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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 57P

Textbook Problem

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8.53 through 8.57 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. P8.57

To determine

Draw the influence lines for the force in member *AD*, *BD*, and *CD*.

**Calculation:**

Find the support reactions.

Apply 1 k moving load from *C* to *F* in the top chord member.

Draw the free body diagram of the member as in Figure 1.

Find the reaction at *A* and *B* when 1 k load placed from *C* to *F*.

Apply moment equilibrium at *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Apply vertical equilibrium.

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

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

Draw the free body diagram of the section *aa* as shown in Figure 3.

Refer Figure 2.

Slope of line *AE* is 4 horizontal and 3 vertical.

Find the equation of member force *AD*.

Apply a 1 k load at *C*

Consider the section *CD*

Apply moment equilibrium equation at *E*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

Consider the section left of line *aa*.

Apply moment equilibrium equation at *E*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute

Thus, the equation of force in the member *AD*,

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

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

0 | C | ||

16 | D | ‑1 | |

32 | E | ||

48 | F | 1 |

Sketch the influence line diagram for ordinate for the force in member *AD* using Table 1 as shown in Figure 3.

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

Refer Figure 4.

Find the force in member *CD*.

Apply 1 k load just the left of *D*

Consider the section *DF*.

Apply moment equilibrium equation at *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute

Structural Analysis

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