Correct Answer - Option 2 : a simply supported beam
Concept
Conjugate beam method:
A Conjugate beam is defined as an imaginary beam with the same dimension as that of the original beam but load at any point on the conjugate beam is equal to bending moment at that point divided by EI (Flexural Rigidity).
Conjugate beam can be made by changing the supports
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Real beam
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Conjugate beam
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Fixed support
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Free support
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Free support
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Fixed support
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Roller support
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Hinge support
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Hinge support
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Roller support
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A simply supported beam consists of a hinge and roller support when ∴ the conjugate beam of this will be of a roller and hinge support. So This method can be directly used for simply supported.
The shear force in the conjugate beam at a point is a slope at the point in the real beam. The bending moment in the conjugate beam at a point is the deflection at the point in the real beam. Since there is no deflection at simple support so the bending moment in the conjugate beam will be zero. There is a slope at simple support in the real beam so the shear force will exist in the conjugate beam. Therefore simple support of a real beam is assumed to be simple support in conjugate beam also.
The shear force in the conjugate beam at a point is a slope at the point in the real beam. The bending moment in the conjugate beam at a point is the deflection at the point in the real beam.
