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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 12P

Textbook Problem

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Draw the influence lines for the shear and bending moment at point *B* and the shears just to the left and just to the right of support *C* of the beam shown in Fig. P8.12.

FIG. P8.12

To determine

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

Draw the influence lines for the shears just to the left and just to the right of support *C*.

**Calculation:**

Apply a 1 k 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 *C* 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

**Influence line for the shear at point B.**

Apply 1 k load at just left of *B*.

Find the equation of shear force 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

Apply 1 k load at just right of *B*.

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

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

Refer Figure 3.

Apply equilibrium equation of forces.

Consider upward force as positive

Thus, the equations of the influence line for

Find the value of influence line ordinate of shear force *x* using the Equations (3) and (4) and summarize the value as in Table 1.

x | Position | Influence line ordinate of |

0 | A | |

4 | ||

4 | 0 | |

10 | 0 | |

30 | D | 0 |

Draw the influence lines for the shear force at point *B* using Table 1 as shown in Figure 4.

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

Refer Figure 2.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

Refer Figure 3.

Consider clockwise moment as negative and anticlockwise moment as positive.

Find the equation of moment at *B* of portion *BD*

Thus, the equations of the influence line for

Find the value of influence line ordinate of moment *x* using the Equations (5) and (6) and summarize the value as in Table 2.

x | Position | Influence line ordinate of Influence line ordinate of |

0 | A | |

4 | 0 | |

10 | 0 | |

30 | D | 0 |

Draw the influence lines for the moment at point *B* using Table 2 as shown in Figure 5.

**Influence line for the shear just to the left of support C.**

Apply 1 k load at just left of *C*.

Find the equation of shear just to the left of support *C* of portion *AC*

Sketch the free body diagram of the section *AC* as shown in Figure 6.

Refer Figure 6.

Apply equilibrium equation of forces.

Consider upward force as positive

Structural Analysis

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