Concept explainers
The wood column is 4 m long and is required to support the axial load of 25 kN. If the cross section is square, determine the dimension a of each of its sides using a factor of safety against buckling of F.S. = 2.5. The column is assumed to be pinned at its top and bottom. Use the Euler equation. Ew = 11 GPa, and σY = 10 MPa.
Find the dimensions a of the square column.
Answer to Problem 1RP
The dimension a of the square column is
Explanation of Solution
Given information:
The length of the column is
The axial load applied on the column is
The factor of safety against buckling is
The column is pinned at its top and bottom.
The modulus of elasticity of the wood column is
The allowable yield stress is
Calculation:
Find the critical load
Substitute 2.5 for F.S. and 25 kN for P.
Calculate the moment of inertia
Here, the dimension of the column is a.
The value of effective-length factor for rectangular column,
Show the expression for Euler’s formula as shown below:
Here,
Substitute 62.5 kN for
Check the validity of using Euler’s formula:
Euler’s formula is valid only when the critical stress
Find the cross-sectional area (A) of the column as follows;
Calculate the critical stress for the column using the relation:
Substitute 62.5 kN for
Thus, the use of Euler Equation is valid.
Therefore, the dimension a of the square column is
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