Question

The column shown has a hollow rectangular cross-section. I-6 meters, the material is cold-drawn steel with E-207 GPa, and Sy=580 MPa. Assume end condition to be C-1; Determine 1. Slendemess ratio 2. Transition Slenderness ratio D-80mm 200mm 3. Short or long column? Why? 4. Is the column safe if the axial load P shown is 1 MN? 100mm Column Cross-section For a rectangular cross-section 1 = bh 12 For a circular cross-section, I = *D* 64

Answer 1

I somh : The column shown bes a hollow rectanguleer cross-sectio. The data for column arrangment are given as, L=6m, E = 207 Gpasy = 580 17 pa The end condition C=L]=6m - 6000mm where c= Effective length of columne D- sony 200mm column loomm Proment of ineartia. foro column For rectangular. Isa bh² column cross-section 12 2 64 For circalar, Ica II D4 ☺ for bollow rectangular cross- section オサナナブ I = Is- Ic p3 Io4 64 I = 100x2003 x 804 T 12 64 I= 64 65 6047.4 mmh) o slenderness ratio (5) - The formula for column arrangment with pirined at both end is S=C where k- Radices of ggration of rad k = 1 А A-cross-sectional area of column A= bb- I a 100x200 - Ix 80² A = 149.73.45 mm mmh 15= i 5= 6000 V64656047.4 14973-43 91:31

2 Transition slenderness ratio Ele) (Stran) It is the value of the slenderness ratio at which the Euler critical stress is equal to half of the material Yield strength (sy). The formula for transition slender ness ratio is, Strana 2172 E - k?s, 2 172 x 207810 (646560474) 14973.45 X 580 Stran=0.01944 The given column is short or long The si condition for column short or long is as, IR Leo < 15 - short column Le D. 6000 Dmin where Domin- mean diameter of column 4A 4x loox 200 2 (100+200) P Domin= 133.33 mm Le - 6000 Dmin 133.33 Le Dmin 45.00 > 15 long column

3. 4 1²x 2077 10x 64 65 604704 Is the column safe if the axial load 'p' is 1PTN. The buckling load for column is aboud calculated as Pь - Д2 ET T2 EI E? L2 60002 Pb=3669245.3 N = 3.669 MN As, the buckling load capacity of column is greater than applied load, then the column is saße Pb=3.669 17N> P= I MN column is safe