WORLD FOR CIVIL

Topic 7.2e: Wood Columns - Example 5

Four twenty five foot long Douglas Fir columns are to support a observation tower. The columns are rought cut and exactly 5" by 5". How heavy can the observation platform be before buckling will occur? (You should assume the wood columns are fixed on both ends.)

We first wish to determine the slenderness ratio we use slenderness ratio = L_e/d = (.5*25' * 12"/ft)/ 5 in. = 30.

We next need to calculate the transition slenderness ratio, k = .671 sqrt(E/allowable compressive stress along grain) = .671 sqrt(1.3 x 10⁶ lb/in² / 6 x 10³ lb/in²) = 9.88

Since the column's slenderness ratio is greater than k, we use the appropriate formula (for wood) for long slender columns. The Allowable Stress = [.3E/(L_e/d)²] = .3*1.3 x 10⁶ lb/in² /(30)² = 433 lb/in².

Finally the Allowable Load = Stress * Area = 433 lb/in² * 25 in² = 10,825 lb./per column. And since there are four columns, the platform weight could be 4 * 10,825 lb. = 44,300 lb.