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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 45P

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. PB.45

To determine

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

**Calculation:**

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

The influence line for the force in member *AB* is determined by place a 1 kN load successively at the points *A, B,* and *C.* The appropriate support reaction is first determined by proportions and then influence line ordinate can be found.

Apply a 1 kN load at *A*.

Find the vertical reaction *A*.

Refer Figure 1.

By proportion,

Find the influence line ordinate for the force in member *AB* at *A*.

Similarly calculate the influence ordinate for the force in member *AB* at different points on the beam and summarize in Table 1.

Apply 1 kN load | Support reaction A (kN) | Support reaction C (kN) | Influence line ordinate for the force in member AB (kN/kN) |

A | 1 | 0 | 0 |

B | 0.5 | 0.5 | 0.5 |

C | 0 | 1 | 0 |

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

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

The influence line for the force in member *AD* is determined by place a 1 kN load at *A*.

Find the force in the member *AD*

Sketch the free body diagram at joint *A* as shown in Figure 3.

Apply force equilibrium along vertical.

Consider upward force as positive and downward force as negative.

Thus, the influence ordinate for the force in member *AD* at *A* is 0 kN/kN.

Find the influence ordinate for the force in member *AD* at *B*.

The influence line for the force in member *AD* is determined by place a 1 kN load at just right of *B*.

Find the force in the member *AD*

Structural Analysis

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