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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 3P

Textbook Problem

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Determine the equations for slope and deflection of the beam shown by the direct integration method. *EI* = constant.

FIG. P6.3

To determine

Find the equations for slope and deflection of the beam using direct integration method.

**Calculation:**

Draw the free body diagram of the beam as in Figure (1).

Refer Figure (1),

Find the reaction at support *A*.

Apply vertical equilibrium along *y*-axis.

Consider upward force as positive.

Find the moment at *A.*

Consider anticlockwise moment as positive.

**Segment AB:**

Consider a section *AB* at a distance of *x* from *A*.

Sketch the free body diagram when section *AB* as shown in Figure 2.

Refer Figure (2),

Take the moment at section

Write the equation for

Find the equation for slope

Integrate Equation (1) with respect to *x*.

Find the equation for deflection

Integrate again Equation (2) with respect to *x*.

Find the integration constants

Apply boundary conditions in Equation (2):

At

Apply boundary conditions in Equation (1):

At

Find the equation for slope of segment *AB*.

Substitute 0 for

Thus, the equation for slope of segment *AB* is

Find the equation for deflection of segment *AB*.

Substitute 0 for

Thus, the equation for deflection is

**Segment BC:**

Consider a section *BC* at a distance of *x* from *A*.

Sketch the free body diagram when section *BC* as shown in Figure 3.

Refer Figure 3.

Write the equation for bending moment at section

Write the equation for

Write the equation for slope.

Integrate Equation (4) with respect to *x*.

Write the equation for deflection

Structural Analysis

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Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - Determine the equations for slope and deflection...Ch. 6 - Determine the equations for slope and deflection...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - 6.7 and 6.8 Determine the slope and deflection at...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point B of...

Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point A of...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beam...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.31 and 6.32 Use the moment-area method to...Ch. 6 - Use the moment-area method to determine the slope...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.33 and 6.34 Use the moment-area method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.39 Determine the slope and deflection at point A...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.57 and 6.58 Use the conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...

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