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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 39P

Textbook Problem

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Draw the influence lines for the vertical reactions at supports *A*, *B*, C, and the shear and bending moment at point *E* of the frame shown in Fig. P8.39.

FIG. PB.39

To determine

Draw the influence lines for the vertical reactions at supports *A*, *B*, *C* and the shear and bending moment at point *E*.

**Calculation:**

Apply a 1 kN unit moving load at a distance of *x* from left end *D*.

Sketch the free body diagram of frame as shown in Figure 1.

**Influence line for vertical reaction at supports C.**

Refer Figure 1.

Find the equation of vertical reaction at supports *C*.

Apply 1 kN load just left of *G*

Consider section *GH*.

Take moment at *G* from *C*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Apply 1 kN load just right of *G*

Consider section *GH*.

Take moment at *G* from *C*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Thus, the equation of vertical reaction at supports *C* as follows,

Find the influence line ordinate of *H* using Equation (2).

Substitute 20 m for

Thus, the influence line ordinate of *H* is

Similarly calculate the influence line ordinate of

x (m) | Points | Influence line ordinate of |

0 | D | 0 |

4 | E | 0 |

8 | F | 0 |

14 | G | 0 |

20 | H | 1 |

Sketch the influence line diagram for vertical reaction at supports *C* using Table 1 as shown in Figure 2.

**Influence line for vertical reaction at support A.**

Apply 1 kN load just left of *F*

Refer Figure 1.

Find the equation of vertical reaction at supports *C*.

Consider section *DF*.

Take moment at *B* from *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Apply 1 kN load just right of *F*.

Consider section *FH*.

Consider moment at *B* from *A* is equal to from *C*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Find the equation of vertical reaction at *A* from *F* to *G*

Substitute 0 for

Find the equation of vertical reaction at *A* from *G* to *H*

Substitute

Thus, the equation of vertical reaction at supports *A* as follows,

Find the influence line ordinate of *G* using Equation (4).

Substitute 14 m for

Thus, the influence line ordinate of *G* is

Similarly calculate the influence line ordinate of

x (m) | Points | Influence line ordinate of |

0 | D | 1 |

4 | E | 0.5 |

8 | F | 0 |

14 | G | |

20 | H | 0 |

Sketch the influence line diagram for the vertical reaction at support *A* using Table 2 as shown in Figure 3.

**Influence line for vertical reaction at support B.**

Apply a 1 kN unit moving load at a distance of *x* from left end *C*.

Refer Figure 1.

Apply vertical equilibrium in the system.

Consider upward force as positive and downward force as negative.

Find the equation of vertical support reaction *D* to *G*

Substitute

Find the equation of vertical support reaction *G* to *H*

Substitute

Thus, the equation of vertical support reaction at *B* as follows,

Find the influence line ordinate of *F* using Equation (7).

Substitute 8 m for

Thus, the influence line ordinate of *F* is

Structural Analysis

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