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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 8, Problem 7P
Textbook Problem
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Draw the influence lines for vertical reactions at supports B and D and the shear and bending moment at point C of the beams shown in Figs. P8.7 and P8.8.

Chapter 8, Problem 7P, Draw the influence lines for vertical reactions at supports B and D and the shear and bending moment

FIG. P8.7

To determine

Draw the influence lines for the vertical reactions at supports B and D.

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

Explanation of Solution

Calculation:

Apply a 1 k unit moving load at a distance of x from right end D.

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

Refer Figure 1.

Find the equation of support reaction (By) at B using equilibrium equation:

Take moment about point D.

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=0By(20)1(x)=020By=xBy=x20 (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 ().

By+Dy=1

Substitute x20 for By.

x20+Dy=1Dy=1x20 (2)

Consider Equation (1).

Find the value of influence line ordinate of reaction By at support B.

Substitute 0 for x in Equation (1).

By=020=0

Similarly calculate the influence line ordinate of reaction By for different value of x and summarize the result in Table 1.

x (ft) from right endBy(k/k)
00
1012
201
2554

Draw the influence line diagram for the vertical reactions at support B using Table 1 as shown in Figure 2.

Consider Equation (2).

Find the influence line ordinate of reaction Dy at support D.

Substitute 0 for x in Equation (1).

Dy=1020=1

Similarly calculate the influence line ordinate of reaction Dy for different value of x and summarize the result in Table 2.

x (ft) from right endDy(k/k)
00
1012
200
2514

Draw the influence line diagram for the vertical reactions at support D using Table 2 as shown in Figure 3.

Find the equation of shear force at C of portion DC (0x<10ft).

Sketch the free body diagram of the section DC as shown in Figure 4.

Refer Figure 4.

Apply equilibrium equation of forces.

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

ΣFy=0

SC+Dy1=0SC=Dy+1

Substitute 1x20 for Dy.

SC=(1x20)+1=1+x20+1=x20

Find the equation of shear force at C of portion CA (10ft<x25ft).

Sketch the free body diagram of the section CA as shown in Figure 5.

Refer Figure 5.

Apply equilibrium equation of forces.

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

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Chapter 8 Solutions

Structural Analysis
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Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical reaction...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the reaction moments...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear in panel CD...Ch. 8 - Draw the influence lines for the shear in panel DE...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence line for the shear in panel CD...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence line for the vertical...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - Draw the influence line for the vertical...

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