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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 15, Problem 4P

Textbook Problem

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Determine the reactions and draw the shear and bending moment diagrams for the beams shown in Figs. P15.1–P15.5 by using the slope-deflection method.

FIG. P15.4, P15.7

To determine

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

Fixed end moment:

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 fixed end moment for *AB*.

Calculate the fixed end moment for *BA*.

Calculate the fixed end moment for *BC*.

Calculate the fixed end moment for *CB*.

Calculate the slope deflection equation for the member *AB*.

Here, *A* and *B*.

Substitute *E*, *I*, 0 for *L* and

Calculate the slope deflection equation for the member *BA*.

Substitute *E*, *I*, 0 for *L*, and

Calculate the slope deflection equation for the member *BC*.

Substitute *E*, *I*, 0 for *L* and

Calculate the slope deflection equation for the member *CB*.

Write the equilibrium equation as below.

Substitute equation (1) and equation (2) in above equation.

Calculate the moment about *AB*.

Substitute

Calculate the moment about *BA*.

Substitute

Calculate the moment about *BC*.

Substitute

Consider the member *AB* of the beam:

Show the section free body diagram of the member *AB* and *BC* as in Figure 2.

Structural Analysis

Show all chapter solutions

Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Solve Problem 15.2 for the loading shown in Fig....Ch. 15 - Solve Problem 15.4 for the loading shown in Fig....Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Determine the reactions and draw the shear and...Ch. 15 - Determine the reactions and draw the shear and...

Ch. 15 - 15.8 through 15.14 Determine the reactions and...Ch. 15 - 15.8 through 15.14 Determine the reactions and...Ch. 15 - 15.8 through 15.14 Determine the reactions and...Ch. 15 - 15.8 through 15.14 Determine the reactions and...Ch. 15 - Solve Problem 15.9 for the loading shown in Fig....Ch. 15 - Solve Problem 15.12 for the loading shown in Fig....Ch. 15 - Determine the member end moments and reactions for...Ch. 15 - Determine the member end moments and reactions for...Ch. 15 - Determine the member end moments and reactions for...Ch. 15 - Determine the member end moments and reactions for...Ch. 15 - Solve Problem 15 .17 for the loading shown in Fig....Ch. 15 - Solve Problem 15.18 for the loading shown in Fig....Ch. 15 - Determine the member end moments and reactions for...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...Ch. 15 - 15.24 through 15.31 Determine the member end...

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