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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 38P

Textbook Problem

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Draw the influence lines for the reaction moment at support *A*, the vertical reactions at supports *A* and *B*, and the shear at the internal hinge *C* of the frame shown in Fig. P8.38.

FIG. PB.38

To determine

Draw the influence lines for the reaction moment at support *A*, the vertical reactions at supports *A* and *B* and the shear at the internal hinge *C*.

**Calculation:**

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

Apply a 1 k unit moving load at a distance of *x* from left end *B*.

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

Refer Figure 1.

Apply 1 k load just left of *C*

Consider section *BC*.

Consider moment equilibrium at *C*.

Take moment at *C* from *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Apply 1 k load just right of *C*

Consider section *BC*.

Consider moment equilibrium at *C*.

Take moment at *C* from *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

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

Substitute 0 for

Thus, the influence line ordinate of *B* is

Similarly calculate the influence line ordinate of

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

0 | B | 1 |

10 | C | 0 |

20 | D | 0 |

30 | E | 0 |

40 | F | 0 |

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

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

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

Refer Figure 1.

Find the vertical support reaction *F* using equilibrium equation:

Apply 1 k load just left of *E*

Consider section *EF*.

Consider moment equilibrium at point *E*.

Consider clockwise moment as positive and anticlockwise moment as negative

Apply 1 k load just right of *E*

Consider section *EF*.

Consider moment equilibrium at point *E*.

Consider clockwise moment as positive and anticlockwise moment as negative

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

Apply a 1 k unit moving load at a distance of *x* from left end *B*.

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 *B* to *C*

Substitute

Find the equation of vertical support reaction *C* to *E*

Substitute

Find the equation of vertical support reaction *E* to *F*

Substitute

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

Find the influence line ordinate of *F* using Equation (8).

Substitute 40 ft for

Thus, the influence line ordinate of *F* is

Similarly calculate the influence line ordinate of

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

0 | B | 0 |

10 | C | 1 |

20 | D | 1 |

30 | E | 1 |

40 | F | 0 |

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

Structural Analysis

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