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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 16, Problem 13P

Textbook Problem

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16.8 through 16.14 Determine the reactions and draw the shear and bending moment diagrams for the beams shown in Figs. P16.8–P16.14 by using the moment-distribution method.

FIG. P16.13

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 unequal length are

Formula to calculate the fixed moment for UDL is

Formula to calculate the fixed moment for UVL are

Formula to calculate the fixed moment for deflection is

Calculation:

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

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

Refer Figure 1,

The beam distance and load are symmetric. Hence, consider right half CE member only.

Calculate the relative stiffness *CD* of the beam as below:

Calculate the relative stiffness *DE* of the beam as below:

Calculate the distribution factor *DC* of the beam.

Substitute

Calculate the distribution factor *DE* of the beam.

Substitute

Check for sum of distribution factor as below:

Substitute 0.571 for

Hence, OK.

Calculate the fixed end moment for *CD*.

Calculate the fixed end moment for *DC*.

Calculate the fixed end moment for *DE*.

Calculate the fixed end moment for *ED*.

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

Due to symmetry, the final moment of members *AB* and *BC* as follows;

Show the section free body diagram of the member *CD* and *DE* as in Figure 2.

Consider the member *CD* of the beam:

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

Calculate the vertical reaction at the right end of the joint *C* by resolving the vertical equilibrium.

Consider the member *DE* of the beam:

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

Structural Analysis

Show all chapter solutions

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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