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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 49P

Textbook Problem

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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. P8.49

To determine

Draw the influence lines for the force in member *DE*, *CG*, *GH* and *BC*.

**Calculation:**

**Influence line for the force in member DE.**

Find the influence ordinate for the force in member *DE* at *E*.

The influence line for the force in member *DE* is determined by place a 1 k load at *E*.

Find the force in the member *DE*

The expressions for the member force *aa* through the members *EI* and *DE* and then apply a moment equilibrium at *I*.

Refer Figure 1.

Apply a 1 k load at *I*.

Apply moment equilibrium equation at *I*.

Take moment at *I* from *E*.

Consider clockwise moment as positive and counterclockwise moment as negative.

Similarly find the force in member *DE* and summarize the value in Table 1.

x (ft) | Apply 1 k load | Influence line ordinate for the force in member DE (k/k) |

0 | E | ‑0.667 |

20 | D | |

40 | C | 0 |

60 | B | 0 |

80 | A | 0 |

Sketch the influence line diagram for ordinate for the force in member *DE* using Table 2 as shown in Figure 2.

**Influence line for the force in member CG.**

Find the force in member *CG*.

The expressions for the member force *aa* through the members *GH, CG,* and *BC* and then apply a moment equilibrium at *G*.

Draw the free body diagram as shown in Figure 3.

Refer Figure 3.

Apply a 1 k load just the left of *G*

Apply force equilibrium along vertical in the right hand section.

Consider upward force as positive and downward force is negative.

Apply a 1 k load just the right of *G*

Apply force equilibrium along vertical in the left hand section.

Consider upward force as positive and downward force is negative.

The equation of force in the member *CG*,

Find the force in member *CG* using the Equation (1), and (2), and summarize the value in Table 2.

x (ft) | Apply 1 k load | Support reaction A (k) | Support reaction D (k) | Influence line ordinate for the force in member CD (k/k) |

0 | A | 1 | 0 | 0 |

20 | B | |||

40 | C | |||

60 | D | |||

80 | E |

Sketch the influence line diagram for ordinate for the force in member *CG* using Table 2 as shown in Figure 4.

**Influence line for the force in member GH.**

Refer Figure 3.

Apply a 1 k load just the left of *C*

Apply moment equilibrium equation at *C*.

Take moment at *C* from *E*.

Consider clockwise moment as negative and counterclockwise moment as positive.

Apply a 1 k load just the right of *C*

Structural Analysis

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