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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 9, Problem 2P
Textbook Problem
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For the beam of Problem 8.6, determine the maximum upward reaction at support A due to a 35 kN/m uniformly distributed live load.

Chapter 9, Problem 2P, For the beam of Problem 8.6, determine the maximum upward reaction at support A due to a 35 kN/m

FIG. P8.6, P8.61

To determine

Find the maximum upward reaction at support A.

Explanation of Solution

Given Information:

The uniformly distributed live load (w) is 35kN/m.

Calculation:

Apply a 1 kN unit moving load at a distance of x from left end A.

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

Refer Figure 1.

Find the equation of support reaction (Cy) at C using equilibrium equation:

Take moment about point C.

Consider moment equilibrium at point C.

Consider clockwise moment as positive and anticlockwise moment as negative.

Sum of moment at point C is zero.

ΣMC=0Ay(14)1(14x)=014Ay=14xAy=1x14        (1)

Consider Equation (1).

Find the value of influence line ordinate of reaction Ay at support A.

Substitute 0 for x in Equation (2).

Ay=1014=1kN/kN

Similarly calculate the influence line ordinate of reaction Ay for different value of x and summarize the result in Table 1.

x (m)Ay(kN/kN)
01
140
1827

Draw the influence line diagram for the vertical reactions at support A using Table 1 as shown in Figure 2

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