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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 7P

Textbook Problem

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Draw the influence lines for vertical reactions at supports *B* and *D* and the shear and bending moment at point *C* of the beams shown in Figs. P8.7 and P8.8.

FIG. P8.7

To determine

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

Draw the influence lines for the shear and bending moment at point *C*.

**Calculation:**

Apply a 1 k unit moving load at a distance of *x* from right end *D*.

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

Refer Figure 1.

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

Take moment about point *D*.

Consider moment equilibrium at point *D*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Sum of moment at point *D* is zero.

Find the equation of support reaction *D* using equilibrium equation:

Apply vertical equilibrium equation of forces.

Consider upward force as positive

Substitute

Consider Equation (1).

Find the value of influence line ordinate of reaction *B*.

Substitute 0 for *x* in Equation (1).

Similarly calculate the influence line ordinate of reaction *x* and summarize the result in Table 1.

x | |

0 | 0 |

10 | |

20 | 1 |

25 |

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

Consider Equation (2).

Find the influence line ordinate of reaction *D*.

Substitute 0 for *x* in Equation (1).

Similarly calculate the influence line ordinate of reaction *x* and summarize the result in Table 2.

x | |

0 | 0 |

10 | |

20 | 0 |

25 |

Draw the influence line diagram for the vertical reactions at support *D* using Table 2 as shown in Figure 3.

Find the equation of shear force at *C* of portion *DC*

Sketch the free body diagram of the section *DC* as shown in Figure 4.

Refer Figure 4.

Apply equilibrium equation of forces.

Consider upward force as positive

Substitute

Find the equation of shear force at *C* of portion *CA*

Sketch the free body diagram of the section *CA* as shown in Figure 5.

Refer Figure 5.

Apply equilibrium equation of forces.

Consider upward force as positive

Structural Analysis

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Ch. 8 - 8.1 through 8.3 Draw the influence lines for...Ch. 8 - 8.1 through 8.3 Draw the influence lines for...Ch. 8 - 8.1 through 8.3 Draw the influence lines for...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical reaction...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for vertical reactions at...Ch. 8 - Draw the influence lines for vertical reactions at...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...

Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical reaction...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the reaction moments...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear in panel CD...Ch. 8 - Draw the influence lines for the shear in panel DE...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence line for the shear in panel CD...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence line for the vertical...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - Draw the influence line for the vertical...

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