If the horizontal cross-sectional area of a wall is 1200 cm², then the basic stress shall be multiplied by a reduction factor equal to:
🔬 Understanding the Area Reduction Factor
In masonry design, the permissible compressive stress is not constant. It is adjusted by several factors to account for real-world conditions. One of these is the Area Reduction Factor (Kₐ). This factor is applied when the load-bearing cross-sectional area of a masonry member (like a wall or column) is relatively small.
The Principle: The code IS 1905: Code of Practice for Structural Use of Unreinforced Masonry recognizes that smaller masonry elements may not achieve the same unit strength as larger ones due to the greater influence of workmanship and edge effects. To ensure safety, a reduction factor is applied to the basic permissible stress for members with a small cross-sectional area.
⚖️ Detailed Analysis of the IS 1905 Provision
Clause 5.4.1.2 of IS 1905 provides the rule for the Area Reduction Factor (Kₐ).
- If the cross-sectional area (A) is greater than 0.2 m², no reduction is needed, and the factor Kₐ is 1.0.
- If the cross-sectional area (A) is less than 0.2 m², the basic stress must be multiplied by a reduction factor calculated using the following formula:
Kₐ = 0.7 + 1.5 × A
(where A is the area in m²)
Calculation for the Given Problem
Step 1: Convert the area to m².
Given Area = 1200 cm²
Since 1 m² = 10,000 cm²,
A = 1200 / 10000 = 0.12 m²
Step 2: Check if the reduction factor applies.
Since 0.12 m² is less than 0.2 m², the reduction factor must be applied.
Step 3: Apply the formula.
Kₐ = 0.7 + 1.5 × A
Kₐ = 0.7 + 1.5 × 0.12
Kₐ = 0.7 + 0.18
Kₐ = 0.88
The calculated value of 0.88 is closest to the option (c) 0.85. (Note: Some interpretations or older versions of the code might lead to slightly different values, but 0.88 is the result from the standard formula, making 0.85 the intended answer).
💡 Study Tips for Masonry Design Factors
- Memorize the Threshold: The key value to remember is 0.2 m² (or 2000 cm²). If the area is smaller than this, you must apply the area reduction factor.
- Learn the Formula: The formula Kₐ = 0.7 + 1.5A is fundamental for this type of problem.
- Watch Your Units: The most common mistake is forgetting to convert the area from cm² to m² before using the formula. Always work in standard units (meters).