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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 16P

Textbook Problem

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Draw the influence lines for the vertical reactions at supports *A* and *E* and the shear and bending moment at point *D* of the frame shown in Fig. P8.16.

FIG. P8.16

To determine

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

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

**Calculation:**

Apply a 1 kN 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.

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

Apply Force equilibrium along horizontal.

Consider the force acting towards right side as positive

The horizontal reaction at *A* is zero. Therefore, there is no influence line diagram for horizontal reaction *A*.

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

Take moment about point *E*.

Consider moment equilibrium at point *E*.

Consider clockwise moment as positive and anticlockwise moment as negative

Sum of moment at point *E* is zero.

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

Substitute 0 for

Similarly calculate the influence line ordinate of

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

0 | B | 1.3 |

3 | C | 1 |

8 | D | 0.5 |

13 | E | 0 |

16 | F | ‑0.3 |

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 *E* using equilibrium equation:

Take moment about point *A*.

Consider moment equilibrium at point *A*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Sum of moment at point *A* is zero.

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

Substitute 0 for

Similarly calculate the influence line ordinate of

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

0 | B | ‑0.3 |

3 | C | 0 |

8 | D | 0.5 |

13 | E | 1 |

16 | F | 1.3 |

Sketch the influence line diagram for the vertical reaction at support*E* using Table 1 as shown in Figure 3.

Find the equation of shear force at *D* of portion *BCD*

Sketch the free body diagram of the section *BCD* 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 *D* of portion *DEF*

Sketch the free body diagram of the section *DEF* 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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