Solution: Stress Distribution in Beams MCQ
This question asks to identify the correct statement regarding stress distribution within a structural member, specifically focusing on bending stress and shear stress.
Analyzing Statement 1: Bending Stress Distribution
Statement: The bending stress in a section is zero at its neutral axis and maximum at the outer fibers.
Reasoning: In beam theory, the neutral axis is the axis within the cross-section where the bending stress is zero. The bending stress increases linearly with the distance from the neutral axis. Therefore, the stress reaches its maximum magnitude at the outermost points of the cross-section, known as the outer fibers.
Conclusion: Statement 1 is correct.
Analyzing Statement 2: Shear Stress Distribution
Statement: The shear stress is zero at the outer fibers and maximum at the neutral axis.
Reasoning: For most common cross-sectional shapes (like rectangles or I-beams), the shear stress distribution across the depth is parabolic. Shear stress is typically zero at the top and bottom surfaces (outer fibers) and attains its maximum value at the neutral axis.
Conclusion: Statement 2 is correct.
Analyzing Statement 3: Bending Stress as Principal Stress
Statement: The bending stress at the outer fibers, is known as principal stress.
Reasoning: Principal stresses represent the maximum and minimum normal stresses acting at a point. In simple bending, the normal stress is maximum at the outer fibers. At these locations, the shear stress is often zero or negligible. Therefore, the maximum bending stress experienced at the outer fibers corresponds to a principal stress.
Conclusion: Statement 3 is correct.
Final Conclusion
Since statements 1, 2, and 3 are all accurate descriptions of stress distribution in beams:
- Statement 1: Correct (Bending stress zero at neutral axis, max at outer fibers).
- Statement 2: Correct (Shear stress zero at outer fibers, max at neutral axis).
- Statement 3: Correct (Bending stress at outer fibers is a principal stress).
Therefore, the option 'All of these' is the correct choice, as it encompasses all the true statements.
Important Questions from Shear Stress and Bending Stress
- For a beam to be classified as a beam of uniform strength, which of the following conditions must be met?
The maximum shear stress in a circular beam is
An increase in load at the free end of a cantilever is likely to cause failure-
The maximum bending stress in a curved beam having symmetrical section always occurs at the
The stresses caused by the bending moment is called -
