tension - group F t,wc,rd(2 + 1) F tj,rd 338,33-187,91 150,42 Column web - tension - group F t,ep,rd(2 + 1) F tj,rd 284,63-187,91 96,72 Front plate - tension - group F t,wb,rd(2 + 1) F tj,rd 459,43-187,91 271,52 Beam web - tension - group The remaining bolts are inactive (they do not carry loads) because resistance of one of the connection components has been used up or these bolts are positioned below the center of rotation. SUMMARY TABLE OF FORCES Nr h j F tj,rd F t,fc,rd F t,wc,rd F t,ep,rd F t,wb,rd F t,rd B p,rd 1 145,8 187,91 207,41 304,93 187,91 321,68 282,24 434, ,8 90,24 218,64 333,72 184,51 300,40 282,24 434, ,2-207,41 304,93 193,24-282,24 434,29 CONNECTION RESISTANCE FOR BENDING M j,rd M j,rd h j F tj,rd M j,rd 31,98 [kn*m Connection resistance for bending [6.2 M b1,ed / M j,rd 1,0 0,11 < 1,00 verified (0,11) CONNECTION RESISTANCE FOR SHEAR v 0,60 Coefficient for calculation of F v,rd [Table 3.4
7 v 0,60 Coefficient for calculation of F v,rd [Table 3.4 F v,rd 94,08 [kn Shear resistance of a single bolt [Table 3.4 F t,rd,max 141,12 [kn Tensile resistance of a single bolt [Table 3.4 F b,rd,int 192,00 [kn Bearing resistance of an intermediate bolt [Table 3.4 F b,rd,ext 192,00 [kn Bearing resistance of an outermost bolt [Table 3.4 Nr F tj,rd,n F tj,ed,n F tj,rd,m F tj,ed,m F tj,ed F vj,rd 1 282,24-0,42 187,91 20,30 19,88 178, ,24-0,42 90,24 9,75 9,33 183, ,24-0,42 0,00 0,00-0,42 188,16 F tj,rd,n Bolt row resistance for simple tension F tj,ed,n Force due to axial force in a bolt row F tj,rd,m Bolt row resistance for simple bending F tj,ed,m Force due to moment in a bolt row F tj,ed Maximum tensile force in a bolt row Reduced bolt row resistance F vj,rd F tj,ed,n N j,ed F tj,rd,n / N j,rd F tj,ed,m M j,ed F tj,rd,m / M j,rd F tj,ed F tj,ed,n + F tj,ed,m F vj,rd Min (n h F v,rd (1 - F tj,ed / (1.4 n h F t,rd,max ), n h F v,rd, n h F b,rd )) V j,rd n h n 1 F vj,rd [Table 3.4 V j,rd 550,57 [kn Connection resistance for shear [Table 3.4 V b1,ed / V j,rd 1,0 0,00 < 1,00 verified (0,00) WELD RESISTANCE A w A wy A wz I wy max max II 45,11 [cm2 19,18 [cm2 Area of all welds Area of horizontal welds 25,94 [cm2 Area of vertical welds 5317,9 [cm 4 Moment of inertia of the weld arrangement with respect to 6 the hor. axis -9,93 [MP a -9,93 [MP a 1,01 [MP a Normal stress in a weld Stress in a vertical weld Tangent stress w 0,85 Correlation coefficient 2) 2) 2) 5) 5) 5) 5) 7) [ 2 max + 3*( 2 max ) f u /( w * M2 ) 19,87 < 376,47 verified (0,05) [ 2 + 3*( II ) f u /( w * M2 ) 19,94 < 376,47 verified (0,05) 0.9*f u / M2 9,93 < 288,00 verified (0,03) CONNECTION STIFFNESS t wash 4,0 [mm Washer thickness [ (2) h head 14,0 [mm Bolt head height [ (2) h nut 20,0 [mm Bolt nut height [ (2) L b 51,2 [mm Bolt length [ (2) k 10 7,7 [mm Stiffness coefficient of bolts [6.3.2.(1) STIFFNESSES OF BOLT ROWS Nr hj k 3 k 4 k 5 k eff,j k eff,j h j 2 k eff,j h j
8 Nr hj k 3 k 4 k 5 k eff,j k eff,j h j k eff,j h j 2 Sum 2,50 31, ,8 4,2 7,2 4,0 1,3 1,92 28, ,8 3,3 5,7 3,7 1,1 0,58 2,94 k eff,j 1 / ( 3 5 (1 / k i,j )) [ (2) z eq j k eff,j h j 2 / j k eff,j h j z eq 123,9 [mm Equivalent force arm [ (3) k eq j k eff,j h j / z eq k eq 2,0 [mm Equivalent stiffness coefficient of a bolt arrangement [ (1) A vc 21,4 [cm 2 EN Shear area 1 1:[6.2.6.(3) 1,00 Transformation parameter [5.3.(7) z 98,3 [mm Lever arm [6.2.5 k 1 8,3 [mm Stiffness coefficient of the column web panel subjected to shear [6.3.2.(1) b eff,c,wc 162,1 [mm Effective width of the web for compression [ (1) t wc 9,1 [mm Effective thickness of the column web [ (6) d c 181,6 [mm Height of compressed web [ (1) k 2 5,7 [mm Stiffness coefficient of the compressed column web [6.3.2.(1) S j,ini E z 2 eq / i (1 / k / k / k eq ) [6.3.1.(4) S j,ini 4069,86 [kn*m Initial rotational stiffness [6.3.1.(4) 1,00 Stiffness coefficient of a connection [6.3.1.(6) S j S j,ini / [6.3.1.(4) S j 4069,86 [kn*m Final rotational stiffness [6.3.1.(4) Connection classification due to stiffness. S j,rig 15804,22 [kn*m Stiffness of a rigid connection [ S j,pin 987,76 [kn*m Stiffness of a pinned connection [ S j,pin S j,ini < S j,rig SEMI-RIGID WEAKEST COMPONENT: COLUMN WEB PANEL - SHEAR REMARKS Plate height is too small. 499,0 [mm > 387,0 [mm Connection conforms to the code Ratio 0,44
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