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Structural Analysis

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

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BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 8, Problem 11P
Textbook Problem
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Draw the influence lines for the shear and bending moment at point E of the beam shown in Fig. P8.10.

Chapter 8, Problem 11P, Draw the influence lines for the shear and bending moment at point E of the beam shown in Fig.

FIG. P8.10, P8.11

To determine

Draw the influence lines for the shear and bending moment at point E.

Explanation of Solution

Calculation:

Find the equation of shear force at just right E (0x3m).

Apply 1 kN load at just right of E.

Consider section EF.

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

Refer Figure 1.

Apply equilibrium equation of forces.

Consider upward force as positive (+) and downward force as negative ().

ΣFy=0

SE1=0SE=1

Find the equation of shear force at just left of E (3mx22m).

Apply 1 kN load at just left of E.

Consider section EF.

Sketch the free body diagram of the section EF as shown in Figure 2.

Refer Figure 2.

Apply equilibrium equation of forces.

Consider upward force as positive (+) and downward force as negative ().

ΣFy=0

SE=0

Thus, the equations of the influence line for SE as follows,

SE=1, 0x3m        (1)

SE=0, 3mx22m        (2)

Find the shear force at various points of x using the Equations (1) and (2) and summarize the value as in Table 1.

Positionx (m)SE (kN/kN)
F01
E3+1
E30
D60
C140
B180
A220

Draw the influence lines for the shear force at point E using Table 1 as shown in Figure 4

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Chapter 8 Solutions

Structural Analysis
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