2 Calculate the critical load for a square Douglas fir timbe

2. Calculate the critical load for a square Douglas fir timber column 300 mm long if it has a cross section of 150 mm by 150 mm and it is fixed at one end and free on the other. Use a Young\'s Modulus of 13.0 GPa and a Yield Strength of 44 MPa.

Solution

Effective length of column fixed at one end and free at the other = 2*L=2*300=600 mm

modulus of elasticity = 13 GPa = 13000 N/mm²

moment of inertia of section = 150*150³/12=42187500 mm⁴

Buckling load capapcity = pi²EI/(KL)² = pi²*13000*42187500/600²=15035725.45 N=15035.7 kN

Yielding load capacity of column = 150*150*44=990000 N=990 kN