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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 24P
Textbook Problem
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Draw the influence lines for the vertical reactions at supports A, C, E, and G of the beams shown in Figs. P8.23 and P8.24.

Chapter 8, Problem 24P, Draw the influence lines for the vertical reactions at supports A, C, E, and G of the beams shown in

FIG. P8.24, P8.26

To determine

Draw the influence lines for the vertical reactions at supports A, C, E and G.

Explanation of Solution

Calculation:

Use Muller-Breslau's principle.

Remove the roller support at A from the given beam and apply a small displacement Δ. Due to the displacement, the structure released in which the deflected shape of the released structure of the beam is drawn.

Sketch the deflected shape of the released beam when roller support A is removed as shown in Figure 1.

The general shape of the influence line for vertical reaction (Ay) at supports A is the similar of deflected shape.

Sketch the general shape of the influence line for vertical reaction (Ay) at supports A as shown in Figure 2.

Apply 1 k unit load at point A.

Find the numerical value of the influence-line ordinate at A.

Generally the influence line ordinate (AA’) at A is 1 k/k when 1 k load is placed at A.

Therefore, the influence line ordinate is 1 k/k at A and 0 at all other points.

Sketch the influence line diagram for the vertical reactions at support A as shown in Figure 3.

Remove the roller support at C from the given beam and apply a small displacement Δ. Due to the displacement, the structure released in which the deflected shape of the released structure of the beam is drawn.

Sketch the deflected shape of the released beam when roller support C is removed as shown in Figure 4.

The general shape of the influence line for vertical reaction (Cy) at supports C is the similar of deflected shape.

Sketch the general shape of the influence line for vertical reaction (Cy) at supports C as shown in Figure 5.

Refer Figure 5.

The influence line ordinate at A, D, E, and G.

Apply 1 k unit load at point C.

Find the numerical value of the influence-line ordinate at C.

Generally the influence line ordinate (CC’) at C is 1 k/k when 1 k load is placed at C. The value of influence line ordinate in the different points on the beam determined by geometry (similar triangle) of the influence line.

Find the numerical value of influence line ordinate (BB’) at point B using similar triangle method.

BBBD=CCCDBB45=130BB=1.5

Similarly calculate the influence line ordinate for Cy in different points on beam and summarize the values as in Table 1.

x (ft)PointsInfluence line ordinate of Cy (k/k)
0A0
15B1.5
30C1
60D0
90E0
105F0
120G0

Sketch the influence line diagram for the vertical reactions at support C as shown in Figure 6.

Remove the roller support at E from the given beam and apply a small displacement Δ. Due to the displacement, the structure released in which the deflected shape of the released structure of the beam is drawn.

Sketch the deflected shape of the released beam when roller support E is removed as shown in Figure 7.

The general shape of the influence line for vertical reaction (Ey) at supports E is the similar of deflected shape.

Sketch the general shape of the influence line for vertical reaction (Ey) at supports E as shown in Figure 8

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Chapter 8 Solutions

Structural Analysis
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