Question

Assuming A_e=0.75A_g, what is the lightest wide-flange shape that can resist a factored tension demand, P_u, of 1749 kips?

a) W14x132

b) W14x176

c) W24x162

Answer 1

a) W14x132

A_g = 38.8 in²

A_e = 0.75A_g = 0.75x38.8 = 29.1 in²

Ultimate Strength = f_u = 58000 psi

Factored tension demand is given by

P_u = f_uA_e = 58000x29.1

= 1687800 lbs = 1687.8 kips < 1749 kips

b) W14x176

A_g = 51.8 in²

A_e = 38.85 in²

f_u = 58000 psi

P_u = 58000x38.85 = 2253300 lb

= 2253.3 kips > 1749 kips

c) W24x162

A_g = 47.7 in²

A_e = 35.775 in²

f_u = 58000 psi

P_u = 58000x35.775 = 2074950 lb

= 2074.95 kips > 1749 kips

Therefore the lightest wide flange shape that can resist factored tension of 1749 kips is W14x176