Question

The rigid bar AB is pinned at A and supported by two aluminum rods (E 10 x 103ksi) with diameter d = 1.2 in and the length shown for each on the figure. If the rigid bar is initially vertical, determine (a) the reaction exerted at A and (b) the average normal stress in each rod when the 40-kip force is applied. 40 kip B 2 ft d= 12 in E O 2 ft- (a) reaction at A 3 ft d=1.2 in D С OCD = 3 ft 2 ft OEF =

Answer 1

40kip Consider the following diagram. 40 kip B 2 ft d=12 in E F -2 ft 2 ft 2 ft FF AEF 3 ft 3 ft 3 ft d = 1.2 in Acol FCD -3 ft 2 ft 2 ft 2 ft 2 1 Consider the middle figure: Write the moment equilibrium equation about point A as follows: M=0 FCD * 2+FpF X5-40x7=0 2FCD +57 g = 280 (1) Write the expression for extension in the bar CD as follows: FCD LCD ADE Aco = Write the expression for extension in the bar EF as follows: FEFLEE AEF = EP

Consider the extreme right figure: By the property of similar triangle, AEF _ ACD 5 2 24 EF = 5ACD FCD LCD 2 = 5 ACDE Fer x 2 Fcp 3 2 = 5 πd πd XE 4 4 FLEE = XE 4 FEF = 15FCD 15F0D-4F2F = 0 (2) ...... Solve the equation (1) and (2). Fcp = 13.49 kip Fee = 50.60 kip Calculation of the normal stress: Calculate the cross-sectional area of the rods as follows: A = AcD = ADF πd 4 1 x1.22 A 4 = A=1.13 in

OCD Calculate the normal stress in the rod CD as follows: FCD A 13.49 kip OCD 1.13 in? CD=11.94 ksi Calculate the normal stress in the rod EF as follows: FCD OEF А 50.60 kip 1.13 in? CD = 44.78 ksi