This question was previously asked in

Gujarat Engineering Service 2017 Official Paper (Civil Part 2)

Option 2 : 0

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

__Explanation:__

Bending Moment Diagram in a Simply Supported Beam:

In the following figure, a unit load is applied to a simply supported beam at point C at mid of beam length.

The bending moment diagram will be an isosceles triangle with maximum ordinate at the center of the beam.

\(B{M_{x - x}} = \frac{W}{2}x\) ( 0 ≤ x ≤ L/2 )

\(B{M_{x - x}} = \frac{W}{2}x - w \times (x - L/2)\) ( 0 ≤ x ≤ L)

So at Ends x = 0 , x = L

BM = 0

At centre x = L/2

\(B{M_{x = \frac{l}{2}}} = \frac{W}{2}\frac{L}{2} = \frac{{WL}}{4}\)

**∴ Bending Moment at Centre is maximum WL/4**

**Bending Moment at ends is zero**

**Ratio of **bending moment at the support to the bending moment at the center is **(0)/(WL/4) = 0**