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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 16, Problem 29P

Textbook Problem

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Determine the member end moments and reactions for the frames shown in Figs. P16.24–P16.31 by using the moment-distribution method.

FIG. 16.29

To determine

Find the member end moments and reactions for the frames.

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 EI of the frame is constant.

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

Refer Figure 1,

Calculate the length of the member *AC*:

Calculate the relative stiffness *AC* of the frame as below:

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

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

Calculate the relative stiffness *BD* of the frame as below:

Calculate the distribution factor *CA* of the frame.

Substitute

Calculate the distribution factor *CD* of the frame.

Substitute

Check for sum of distribution factor as below:

Substitute 0.556 for

Hence, OK.

Calculate the distribution factor *DC* of the frame.

Substitute

Calculate the distribution factor *DB* of the frame.

Substitute

Check for sum of distribution factor as below:

Substitute 0.571 for

Hence, OK.

Calculate the fixed end moment for *AC*.

Calculate the fixed end moment for *CA*.

Calculate the fixed end moment for *CD*.

Calculate the fixed end moment for *DC*.

Calculate the fixed end moment for *DB* and *BD*.

Show the calculation of

Show the free body diagram of the member *AC*, *CD* and *DB* for side-sway prevented as in Figure 2.

Consider member *CD*:

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

Calculate the vertical reaction at joint *D* by resolving the horizontal equilibrium.

Consider member *AC*

Calculate vertical reaction at joint *A* using the relation:

Calculate horizontal reaction at joint *A* by taking moment about point *C*.

Calculate the horizontal reaction at joint *C* by resolving the horizontal equilibrium.

Consider member *DB*:

Calculate vertical reaction at joint *B*:

Calculate horizontal reaction at joint *B* by taking moment about point *D*.

Calculate the horizontal reaction at joint *D* by resolving the horizontal equilibrium.

Show the unknown load *R* as in Figure 3.

Calculate the reaction *R*:

Show the arbitrary translation as in Figure 4.

Calculate the relative translation *AC*:

Calculate the relative translation *CD*:

Calculate the relative translation *BD*:

Calculate the fixed end moment for *AC* and *CA*.

Substitute

Calculate the fixed end moment for *CD* and *DC*.

Substitute

Calculate the fixed end moment for *BD* and *DB*.

Substitute

Assume the Fixed-end moment at *AC*, and *CA* as

Calculate the value of

Substitute

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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