
(a)
Draw the influence lines for the horizontal and vertical reactions at support A and the member forces in members BC, CM, and ML.
(a)

Explanation of Solution
Influence line for the vertical reaction at A.
The influence line ordinate of
Apply 1 kip at D.
Find the vertical reaction at support A.
The reaction is determined by applying a 1-kip load at successive panel points.
Apply 1 kip load at C.
Draw the free body diagram as shown in Figure 1.
Refer Figure 1.
Consider moment equilibrium at I.
Thus, the influence line ordinate of vertical reaction at A is 0.667.
Similarly find the influence line ordinate of
Points | x (ft) | Influence line ordinate of |
B | 0 | 1 |
C | 24 | 0.833 |
D | 48 | 0.667 |
E | 72 | 0.5 |
F | 96 | 0.333 |
G | 120 | 0.167 |
H | 144 | 0 |
Draw the influence line ordinate of
Influence line for the horizontal reaction at A.
The influence line ordinate of
Apply 1 kip at D.
Find the horizontal reaction at support A.
The reaction is determined by applying a 1-kip load at successive panel points.
Apply 1 kip load at C.
Draw the free body diagram as shown in Figure 3.
Refer Figure 4.
Consider moment equilibrium at E.
Thus, the influence line ordinate of horizontal reaction at A is 0.667.
Similarly find the influence line ordinate of
Points | x (ft) | Influence line ordinate of |
B | 0 | 0 |
C | 24 | 0.333 |
D | 48 | 0.667 |
E | 72 | 1 |
F | 96 | 0.667 |
G | 120 | 0.333 |
H | 144 | 00 |
Draw the influence line ordinate of
Influence line for the force in member BC.
Find the force
The influence line ordinate of
Apply 1 kip at C and consider a section passes through members BC, CM, and ML.
Sketch the free body diagram of the section as in Figure 5.
Refer Figure 5.
Find the member force BC.
Consider moment equilibrium at M.
Thus, the influence line ordinate of member force BC at D is ‑0.167.
Similarly find the influence line ordinate of
Points | x (ft) | Influence line ordinate of |
B | 0 | 0 |
C | 24 | ‑0.833 |
D | 48 | ‑0.167 |
E | 72 | 0.5 |
F | 96 | 0.333 |
G | 120 | 0.167 |
H | 144 | 0 |
Draw the influence line ordinate of
Influence line for the force in member ML.
Find the force
The influence line ordinate of
Apply 1 kip at C and consider a section passes through members BC, CM, and ML.
Sketch the free body diagram of the section as in Figure 7.
Refer Figure 7.
The slope of member ML is 24 ft horizontal and 12 ft vertical.
Find the member force ML.
Consider horizontal equilibrium equation.
Thus, the influence line ordinate of member force ML at D is ‑0.56.
Similarly find the influence line ordinate of
Points | x (ft) | Influence line ordinate of |
B | 0 | 0 |
C | 24 | 0.56 |
D | 48 | ‑0.56 |
E | 72 | ‑1.68 |
F | 96 | ‑1.12 |
G | 120 | ‑0.56 |
H | 144 | 0 |
Draw the influence line ordinate of
Influence line for the force in member CM.
Find the force
The influence line ordinate of
Apply 1 kip at C and consider a section passes through members BC, CM, and ML.
Sketch the free body diagram of the section as in Figure 9.
Refer Figure 9.
The slope of member ML is 24 ft horizontal and 12 ft vertical.
Find the member force CM.
Consider vertical equilibrium equation.
Thus, the influence line ordinate of member force CM at D is ‑0.416.
Similarly find the influence line ordinate of
Points | x (ft) | Influence line ordinate of |
B | 0 | 0 |
C | 24 | ‑1.083 |
D | 48 | ‑0.416 |
E | 72 | 0.25 |
F | 96 | 0.167 |
G | 120 | 0.083 |
H | 144 | 0 |
Draw the influence line ordinate of
(b)
Find the forces (compression and tension) in bars CM and ML produced by the dead load.
(b)

Answer to Problem 40P
The dead load force in member CM is
The dead load force in member ML is
Explanation of Solution
Given Information:
The uniform dead load,
Calculation:
Refer Figure 11.
Sketch the influence line diagram of member CM as in Figure 11.
Refer Figure 11.
Find the length
Find the length
Refer Figure 11.
Find the dead load force in member CM using the equation.
Therefore, the dead load force in member CM is
Refer Figure 9.
Sketch the influence line diagram of member ML as in Figure 12.
Refer Figure 12.
Find the length
Find the length
Refer Figure 11.
Find the dead load force in member CM using the equation.
Therefore, the dead load force in member ML is
(c)
Find the forces (compression and tension) in bars CM due to live load.
(c)

Answer to Problem 40P
The maximum compression force in member CM due to live load is
The maximum tension force in member CM due to live load is
Explanation of Solution
Given Information:
The uniform live load,
The concentrated live load, P is 20 k.
Calculation:
Refer Figure 11.
Sketch the influence line diagram of member CM as in Figure 13.
Refer Figure 13.
Find the maximum compression force in member CM using the equation.
Therefore, the maximum compression force in member CM due to live load is
Find the maximum tension force in member CM using the equation.
Therefore, the maximum tension force in member CM due to live load is
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Chapter 12 Solutions
Fundamentals of Structural Analysis
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