   # Draw the influence line for the shear in panel CD and the bending moment at D of the girder with the floor system shown in Fig. P8.44. FIG. PB.44

#### Solutions

Chapter
Section
Chapter 8, Problem 44P
Textbook Problem
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## Draw the influence line for the shear in panel CD and the bending moment at D of the girder with the floor system shown in Fig. P8.44. FIG. PB.44

To determine

Draw the influence lines for the shear in the panel CD and the bending moment at D.

### Explanation of Solution

Calculation:

Influence line for the shear in the panel CD.

The influence line for the shear in panel CD is determined by placing a 1kN load successively at the panel points A, B, C, D E and F. The appropriate support reaction is first determined by proportions, and the shear in panel CD is computed.

Apply 1kN at A.

Sketch the free body diagram as shown in Figure 1.

Refer Figure 1.

Find the support reaction (Ay) at A using moment equilibrium.

Take moment at G.

Consider clockwise moment as positive and counterclockwise moment as negative.

ΣMG=0Ay(9)1(9)=0Ay=1kN

Hence, the support reaction at D and F are zero.

Find the shear (SCD) in the panel CD at A.

SCD=Fy=0

Thus, the influence line ordinate of SCD at A is 0kN.

Apply 1kN at B.

Sketch the free body diagram as shown in Figure 2.

Find the support reaction (Ay) at A using moment equilibrium.

Take moment at G.

Consider clockwise moment as positive and counterclockwise moment as negative.

ΣMG=0Ay(9)1(3)=0Ay=39Ay=13kN

Find the reaction (R) at hinge G.

Apply force equilibrium.

Ay1+R=0131+R=023+R=0R=23kN

Consider portion GF.

Find the support reaction (Dy) at D using moment equilibrium.

Take moment at F.

Consider clockwise moment as positive and counterclockwise moment as negative.

ΣMF=0R(21)+Dy(12)=023(21)+12Dy=012Dy=14Dy=76kN

Find the reaction (Fy) at F.

Apply force equilibrium.

Ay+Dy+Fy1=013+76+Fy=1Fy=11376Fy=12

Find the shear in the panel CD at B

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