   # Draw the influence lines for the shear and bending moment at point E of the beam shown in Fig. P8.10. FIG. P8.10, P8.11

#### Solutions

Chapter
Section
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. 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.

 Position x (m) SE (kN/kN) F 0 1 E 3+ 1 E 3− 0 D 6 0 C 14 0 B 18 0 A 22 0

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

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