Page 174 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.157

The modified modulus of elasticity for composite design is
28.9 sq.in.
E m 29,000 ksi + 0.4 3267 ksi
5.6 sq.in.
35,744 ksi (246,276 MPa)

The radius of gyration of a hollow circular shape
D + D i 2
2
r (See AISC LRFD Manual, p. 7-21.)
4

(6.625 in.) + (6.065 in.) 2
2
2.25 in. (5.72 cm)
4
for the bare steel pipe.
The modified radius of gyration for composite design
r m r 0.3D (the overall dimension)
2.25 in. (0.3 6.625 in. 1.99 in.)
2.25 in. (5.72 cm)
The slenderness parameter
Kl
F my
c
r m
E m
10.0 ft × 12 in./ft 51.4 ksi
0.64

2.25 in. × 35,744 ksi
Because c < 1.5
2
F cr (0.658 c)F my
0.658 (0.64) 2 51.4 ksi 43.2 ksi (297.6 MMPa)
The design compressive strength
c P n c A s F cr
0.85 5.6 sq.in. 43.2 kips/sq.in.
205 kips > 200 kips required
c P n 205 kips (911.8 kN) for this case is also tabulated on p. 4-100 of the AISC LRFD
Manual.
The 6-in. (15.2 cm) standard-weight concrete-filled pipe-column is satisfactory.
Related Calculations. This procedure is the work of Abraham J. Rokach, MSCE, As-
sociate Director of Education, American Institute of Steel Construction. SI values were
prepared by the handbook editor.