   # Draw the influence lines for the forces in the members identified by an “×” of the trusses shown in Figs. P8.53–P8.57. Live loads are transmitted to the top chords of the trusses. FIG. PB.56

#### Solutions

Chapter
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Chapter 8, Problem 56P
Textbook Problem
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## Draw the influence lines for the forces in the members identified by an “×” of the trusses shown in Figs. P8.53–P8.57. Live loads are transmitted to the top chords of the trusses. FIG. PB.56

To determine

Draw the influence lines for the force in member AE, AC, and EF.

### Explanation of Solution

Calculation:

Influence line for the force in member AE.

Find the force in member AE.

The expressions for the member force FAE can be determined by passing an imaginary section aa through the members AE and AC and then apply a moment equilibrium at F.

Draw the free body diagram as shown in Figure 1.

Refer Figure 1.

Apply a 1 kN load just the left of F (0x8m).

Consider above line aa.

Apply moment equilibrium equation at F.

ΣMF=0

Take moment at F from E.

Consider clockwise moment as negative and counterclockwise moment as positive.

FAE(8)1(8x)=08FAE=(8x)FAE=x81

Apply a 1 kN load just the right of F (8mx16m).

Apply moment equilibrium equation at F.

ΣMC=0

Take moment at C from E.

Consider clockwise moment as negative and counterclockwise moment as positive.

FAE(8)=0FAE=0

The equation of force in the member AE,

FAE=x81, 0x8m (1)

FAE=0, 8mx16m (2)

Find the force in member AE using the Equation (1) and (2) and summarize the value in Table 1.

 x (m) Apply 1 kN load Influence line ordinate for the force in member AE (kN/kN) 0 E x8−1=08−1=−1 8 F x8−1=88−1=0 16 G 0

Sketch the influence line diagram for ordinate for the force in member AE using Table 1 as shown in Figure 2.

Influence line for the force in member AC.

The influence line for the force in member AC is determined by apply force equilibrium along vertical.

Consider the section below line aa.

Consider upward force as positive and downward force as negative.

Apply a 1 kN load just the left of F (0x8m).

ΣFy=0Ay+FAE+FAC(35)=035FAC=AyFAE

Substitute x81 for FAE

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