Problem: A flat concrete ceiling 40 ft x 30 ft x 8 inches thick is supported by steel pipe columns 9 ft long. The pipes are 2 inch OD with 1/8 inch wall thicknesses. Determine how many supports are needed if a factor of safety of 3 is to be applied to the critical load. Find the stress in each pipe and compare it with the yield stress.
Solution: From Appendix B, the specific weight of concrete is 0.084 lb/in3. The weight of the ceiling is
Assuming that the pipes are either buried in a concrete base or rest on a flat bearing plate (standard in residential construction) and that the top of each pipe has a similar flat bearing surface, case d of Figure 10.18 applies and the effective length is
The moment of inertia of each pipe's cross section is
The critical load is
Applying the factor of safety, the allowable load is 1.063 x 104 lb. Dividing the ceiling weight by this value, I get 10.92, or 11 columns.
The cross sectional area of each pipe is
Therefore the stress is 14.44 ksi, whereas the yield stress is 36 ksi. So the design is OK.