   # Draw the influence lines for the shear in panel DE and the bending moment at E of the girder with the floor system shown in Fig. P8.41. FIG. PB.41, PB.42

#### Solutions

Chapter
Section
Chapter 8, Problem 41P
Textbook Problem
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## Draw the influence lines for the shear in panel DE and the bending moment at E of the girder with the floor system shown in Fig. P8.41. FIG. PB.41, PB.42

To determine

Draw the influence lines for the shear in the panel DE and the bending moment at E.

### Explanation of Solution

Calculation:

Influence line for the shear in the panel DE.

The shear in the panel DE when unit load is located to the left of panel point D.

SDE=Fy, 0x<36ft

SDE=Fy, 36ft<x<54ft

The shear in the panel DE when unit load is located to the right of panel point E.

SCD=Ay, 90ft<x126ft

The influence line for the shear in panel DE is determined by place a 1 k load successively at the panel points A, B, C, D E, F G and H. The appropriate support reaction is first determined and then the shear in panel DE is computed.

Apply 1 k at A.

Sketch the free body diagram as shown in Figure 1.

Refer Figure 1.

Find the support reaction (Fy) at F using moment equilibrium.

ΣMC=0Fy(54)=1(36)Fy=3654Fy=23k

Find the support reaction (Cy) at C using force equilibrium.

ΣFy=0Cy+Fy=1Cy+23=1Cy=13k

Find the shear in the panel DE at A. (left of point C)

SDE=Fy

Substitute 23k for Fy.

SDE=23k

Thus, the influence line ordinate of panel DE at A is 23k/k

Similarly calculate the influence ordinate of panel DE at different points on the beam and summarize in Table 1.

 Apply 1 k Cy (k) Fy(k) Shear in the panel DE (k) Influence line ordinate for the panel DE (k/k) At A 13 23 Fy=23 23 At B 23 13 Fy=13 13 At C 1 0 Fy=0 0 At D 23 13

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