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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 35P

Textbook Problem

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8.35 and 8.36 Draw the influence lines for the horizontal and vertical reactions at supports *A* and *B* of the frames shown in Figs. P8.35 and P8.36.

FIG. P8.35

To determine

Draw the influence lines for the vertical reactions at supports *A* and *B*.

**Calculation:**

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

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

Refer Figure 1.

Find the vertical equation of support reaction *A* using equilibrium equation:

Take moment about point *B*.

Consider moment equilibrium at point *B*.

Consider clockwise moment as positive and anticlockwise moment as negative

Sum of moment at point *B* is zero.

Find the influence line ordinate of *C* using Equation (1).

Substitute 0 for

Similarly calculate the influence line ordinate of

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

0 | C | 1 |

6 | D | |

12 | E | 0 |

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

Refer Figure 1.

Find the equation of support reaction *B* using force equilibrium equation:

Consider force equilibrium along vertical.

Consider the upward force as positive

Substitute

Find the influence line ordinate of *C* using Equation (1).

Substitute 0 for

Similarly calculate the influence line ordinate of

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

0 | C | 0 |

6 | D | |

12 | E | 1 |

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

Refer Figure 1.

Apply 1 kN load at just left of *D*.

Consider the section *DE*.

Find the horizontal support reaction *B* using moment equilibrium equation:

Apply moment equilibrium at *D* from *B*.

Consider the clockwise moment as negative and counter clockwise moment as positive.

Substitute

Apply 1 kN load at just right of *D*.

Consider the section *DE*.

Find the horizontal support reaction *B* using moment equilibrium equation:

Apply moment equilibrium at *D* from *B*

Structural Analysis

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