
Concept explainers
(a)
Draw the influence lines for the reactions
Determine the reactions at B, C, D and E, moments at C and D.
(a)

Explanation of Solution
Given Information:
The uniform load (w) is 2 kips/ft.
Calculation:
Influence line for reaction at
Consider the portion AF
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 1.
Refer Figure 1.
Find the equation support reaction
Take moment about point F from H.
Consider clockwise moment as negative and anticlockwise moment as positive
Consider the portion FH
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 2.
Refer Figure 2.
Consider clockwise moment as negative and anticlockwise moment as positive.
Find the equation support reaction
Take moment about point F from H.
Thus, the equations of the influence line for
Find the value of influence line ordinate of
Points | x | |
A | 0 | 0 |
12 | 0 | |
C | 42 | 0 |
D | 50 | 0 |
E | 72 | 0 |
F | 80 | 0 |
G | 102 | 1 |
H | 114 | 1.55 |
Draw the influence lines for
Refer Figure 3.
Determine the reaction at G.
Therefore, the reaction at G is
Influence line for reaction
Consider the portion AD
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 4.
Refer Figure 4.
Find the equation support reaction
Take moment about point D from H.
Consider clockwise moment as negative and anticlockwise moment as positive
Consider the portion DF
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 5.
Refer Figure 5.
Find the equation support reaction
Take moment about point F from H.
Consider the portion FH
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 6.
Refer Figure 6.
Find the equation support reaction
Take moment about point F from H.
Thus, the equations of the influence line for
Find the value of influence line ordinate of
Points | x | |
A | 0 | 0 |
12 | 0 | |
C | 42 | 0 |
D | 50 | 0 |
E | 72 | 1 |
F | 80 | 1.364 |
G | 102 | 0 |
H | 114 | ‑0.744 |
Draw the influence lines for
Refer Figure 7.
Determine the reaction at E.
Therefore, the reaction at E is
Influence line for reaction
Consider the portion AD
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 8.
Refer Figure 8.
Find the equation support reaction
Take moment about point B from H.
Consider the portion DF
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 9.
Refer Figure 9.
Find the equation support reaction
Take moment about point B from H.
Consider the portion FH
Apply a 1 kip unit moving load at a distance of
Sketch the free body diagram of beam as shown in Figure 10.
Refer Figure 6.
Find the equation support reaction
Take moment about point B from H.
Consider clockwise moment as negative and anticlockwise moment as positive
Thus, the equations of the influence line for
Find the value of influence line ordinate of
Points | x | |
A | 0 | ‑0.4 |
12 | 0 | |
C | 42 | 1 |
D | 50 | 1.27 |
E | 72 | 0 |
F | 80 | ‑0.46 |
G | 102 | 0 |
H | 114 | 0.25 |
Draw the influence lines for
Refer Figure 11.
Determine the reaction at C.
Therefore, the reaction at C is
Influence line for reaction
Consider the portion AD
Refer Figure 8.
Consider upward force as positive and anticlockwise moment as negative.
Find the equation support reaction
Consider vertical equilibrium equation.
Consider the portion DF
Refer Figure 9.
Find the equation support reaction
Consider vertical equilibrium equation.
Consider the portion FH
Refer Figure 6.
Find the equation support reaction
Consider vertical equilibrium equation.
Consider upward force as positive and anticlockwise moment as negative.
Thus, the equations of the influence line for
Find the value of influence line ordinate of
Points | x | |
A | 0 | 1.4 |
12 | 1 | |
C | 42 | 0 |
D | 50 | ‑0.25 |
E | 72 | 0 |
F | 80 | 0.1 |
G | 102 | 0 |
H | 114 | 0.063 |
Draw the influence lines for
Refer Figure 12.
Determine the reaction at B.
Therefore, the reaction at B is
Influence line for the moment at section C:
Consider portion AC
Find the equation of moment at C for portion AC.
Apply a 1 kip in the portion AC from A.
Sketch the free body diagram of the section CH as shown in Figure 13.
Find the equation of moment at C of portion AC.
Consider portion CD
Find the equation of moment at C for portion CD.
Apply a 1 kip in the portion CD from A.
Sketch the free body diagram of the section AC as shown in Figure 14.
Find the equation of moment at C of portion CD.
Consider portion DF
Find the equation of moment at C for portion DF.
Apply a 1 kip in the portion DF from A.
Sketch the free body diagram of the section AC as shown in Figure 15.
Find the equation of moment at C of portion DF.
Consider portion FH
Find the equation of moment at C for portion FH.
Apply a 1 kip in the portion FH from A.
Sketch the free body diagram of the section AC as shown in Figure 16.
Find the equation of moment at C of portion FH.
Thus, the equations of the influence line for
Find the value of influence line ordinate of
Points | x | |
A | 0 | 0 |
12 | 0 | |
C | 42 | 0 |
D | 50 | ‑8 |
E | 72 | 0 |
F | 80 | +2.73 |
G | 102 | 0 |
H | 114 | ‑1.89 |
Draw the influence lines for
Refer Figure 17.
Determine the moment at C.
Therefore, the moment at C is
Influence line for the moment at section E:
Consider portion AE
Find the equation of moment at D for portion AE.
Apply a 1 kip in the portion AE from A.
Sketch the free body diagram of the section EH as shown in Figure 18.
Find the equation of moment at E of portion AE.
Consider portion EF
Find the equation of moment at E for portion EF.
Apply a 1 kip in the portion DF from A.
Sketch the free body diagram of the section AC as shown in Figure 19.
Find the equation of moment at E of portion EF.
Consider portion FH
Find the equation of moment at E for portion FH.
Apply a 1 kip in the portion FH from A.
Sketch the free body diagram of the section AC as shown in Figure 20.
Find the equation of moment at D of portion FH.
Thus, the equations of the influence line for
Find the value of influence line ordinate of
Points | x | |
A | 0 | 0 |
12 | 0 | |
C | 42 | 0 |
D | 50 | 0 |
E | 72 | 0 |
F | 80 | ‑8 |
G | 102 | 0 |
H | 114 | 4.04 |
Draw the influence lines for
Refer Figure 21.
Determine the moment at E.
Therefore, the moment at E is
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