Autodesk Robot Structural Analysis Professional 2015 Design of fixed beam-to-beam connection BS 5950-1:2000/AC:2009 Ratio 0.17 GENERAL Connection no.: 2 Connection name: Beam-Beam Structure node: 40 Structure bars: 24, 25 GEOMETRY LEFT SIDE BEAM Section: UB 305x165x40 Bar no.: 24 = -168.7 [Deg] Inclination angle h bl = 303 [mm] Height of beam section b fbl = 165 [mm] Width of beam section t wbl = 6 [mm] Thickness of the web of beam section t fbl = 10 [mm] Thickness of the flange of beam section r bl = 9 [mm] Radius of beam section fillet A bl = 5130 [mm 2 ] Cross-sectional area of a beam I xbl = 85030000 [mm 4 ] Moment of inertia of the beam section Material: S275 f yb = 275000.00 [kpa] Resistance RIGHT SIDE BEAM Section: UB 305x165x40 Bar no.: 25 = -11.3 [Deg] Inclination angle h br = 303 [mm] Height of beam section
= -11.3 [Deg] Inclination angle b fbr = 165 [mm] Width of beam section t wbr = 6 [mm] Thickness of the web of beam section t fbr = 10 [mm] Thickness of the flange of beam section r br = 9 [mm] Radius of beam section fillet A br = 5130 [mm 2 ] Cross-sectional area of a beam I xbr = 85030000 [mm 4 ] Moment of inertia of the beam section Material: S275 f yb = 275000.00 [kpa] Resistance BOLTS The shear plane passes through the UNTHREADED portion of the bolt. d = 16 [mm] Bolt diameter Class = 10.9 Bolt class F trd = 113.04 [kn] Tensile resistance of a bolt n h = 2 Number of bolt columns n v = 5 Number of bolt rows h 1 = 85 [mm] Distance between first bolt and upper edge of front plate Horizontal spacing e i = 70 [mm] Vertical spacing p i = 60;60;160;45 [mm] PLATE h pr = 468 [mm] Plate height b pr = 165 [mm] Plate width t pr = 20 [mm] Plate thickness Material: STEEL 43-245 f ypr = 245000.00 [kpa] Resistance LOWER STIFFENER w rd = 165 [mm] Plate width t frd = 10 [mm] Flange thickness h rd = 140 [mm] Plate height t wrd = 6 [mm] Web thickness l rd = 300 [mm] Plate length d = 15.4 [Deg] Inclination angle Material: STEEL 43-245 f ybu = 245000.00 [kpa] Resistance FILLET WELDS a w = 5 [mm] Web weld a f = 8 [mm] Flange weld a fd = 5 [mm] Horizontal 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: 13: ULS /24/ 1*1.20 + 2*1.20 + 3*1.20 + 7*1.20 M b1,ed = -29.80 [kn*m] Bending moment in the right beam V b1,ed = 1.26 [kn] Shear force in the right beam N b1,ed = 2.65 [kn] Axial force in the right beam
RESULTS BEAM RESISTANCES TENSION A b = 5130 [mm 2 ] Area EN1993-1-1:[6.2.3] N tb,rd = A b f yb / M0 N tb,rd = 1410.75 [kn] Design tensile resistance of the section EN1993-1-1:[6.2.3] SHEAR A vb = 2847 [mm 2 ] Shear area EN1993-1-1:[6.2.6.(3)] V cb,rd = A vb (f yb / 3) / M0 V cb,rd = 451.98 [kn] Design sectional resistance for shear EN1993-1-1:[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 = 626000 [mm 3 ] Plastic section modulus EN1993-1-1:[6.2.5.