Page 176 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.159

2. Determine the modified yield stress and modulus of elasticity
Determine F my and E m :

A r A c
F my F y + c 1 F yr + c 2 f c
A s A s
whereA r the cross-sectional area of four No. 7 longitudinal bars 4 0.6 sq.in. 2 4
2
sq.in. (15.5 cm )
2
A s cross-sectional area of W8 40 11.7 sq.in. (75.5 cm )
2
A c 16 in. l6 in. – (11.7 sq.in. + 2.4 sq.in.) 242 sq.in. (1561 cm )
For concrete-encased shapes, c 1 0.7 and c 2 0.6.
2.4 sq.in. 242 sq.in.
F my 36 ksi + 0.7 55 ksi + 0.6 3.5 ksi
11.7 sq.in. 11.7 sq.in.
87.3 ksi (601.5 MPa)

A c
E m E + c e E c
A s
where c 3 0.2 for concrete-encased shapes

1.5
E c w f c
145 1.5 3.5 3267 ksi (24,577 MPa) for 3.5-ksi normal-weight
3
(145 lb/ft ) (2320 kg/cu m) concrete
E m 29,000 ksi + 0.2 3267 ksi 242 sq.in./11.7 sq.in. 42,513 ksi (292,915 MPa)
The modified radius of gyration
r m r y (W8 40) 0.3 16 in. (overall dimension)
2.04 in. 4.80 in. (12.2 cm)
4.80 in. (12.2 cm)

The slenderness parameter
kl
c
E my

R m
E m
15.0 ft × 12 in.ft 87.3 ksi
0.54

4.80 in. × 42,513 ksi
The critical stress
2
F cr (0.658 c)F my
0.658 (0.54) 2 87.3 ksi 77.2 ksi (531.9 MPa)
3. Compute the design compressive strength
The design compressive strength

c P n c A s F cr
0.85 11.7 sq.in. 77.2 kips/sq.in. (531.9 MPa)
768 kips (5292 MPa)