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Strength of Materials

Double Integration-Simply Supported - Standard Cases

Mid - span de...

Question

Mid - span deflection for the beam load system shown below can be obtained by

A

1, 2 and 3 only

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B

1, 2 and 4 only

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C

2, 3 and 4 only

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D

1, 2, 3 and 4

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Solution

The correct option is D 1, 2, 3 and 4
Real beam Conjugate beam

Hinged support
Fixed support
Free support
Internal hinge
Internal roller Hinged support
Free support
Fixed support
Internal roller
Internal hinge

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Q. Assertion (A): Macaulay's method to determine the slope and deflection at a point in a beam is suitable for beams subjected to concentrated loads and can be extended to uniformly distributed loads.
Reason (R): Macaulay's method is based upon the modification of moment area method. This is applicable to a simple beam carrying a single concentrated load but by superposition, this -method can be extended to cover any kind of loading.

Q. A cantilever beam of span L is subjected to a load W at a distance 'a' from support. It is desired to obtain the vertical displacement at the free end by unit load method. The expression for deflection is

Q. The mid-span deflection simply supported beam

A B

with loading as shown in figure is given by

Q. For the beam shown below

M_{0}

is the applied moment at mid span, slope of the beam at end

A

Q. For determining the deflection 'y' of a loaded beam at a distance 'x' by Macaulay's method, which one or more of the following is/are used?
1. The basic differential equation for deflection

E l \frac{d^{2} y}{d x^{2}} = - M;

where El is the flexural rigidity of the beam, M is the bending moment.
2. Successive integration of the differential equation given in 1.
3. Known positions of zero deflection in the beam.
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