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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 21P

Textbook Problem

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Draw the influence lines for the shear and bending moment at point *B* and the shear at internal hinge *C* of the beam shown in Fig. P8.20.

FIG. P8.20, P8.21, P8.22

To determine

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

Draw the influence lines for the shear at internal hinge *C*.

**Calculation:**

**Influence line for shear at point B:**

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

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

Refer Figure 1.

Consider the unit load at a variable position *x* to the left hinge *C*. (placed portion *AC* of the beam

Find the vertical support reaction *A* for portion *AC*.

Take Moment at hinge *C* from left end *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Consider the unit load at a variable position *x* to the right hinge *C*. (Place portion *CG* of the beam

Find the vertical support reaction *A* for portion *CG*.

Take Moment at hinge *C* from left end *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Thus, the equations of the influence line ordinate for

Refer Figure 1.

Find the equation of influence line ordinate for the vertical reaction

Apply moment equilibrium at *F*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Find the influence line ordinate of vertical reaction *AC*

Substitute

Find the influence line ordinate of vertical reaction *CG*

Substitute

Thus, the equations of the influence line ordinate for

Refer Figure 1.

Find the equation of influence line ordinate for the vertical reaction

Consider the vertical forces equilibrium condition, take the upward force as positive

Find the influence line ordinate of vertical reaction *AC*

Substitute

Find the influence line ordinate of vertical reaction *AC*

Substitute

Thus, the equations of the influence line ordinate for

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

Sketch the free body diagram of the section *AB* as shown in Figure 2.

Refer Figure 2.

Apply equilibrium equation of forces.

Consider upward force as positive

Substitute

Find the equation of shear at *B* of portion *BG*

Sketch the free body diagram of the section *BG* as shown in Figure 3.

Refer Figure 3.

Apply equilibrium equation of forces.

Consider upward force as positive

Find the influence line ordinate of shear at *B**BC*

Substitute

Find the influence line ordinate of shear at *B**CG*

Substitute

Thus, the equations of the influence line ordinate for

Find the influence line ordinate of

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

0 | A | 0 |

6 | ‑0.5 | |

6 | 0.5 | |

12 | C | 0 |

18 | D | 0 |

21 | E | 0 |

24 | F | 0 |

30 | G | 0 |

Sketch the influence line diagram for the shear at point*B* as shown in Figure 4.

**Influence line for moment at point B:**

Refer Figure 2.

Find the equation of bending moment at *B* of portion *AB*

Take moment at *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute

Refer Figure 3.

Find the equation of bending moment at *B* of portion *BG*

Take moment at *B*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Find the influence line ordinate of moment at *B**BC*

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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