Question

Column A buckles more easily than Column B. Which of the following statements is true?1.Column A must have a smaller cross-sectional area than Column B.2.Column A must have a smaller Young’s modulus than Column B.3.Column A must be shorter than Column B.4.Column A must have a smaller Euler buckling load than Column B.

Answer 1

Euler's buckling load is the maximum compressive load hat a slender column can resist before bending or buckling. It is proportional to the Young's modulus of the column material, as well as the cross-sectional area of the column. It is inversely proportional to the square of the length of the column:

`P_(cr)=(\pi^2EI)/(L^2)`

Where P_cr is the Euler's buckling load, E is the Young's modulus of the material, L is the length of the column and I is the area moment of inertia.

Since column A buckles more easily than column B, then the Euler's buckling load of column B must be greater than that of column A. This situation could be produced whenever column A has a smaller cross-sectional area, a smaller Young's modulus, or a greater length, or a combination of those factors.

Since the Euler's buckling load depends on various factors, we cannot be sure that column A has a smaller cross-sectional area, a smaller Young's modulus or a greater length than column B. The only statement that must be true, is:

`\begin{gathered} 4) \\ \text{Column A must have a smaller} \\ \text{Euler buckling load than Column B} \end{gathered}`