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A beam of overall length l rests on two simple supports with equal overhangs on both sides. Two equal loads act at the free ends. If the deflection at the centre of the beam is the same as at either end, then the length of either overhang is ? a) 0.152l b) 0.207l c) 0.252l d) 0.277l?
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A beam of overall length l rests on two simple supports with equal ove...
Given Information:
- The beam has an overall length of l.
- The beam rests on two simple supports with equal overhangs on both sides.
- Two equal loads act at the free ends.
- The deflection at the centre of the beam is the same as at either end.

To find:
- The length of either overhang.

Solution:
Let us assume that the length of each overhang is 'x'.

We know that the deflection at the centre of the beam is given by:

δc = (5wL^4)/(384EI)

where,
δc = deflection at the centre of the beam
w = load acting at the free ends
L = length of the beam
E = modulus of elasticity
I = moment of inertia

We also know that the deflection at the end of a simply supported beam with a point load at the end is given by:

δe = (FL^3)/(3EI)

where,
δe = deflection at the end of the beam
F = load acting at the end of the beam

Since the deflection at the centre of the beam is the same as at either end, we can equate the above two equations as follows:

(5wL^4)/(384EI) = (FL^3)/(3EI)

Simplifying the above equation, we get:

F = (5wL)/64

Now, let us consider a section of the beam between the centre and one of the supports. The bending moment at this section is given by:

M = F(x/2)

where,
x/2 = distance of the section from the support

The maximum deflection at this section is given by:

δmax = (FL^3)/(48EI)

Substituting the value of F, we get:

δmax = (5wx^3)/(384EI)

Since the deflection at the centre and at this section is the same, we get:

δc = δmax

(5wL^4)/(384EI) = (5wx^3)/(384EI)

Simplifying the above equation, we get:

x = (L/2)∛2

Therefore, the length of either overhang is:

x = (L/2)∛2 = 0.277L

Hence, the correct option is (d) 0.277L.
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A beam of overall length l rests on two simple supports with equal overhangs on both sides. Two equal loads act at the free ends. If the deflection at the centre of the beam is the same as at either end, then the length of either overhang is ? a) 0.152l b) 0.207l c) 0.252l d) 0.277l?
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A beam of overall length l rests on two simple supports with equal overhangs on both sides. Two equal loads act at the free ends. If the deflection at the centre of the beam is the same as at either end, then the length of either overhang is ? a) 0.152l b) 0.207l c) 0.252l d) 0.277l? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A beam of overall length l rests on two simple supports with equal overhangs on both sides. Two equal loads act at the free ends. If the deflection at the centre of the beam is the same as at either end, then the length of either overhang is ? a) 0.152l b) 0.207l c) 0.252l d) 0.277l? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of overall length l rests on two simple supports with equal overhangs on both sides. Two equal loads act at the free ends. If the deflection at the centre of the beam is the same as at either end, then the length of either overhang is ? a) 0.152l b) 0.207l c) 0.252l d) 0.277l?.
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