Question

Acolumn ABC is supported at ends A and Cand compressed by an axial load Plfigure a). The column is pin-supported at the ends (support A and C). Lateral support is provided at point 8 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-262 in 1y-2.627 in', E = 29,500 ksi and oy - 36 ksi) 1. Determine the largest vertical force Pthat 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 I

Answer 1

Given Data Section : C688.2 С 22/15ft Area (A)= 4.78 in² IX = 26.2 in" Iy = 2.627 in" E = 29,500 ksi L 36 ksi 2/2=15ft Comersions. Iksi 6.39476 mea. ift = 0.3048 m. link = 401623 x 10-7 mu Case 1: If Column buckles in the plane of the figure. T² EI 422 EIA 42?x 29 500 x 26 27 (2/2)² L2 (30x12) ² Per - - 23.6067 kip Case 2: I Column buckles perpendiculas to the plane of figure X²E IX X² X 29500x 26.2 L² (30x12) 2 kip Pes = 58.86

So, Design will proceed based on the load (Per Dosare 2 obtained in Case 2 > (Per cases. 2 oca 58.86 4.78 12.31 ksi The Critical stress do not exceed the proportional limit in the Case of larger Critical load. le 12-31 < 36 ksi Yield stren. Allowable Load Pallowable = Per fos 23.6067 2.5 Pollowable 9.44 kip