(2)] M b,pl,rd = W plb f yb / M0 M b,pl,rd = 172.15 [kn*m] Plastic resistance of the section for bending (without stiffeners) EN1993-1-1:[6.2.5.(2)] BENDING ON THE CONTACT SURFACE WITH PLATE OR CONNECTED ELEMENT W pl = 1028066 [mm 3 ] Plastic section modulus EN1993-1-1:[6.2.5] M cb,rd = W pl f yb / M0 M cb,rd = 282.72 [kn*m] Design resistance of the section for bending EN1993-1-1:[6.2.5] FLANGE AND WEB - COMPRESSION M cb,rd = 282.72 [kn*m] Design resistance of the section for bending EN1993-1-1:[6.2.5] h f = 439 [mm] Distance between the centroids of flanges [6.2.6.7.(1)] F c,fb,rd = M cb,rd / h f F c,fb,rd = 643.97 [kn] Resistance of the compressed flange and web [6.2.6.7.(1)] GEOMETRICAL PARAMETERS OF A CONNECTION 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 26-48 - 45 166 181 166 181 128 121 121 121 2 26-48 - 103 166 165 165 165 205 103 103 103 3 26-48 - 110 166 165 165 165 220 110 110 110 4 26-48 - 60 166 165 165 165 120 60 60 60 5 26-48 - 60 166 165 165 165 143 112 112 112 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 TENSION F t,rd = 113.04 [kn] Bolt resistance for tension [Table 3.4] B p,rd = 311.24 [kn] Punching shear resistance of a bolt [Table 3.4] N j,rd = Min (N tb,rd, n v n h F t,rd, n v n h B p,rd) N j,rd = 1130.40 [kn] Connection resistance for tension [6.2] N b1,ed / N j,rd 1,0 0.00 < 1.00 verified (0.00)
CONNECTION RESISTANCE FOR BENDING F t,rd = 113.04 [kn] Bolt resistance for tension [Table 3.4] B p,rd = 311.24 [kn] Punching shear resistance of a bolt [Table 3.4] 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) [6.2.6.4], [Tab.6.2] F t,wc,rd = b eff,t,wc t wc f yc / M0 [6.2.6.3.(1)] F t,ep,rd = Min (F T,1,ep,Rd, F T,2,ep,Rd, F T,3,ep,Rd) [6.2.6.5], [Tab.6.2] F t,wb,rd = b eff,t,wb t wb f yb / M0 [6.2.6.8.(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) 226.08 Bolt row resistance F t,ep,rd(1) = 226.08 226.08 Front plate - tension F t,wb,rd(1) = 273.11 273.11 Beam web - tension F c,fb,rd = 643.97 643.97 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) 142.86 Bolt row resistance F t,ep,rd(2) = 226.08 226.08 Front plate - tension F t,wb,rd(2) = 271.83 271.83 Beam web - tension F c,fb,rd - 1 1 F tj,rd = 643.97-226.08 417.89 Beam flange - compression F t,ep,rd(2 + 1) - 1 1 F tj,rd = 436.05-226.08 209.97 Front plate - tension - group F t,wb,rd(2 + 1) - 1 1 F tj,rd = 368.94-226.08 142.86 Beam web - tension - group RESISTANCE OF THE BOLT ROW NO. 3 F t3,rd,comp - Formula F t3,rd,comp Component F t3,rd = Min (F t3,rd,comp) 181.50 Bolt row resistance F t,ep,rd(3) = 226.08 226.08 Front plate - tension F t,wb,rd(3) = 271.83 271.83 Beam web - tension F c,fb,rd - 2 1 F tj,rd = 643.97-368.94 275.03 Beam flange - compression F t,ep,rd(3 + 2) - 2 2 F tj,rd = 426.87-142.86 284.01 Front plate - tension - group F t,wb,rd(3 + 2) - 2 2 F tj,rd = 350.63-142.86 207.76 Beam web - tension - group F t,ep,rd(3 + 2 + 1) - 1 2 F tj,rd = 652.59-368.94 283.64 Front plate - tension - group F t,wb,rd(3 + 2 + 1) - 1 2 F tj,rd = 550.44-368.94 181.50 Beam web - tension - group Additional reduction of the bolt row resistance F t3,rd = F t1,rd h 3/h 1 F t3,rd = 108.69 [kn] Reduced bolt row resistance [6.2.7.2.