Question

A column ABC is supported at ends A and Cand compressed by an axial load P (figure a). The column is pin-supported at the ends (support A and C). Lateral support is provided at point B but only in the plane ZX. The column is constructed of two channel sections (C6 x 8.2) back to back (see figure). (Given: A=4.78 in?, Ix=26.2 in4, ly=2.627 in4, E = 29,500 ksi and Oy = 36 ksi) 1. Determine the largest vertical force P that can be applied without causing buckling. 2. Compared the critical stress to the yield stress. 3. If the FS =2.5, what is the allowable value of load P. Z P с ENK I A

Answer 1

Griven Data: - B I min - A-4.78 in2 Ix=26.21 Iy= 2.627 int E = 29,500ksi A Jp = 36ksi Buckling load (Pe) - min of [Ix and Iy ia Actual length of column Le = effective length of column. Pe LE Pe L Imin Pc at 22 Pe=²E I min Here fixed and Hinged Lez Support. Bc = ²E I min (2L) 2 - A² x 29,500x 2.627 (usxa)? = 1888544271 16 Far AB there Both side fixed suppart. Pe=7²E Imin 7²x29,500X2.627 Le² (3 x 92 = 37077085216

Largest fance p is 37,170 lb we have to Not much exceed the force otherwise it can Bucle. di critical storess to yield storess. ind permissible. Pe A - Iper. 37.770 4.78 7.90 16 ksi < 36ksi It is safe has stress design. di when factar of safety is 2.5 then allowable boad is :- Fos Tindused allowable 36 2.5 = allowable allowable = 36 - 14.4 asi Tallonable = Pe A 14.4 4.78 Pe = 68.832 lb When FS = 2.5 Allowable coast is become 68.832 18.