Question

2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature change, determine the stress in the cylinder. Material data: Steel E = 200 GPa, a = 11.7 x 10-6/°C; Brass: E = 105 GPa, Q = 20.9 x 10-6/°C. 10.45 m 0.3 m D 0.3 m B 0.9 m А

Answer 1

Giren that diameter of braws Cylinder (db)= 30MM diameter of steel cylinder (da)= 22mm Initial temperature in the assembly (61)=20°c final temperature in the brais (T2) b=56c final temperature in the nteel (72) = 20 200 Gpa, La = 11.7x10flec E6=185 Gpa, ah= 20.98100% No. Stresses in system before temperature Es length of (s) = 0.9m Change steelrod length of brass cylinder (do): 0.3m Because the intial and final temperature of the atal rod same There is no Thermal strela developed in steel rod. / 8l=last sequanion in thermal stressy, (526 loc 407) (Comb = (2) b-7) (815- 0.3% 20.9410" (50-20) (se) 1.881 X10 6

1. 88 ] xio ។ 11 €ь (81), es О, 3 &ь= 6.28 xio 1 stress E-young's modules с We know 8 strain ", - Eь Сь съ - Бьхь 105 xo1x 6. 27 xjo 4 съ= 65.8 35 x 10 2. ". 3. 65. 835 чра. stress in the brass Cylinder (15) = 65.835 mpa