Which one of the following is NOT the assumption of Euler's column theory?
- AThe direct stress is very small compared to the bending stress.
- BThe self-weight of the column is considerable.Correct
- CThe cross-section of the column is uniform throughout.
- DThe column will fail by buckling only.
Solution
Concept
Euler's theory assumes an ideal column that is straight, uniform and loaded axially, with its self-weight neglected.
Formula
Pcr = π² E I / Le2
Step-by-step solution
1. List the Euler assumptions: the column is initially straight, the load is axial, the section is uniform, the material is homogeneous and elastic, the column fails by buckling only, direct stress is small compared to bending stress, and self-weight is neglected. 2. Option (B) says self-weight is considerable. This is the opposite of the real assumption. 3. So the answer is (B).
Explanation
Euler's theory neglects the self-weight of the column. Option (B) says the self-weight is considerable, so it is not an assumption. All other options are standard Euler assumptions.
Why the other options are wrong
A, C and D are all true assumptions of Euler's theory, so they cannot be the answer.
Shortcut
Euler's column is an ideal column, so self-weight is always neglected.
Common mistake
Thinking that (A) is wrong. Small direct stress compared to bending stress is a listed assumption, because the theory is for long columns.
Correct answer: B) The self-weight of the column is considerable.