A 15by55in strut has a ength of 10ft t is made from southern

A 1.5-by-5.5in strut has a ength of 10ft. t is made from southern pine having a modulus, E 1,500 ksi and allowa ble strength parallel to grain, oyp= 2 ksi. With P\"-?4.?\"(KI r\' and a pin-end connection, determine a) its critical buckling load and b) the allowable capacity of column lond at F2. c) The maximum length in feet so that it will not fa by buckle. cv 1,Sin 5.5in HW # 13-1 a 10f

Solution

a) E=1500 ksi

moment of inertia about minor axis=I=5.5*1.5³/12=1.55 in⁴

length=10 ft=120 in

Euler buckling load = pi²*E*I/L² = pi²*1500*1.55/120² = 1.59 kips

b)allowable capapcity of column at FS=2 = 1.59/2=0.795 kips

c)for the column to not fail by buckle, its length has to such that its Euler capapcity is > yielding capacity

yielding capapcity = 2*1.5*5.5=16.5 kips

let the required length be L

pi²*1500*1.55/L² = 16.5

L=37.29 in=3.1 ft

Answer is 3.1 ft