Page 119 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.51

CONNECTIONS

CONNECTIONS 3.51

Tear-out at extreme bolt no. 1:
• At end plate φR n =φ1.2L c tF u φR b = 0.75 × 1.2 × 2.06 × 0.375 × 58 × 2 = 80.7 kips
Tear-out at extreme bolt no. 2:
• At W30 × 99, φR n = 0.75 × 1.2 × 2.06 × 0.52 × 65 × 2 = 125 kips
• At end plate, φR n = 0.75 × 1.2 × 0.781 × 0.375 × 58 × 2 = 30.6 kips
Tear-out at intermediate bolts:
• At W30 × 99, φR n = 0.75 × 1.2 × 2.06 × 0.52 × 65 × 2 = 125 kips
• At end plate, φR n = 0.75 × 1.2 × 2.06 × 0.375 × 58 × 2 = 80.7 kips
Design strength with four rows of bolts (n = 4):
φR n =φR n ext bolt 1 min +φR n ext bolt 2 min +φR n int bolt min × (n − 2)
= 43.3 + 30.6 + 43.3 × (4 − 2) = 161 kips ≥ 80 kips OK
Design strength of welds (assume F EXX = 70 ksi):

1
1
φR n =φF w A w = 0.75 × 0.60 × 70 × / 16 × 0.707 = 1.392 kips/in for / 16-in fillet
3
φR n = 1.392 × 3 × 11.125 × 2 = 92.916 kips for the two / 16-in fillets
Since t w = 0.275 in is less than the AISC base metal minimum of 0.286 in,
.
φR = 92 916 × 0 275 = 89 4 . kips ≥ P = 80 kips OK
.
n
0 286
.
The minimum thickness noted assures that the base metal has sufficient strength to transmit the
load from the weld, that is, the design shear rupture strength of the base metal matches the design
shear rupture strength of the welds. It is calculated from
t min = . 309 D = ×23 .09 × 3 = . 0 286 in
F u 65
1
where D is the weld size in / 16ths and the multiple of 2 accounts for the pair of welds.
Design strength for shear in end plate and beam web:
Gross shear on end plate:

φR n =φ× 0.60A g F y = 0.90 × 0.60 × 11.5 × 0.75 × 36 = 168 kips ≥ 80 kips OK
Net shear on end plate:
φR n =φ× 0.60A nv F u = 0.75 × 0.60 × [11.5 – (4 × 1)] × 0.375 × 2 × 58
= 147 kips ≥ 80 kips OK
Gross shear on beam web:

φR n = 0.90 × 0.60 × 15.9 × 0.275 × 50 = 118 kips ≥ 80 kips OK
Shear on remaining W16 × 31 web:

φR n = 0.90 × 0.60 × 14.1 × 0.275 × 50 = 105 kips ≥ 80 kips OK
Design strength for bending in net section of single cope:

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