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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 15P

Textbook Problem

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For the beam of Problem 8.23, determine the maximum positive bending moment at point *D* due to the wheel loads of the moving HS15-44 truck shown in Fig. P9.15.

FIG. P9.15, P9.21

FIG. P8.23, P8.25

To determine

Find the maximum positive bending moment at point *D*.

**Calculation:**

Apply 1 k load at *D*.

Sketch the free body diagram of beam as shown in Figure 1.

Find the vertical reaction *A*.

Consider moment at *B* from *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Find the vertical reaction *G*.

Consider moment at *F* from *G*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Find the vertical reactions

Consider moment at *B* from *G*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Substitute 0 for

Consider moment at *F* from *A*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute 0 for

Solve Equations (1) and (2),

Insert a hinge at *D* to obtain the released structure of the beam. Next apply a small rotation *D* in the released structure. The rotation *CD* in counterclockwise and the portion *DE* in clockwise to obtain the deflected shape.

Sketch the deflected shape of the released beam when insert a hinge at *D* as shown in Figure 2.

The general shape of the influence line for bending moment *D* is the similar of deflected shape.

Sketch the general shape of the influence line for bending moment *D* as shown in Figure 3.

Find the numerical value of influence line ordinate for *D*.

Refer Figure 3.

Find the moment at *D*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute 0 for

Thus, the value of influence line ordinate at *D* is

The remaining values of influence line ordinate at different points on the beam determined by geometry (similar triangle) of the influence line and summarize the values as in Table 1.

x (ft) | Points | Influence line ordinate of |

0 | A | 0 |

20 | ||

40 | C | 0 |

70 | D | |

100 | E | 0 |

115 | F | |

130 | G | 0 |

Sketch the influence line diagram for moment at point *D* as shown in Figure 4.

Refer Figure 4.

The slope *AB* of influence diagram is equal to slope *BC* of influence diagram.

Find the slope *D* in the portion *AC*.

Here, *A* to *B*.

Substitute 20 ft for

The slope *CD* of influence diagram is equal to slope *DE* of influence diagram.

Find the slope *D* in the portion *CE*.

Here, *C* to *D*.

Substitute 30 ft for

The slope *EF* of influence diagram is equal to slope *FG* of influence diagram

Structural Analysis

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