Question

Pinned End UIL Fixed End 18 ft Brace|| Brace 18 ft 54 ft Bracell Brace 18 ft Fixed End Pinned End I Weak-axis buckling Cross-section Strong-axis buckling 0.5 inch I 5 inches 0.5 inch 0.5 inch 5 inches A steel column (E = 29,000 ksi) has the cross-section indicated and is supported and braced as shown. Complete the following: 1. Calculate the strong-axis moment of inertia Ix. 2. Calculate the weak-axis moment of inertia Iy. 3. Calculate the critical buckling stress ocr for strong-axis buckling. 4. Calculate the critical buckling stress ocr for weak-axis buckling. 5. Determine the governing critical buckling load Pcr-

Please show all work and steps. Any help will be appreciated and thank you for your time!

Answer 1

given Column: freuderd pinned 7 oft -Iosin 1 suf av BOD T o-sin SM SEB 9 vist - O SMT pingen freed to Sincht ene ។ Chars section for Stel E229000ksi ) Stoong anis moment of Inertia Ips slated (4.5) (5) Ix=43.125 int 5.(0:53 12 2) Weak axis moment of Inertia Ty z PC oscent) + # Iy - 10.46875 in? area of Cooss sedim. ; A= 6.5x5) + Co.sxs) + (o.sxs) A=7.sin? so rading of gyration of A * Bax = 2.3979 in rading of groothan one semaine Ž. Rum= 1.1814 in So slenderness ratio , for Strong (54812)in 143.125 7.5 10.46875 7.S Axis lexx Now - DAF 324 in 2-3979 in 7 day= 135.118 for weak axis ri dex = 18+= 18x12m=2164 din - 216 1.1814 diny ? 2182.833

3) So Critical buckling Stress for story ax's backling (M) x- TTE Ter), - 1506773 ks! TT2X (29000 ksi) 135.1182 4) Critical buckling stress for weakºaxis buckling 7 Gra), The (29000 ksi) 182-833) Er),= 8.3622 ksi s) governing Buckling critical Loced Per= (min.) A (a), = 85622651 Po = 84622 ksi)ftasin) Po = 64.216 kips about weak axis
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