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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 51P

Textbook Problem

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8.45 through 8.52 Draw the influence lines for the forces in the members identified by an “×” of the trusses shown in Figs. P8.45–P8.52. Live loads are transmitted to the bottom chords of the trusses.

FIG. P8.51

To determine

Draw the influence lines for the force in member *CD*, *CI*, *DI*, and *DJ*.

**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 *aa* through the members *HI*, *CI*, and *CD* and then apply a moment equilibrium at *I*.

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 *bb* through the members *IJ*, *DI* and *CD* and then apply a moment equilibrium at *J*.

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.

Structural Analysis

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