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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 1P

Textbook Problem

For the beam of Problem 8.6, determine the maximum negative bending moment at point *B* due to a 75 kN concentrated live load.

FIG. P8.6, P8.61

Expert Solution

To determine

Find the maximum negative bending moment at point *B*.

The maximum negative bending moment at point *B* is

**Given Information:**

The concentrated live load (*P*) is 75 kN.

**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 *C* using equilibrium equation:

Take moment about point *A*.

Consider moment equilibrium at point *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Sum of moment at point *A* is zero.

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

Apply vertical equilibrium equation of forces.

Consider upward force as positive

Substitute

Find the equation of moment at *B*.

Apply 1 kN at just left of *B*

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

Refer Figure 2.

Consider moment at *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute

Apply 1 kN at just right of *B*

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

Refer Figure 3.

Consider moment at *B*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

Substitute

Thus, the equations of the influence line for

Find the value of influence line ordinate of moment at various points of *x* using the Equations (3) and (4) and summarize the value as in Table 1.

x | |

0 | 0 |

7 | |

14 | 0 |

28 | –2 |

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

Refer Figure 4,

The maximum negative influence line ordinate of bending moment at *B* is

**Find the maximum negative bending moment at point B using the equation.**

Substitute 75 kN for *P* and

Therefore, the maximum negative bending moment at point *B* is

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