Question

For a cantilever slab of 1.4 m span, the minimum thickness required from serviceability criteria is

• A. 100 mm
• B. 140 mm
• C. 180 mm
• D. 200 mm

Hint:

Memorize the basic Span/Effective Depth ratios from IS 456 for deflection control:
- Cantilever: 7
- Simply Supported: 20
- Continuous: 26
These are fundamental for the initial sizing of beams and slabs.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the minimum required total thickness (or depth) of a cantilever slab to satisfy the deflection control criteria (a serviceability limit state) as per IS 456.

Step 2: Key Formula or Approach:
IS 456:2000 (Clause 23.2.1) provides basic span-to-effective depth ratios for beams and slabs to control deflection without detailed calculations, for spans up to 10 m.
For a

cantilever beam or slab, the basic ratio of span to effective depth ($L/d$) should not exceed 7.
\[ \frac{\text{Span}}{\text{Effective Depth}} \le 7 \] This basic ratio can be modified by factors for tension and compression reinforcement, but for a preliminary estimate, we use the basic value. The question asks for minimum thickness, which implies we should use the maximum allowable ratio.
\[ d_{min} = \frac{\text{Span}}{7} \]

Step 3: Detailed Explanation:
We are given:
- Span ($L$) = 1.4 m = 1400 mm.
First, calculate the minimum required effective depth ($d_{min}$):
\[ d_{min} = \frac{1400 \text{ mm}}{7} = 200 \text{ mm} \] The question asks for the "minimum thickness". Thickness usually refers to the overall depth ($D$), which is the effective depth plus the clear cover and half the bar diameter ($D = d + \text{cover} + \phi/2$).
The calculated minimum effective depth is 200 mm. This means the overall thickness must be even greater (e.g., around 220-230 mm).
Let's re-read the options. Option (D) is 200 mm. It is possible that the question is asking for the effective depth, or that it is a simplified question where the overall thickness is taken to be equal to the calculated minimum effective depth. Given the options, 200 mm is the direct result of the code's span/depth ratio calculation. The other options are significantly different.

Step 4: Final Answer:
The minimum effective depth required is 200 mm. Assuming the question uses "thickness" to refer to this controlling dimension, the answer is 200 mm.