Consider a portal frame shown in the figure. The horizontal shear equation at D is

H_{D} = \frac{M_{C D} + M_{D C} - P h}{L_{2}}

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H_{D} = \frac{M_{C D} + M_{D C} - \frac{W L_{2}^{2}}{2}}{L_{2}}

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H_{D} = \frac{M_{C D} + M_{D C} + P h}{L_{2}}

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H_{D} = \frac{M_{C D} + M_{D C} + \frac{W L_{2}^{2}}{2}}{L_{2}}

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Solution

The correct option is D $H_{D} = \frac{M_{C D} + M_{D C} + \frac{W L_{2}^{2}}{2}}{L_{2}}$
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$Σ M_{C} = 0$

$H_{D} \times L_{2} = M_{D C} + M_{C D} + w L_{2} \times \frac{L_{2}}{2}$

$H_{D} = \frac{M_{C D} + M_{D C} + \frac{W L_{2}^{2}}{2}}{L_{2}}$

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