   # Determine the reactions at the supports for the structures shown. FIG.P3.31

#### Solutions

Chapter
Section
Chapter 3, Problem 31P
Textbook Problem
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## Determine the reactions at the supports for the structures shown. FIG.P3.31

To determine

Calculate the support reactions for the given structure.

### Explanation of Solution

Given information:

The structure is given in the Figure.

Apply the sign conventions for calculating reaction forces and moments using the three equations of equilibrium as shown below.

• For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
• For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
• For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as negative and the counter clockwise moment as positive.

Calculation:

Let Ax and Ay be the horizontal and vertical reactions at the hinged support A.

Let Bx and By be the horizontal reaction and vertical reaction at the hinged support B.

Sketch the free body diagram of the structure as shown in Figure 1.

Use equilibrium equations:

Summation of moments about B is equal to 0.

MB=0Ay(48)+2.5(24)(242+24)+90(2424cos60°)=0Ay(48)+2,160+1,080=048Ay=3,240

Ay=67.5k

Therefore, the vertical reaction at A is Ay=67.5k_.

For the member AC, the summation of moments about C is equal to 0.

MCAC=0Ay(24)+Ax(24)+(2

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