146 The beam is supported by two rods AB and CD that have cr

1-46. The beam is supported by two rods AB and CD that have cross-sectional areas of 12 mm2 and 8 mm2, respectively. If d= 1 m, determine the average normal stress in each rod.

Solution

>> Let, force in rod AB & CD are :- F_ab & F_cd

Now, on beam, a Force, F = 6 kN, is acting \'d\' = 1 m from A

>> As, rod is in equilibrium

So, Net Forces in Y Direction = 0

=> F_ab + F_cd = F = 6 ........(1)....

>> As, also, Net moment about A, Ma = 0

=> Ma = 1*F - 3*F_cd = 0

=> F_cd = 2 kN

from (1), F_ab = 4 kN

>> Now, crosssection of rod AB, A_ab = 12 mm²

and, CrossSection of rod CD, A_cd = 8 mm²

=> Normal Stress in rod AB = F_ab/A_ab = 4*10³/(12*10^-6) = 333 MPa

&, Normal Stress in rod CD = F_cd/Acd = 2*10³/(8*10^-6) = 250 MPa