The bending stress in a wall or column subjected to effective vertical load need not be considered, if the eccentricity ratio is:
Try it first: pick an option, then read the explanation.
Understanding Eccentricity and Bending Stress
When a vertical load is applied to a wall or column, its position relative to the center of the cross-section is critical. An off-center, or "eccentric," load creates both direct compressive stress and bending stress. The eccentricity ratio (e/t) is the distance of the load from the center (e) divided by the thickness of the member (t).
The Question: The question asks at what point the eccentricity is so small that the bending effect can be ignored for design purposes, and the load can be treated as purely axial (centered).
Detailed Analysis of IS 1905 Code Provisions
The design of unreinforced masonry is governed by IS 1905. This code provides specific limits for eccentricity to simplify the design process.
(a) Less than or equal to 1/24
Why it's correct: According to Clause 5.4.2.1 of IS 1905, if the eccentricity ratio (e/t) is less than or equal to 1/24, the effect of bending is considered negligible. In this case, the stress is assumed to be uniformly distributed across the section, and the design is checked for direct compression only. The bending stress "need not be considered."
Analysis of Other Ratios:
- (c) More than 1/24: If the ratio is greater than 1/24 (but not more than 1/6), the bending stress is significant and must be considered. The code allows for a 25% increase in permissible compressive stress to account for this.
- (b) Less than or equal to 1/6: This is another critical limit, known as the "middle third rule." If the eccentricity is within the middle third of the section (e/t ≤ 1/6), no tensile stress will develop. However, bending stress is still present and must be accounted for if e/t is greater than 1/24.
- (d) Less than or equal to 1/12: This is another value within the moderate eccentricity range. Bending stress must be considered at this level.
Study Tips for Eccentricity in Masonry
- 1/24 is the "Ignore It" Limit: This is the key value to memorize. If the eccentricity is very small (≤ 1/24 of the thickness), you can treat the load as if it's perfectly centered.
- 1/6 is the "No Tension" Limit: This is the middle third rule. As long as the load is within the middle third of the wall's thickness, the entire cross-section will remain in compression.
- Visualize the Stress Diagram:
- e/t ≤ 1/24: The stress is an almost perfect rectangle (uniform).
- 1/24 < e/t ≤ 1/6: The stress is a trapezoid (non-uniform compression).
- e/t > 1/6: The stress becomes a triangle, with zero stress at one face and tension trying to develop.