A compression member of 9-m effective length is obtained by welding two 10 -mm-thick steel plate

step 1 Let us first calculate the moment of inertia. So it is equal to Phi divided by 4, outer radius t

A compression member of 9-m effective length is obtained by...

A compression member of $9-\mathrm{m}$ effective length is obtained by welding two 10 -mm-thick steel plates to a $\mathrm{W} 250 \times 80$ rolled-steel shape as shown. Knowing that $\sigma_{Y}=345 \mathrm{MPa}$ and $E=200 \mathrm{GPa}$ and using allowable stress design, determine the allowable centric load for the compression member.

Key Concepts

Compression Members

Compression members are structural elements that carry axial loads, and their design must ensure that they are capable of withstanding applied forces without failing. In structural engineering, both material yielding and instability (buckling) are of concern for such members, and proper analysis is required to avoid a catastrophic failure.

Euler Buckling Theory

Euler Buckling Theory is fundamental in determining the critical load at which a slender column will buckle when subjected to axial compression. This theory takes into account the modulus of elasticity, the column’s effective length, and its moment of inertia, and it is especially relevant for long, slender columns where buckling governs the design.

Allowable Stress Design

Allowable Stress Design (ASD) is a conventional engineering method that involves designing structural members such that the applied stresses do not exceed specified allowable limits, usually derived by applying a safety factor to the material’s yield or ultimate strength. This method ensures that structures have adequate safety margins against failure under service loads.

Effective Length

The effective length of a column is a critical parameter in buckling analysis that accounts for the actual support and boundary conditions of the column. It represents the length between points of inflection or restraint, and influences the buckling capacity by effectively lengthening or shortening the column in the analysis.

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