WORLD FOR CIVIL

Topic 6.3: Columns & Buckling - Problem Assignment

1. A 10 foot long wood beam, nominally 2" by 4" (actual 1.5" by 3.5"), is used as a pinned-pinned column. Determine the slenderness ratio, and the Euler Buckling load for this column. Young's modulus is 1.8 x 10 ⁶ lb/in², and the allowable yield stress is 6000 psi.
(277, 1220 lb.)

2. A 16 foot long wood beam, nominally 4" by 8" (actual 3.5" by 7.25"), is used as a fixed - pinned column. Determine the slenderness ratio, and the Euler Buckling load for this column. Young's modulus is 2 x 10 ⁶ lb/in², and the allowable yield stress is 6600 psi.
(133, 28,360 lb.)

3. A 16 foot long WT 6 x 46 steel T-beam is used as a fixed - free column. Determine the slenderness ratio, the Euler Buckling load, and the axial stress when the Euler Buckling load is applied. Young's modulus is 30 x 10 ⁶ lb/in², and the allowable yield stress is 38 x 10 ³ lb/in².
(254, 61,810 lb., 4580 psi.)

4. A wood yard stick has dimensions, length = 36", width = 2", thickness = 3/8". If one end of the year stick is held fixed and a person pushes on the other end, what force will cause the yard stick to fail in Euler buckling. Assume both fixed-free, and fixed - pinned columns and compare your answers. Use a Young's modulus of 2 x 10 ⁶ lb/in², and the allowable yield stress of 6000 psi.
[fixed-free: 34 lb. (45psi.); fixed-pinned: 274 lb. (365 psi.)]

5. A 40 foot long W8 x 40 structural steel I-beam is used as a column. Young's modulus is 30 x 10 ⁶ lb/in² , and the allowable yield stress is 35 x 10 ³ lb/in² . Determine the maximum safe load assuming:
a) pinned-pinned; b) pinned-fixed; c) fixed - free; d) fixed - fixed conditions for ends of the beam.
[ a. 32,950 lb (2790 psi), b. 67100 lb. (5680 psi), c. 8200 lb. (695 psi), d. 127,200 lb. (10,780 psi)]

6. Select the best (safe & lightest) structural steel wide flange I-beam (from web table) to be used as a 16 foot long, pinned-pinned, column to support an axial load of 120,000 lb. Young's modulus is 30 x 10 ⁶ lb/in² , and the allowable yield stress is 36 x 10 ³ lb/in² .
(W8x31)