Question

Required Information A steel rod AD and a brass rod BE are connected by a rigid bar ACB, which is fixed at a pivot point. The stiffness of th steel rod is greater than the brass rod. The distances from the pivot point to the connections are 240 mm and 150 mm respectively, as shown in the figure. It is known that rod AD has a cross-section area 41 = 100 mm, length L1 = 330 mm, Young's modulus G 200 GPa, and thermal expansion coefficient a1 = 12.5 X 105 C. Rod BE has a cross-secti area A2 = 200 mm length L2 = 220 mm, Young's modulus E2 = 100 GPa, and thermal expansion coefficient a2 = 16 * 106 rc. If there is a temperature increase of 35°C. 330 mm 220 mm --240 mm -150 mm What are the values of the Internal stress in each of the rods? OBE= 5.775 102 GPa OAD- 8.75 10-2 GPa

Answer 1

LL 220 mm 2 330mm m m 2 1 > 9 .40 mm biven, Rod ACB is a ligid bar L = 330 mm , A, = 100 mm, E = 200 lepa 2, 12-5 *10°C L₂ = 220 mm, A = 200 mm², E = 100 MPa 42 = 16.5x100/°C Now, As temperature increases by 35°, both lod 1 and 2 tend to elongate. But the rod AB BCB is rigid, Point A and B Cannot simultaneously go down . So they remain at their auginal position

As a result, compressive stress o, and a generates in od 1 and 2 as they are restricted for elongation For Mod 1, Total elongation to 3) NOT h - 5410 = 6,= EAST : 200 * 12:5*10 %35 Gopa = 8.75 X 102 Gepa For Mod 2, 62 - E22207 100x 16.5x10 % 35 Gopal WAS 5.775 x 10-2 Gepa
The elongation of the rods is restricted due to rigidity of the pivoted bar. Use the formula for compressive stress generated when there is temperature increase but the rod is fixed from both end.