Page 253 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.33

CRITERIA FOR BUILDING DESIGN

CRITERIA FOR BUILDING DESIGN 5.33

concrete encasement of the steel core must be reinforced with continuous longitudinal bars and
2
2
lateral ties or spirals, with a minimum transverse reinforcement of at least 0.009 in /in (0.225 mm /
mm) of tie spacing, and (3) the reinforcement ratio (ratio of area of continuous longitudinal rein-
forcing to gross area of composite member) must be at least 0.004. Additional requirements for shear
connectors and detailing are discussed subsequently.
To determine the available compressive strength (design compressive strength φ c P n and allowable
compressive strength P n /Ω c ) of an axial-loaded encased column for the limit state of flexural buck-
ling, use φ c = 0.75 (LRFD) and Ω c = 2.00 (ASD). First calculate the following:

P o = A s F y + A sr F yr + 0.85A c f c ′ (5.118)
π 2 EI
P = eff (5.119)
e
( KL) 2
(5.120)
EI eff = E s I s + 0.5E s I sr + C 1 E c I c
 A 
01 2 
C = . +  A + s A   ≤ 03 . (5.121)
1
s
c
The following definitions apply:
2
2
A s = area of steel section, in (mm )
2
2
A c = area of concrete, in (mm )
2
2
A sr = area of continuous reinforcing bars, in (mm )
E c = modulus of elasticity of concrete
.
= w 15 f ′ ksi (5000 f ′ MPa)
c c c
E s = modulus of elasticity of steel = 29,000 ksi (210 MPa)
2
2
EI eff = effective rigidity of composite section, kip⋅in (N⋅mm )
f c ′= specified minimum concrete compressive strength, ksi (MPa)
F y = specified minimum yield stress of steel section, ksi (MPa)
F yr = specified minimum yield strength of reinforcing bars, ksi (MPa)
4
4
I c = moment of inertia of concrete section, in (mm )
4
4
I s = moment of inertia of steel shape, in (mm )
4
4
I sr = moment of inertia of reinforcing bars, in (mm )
K = effective length factor (see Art. 5.2)
L = laterally unbraced length of the member, in (mm)
P e = elastic axial buckling strength, kips (kN)
P o = nominal axial compressive strength without length effects, kips (kN)
w c = weight of concrete per unit volume
3
3
= 90 ≤ w c ≤ 150 lb/ft (1440 ≤ w c ≤ 2450 kg/m )
The nominal compressive strength is then calculated as
o[
PP e )
When P e ≥ 0.44 P o , P = P 0 658 (/ ] (5.122)
.
o
n
When P e < 0.44 P o , P n = 0.877 P e (5.123)
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