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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 42P

Textbook Problem

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Draw the influence lines for the shear in panel *BC* and the bending moment at *F* of the girder with the floor system shown in Fig. P8.41.

FIG. P8.41, P8.42

To determine

Draw the influence lines for the shear in the panel *BC* and the bending moment at *F*.

**Calculation:**

**Influence line for the shear in the panel BC.**

Consider panel *AB*.

Apply a 1 k load over a region *AB*

Sketch the free body diagram when 1 k load on *AB* as shown in Figure 1.

Refer Figure 1.

Apply force equilibrium equation:

Apply upward force as positive and downward force as negative.

Therefore, the influence line ordinate for panel *BC* in the portion *AB* is ‑1 k/k.

Similarly apply the 1 k load in the different panel and find the influence line ordinate for the shear in the panel *BC*.

Summarize the value of influence line ordinate for the shear in the panel *BC* as in Table 1.

Apply 1 k load | Points | Shear in the panel BC (k) | Influence line ordinate for the shear in the panel BC (k/k) |

AB | A | ‑1 | ‑1 |

AB | B | ‑1 | ‑1 |

BC | C | 0 | 0 |

CD | D | 0 | 0 |

DE | E | 0 | 0 |

EF | F | 0 | 0 |

FG | G | 0 | 0 |

GH | H | 0 | 0 |

Sketch the influence line diagram for the shear in the panel *BC* using Table 1 as shown in Figure 2.

**Influence line for the bending moment at F.**

Consider panel *GH*.

Apply a 1 k load over a region *GH* from *H*.

Sketch the free body diagram when 1 k load on *GH* as shown in Figure 3.

Refer Figure 3.

Find the reaction *F*

Structural Analysis

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