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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 16P

Textbook Problem

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For the truss of Problem 8.49, determine the maximum compressive axial force in member *GH* due to the series of four moving concentrated loads shown in Fig. P9.14.

FIG. P9.14, P9.16, P9.19, P9.23

FIG. P8.49

To determine

Find the maximum compressive axial force in member *GH*.

**Calculation:**

Find the equation of support reactions using equilibrium.

Apply 1 k load from *A* to *E*.

Sketch the free body diagram as shown in Figure 1.

Refer Figure 1.

Find the equation of support reaction at *D* using moment equilibrium at *A*.

Consider clockwise moment as positive.

Find the equation of support reaction at *A* using force equilibrium at *A*.

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

Find the force in member *GH*.

The expressions for the member force *aa* through the members *GH, CG,* and *BC* and then apply a moment equilibrium at *G*.

Draw the free body diagram as shown in Figure 2.

Refer Figure 3.

Apply a 1 k load just the left of *C*

Apply moment equilibrium equation at *C*.

Take moment at *C* from *E*.

Consider clockwise moment as negative and counterclockwise moment as positive.

Apply a 1 k load just the right of *C*

Apply moment equilibrium equation at *C*.

Take moment at *C* from *A*.

Consider clockwise moment as positive and counterclockwise moment as negative.

The equation of force in the member *GH*,

Find the support reactions using Equations (1) and (2), force in member *GH* using the Equations (3) and (4) and summarize the value in Table 1.

x (ft) | Apply 1 k load | Support reaction A (k) | Support reaction D (k) | Influence line ordinate for the force in member GH (k/k) |

0 | A | 1 | 0 | 0 |

20 | B | |||

40 | C | |||

60 | D | |||

80 | E |

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

Refer Figure 3.

Find the slope *GH*.

Here, *A* to *C*.

Substitute 40 ft for

Find the slope *GH*.

Here, *C* to *D*.

Substitute 20 ft for

Find the slope *GH*.

Here, *D* to *E*.

Substitute 20 ft for

Sketch the loading position as shown in Figure 4.

Find the maximum compressive axial force in member *GH*.

Sketch the loading position on the truss when the load 1 placed at just right of *C* as shown in Figure 5.

Structural Analysis

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