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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 6P

Textbook Problem

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For the beam of Problem 8.10, determine the maximum positive and negative shears and the maximum positive and negative bending moments at point *C* due to a concentrated live load of 150 kN, a uniformly distributed live load of 50 kN/m, and a uniformly distributed dead load of 25 kN/m.

FIG. P8.10, P8.11

To determine

Find the maximum positive and negative shears and the maximum positive and negative bending moments at point *C*.

**Given Information:**

The concentrated live load (*P)* is 150 kN.

The uniformly distributed live load

The uniformly distributed dead load

**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 *B* 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 C.**

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

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

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

Refer Figure 2.

Apply equilibrium equation of forces.

Consider upward force as positive

Substitute

Apply 1 kN load at just right of *C*.

Find the equation of shear force at *C* of portion *CF*

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

Refer Figure 3.

Apply equilibrium equation of forces.

Consider upward force as positive

Substitute

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 | B | |

8 | ||

8 | ||

16 | D | 0 |

19 | E | |

22 | F |

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

Refer Figure 4.

The maximum positive ILD ordinate at point *C* is

The maximum negative ILD ordinate at point *C* is

Find the positive area *C*.

Here, *A* to *B* and *C* to *D*.

Substitute 4 m for

Find the negative area *C*.

Here, *B* to *C* and *E* to *F*.

Substitute 4 m for

**Find the maximum positive shear at point C using the equation.**

Substitute 150 kN for *P*,

Structural Analysis

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