Limit State of Serviceability - Deflection Control MCQ with answer and solution

Concept

Span-to-Effective Depth Ratio for Long Spans

Formula

Modified (L/d) = Basic (L/d) × (10 / L)

Step-by-step solution

1. Identify the basic span-to-depth ratio for a simply supported beam: Basic (L/d) = 20. 2. Apply the span correction factor for span \> 10 m: Factor = 10 / L = 10 / 16 = 0.625. 3. Calculate the modified ratio: Modified (L/d) = 20 × 0.625 = 12.5.

Explanation

For a span greater than 10 meters, the standard basic span-to-effective-depth ratio (which is 20 for a simply supported beam) must be multiplied by a factor of 10 divided by the actual span in meters. For a 16m span, the modified ratio is calculated as 20 multiplied by (10 / 16), which equals 12.5 (Option B).

Shortcut

For spans over 10 m, multiply the basic ratio (20) by 10/span. For 16 m, calculate 20 x 10/16 = 12.5.

Common mistake

Many students select Option C (20) by directly taking the basic span-to-effective depth ratio for a simply supported beam without applying the modification factor (10 / span) required for spans exceeding 10 meters.