# Draw the influence lines for the shear and bending moment at point B and the shears just to the left and just to the right of support C of the beam shown in Fig. P8.12. FIG. P8.12

### Structural Analysis

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

Chapter
Section

### Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 8, Problem 12P
Textbook Problem
160 views

## Draw the influence lines for the shear and bending moment at point B and the shears just to the left and just to the right of support C of the beam shown in Fig. P8.12.FIG. P8.12

To determine

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

Draw the influence lines for the shears just to the left and just to the right of support C.

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

Consider moment equilibrium at point D.

Consider clockwise moment as positive and anticlockwise moment as negative.

Sum of moment at point D is zero.

ΣMD=0Cy(20)1(30x)=020Cy=30xCy=32x20        (1)

Find the equation of support reaction (Dy) at D using equilibrium equation:

Apply vertical equilibrium equation of forces.

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

Cy+Dy=1

Substitute 32x20 for Cy.

32x20+Dy=1Dy=132+x20Dy=x2012        (2)

Influence line for the shear at point B.

Apply 1 k load at just left of B.

Find the equation of shear force at B of portion AB (0x4ft).

Sketch the free body diagram of the section AB 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

SB1=0SB=1k

Apply 1 k load at just right of B.

Find the equation of shear force at B of portion BD (4ftx30ft).

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

Refer Figure 3.

Apply equilibrium equation of forces.

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

ΣFy=0SB=0SB=0

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

SB=1k/k, 0x4ft        (3)

SB=0, 4ftx30ft        (4)

Find the value of influence line ordinate of shear force SB at various points of x using the Equations (3) and (4) and summarize the value as in Table 1.

 x (ft) Position Influence line ordinate of SB (k/k) 0 A −1 4 B− −1 4 B+ 0 10 C 0 30 D 0

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

Influence line for moment at point B.

Refer Figure 2.

Consider clockwise moment as positive and anticlockwise moment as negative.

Find the equation of moment at B of portion AB (0x4ft).

MB=1(4x)=x4

Refer Figure 3.

Consider clockwise moment as negative and anticlockwise moment as positive.

Find the equation of moment at B of portion BD (4ftx30ft).

MB=0

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

MB=x4, 0x4ft        (5)

MB=0, 4ftx30ft        (6)

Find the value of influence line ordinate of moment MB at various points of x using the Equations (5) and (6) and summarize the value as in Table 2.

 x (ft) Position Influence line ordinate of Influence line ordinate of MB (k-ft/k) 0 A −4 4 B 0 10 C 0 30 D 0

Draw the influence lines for the moment at point B using Table 2 as shown in Figure 5.

Influence line for the shear just to the left of support C.

Apply 1 k load at just left of C.

Find the equation of shear just to the left of support C of portion AC (0x10ft).

Sketch the free body diagram of the section AC as shown in Figure 6.

Refer Figure 6.

Apply equilibrium equation of forces.

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

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