Determine the load bearing capacity of the 3 m high column, the cross section of which is given in the Figure. Both ends of the column are built-in. Material is glued laminated timber, grade of material is Gl36h, its compressive strength is: f = 31 MPa, the Euler slenderness is: λ1 = 61.6. Buckling reduction factor (χc) can be calculated in the function of the relative slenderness, λ by the following formula based on Eurocode (χc ≤ 1):
χc=1χ+√χ2–λ2,
Solve Problem
Load bearing capacity, Nb [kN]=Solve
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Steps
Step 1. Calculate the section properties. Step 2. Give the relevant slenderness. Since the support conditions are the same in both directions, buckling occurs first about the axis of the smaller radius of gyration: iy . The relevant slenderness is Step 3. Determine the buckling reduction factor. Step 4. Calculate the load bearing capacity of the column.Step by step
Check section properties
Check slenderness
Check buckling reduction factor
Check capacity
Results
First the section properties are calculated: Since the support conditions are the same in both directions, buckling occurs first about the axis of the smaller radius of gyration: iy . The relevant slenderness is Load bearing capacity of the column must be reduced by the buckling reduction factor: The capacity of the column becomesWorked out solution