Bracing gusset (Whitmore, Thornton, block shear) calculator

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Worked example — results

• ✓ Whitmore tension
• ✓ Gusset buckling (compression)
• ✓ Block shear
• ✓ Bolts

Method, formulas and assumptions

• Bolt diameter df = CHOOSE(3,12,16,20,24,30,36) = 20 mm
• Bolt tensile strength fuf = IF(2=1,400,830) = 830 MPa
• Tensile stress area As = CHOOSE(3,84.3,157,245,353,561,817) = 245 mm²
• Core area Ac (threads) = CHOOSE(3,76.2,144,225,324,519,759) = 225 mm²
• Shank area Ao = CHOOSE(3,113,201,314,452,707,1018) = 314 mm²
• Plate yield stress fy (AS/NZS 3678) = CHOOSE(1,IF(12<=8,280,IF(12<=12,260,250)),IF(12<=8,320,IF(12<=12,310,IF(12<=20,300,280))),IF(12<=12,360,IF(12<=20,350,340))) = 260 MPa
• Plate tensile strength fu = CHOOSE(1,410,430,450) = 410 MPa
• Joint length (n − 1)p = (3-1)*70 = 140 mm
• Whitmore width g + 2 Lj tan30° = 60+2*140*TAN(RADIANS(30)) = 221.66 mm
• Hole = 20+2 = 22 mm
• Whitmore gross area = 221.66*12 = 2659.9 mm²
• Whitmore net area = (221.66-2*22)*12 = 2131.9 mm²
• φNt = 0.9 min(Ag fy, 0.85 An fu) = 0.9*MIN(2659.9*260,0.85*2131.9*410)/1000 = 622.42 kN
• r = t/√12 = 12/SQRT(12) = 3.4641 mm
• λn = (le/r)√kf √(fy/250) = 0.65*180/3.4641*SQRT(1)*SQRT(260/250) = 34.444
• αa = 2100*(34.444-13.5)/(34.444^2-15.3*34.444+2050) = 16.233
• λ = λn + αa·αb = 34.444+16.233*0.5 = 42.56
• η = MAX(0,0.00326*(42.56-13.5)) = 0.094737
• ξ = ((42.56/90)^2+1+0.094737)/(2*(42.56/90)^2) = 2.9477
• Slenderness reduction αc = MIN(1,2.9477*(1-SQRT(1-(90/(2.9477*42.56))^2))) = 0.89412
• φNc = 0.9 αc Ag fy = 0.9*0.89412*2659.9*260/1000 = 556.52 kN
• Block shear gross shear area 2(Lj + e)t = 2*(140+40)*12 = 4320 mm²
• Net shear area = 2*(140+40-(3-0.5)*22)*12 = 3000 mm²
• Net tension area (g − dh)t = (60-22)*12 = 456 mm²
• φRbs = 0.75 (min(0.6fu Anv, 0.6fy Agv) + fu Ant) = 0.75*(MIN(0.6*410*3000,0.6*260*4320)+410*456)/1000 = 645.66 kN
• Bolts (2nr, single shear, bearing) = 2*3*MIN(0.8*0.62*830*225/1000,0.9*3.2*20*12*410/1000) = 555.77 kN

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