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Structural Analysis

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

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Chapter
Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 7, Problem 24P
Textbook Problem
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7.24 through 7.27 Use the virtual work method to determine the deflection at point C of the beam shown.

Chapter 7, Problem 24P, 7.24 through 7.27 Use the virtual work method to determine the deflection at point C of the beam

FIG. P7.24, P7.28, P7.59

To determine

Find the deflection at point C of the beam using virtual work method.

Explanation of Solution

Given information:

The beam is given in the Figure.

Calculation:

Consider the real system.

Let the bending moment due to real load be M.

Sketch the real system of the beam as shown in Figure 1.

Consider the virtual system.

Remove all the real loads and apply unit load where the point to find the deflection.

Let the bending moment due to virtual load be Mv.

Sketch the virtual system of the beam with unit load at point C as shown in Figure 2.

Find the equations for M and Mv for the 2 segments of the beam as shown in Table 1.

Segmentx-coordinateMMv
OriginLimits
CBC0L2Px1x
BACL2LPx1x

Find the deflection at C using the virtual work expression:

1(ΔC)=0LMvMEIdx (1)

Substitute 2I for span AB and I for span BC.

Rearrange Equation (1) for the limits 0L2 and L2L as follows.

ΔC=0L/2MvMEIdx+12L/2LMvMEIdx=1EI[0L/2(MvM)dx+12L/2L(MvM)dx]

Substitute x for Mv, Px for M for the limits 0L2, x for Mv, and Px for M for the limits L2L

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Chapter 7 Solutions

Structural Analysis
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