A beam is said to be of uniform strength if the
- Abending moment is same throughout the beam
- Bdeflection is same throughout the beam
- Cbending stress is same throughout the beamCorrect
- Dshear stress is same throughout the beam
Solution
Concept
In a beam of uniform strength, the maximum bending stress is the same at every section.
Formula
σ = M/Z = constant
Step-by-step solution
1. Bending stress at any section is σ = M/Z. 2. M changes along the beam. 3. For uniform strength, Z is changed so that M/Z stays constant. 4. So the bending stress is the same throughout the beam.
Explanation
A beam of uniform strength has the same maximum bending stress at every section. To get this, the section (width or depth) is changed along the length as the bending moment changes. This saves material.
Why the other options are wrong
A: Bending moment changes with loading and support, so it is not constant. B: Deflection is not kept constant in such a beam. D: The design is based on bending stress, not shear stress.
Shortcut
Uniform strength means uniform bending stress (M/Z constant).
Common mistake
Students choose 'bending moment same', but it is the stress that is kept constant.
Correct answer: C) bending stress is same throughout the beam