Solid cylindrical rods AB and BC are welded together at B and loaded as shown. Determine the magnitude of the force P for which the tensile stresses in rods AB and BC are equal. Take W = 10 kips. Find force P?

Solid cylindrical rods AB and BC are welded together at B and loaded as shown. Determine the magnitude of the force P for which the tensile stresses in rods AB and BC are equal. Take W = 10 kips. Find force P?

Answer:-

For the rod AB :-

Force on AB, Fab = P+10

Area of AB , Aab = π (1.25)^2/4 = 1.22718 m^2

So  stress on AB is , σab = Fab/Aab = P+10/1.22718

For the rod BC :-

Force on AB, Fab = P

Area of AB , Aab = π (0.75)^2/4 = 0.44179 m^2

So  stress on AB is , σab = Fbc/Abc = P/0.44179

Now,  σab= σbc

        P+10/1.22718 = P/0.44179

So,  the value of force P = 12.7325 kips