Question

A tubular steel column CD supports horizontal cantilever arm ABC, as shown in the figure. Column CD has an outside diameter of 8.000 in. and a wall thickness of 0.400 in. The loads are PA = 370 lb and PB = 570 lb. Dimensions of the structure are a = 5.9 ft, b = 8.1 ft, and c = 12.2 ft. Determine the maximum compression stress at the base of column CD. b a PB PA B A D

Answer 1

Consider the Civen dataas shown below:- outside lia (do) = (8.0004) wall thickness (A) = (0.400) an. loads (PA) = 370 lb, QB) - a= 5.9ft, b= 8.1ft, I/ 570 lb. C = 12:2ft, Now, Consider the following diagram as showsi below: !PB: 570lb) b= 8.1ft (a=5.9ft ||PA = 37016) с B A (²12.224 D Figla)

Now, Section profsties detsmine the of Columnco, as shown below:- Internal diameter (di) (de) = loat put value of do, &t in above Eqn, (di) - 8- 2xC 0.4) [ (de) = 72 in The cross-sectional area (A) is, A= 6( 1de)? (da) value of put the value do, & di in above eqn, as shown below:- A- A(CD)*- (7.2)

A = 9.550 in 2 moment of inertia oft (I) = do)? (di)4) 64 put Equas as shown below: the value of do, di in above I= म (3) 4 (7-2) } 69 I= 69.145 tine tiny Now, Evaluate the Intsnal forces & moments" as shown below!

F = PA+PB of F = 370+ 570 940 lb & moment (M) = PAX(a+b) + pex (6) (Clockwise moment tre) (M) = 370x (5.9+8.1) +570x(8.1) ME (370x14) +(570x8-1 3.1) M = 9797 16-ft Now, deframine the axial & bending stress by using following formulare a as

Shown below: (6a) an ca put the value of. F, &A in Eqn 19, as shown below (64) (940) (9.559 =98-429 psi & be 11 Mх с OOD (6) where, C= do 8=4 in 2 put the value valere of My C, f I in Eqn 16) as shown below! (56) - 979784 (69.145) - 566.751 psi

11 Now, / detsemine the maximum Compressive Stress at the base of the Coloumm co is as shown below! (compression) = -(6 a)- (66) = t 98.429 - 566.751) =-665.180 psi) (compression) 66 5. 180 psi (c) Therefore, the maximum Compressive spess the Coloumn Cois, at the base of compression ssion = 665.180 psi (c) And