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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 11P

Textbook Problem

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For the truss of Problem 8 .51, determine the maximum tensile and compressive axial forces in member *DI* due to a concentrated live load of 40 k, a uniformly distributed live load of 4 k/ft, and a uniformly distributed dead load of 2 k/ft.

FIG. P8.51

To determine

Find the maximum tensile and compressive axial forces in member *DI*.

**Given Information:**

The concentrated live load (*P)* is 40 k.

The uniformly distributed live load

The uniformly distributed dead load

**Calculation:**

Find the support reactions.

Apply 1 k moving load from *A* to *G* in the bottom chord member.

Draw the free body diagram of the truss as in Figure 1.

Refer Figure 1,

Find the reaction at *C* and *E* when 1 k load placed from *A* to *G*.

Apply moment equilibrium at *C*.

Apply force equilibrium equation along vertical.

Consider the upward force as positive

**Equation member force CD.**

The expressions for the member force *aa* through the members *HI*, *CI*, and *CD* and then apply a moment equilibrium at *I*.

Draw the free body diagram of the section as shown in Figure 2.

Refer Figure 2.

Apply 1 k load just the left of *C*

Find the equation of member force *CD* from *A* to *C*.

Consider the section *DG*.

Apply moment equilibrium equation at *I*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Substitute

Apply 1 k load just the right of *C*

Find the equation of member force *CD* from *C* to *G*.

Consider the section *AC*.

Apply moment equilibrium equation at *I*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Thus, the equation of force in the member *CD*,

**Influence line for the force in member DI.**

The expressions for the member force *bb* through the members *IJ*, *DI* and *CD* and then apply moment equilibrium at *J*.

Draw the free body diagram of the section *bb* as shown in Figure 3.

Refer Figure 3.

Apply 1 k load just the left of *C*

Find the equation of member force *DI* from *A* to *C*.

Consider the section *DG*.

Apply moment equilibrium equation at *J*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Substitute

Apply 1 k load just the right of *C*

Find the equation of member force *DI* from *C* to *G*.

Consider the section *AC*.

Apply moment equilibrium equation at *J*.

Consider clockwise moment as positive and anticlockwise moment as negative.

Substitute

Thus, the equation of force in the member *DI*,

Find the force in member *DI* using the Equation (5) and (6) and then summarize the value in Table 1

Structural Analysis

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