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Vector Component

For the frame...

Question

For the frame shown below, the fixed end moment developed at support A is $\frac{P L}{k}$ .
The value of k (correct upto one decimal place) is_____.

12

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Solution

The correct option is A 12

$k_{D A} = \frac{4 E I}{2 L} = \frac{2 E I}{L}$

$k_{D B} = \frac{3 (2 E I)}{L} = \frac{6 E I}{L}$

$k_{D C} = \frac{4 E I}{L}$

$M_{A} = \frac{P L}{2} ⎡ ⎢ ⎢ ⎢ ⎣ \frac{\frac{2 E I}{L}}{\frac{2 E I}{L} + \frac{6 E I}{L} + \frac{4 E I}{L}} ⎤ ⎥ ⎥ ⎥ ⎦$

$= \frac{P L}{12}$

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