Which of the following assumptions is NOT valid in case of design of axially loaded compression members in the steel design?
- ASecondary stresses are neglected.
- BThe ideal column is assumed to be absolutely straight with no crookedness.
- CThe modulus of elasticity is assumed to be constant in a built-up column.
- DThe modulus of elasticity is assumed to vary in a built-up column.Correct
Solution
Concept
Ideal column theory assumes a perfectly straight, homogeneous column with constant modulus of elasticity and neglects secondary stresses.
Formula
Pcr = π2 E I / Le2
Step-by-step solution
1. List the standard assumptions for an axially loaded ideal column: column is perfectly straight, load is exactly axial, material is homogeneous and isotropic, E is constant, and secondary stresses are neglected. 2. Options A, B and C match these assumptions, so they are valid. 3. Option D says E varies in a built-up column. This goes against the constant-E assumption. 4. So the assumption that is NOT valid is D.
Explanation
In compression member design, the column is taken as perfectly straight and made of uniform material, so E is constant everywhere. Secondary stresses are ignored. Saying that E varies is against these assumptions, so D is not valid.
Why the other options are wrong
A: Neglecting secondary stresses is a valid assumption. B: A perfectly straight ideal column is a valid assumption. C: Constant E in a built-up column is a valid assumption.
Shortcut
Options C and D are opposites. Ideal theory needs constant E, so the 'varies' option is the wrong assumption.
Common mistake
Students may think a built-up section has different E for each part. Steel components have the same E, and the theory assumes it is constant.
Correct answer: D) The modulus of elasticity is assumed to vary in a built-up column.