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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 3P

Textbook Problem

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8.1 through 8.3 Draw the influence lines for vertical reactions at supports *A* and *C* and the shear and bending moment at point *B* of the beams shown in Figs. P8.1 through P8.3.

FIG. P8.3

To determine

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

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

**Calculation:**

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

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

Refer Figure 1.

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

Take moment about point *C*.

Consider moment equilibrium at point C.

Consider clockwise moment as positive and anticlockwise moment as negative

Sum of moment at point C is zero.

Find the equation of support reaction *B* 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 *A*.

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 | 1 |

10 | |

15 | 0 |

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

Consider Equation (2).

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

Substitute 15 for *x* in Equation (2).

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

x | |

0 | 0 |

10 | |

15 | 1 |

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

Find the equation of shear force at *B* of portion *AB*

Sketch the free body diagram of the section *AB* 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 *B* of portion *BC*

Sketch the free body diagram of the section *BC* 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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