   # 8.35 and 8.36 Draw the influence lines for the horizontal and vertical reactions at supports A and B of the frames shown in Figs. P8.35 and P8.36. FIG. P8.35

#### Solutions

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Chapter 8, Problem 35P
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## 8.35 and 8.36 Draw the influence lines for the horizontal and vertical reactions at supports A and B of the frames shown in Figs. P8.35 and P8.36.FIG. P8.35 To determine

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

### Explanation of Solution

Calculation:

Apply a 1 kN unit moving load at a distance of x from left end C.

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

Refer Figure 1.

Find the vertical equation of support reaction (Ay) at A using equilibrium equation:

Consider moment equilibrium at point B.

Consider clockwise moment as positive and anticlockwise moment as negative

Sum of moment at point B is zero.

ΣMB=0Ay(12)1(12x)=012Ay=12xAy=1x12 (1)

Find the influence line ordinate of Ay at C using Equation (1).

Substitute 0 for x in Equation (1).

Ay=1012=1kN/kN

Similarly calculate the influence line ordinate of Ay at various points on the beam and summarize the values in Table 1.

 x (m) Points Influence line ordinate of Ay(kN/kN) 0 C 1 6 D 12 12 E 0

Sketch the influence line diagram for the vertical reaction at support A using Table 1 as shown in Figure 2.

Refer Figure 1.

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

Consider force equilibrium along vertical.

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

Ay+By=1

Substitute 1x12 for Ay.

1x12+By=1By=11+x12By=x12 (2)

Find the influence line ordinate of By at C using Equation (1).

Substitute 0 for x in Equation (2).

By=012=0

Similarly calculate the influence line ordinate of By at various points on the beam and summarize the values in Table 2.

 x (m) Points Influence line ordinate of By(kN/kN) 0 C 0 6 D 12 12 E 1

Sketch the influence line diagram for the vertical reaction at support E using Table 2 as shown in Figure 3.

Refer Figure 1.

Apply 1 kN load at just left of D. (0x6m)

Consider the section DE.

Find the horizontal support reaction (Bx) at B using moment equilibrium equation:

Apply moment equilibrium at D from B.

Consider the clockwise moment as negative and counter clockwise moment as positive.

ΣMD=0Bx(6)By(6)=0Bx=By

Substitute x12 for By.

Bx=x12(+)

Apply 1 kN load at just right of D. (6mx12m)

Consider the section DE.

Find the horizontal support reaction (Bx) at B using moment equilibrium equation:

Apply moment equilibrium at D from B

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