Page 122 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.54

CONNECTIONS

3.54 CHAPTER THREE

Design strength for block shear on beam web [Eq. (3.32)]:
φR n =φ[U bs F u A nt + min(0.6F y A gv , 0.6F u A nv )]
Check block shear for vertical force:
A gt = 0.355 × 1.75 = 0.621 in 2
A nt = 0.355 × (1.75 − 0.5 × 0.875) = 0.466 in 2
A gv = 0.355 × [1.25 + (3 − 1) × 3] = 2.57 in 2
A nv = 0.355 × [1.25 + (3 − 1) × 3 − (3 − 0.5) × 0.875] = 1.8 in 2
φR n = 0.75[1 × 65 × 0.466 + min(0.6 × 50 × 2.57, 0.6 × 65 × 1.8)]
= 0.75[30.3 + min(77.1, 70.2)] = 80.5, 75.4
= 75.4 kips
Check block shear for horizontal force:
A gv = 0.355 × 1.75 = 0.621 in 2
A nv = 0.355 × (1.75 − 0.5 × 0.875) = 0.466 in 2
A gt = 0.355 × [1.25 + (3 − 1) × 3] = 2.57 in 2
A nt = 0.355 × [1.25 + (3 − 1) × 3 − (3 − 0.5) × 0.875] = 1.8 in 2
φR n = 0.75[1 × 65 × 1.8 + min(0.6 × 50 × 0.621, 0.6 × 65 × 0.466)]
= 0.75[117.0 + min(18.6, 18.2)] = 101.7, 101.4
= 101 kips
Check block shear for combined force:
 V  2  T  2  33  2  39  2
  +   = + = 0 340 1. ≤ OK
 φ R   φ R   75 4.   101 
n
n
Design strength for bending in net section of single cope:
Follow procedure in AISC Manual.
Area of remaining tee = 9.85 in 2
Center of gravity of remaining tee = 4.88 in above bottom of beam
Moment of inertia of remaining tee = 274 in 4
Section modulus at top of tee = 24.1 in 3
Section modulus at bottom of tee = 56.1 in 3
M u = R u e = 33 × (4.00 + 0.50) = 148 in⋅kips
φM n =φF u S net = 0.75 × 65 × 24.1 = 1175 in⋅kips ≥ 148 in⋅kips OK
Design strength for web buckling in net section of single cope:
Follow procedure in AISC Manual.
c = cope length = 4.00 in; d = beam depth = 18.0 in; h o = net depth = 16.25 in
c/d = 0.222 ≤ 1; therefore, adjustment factor is f = 2(c/d) = 0.444
c/h o = 0.246 ≤ 1; therefore, plate buckling coefficient is f = 2.2(h o /c) 1.65 = 22.2
2
t w
φF = 23 590 ( h o fk )
,
cr
2
.
,
φF = 23 590 0 355 ) × 0 444 22 22 111. × . = ksi < 0 .9 F = 45 ksi
cr ( 16 25. y
φM n =φF cr S net = 45 × 13.8 = 621 in⋅kips ≥ 490 in⋅kips OK
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