(9)] RESISTANCE OF THE BOLT ROW NO. 4 F t4,rd,comp - Formula F t4,rd,comp Component F t4,rd = Min (F t4,rd,comp) 166.34 Bolt row resistance F t,ep,rd(4) = 226.08 226.08 Front plate - tension F t,wb,rd(4) = 271.83 271.83 Beam web - tension F c,fb,rd - 3 1 F tj,rd = 643.97-477.63 166.34 Beam flange - compression F t,ep,rd(4 + 3) - 3 3 F tj,rd = 391.74-108.69 283.05 Front plate - tension - group F t,wb,rd(4 + 3) - 3 3 F tj,rd = 280.50-108.69 171.81 Beam web - tension - group F t,ep,rd(4 + 3 + 2) - 2 3 F tj,rd = 602.07-251.55 350.52 Front plate - tension - group F t,wb,rd(4 + 3 + 2) - 2 3 F tj,rd = 449.63-251.55 198.07 Beam web - tension - group F t,ep,rd(4 + 3 + 2 + 1) - 1 3 F tj,rd = 827.79-477.63 350.16 Front plate - tension - group F t,wb,rd(4 + 3 + 2 + 1) - 1 3 F tj,rd = 649.44-477.63 171.81 Beam web - tension - group Additional reduction of the bolt row resistance
F t4,rd = F t1,rd h 4/h 1 F t4,rd = 74.33 [kn] Reduced bolt row resistance [6.2.7.2.(9)] RESISTANCE OF THE BOLT ROW NO. 5 F t5,rd,comp - Formula F t5,rd,comp Component F t5,rd = Min (F t5,rd,comp) 92.01 Bolt row resistance F t,ep,rd(5) = 226.08 226.08 Front plate - tension F t,wb,rd(5) = 271.83 271.83 Beam web - tension F c,fb,rd - 4 1 F tj,rd = 643.97-551.96 92.01 Beam flange - compression F t,ep,rd(5 + 4) - 4 4 F tj,rd = 393.70-74.33 319.37 Front plate - tension - group F t,wb,rd(5 + 4) - 4 4 F tj,rd = 284.42-74.33 210.09 Beam web - tension - group F t,ep,rd(5 + 4 + 3) - 3 4 F tj,rd = 610.24-183.02 427.22 Front plate - tension - group F t,wb,rd(5 + 4 + 3) - 3 4 F tj,rd = 465.92-183.02 282.90 Beam web - tension - group F t,ep,rd(5 + 4 + 3 + 2) - 2 4 F tj,rd = 820.57-325.88 494.69 Front plate - tension - group F t,wb,rd(5 + 4 + 3 + 2) - 2 4 F tj,rd = 635.04-325.88 309.16 Beam web - tension - group F t,ep,rd(5 + 4 + 3 + 2 + 1) - 1 4 F tj,rd = 1046.29-551.96 494.33 Front plate - tension - group F t,wb,rd(5 + 4 + 3 + 2 + 1) - 1 4 F tj,rd = 834.86-551.96 282.90 Beam web - tension - group Additional reduction of the bolt row resistance F t5,rd = F t1,rd h 5/h 1 F t5,rd = 39.97 [kn] Reduced bolt row resistance [6.2.7.2.