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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 13P

Textbook Problem

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For the beam of Problem 8.3, determine the maximum positive shear and bending moment at point *B* due to the series of three moving concentrated loads shown in Fig. P9.13.

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

FIG. P8.3

To determine

Find the maximum positive shear and bending moment at point *B*.

**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 *A* using equilibrium equation:

Take moment about point *C*.

Consider moment equilibrium at point *C*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Sum of moment at point *C* is zero.

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

Apply vertical equilibrium equation of forces.

Consider upward force as positive

Substitute

**Influence line for shear at point 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

Substitute

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

Sketch the free body diagram of the section *BC* 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 at various points of *x* using the Equations (3) and (4) and summarize the value as in Table 1.

x | |

0 | 0 |

16 | 0 |

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

Refer Figure 4.

Find the slope *B* in the portion *AB*.

Here, *A to B*.

Substitute 10 m for

Find the slope *B* in the portion *BC*.

Here, *B to C*.

Substitute 5 m for

Sketch the loading position as shown in Figure 5.

Find the maximum positive shear force at *B*.

Sketch the loading position on the beam when the load 1 placed at just right of *B* as shown in Figure 6.

Refer Figure 6.

Find the shear force at *B* when the load 1 placed at just right of *B*.

Substitute 5 m for

Sketch the loading position on the beam when the load 2 placed at just right of *B* as shown in Figure 7.

Refer Figure 7.

Find the shear force at *B* when the load 2 placed at just right of *B*.

Substitute 10 m for

Sketch the loading position on the beam when the load 3 placed at just right of *B* as shown in Figure 8.

Refer Figure 8.

Find the shear force at *B* when the load 3 placed at just right of *B*.

Substitute 10 m for

Structural Analysis

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Ch. 9 - For the beam of Problem 8.6, determine the maximum...Ch. 9 - For the beam of Problem 8.6, determine the maximum...Ch. 9 - For the beam of Problem 8.6, determine the maximum...Ch. 9 - For the beam of Problem 8.7, determine the maximum...Ch. 9 - For the cantilever beam of Problem 8.5, determine...Ch. 9 - For the beam of Problem 8.10, determine the...Ch. 9 - For the beam of Problem 8.23, determine the...Ch. 9 - For the beam of Problem 8.29, determine the...Ch. 9 - For the truss of Problem 8.47, determine the...Ch. 9 - For the truss of Problem 8.50, determine the...

Ch. 9 - For the truss of Problem 8 .51, determine the...Ch. 9 - For the beam of Problem 8.2, determine the maximum...Ch. 9 - For the beam of Problem 8.3, determine the maximum...Ch. 9 - For the beam of Problem 8.1, determine the maximum...Ch. 9 - For the beam of Problem 8.23, determine the...Ch. 9 - For the truss of Problem 8.49, determine the...Ch. 9 - For the truss of Problem 8.53, determine the...Ch. 9 - Determine the absolute maximum shear in a 15 m...Ch. 9 - Determine the absolute maximum shear in a 60 ft...Ch. 9 - Determine the absolute maximum bending moment in...Ch. 9 - Determine the absolute maximum bending moment in a...Ch. 9 - Determine the absolute maximum bending moment in a...Ch. 9 - Determine the absolute maximum bending moment in a...

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