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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 18P

Textbook Problem

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Determine the absolute maximum shear in a 15 m long simply supported beam due to the series of three moving concentrated loads shown in Fig. P9.13.

FIG. P9.13, P9.17, P9.18, P9.22

To determine

Find the absolute maximum shear in a 15 m long simply supported beam.

**Calculation:**

Sketch the simply supported beam as shown in Figure 1.

The simply supported beam the maximum shear occurs at support. Hence, find the influence line diagram for support reactions.

Case 1: Consider the Absolute Maximum Shear occurs at Support *A*.

**Influence line diagram for support reaction at A.**

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 *A* using equilibrium equation:

Take moment about point *B*.

Consider moment equilibrium at point *B*.

Consider clockwise moment as positive and anticlockwise moment as negative

Sum of moment at point *B* is zero.

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

Apply vertical equilibrium equation of forces.

Consider upward force as positive

Substitute

Consider Equation (1).

Find the value of influence line ordinate of reaction *A*.

Substitute 0 for *x* in Equation (1).

Similarly calculate the influence line ordinate of reaction *x* and summarize the result in Table 1.

x | |

0 | 1 |

15 | 0 |

Draw the influence line diagram for the vertical reactions at support *A* using Table 1 as shown in Figure 3.

Refer Figure 3.

Find the slope

Here,

Substitute 15 m for

Sketch the loading position as shown in Figure 4.

Find the maximum absolute maximum shear for case 1.

Sketch the loading position on the beam when the load 1 placed at just right of *A* as shown in Figure 5.

Refer Figure 5.

Find the shear force of case 1.

Substitute 15 m for *L* and

Structural Analysis

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