FUNDAMENTALS OF STRUCTURAL ANALYSIS
FUNDAMENTALS OF STRUCTURAL ANALYSIS
5th Edition
ISBN: 9781260170276
Author: Leet
Publisher: MCG
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Question
Chapter 3, Problem 1P
To determine

Calculate the support reactions of the beam.

Expert Solution & Answer
Check Mark

Answer to Problem 1P

The horizontal reaction at A is Ax=6kips()_.

The vertical reaction at A is Ay=8.62kips()_.

The vertical reaction at B is By=19.38kips()_.

Explanation of Solution

Given information:

The structure is given in the Figure.

Apply the sign conventions for calculating reactions 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 and By be the vertical reaction at the roller support B.

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

FUNDAMENTALS OF STRUCTURAL ANALYSIS, Chapter 3, Problem 1P

Refer to Figure 1.

Use equilibrium equations:

Find the vertical reaction at B:

Summation of moment about A is equal to 0.

MA=0By×13+5×4×(42+9)+10(45)×4=0By=19.38kips()

Therefore, the vertical reaction at B is By=19.38kips()_.

Find the horizontal reaction at A:

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

+Fx=0Ax10(35)=0Ax=6kips()

Therefore, the horizontal reaction at A is Ax=6kips()_.

Find vertical reaction at A:

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

+Fy=0Ay10(45)5×4+19.38=0Ay=8.62kips()

Therefore, the vertical reaction at A is Ay=8.62kips()_.

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