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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 56P

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. P8.53–P8.57. Live loads are transmitted to the top chords of the trusses.

FIG. PB.56

To determine

Draw the influence lines for the force in member *AE*, *AC*, and *EF*.

**Calculation:**

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

Find the force in member *AE*.

The expressions for the member force *aa* through the members *AE* and *AC* and then apply a moment equilibrium at *F*.

Draw the free body diagram as shown in Figure 1.

Refer Figure 1.

Apply a 1 kN load just the left of *F*

Consider above line *a*‑*a*.

Apply moment equilibrium equation at *F*.

Take moment at *F* from *E*.

Consider clockwise moment as negative and counterclockwise moment as positive.

Apply a 1 kN load just the right of *F*

Apply moment equilibrium equation at *F*.

Take moment at *C* from *E*.

Consider clockwise moment as negative and counterclockwise moment as positive.

The equation of force in the member *AE*,

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

x (m) | Apply 1 kN load | Influence line ordinate for the force in member AE (kN/kN) |

0 | E | |

8 | F | |

16 | G |

Sketch the influence line diagram for ordinate for the force in member *AE* using Table 1 as shown in Figure 2.

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

The influence line for the force in member *AC* is determined by apply force equilibrium along vertical.

Consider the section below line *a*‑*a*.

Consider upward force as positive and downward force as negative.

Apply a 1 kN load just the left of *F*

Substitute

Structural Analysis

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