(9)] 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 1 395 226.08 - - 226.08 273.11 226.08 622.49 2 350 142.86 - - 226.08 271.83 226.08 622.49 3 190 108.69 - - 226.08 271.83 226.08 622.49 4 130 74.33 - - 226.08 271.83 226.08 622.49 5 70 39.97 - - 226.08 271.83 226.08 622.49 CONNECTION RESISTANCE FOR BENDING M j,rd M j,rd = h j F tj,rd M j,rd = 172.30 [kn*m] Connection resistance for bending [6.2] M b1,ed / M j,rd 1,0 0.17 < 1.00 verified (0.17) CONNECTION RESISTANCE FOR SHEAR v = 0.60 Coefficient for calculation of F v,rd [Table 3.4] Lf = 0.97 Reduction factor for long connections [3.8] F v,rd = 93.95 [kn] Shear resistance of a single bolt [Table 3.4] F t,rd,max = 113.04 [kn] Tensile resistance of a single bolt [Table 3.4] F b,rd,int = 160.53 [kn] Bearing resistance of an intermediate bolt [Table 3.4] F b,rd,ext = 275.20 [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 1 226.08 0.53 226.08 39.10 39.63 164.36 2 226.08 0.53 142.86 24.71 25.24 172.91 3 226.08 0.53 108.69 18.80 19.33 176.42 4 226.08 0.53 74.33 12.86 13.39 179.95 5 226.08 0.53 39.97 6.91 7.44 183.47 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,ed (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 1 n F vj,rd [Table 3.4] V j,rd = 877.11 [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 = 11284 [mm 2 ] Area of all welds [4.5.3.2(2)] A wy = 7283 [mm 2 ] Area of horizontal welds [4.5.3.2(2)] A wz = 4001 [mm 2 ] Area of vertical welds [4.5.3.2(2)] I wy = 312665466 [mm 4 ] Moment of inertia of the weld arrangement with respect to the hor. axis [4.5.3.2(5)] max= max = -16520.85 [kpa] Normal stress in a weld [4.5.3.2(5)] = = -14926.10 [kpa] Stress in a vertical weld [4.5.3.2(5)] II = 314.00 [kpa] Tangent stress [4.5.3.2(5)] w = 0.85 Correlation coefficient [4.5.3.2(7)] [ 2 max + 3*( 2 max )] f u/( w* M2) 33041.70 < 404705.88 verified (0.08) [ 2 + 3*( 2 + 2 II )] f u/( w* M2) 29857.16 < 404705.88 verified (0.07) 0.9*f u/ M2 16520.85 < 309600.00 verified (0.05) CONNECTION STIFFNESS t wash = 4 [mm] Washer thickness [6.2.6.3.(2)] h head = 12 [mm] Bolt head height [6.2.6.3.(2)] h nut = 16 [mm] Bolt nut height [6.2.6.3.(2)] L b = 52 [mm] Bolt length [6.2.6.3.(2)] k 10 = 5 [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 k eff,j h j 2 Sum 4407 1318308 1 395 48 4 1581 624127 2 350 40 4 1359 475468 3 190 43 4 747 141844 4 130 24 3 444 57612 5 70 44 4 276 19257 k eff,j = 1 / ( 3 5 (1 / k i,j)) [6.3.3.1.(2)] z eq = j k eff,j h j 2 / j k eff,j h j z eq = 299 [mm] Equivalent force arm [6.3.3.1.(3)] k eq = j k eff,j h j / z eq k eq = 15 [mm] Equivalent stiffness coefficient of a bolt arrangement [6.3.3.1.(1)] S j,ini = E z eq 2 k eq [6.3.1.(4)] S j,ini = 270253.08 [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 = 270253.08 [kn*m] Final rotational stiffness [6.3.1.(4)] Connection classification due to stiffness. S j,rig = 27348.24 [kn*m] Stiffness of a rigid connection [5.2.2.5] S j,pin = 1709.26 [kn*m] Stiffness of a pinned connection [5.2.2.5] S j,ini S j,rig RIGID WEAKEST COMPONENT: BEAM FLANGE AND WEB - COMPRESSION REMARKS The thickness of bracket flange is less than the thickness of beam flange 10 [mm] < 10 [mm] Connection conforms to the code Ratio 0.17