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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 16, Problem 1P

Textbook Problem

Determine the reactions and draw the shear and bending moment diagrams for the beams shown in Figs. P16.1–P16.5 by using the moment-distribution method.

FIG. P16.1

Expert Solution

To determine

Find the reaction and plot the shear and bending moment diagram.

Fixed end moment:

Formula to calculate the relative stiffness for fixed support

Formula to calculate the fixed moment for point load with equal length are

Formula to calculate the fixed moment for point load with equal length are

Formula to calculate the fixed moment for point load with unequal length are

Formula to calculate the fixed moment for UDL is

Calculation:

Consider the flexural rigidity *EI* of the beam is constant.

Show the free body diagram of the entire beam as in Figure 1.

Refer Figure 1,

Calculate the relative stiffness *CA* of the beam:

Calculate the relative stiffness *CE* of the beam:

In the above beam, only joint C is free to rotate. Hence, calculate the distribution factor at joint C.

Calculate the distribution factor *AC* of the beam.

Substitute

Calculate the distribution factor *CE* of the beam.

Substitute

Check for sum of distribution factor:

Substitute 0.5 for

Hence, OK.

Calculate the fixed end moment for *AC*.

Calculate the fixed end moment for *CA*.

Calculate the fixed end moment for *CE*.

Calculate the fixed end moment for *EC*.

Show the calculation of final moments using moment distribution method as in Table 1.

Consider the member *AC* of the beam:

Show the free body diagram of the member *AC* as in Figure 2.

Calculate the vertical reaction at the left end of the joint *C* by taking moment about point *A*.

Calculate the horizontal reaction at point *A* by resolving the horizontal equilibrium.

Calculate the vertical reaction at point *A* by resolving the vertical equilibrium.

Consider the member *CE* of the beam:

Show the free body diagram of the member *CE* as in Figure 3.

Calculate the vertical reaction at the right end of the joint *C* by taking moment about point *E*.

Calculate the horizontal reaction at point *E* by resolving the horizontal equilibrium.

Calculate the vertical reaction at point *E* by resolving the vertical equilibrium.

Calculate the total reaction at point *C*.

Substitute

Show the reaction of the beam in Figure 4.

Refer Figure 4,

Shear diagram:

Point *A*:

Point *B*:

Point *C*:

Point *D*:

Point *E*:

Plot the shear force diagram of the beam as in Figure 5.

Refer Figure 4,

Bending moment diagram:

Point *A*:

Point *B*:

Point *C*:

Point *D*:

Point *E*:

Plot the bending moment diagram of the beam as in Figure 6.

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Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - Solve Problem 16.2 for the loading shown in Fig....Ch. 16 - Solve Problem 16.4 for the loading shown in Fig....Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - Determine the reactions and draw the shear and...Ch. 16 - 16.8 through 16.14 Determine the reactions and...

Ch. 16 - 16.8 through 16.14 Determine the reactions and...Ch. 16 - 16.8 through 16.14 Determine the reactions and...Ch. 16 - 16.8 through 16.14 Determine the reactions and...Ch. 16 - 16.8 through 16.14 Determine the reactions and...Ch. 16 - Solve Problem 16.9 for the loading shown in Fig....Ch. 16 - Solve Problem 16.12 for the loading shown in Fig....Ch. 16 - 16.17 through 16.20 Determine the member end...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Solve Problem 16.17 for the loading shown in Fig....Ch. 16 - Solve Problem 16.18 for the loading shown in Fig....Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - 16.24 through 16.31 Determine the member end...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - Determine the member end moments and reactions for...Ch. 16 - 16.24 through 16.31 Determine the member end...Ch. 16 - 16.24 through 16.31 Determine the member end...

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