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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 17P

Textbook Problem

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For the truss of Problem 8.53, determine the maximum tensile axial force in member *DI* due to the series of three moving concentrated loads shown in Fig. P9.13.

FIG. P9.13, P9.17, P9.18, P9.22

FIG. P8.53

To determine

Find the maximum tensile axial force in member *DI*.

**Calculation:**

Find the support reactions.

Apply 1 kN moving load from *A* to *G* in the top chord member.

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

Refer Figure 1.

Find the reaction at *A* and *G* when 1 kN load placed from *A* to *G*.

Apply moment equilibrium at *A*.

Apply force equilibrium equation along vertical.

Consider the upward force as positive

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

The expressions for the member force *aa* through the members *CD*, *DI*, and *IJ* and then apply a vertical force equilibrium.

Draw the free body diagram as shown in Figure 2.

Refer Figure 2.

Find the equation of member force *DI*.

Apply a 1 kN load at just left of *C*

Consider the section *DG*.

Apply force equilibrium equation along vertical.

Consider upward force as positive and downward force as negative.

Substitute

Apply a 1 kN load at just right of *C*

Consider the section *AC*.

Apply force equilibrium equation along vertical.

Consider upward force as positive and downward force as negative.

Substitute

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

Find the force in member *DI* using the Equation (1) and (2) and then summarize the value in Table 1.

x (m) | Apply 1 kN load | Force in member DI | Influence line ordinate for the force in member DI (kN/kN) |

0 | A | 0 | 0 |

8 | C | 0.556 | |

12 | D | ||

24 | G | 0 |

Sketch the influence line diagram for ordinate for the force in member *DI* using Table 1 as shown in Figure 3.

Refer Figure 3.

Find the slope *DI*.

Here, *A* to *C*.

Substitute 8 m for

Find the slope *DI*.

Here, *C* to *D*.

Substitute 4 m for

The slope of portion *C* to *O* is positive and *O* to *D* is negative.

Find the distance of *OD* using similar triangle rule.

Find the distance of *CO*.

Substitute 4 m for

Structural Analysis

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