Base width for “no tension” condition — triangular vs rectangular sections of the same height For two gravity-type sections of the same height (one triangular, one rectangular), compare the required bottom width to satisfy the “no tension at the base” criterion under similar loading direction. Which statement is correct?

Introduction / Context:In gravity structures (e.g., retaining walls, small dams, masonry sections), a common serviceability requirement is that the resultant at the base stays within the middle kernel so that no tensile stress develops. The base width needed to prevent tension depends on how the section distributes self-weight relative to the toe and heel where overturning acts.

Given Data / Assumptions:

• Two sections have the same height.
• Overturning direction is the same for both shapes.
• Self-weight provides stabilizing moment; tensile stress at the base is not allowed (resultant within the middle third for rectangular sections and within the elastic core for the actual shape).

Concept / Approach:

For equal height, a triangular section concentrates more of its self-weight near the base, creating a larger stabilizing lever arm against overturning compared with a rectangular section of the same base width. Consequently, to keep the resultant within the permitted kernel and avoid tension, a rectangular section generally needs a larger base width than a triangular section subjected to similar actions.

Step-by-Step Solution:

Verification / Alternative check:

Illustrative computations with a simple overturning couple and self-weight show that the eccentricity of the resultant relative to the base midpoint is smaller for a triangular profile at the same base width, hence it reaches the “no tension” kernel more easily. Therefore, for equal height, the rectangular section must be made wider to meet the same criterion.

Why Other Options Are Wrong:

• Triangular requires more width: Opposite to the stabilizing leverage effect described.
• Same width: Neglects the differing weight centroids and lever arms.
• Triangular never satisfies no-tension: Incorrect; with adequate base it certainly can.

Common Pitfalls:

• Ignoring the centroid location and its influence on stabilizing moment.
• Confusing the kernel (core) condition with a pure middle-third rule for all shapes.

Final Answer:

for rectangular section the required bottom width is more than that for a triangular section.