Concept explainers
Draw the influence lines for the force in member CD, CI, DI, and DJ.
Explanation of Solution
Calculation:
Find the support reactions.
Apply 1 k moving load from A to G in the bottom chord member.
Draw the free body diagram of the truss as in Figure 1.
Refer Figure 1,
Find the reaction at C and E when 1 k load placed from A to G.
Apply moment equilibrium at C.
Apply force equilibrium equation along vertical.
Consider the upward force as positive
Influence line for the force in member CD.
The expressions for the member force
Draw the free body diagram of the section as shown in Figure 2.
Refer Figure 2.
Apply 1 k load just the left of C
Find the equation of member force CD from A to C.
Consider the section DG.
Apply moment equilibrium equation at I.
Consider clockwise moment as negative and anticlockwise moment as positive.
Substitute
Apply 1 k load just the right of C
Find the equation of member force CD from C to G.
Consider the section AC.
Apply moment equilibrium equation at I.
Consider clockwise moment as positive and anticlockwise moment as negative.
Thus, the equation of force in the member CD,
Find the force in member CD using the Equation (1) and (2) and then summarize the value in Table 1.
x (ft) | Apply 1 k load | Force in member CD (k) | Influence line ordinate for the force in member CD (k/k) |
0 | A | ||
16 | B | ||
32 | C | 0 | 0 |
48 | D | 0 | 0 |
64 | E | 0 | 0 |
80 | F | 0 | 0 |
96 | G | 0 | 0 |
Sketch the influence line diagram for ordinate for the force in member CD using Table 1 as shown in Figure 3.
Influence line for the force in member CI.
Refer Figure 2.
Apply 1 k load just the left of C
Find the equation of member force CI from A to C.
Consider the section AC.
Apply moment equilibrium equation at H.
Consider clockwise moment as negative and anticlockwise moment as positive.
Substitute
Apply 1 k load just the right of C
Find the equation of member force CI from C to G.
Consider the section AC.
Apply moment equilibrium equation at H.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Thus, the equation of force in the member CI,
Find the force in member CI using the Equation (1) and (2) and then summarize the value in Table 2.
x (ft | Apply 1 k load | Force in member CI (k) | Influence line ordinate for the force in member CI (k/k) |
0 | A | ||
16 | B | ||
32 | C | 0 | |
48 | D | ||
64 | E | 0 | |
80 | F | 0.5 | |
96 | G | 1 |
Sketch the influence line diagram for ordinate for the force in member CI using Table 2 as shown in Figure 4.
Influence line for the force in member DI.
The expressions for the member force
Draw the free body diagram of the section bb as shown in Figure 5.
Refer Figure 5.
Apply 1 k load just the left of C
Find the equation of member force DI from A to C.
Consider the section DG.
Apply moment equilibrium equation at J.
Consider clockwise moment as negative and anticlockwise moment as positive.
Substitute
Apply 1 k load just the right of C
Find the equation of member force DI from C to G.
Consider the section AC.
Apply moment equilibrium equation at J.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Thus, the equation of force in the member DI,
Find the force in member DI using the Equation (5) and (6) and then summarize the value in Table 3.
x (ft) | Apply 1 k load | Force in member DI (k) | Influence line ordinate for the force in member DI (k/k) |
0 | A | 1.494 | |
16 | B | 0.747 | |
32 | C | 0 | |
48 | D | 0.534 | |
64 | E | 0 | 0 |
80 | F | ||
96 | G |
Sketch the influence line diagram for ordinate for the force in member DI using Table 3 as shown in Figure 6.
Influence line for the force in member DJ.
The expressions for the member force
Draw the free body diagram of the section cc as shown in Figure 7.
Refer Figure 7.
Apply 1 k load just the left of C
Find the equation of member force DJ from A to C.
Consider the section DG.
Apply moment equilibrium equation at C.
The member force DI is resolved in horizontal and vertical.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute
Apply 1 k load just the right of C
Find the equation of member force DJ from C to G.
Consider the section DG.
Apply moment equilibrium equation at K.
The member force DI is resolved in horizontal and vertical.
Consider clockwise moment as positive and anticlockwise moment as negative.
Substitute 0 for
Thus, the equation of force in the member DJ,
Find the force in member DJ using the Equation (7) and (8) and then summarize the value in Table 4.
x (ft) | Apply 1 k load | Force in member DJ (k) | Influence line ordinate for the force in member DJ (k/k) |
0 | A | ||
16 | B | ||
32 | C | 0 | |
48 | D | 0.167 | |
64 | E | 0 | |
80 | F | ||
96 | G |
Sketch the influence line diagram for ordinate for the force in member DJ using Table 4 as shown in Figure 8.
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