   # Draw the influence lines for the shear and bending moment at point B of the cantilever beam shown in Fig. P8.4. FIG. 8.4

#### Solutions

Chapter
Section
Chapter 8, Problem 4P
Textbook Problem
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## Draw the influence lines for the shear and bending moment at point B of the cantilever beam shown in Fig. P8.4. FIG. 8.4

To determine

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

### Explanation of Solution

Calculation:

Apply a 1 k 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 support reaction (Cy) at C using force equilibrium equation:

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

ΣFy=0Cy1=0Cy=1k

Find the moment equation at C.

Consider clockwise moment as positive and anticlockwise moment as negative

ΣMC=01(18x)+MC=0MC=18x (1)

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

Refer Figure 2.

Find the shear force at B of portion BC (0ftx<9ft).

Apply equilibrium equation of forces.

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

ΣFy=0

SB1=0SB=1k

Find the equation of shear force at B of portion BC (9ft<x18ft).

Sketch the free body diagram of the section BC as shown in Figure 3.

Refer Figure 3.

Apply equilibrium equation of forces.

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

ΣFy=0

SB1+Cy=0SB=1Cy

Substitute 1k for Cy.

SB=11=0

Find the value of influence line ordinate of shear force at various points of x and summarize the value as in Table 1

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