A 200 mm thick wall made of modular bricks is 5 m long between cross walls and 3.8 m clear height between RCC slabs at top and bottom. The slenderness ratio of the wall is:
🔬 Understanding Slenderness Ratio
The slenderness ratio is a critical parameter in the design of masonry walls and columns. It measures the wall's susceptibility to buckling under compressive loads. A higher ratio indicates a more slender wall, which has a lower load-carrying capacity.
Formula: According to IS 1905, the slenderness ratio (SR) is the lesser of the following two values:
1. SR (height) = Effective Height (hₑꜰ) / Effective Thickness (tₑꜰ)
2. SR (length) = Effective Length (lₑꜰ) / Effective Thickness (tₑꜰ)
⚖️ Detailed Calculation Steps
First, let's identify the given data:
- Actual Thickness (t): 200 mm = 0.2 m
- Clear Length (l): 5 m
- Clear Height (h): 3.8 m
- Support Conditions: Supported by cross walls (laterally) and RCC slabs (at top and bottom).
Step 1: Determine Effective Thickness (tₑꜰ)
For a single-leaf solid brick wall, the effective thickness is equal to its actual thickness.
tₑꜰ = 0.2 m
Step 2: Determine Effective Height (hₑꜰ)
The wall is supported by RCC slabs at the top and bottom. According to IS 1905, this condition provides "enhanced resistance" to lateral movement. For this condition, the effective height is taken as 0.75 times the clear height.
hₑꜰ = 0.75 × h = 0.75 × 3.8 m = 2.85 m
Step 3: Determine Effective Length (lₑꜰ)
The wall is supported by cross walls at its ends. For this condition, the effective length is taken as the clear distance between the supports.
lₑꜰ = l = 5.0 m
Step 4: Calculate and Compare Slenderness Ratios
Now we calculate the two possible slenderness ratios and choose the smaller one.
SR (based on height) = hₑꜰ / tₑꜰ = 2.85 m / 0.2 m = 14.25
SR (based on length) = lₑꜰ / tₑꜰ = 5.0 m / 0.2 m = 25
The final slenderness ratio for the wall is the lesser of these two values.
SR = 14.25
This value is closest to 15, making option (a) the correct answer.