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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 55P

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. P8.55

To determine

Draw the influence lines for the force in member *BC*, *BF*, *BG*, and *FG*.

**Calculation:**

Find the support reactions.

Apply 1 kN moving load from *E* to *D* 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 kN load placed from *E* to *G*.

Apply moment equilibrium at *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Apply force equilibrium equation along horizontal.

Consider the force acting towards right side as positive

Consider joint *E*.

Sketch the free body diagram of the joint *E* as shown in Figure 2.

Refer Figure 2.

Apply vertical equilibrium at * E*.

Consider the upward force as positive

Refer Figure 1.

Apply vertical equilibrium at * E*.

Consider the upward force as positive

**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 3.

Slope of line *BC* is 4 horizontal and 1 vertical.

Find the equation of member force *BG*.

Apply a 1 kN load at just left of *G*

Consider the section *GD*.

Apply moment equilibrium equation at *G*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Apply a 1 kN load at just right of *G*

Consider the section *GD*

Apply moment equilibrium equation at *G*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

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

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

0 | E | ||

4 | F | 0 | |

8 | G | ||

12 | D | 4.123 |

Sketch the influence line diagram for ordinate for the force in member *BC* using Table 1 as shown in Figure 4.

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

Refer Figure 4.

Find the force in member *FG*.

Apply 1 kN load just left of *F*

Consider the section *GD*.

Apply moment equilibrium equation at *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

Consider the section *FG.*

Apply moment equilibrium equation at *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

Find the force in member *FG* using the Equation (3) and (4) and then summarize the value in Table 2.

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

0 | E | ||

4 | F | 0 | |

8 | G | 2 | 2 |

12 | D | 4 |

Sketch the influence line diagram for ordinate for the force in member *FG* using Table 2 as shown in Figure 5.

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

Refer Figure 4.

Slope of member is 4 horizontal and 2 vertical.

Find the force in member *BG*.

Apply 1 k load just left of *F*

Consider the section *GD*.

Apply vertical force equilibrium equation.

Consider the upward force as positive

Structural Analysis

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