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Structural Analysis

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

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BuyFindarrow_forward

Structural Analysis

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

Chapter 8, Problem 41P, Draw the influence lines for the shear in panel DE and the bending moment at E of the girder with

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 kCy (k)Fy(k)Shear in the panel DE (k)Influence line ordinate for the panel DE (k/k)
At A1323Fy=2323
At B2313Fy=1313
At C10Fy=00
At D2313

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Chapter 8 Solutions

Structural Analysis
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