Consider the following statements :

If at section away from the ends of the beam, M represents the bending moment, V the shear force, w the intensity of loading and y represents the deflection of the beam at the section, then

1. $\frac{d M}{d x} = V$

2. $\frac{d V}{d x} = w$

3. $\frac{d w}{d x} = y$

Of these statements:

1 and 2 are correct 1 and 3 are correct 2 and 3 are correct 1, 2 and 3 are correct

Explanation:

The relation between shear force (V) and loading rate (w) is:

$\frac{d V}{d x} = w$

it means a positive slope of the shear force diagram represents an upward loading rate.

The relation between shear force (V) and bending moment (M) is:

$\frac{d M}{d x} = V$

it means the slope of a bending moment diagram will represent the magnitude of shear force at that section.

The relation between loading rate and shear force can be written as:

$\frac{d^{2} M}{d x^{2}} = w$

Additional Information

If y is the deflection then relation with moment M, shear force V and load intensity w.

$E I \frac{d^{2} y}{d x^{2}} = M$

$E I \frac{d^{3} y}{d x^{3}} = V$

$E I \frac{d^{4} y}{d x^{4}} = w$

Hint Answer

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1 and 2 are correct

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Consider the following statements : If at section away from the ends of the beam, M represents the bending moment, V the shear force, w the intensity of loading and y represents the deflection of the beam at the section, then 1. dMdx=V 2. dVdx=w 3. dwdx=y Of these statements: