   # Determine the reactions at the supports for the structures shown. FIG.P3.23

#### Solutions

Chapter
Section
Chapter 3, Problem 23P
Textbook Problem
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## Determine the reactions at the supports for the structures shown. FIG.P3.23

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

Let Ay be the vertical reaction at the roller support A.

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

Use equilibrium equations:

Summation of forces along x-direction is equal to 0.

+Fx=0Bx+(20+402)(10)(45)=0Bx+240=0Bx=240kN

Therefore, the horizontal reaction at B is Bx=240kN_.

Summation of moments about A is equal to 0

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