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A T-shaped bracket supports the four loads shown. Determine the reactions at A and B (a) if a=...

A T-shaped bracket supports the four loads shown. Determine the reactions at A and B (a) if a = 10 in., (b) if a = 7 in.

Fig. P4.99

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Answer #1

Draw the free-body diagram for the bracket.

Picture 1

Here, the unknowns vertical reactions acting at the points A and B are represented by and respectively.

(a)

Apply moment equilibrium condition about the point A.

…… (1)

Here, the distance between the points B and D is represented by a.

Substitute 10 in for a

Therefore, the reaction at the point B is .

Apply force equilibrium condition along vertical direction

Therefore, the reaction at the point A is .

Consider equation (1).

Substitute 7 in. for a

Therefore, the reaction at point B is

Apply force equilibrium condition along vertical direction

Therefore, the reaction at the point A is .

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