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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 34P

Textbook Problem

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Draw the influence lines for the shears and bending moments at points *D* and *F* of the beam shown in Fig. P8.33.

FIG. P8.33, P8.34

To determine

Draw the influence lines for the shear and bending moment at point *D* and *F*.

**Calculation:**

Use Muller-Breslau's principle.

**Influence line ordinate for shear at D.**

Cut the beam at *D* to obtain the released structure of the beam. Next apply a small relative displacement in positive direction of *D* of the portion *CD* downward by *D* of the portion *DE* upward by

Sketch the deflected shape of the released beam when the beam cut at *D* as shown in Figure 1.

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

Sketch the general shape of the influence line for shear *D* as shown in Figure 2.

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

Place the 1 kN load first just to the left of *D* and then just to the right of *D*.

Sketch the free body diagram of beam as shown in Figure 3.

Refer Figure 3.

The reaction at the hinge *E* and *C* is *D* is center of the hinge *CD*.

Find the shear at *D**D* using the equation:

Thus, the value of influence line ordinate just left of *D* is

Find the shear at *D**D* using the equation:

Thus, the value of influence line ordinate just right of *D* is

The numerical value of influence line ordinate in different points on the beam for shear

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

0 | A | 0 |

8 | ||

14 | ||

18 | ||

22 | ||

25 | E | |

28 | ||

36 | G | 0 |

Sketch the influence line diagram for shear at point *D* using Table 1 as shown in Figure 4.

**Influence line ordinate for moment at D.**

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 counterclockwise to obtain the deflected shape.

Sketch the deflected shape of the released beam when insert a hinge at *D* as shown in Figure 5.

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

Sketch the general shape of the influence line for bending moment *D* as shown in Figure 6.

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

Refer Figure 3.

Find the moment at *C* from *B*.

Apply 1 kN load at *D*.

Consider clockwise moment as positive and anticlockwise moment as negative.

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

The remaining values of influence line ordinate are determined by geometry (similar triangle) of the influence line and summarize the values as in Table 2.

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

0 | A | 0 |

8 | 0 | |

14 | 0 | |

22 | 2 | |

25 | E | 0 |

28 | 0 | |

36 | G | 0 |

Sketch the influence line diagram for moment at point *D* using Table 2 as shown in Figure 7

Structural Analysis

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