Question

dll. TC Wicu dgie 15 Part II: Show the detail steps of the following calculation problems. 2. (15 pts) A circular cross-section beam is shown below. Assume E = 29 Mpsi. Calculate the diameter of the beam so the deflection at midspan (point B) will not exceed 1.2 in.

Answer 1

400 lbf goodbf. Rc 1 3 Ź o =0 - (600x4)+(800x8) = R(x14 - Rc=5714285 lbf.. • Rot 571.4285= 1200 - Ro = 628.5714 lbf. :. Moment ean. MCX)= EID = 628.5114321-400(2-4);-800 (7-8) Integrating twice . - Eldy = 314.2857x²+4 -200 (x-4) 2! 2400 (8-872 EI Y(x) = 104.7619 2²+ ( x + (o!-200 (x-2) 3 - 500 (x-83 at = 0, y=0 ) 6 =0. at ze = 14 ft y=o. 0=104.7619 (19) * 146,- 200 (10) - 500 (6)? <=-13714.2857 Now, E = 29x100 psi = 29x10x (12) ablat. $ = 1.2 in = 0.1 ft. = 4 (B). at se = 7ft at pt. B. , y =o.lft. Ix (29x109x12) (0,1)=106.7619 x604-13719.2967() -200 (3) I=1.48148x10 fts. I = π d = 1.48148 x 105 = d =0.23 438 ft 32-8126 in 3 .