A simply supported beam 'A' of lengthl, breadthband depthdcarries a central loadW. Another beam 'B' of the same dimensions carries a central load equal to 2W. The deflection of beam 'B' will be __________ as that of beam 'A'.a)one-fourthb)one-halfc)doubled)four timesCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given information:
- Beam A: Length l, Breadth b, Depth d, Central load W
- Beam B: Same dimensions as A, Central load 2W

To find: Deflection of beam B compared to beam A

Solution:
1. Calculate the deflection of beam A using the formula: δ = (WL³)/(48EI)
where δ = deflection, W = load, L = length, E = modulus of elasticity, I = moment of inertia

2. Calculate the deflection of beam B using the same formula but with load 2W.

3. Ratio of deflection of beam B to A = δB/δA = [(2W)(L³)]/[(W)(L³)] = 2

Therefore, the deflection of beam B will be doubled compared to beam A.

Explanation:
- The deflection of a beam under a load depends on various factors such as length, breadth, depth, material, and load magnitude.
- The formula for deflection of a simply supported beam is proportional to the load and inversely proportional to the moment of inertia, which is a function of the beam's dimensions.
- In this case, both beams have the same dimensions, so their moment of inertia will be the same.
- Beam B has double the load of beam A, so its deflection will be twice as much as beam A.
- Therefore, the correct answer is option C, doubled.

Answer

Deflection for SSB at central point load=wl^3/48EI

SO, Deflection is directly proportional to load W

for beam B load is 2W ,so Deflection of beam B = 2WL^3/48EI

for beam A load is W ,so Deflection of beam A = WL^3/48EI

so the ratio will be double.

Answer

Type of questions level is so good so again and again show this test

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