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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 16, Problem 31P

Textbook Problem

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16.24 through 16.31 Determine the member end moments and reactions for the frames shown in Figs. P16.24–P16.31 by using the moment-distribution method.

FIG. P16.31

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 elastic modulus *E* of the frame is constant.

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

Refer Figure 1,

Calculate the relative stiffness *CA*, *DB*, *CE* and *DF* of the frame as below:

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

Calculate the distribution factor *CA* of the frame.

Substitute

Calculate the distribution factor *CD* of the frame.

Substitute

Calculate the distribution factor *CE* of the frame.

Substitute

Check for sum of distribution factor as below:

Substitute

Hence, OK.

Calculate the distribution factor *EC* of the frame.

Substitute

Calculate the distribution factor *EF* of the frame.

Substitute

Check for sum of distribution factor as below:

Substitute

Hence, OK.

Calculate the distribution factor *EC* of the frame.

Substitute

Calculate the distribution factor *FD* of the frame.

Substitute

Check for sum of distribution factor as below:

Substitute

Hence, OK.

Calculate the distribution factor

Substitute

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

Hence, OK.

Show the translation

Write the expression to calculate the Fixed-end moment of the member.

Assume the Fixed-end moment of the members *AC*, *CA*, *BD* and *DB* as

Write the expression to calculate the Fixed-end moment of the member.

Assume the Fixed-end moment of the members *CE*, *EC*, *DF* and *FD* as

Show the calculation of

Show the free body diagram of the frame with unknown reaction

Consider member *EC*:

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

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

Consider member *FD*:

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

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

Calculate the reaction

Show the free body diagram of the frame with unknown reaction

Consider member *AC*:

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

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

Consider member *BD*:

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

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

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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