Using Appendix D

Problem: A T-shaped cantilever steel beam has a circular cross section of diameter 3 inches. (The supporting wall is in red.) It is loaded with a 2 kip force perpendicular to its plane as shown. Determine the y-direction displacement at points A, B, and C.

Solution: The moment of inertia of the rod BD is

The 20 kip force is first moved to point B and a couple of 60 kip-ft included. The displacement at B is entirely due to the 20 kip force and can be determined from Case 1 of Appendix D:

Points A and C have the same vertical displacement due to P, but also a displacement due to the twisting action of the 60 kip-ft couple. This causes BD to turn through an angle which, when multiplied by the length of the radial arm AB, produces inches of additional displacement. From an earlier chapter,

Multiplying this by 36 inches, the additional displacement at A is - 1.746 inches, and at C it is + 1.746 inches. Adding these to the displacement caused by the force, I get:

at A: -1.746 - 1.249 = - 2.995 in

at C: +1.746 - 1.249 = + 0.497 in

This does not take into account the vertical displacement of A due to the bending moment of the 2 kip force acting there (since no force acts at C there is no such consideration at that point). That requires the use of the Case 1 equation again:

The deflection at A is, therefore, - 2.995 - 0.270 = - 3.265 in.