Concept explainers
Draw the influence lines for the force in member AB, BG, DF, and FG.

Explanation of Solution
Calculation:
Find the support reactions.
Apply 1 k moving load from E to G in the top chord member.
Draw the free body diagram of the member as in Figure 1.
Find the reaction at A and B when 1 k load placed from E to G.
Apply moment equilibrium at A.
Apply force equilibrium equation along vertical.
Consider the upward force as positive
Influence line for the force in member AB.
The expressions for the member force
Draw the free body diagram of member with section aa as shown in Figure 2.
Refer Figure 2.
Find the equation of member force AB.
Apply a 1 k load at just left of F
Consider the right hand portion to section a-a.
Apply moment equilibrium equation at F.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Apply a 1 k load at just right of F
Consider the left hand portion to section a-a.
Apply moment equilibrium equation at F.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Thus, the equation of force in the member AB,
Find the force in member AB using the Equation (1) and (2) and then summarize the value in Table 1.
x (ft) | Apply 1 k load | Force in member AB (k) | Influence line ordinate for the force in member AB (k/k) |
0 | E | ||
18 | F | 0.375 | |
36 | G |
Sketch the influence line diagram for ordinate for the force in member AB using Table 2 as shown in Figure 3.
Influence line for the force in member BG.
The expressions for the member force
Draw the free body diagram of section a-a as shown in Figure 4.
Refer Figure 4.
Find the force in member BG.
Apply 1 k load just left of F
Consider the section EF.
The member force of EF not affected when 1 k load applied from E to F. Therefore, the influence line ordinate of member force BG is 0 k/k from E to F.
Apply a 1 k load just the right of F
Apply moment equilibrium at F.
Consider the section right of line a-a.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Thus, the equation of force in the member BG,
Find the force in member BG using the Equation (3) and (4) and then summarize the value in Table 2.
x (ft) | Apply 1 k load | Force in member BG (k) | Influence line ordinate for the force in member BG (k/k) |
0 | E | 0 | |
18 | F | 0 | |
36 | G | ‑1.07 |
Sketch the influence line diagram for ordinate for the force in member BG using Table 2 as shown in Figure 5.
Influence line for the force in member DF.
The expressions for the member force
Draw the free body diagram of section a-a as shown in Figure 6.
Refer Figure 6.
Find the force in member DF.
Apply 1 k load just left of F
Consider the section right of line bb.
Apply moment equilibrium at G.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Apply 1 k load just right of F
Consider the section left of line bb.
Apply moment equilibrium at E.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Thus, the equation of force in the member DF,
Find the force in member DF using the Equation (5) and (6) and then summarize the value in Table 3.
x (ft) | Apply 1 k load | Force in member DF (k) | Influence line ordinate for the force in member DF (k/k) |
0 | E | 0.3125 | |
18 | F | ‑0.625 | ‑0.625 |
36 | G | ‑0.3125 | ‑0.3125 |
Sketch the influence line diagram for ordinate for the force in member DF using Table 3 as shown in Figure 7.
Influence line for the force in member FG.
Refer Figure 6.
Find the force in member FG.
Apply 1 k load just left of F
Consider the section right of line bb.
Apply moment equilibrium at B.
Consider clockwise moment as positive and anticlockwise moment as negative.
Apply 1 k load just right of F
Consider the section left of line bb.
Apply moment equilibrium at A.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Thus, the equation of force in the member FG,
Find the force in member FG using the Equation (7) and (8) and then summarize the value in Table 4.
x (ft) | Apply 1 k load | Force in member FG (k) | Influence line ordinate for the force in member FG (k/k) |
0 | E | 0.3125 | |
18 | F | ‑0.625 | ‑0.625 |
36 | G | ‑0.3125 | ‑0.3125 |
Sketch the influence line diagram for ordinate for the force in member FG using Table 4 as shown in Figure 8.
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Chapter 8 Solutions
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