Question

47. the beam is supported by two rods ab and cd that have cross-sectional areas of 12mm^2 and 8mm^2, respectively. determine the position d of the 6-kn load so that the average normal stress in each rod is the same.

Answer 1

Let the beam is of length L

Now the stress on both the end is same

now we can say that torque on the beam due to two forces must be zero

$N_1* x = N_2* (L - x)$

also we know that stress at both ends are same

$\frac{N_1}{12} = \frac{N_2}{8}$

$2*N_1 = 3*N_2$

Now from two equations we have

$\frac{3}{2}N_2*x = N_2* (L - x)$

solving above equation we have

$x = \frac{2}{5}L$

so the load is placed at distance 0.4L from the end of 12 mm^2 area