Sample Solution from

Mechanics of Materials (10th Edition)

10th Edition

ISBN: 9780134319650

Chapter 1

Problem 1.1RP

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To determine

**To determine:** The resultant internal loadings acting on cross sections located at *D* and *E*.

**Answer:**

The resultant internal loadings at cross section at *D* are

The resultant internal loadings at cross section at *E* are

**Explanation:**

**Given information:**

The beam *AB* is pin supported at *A* and supported by a cable *BC*.

The weight of the beam *AB* is

The weight of the column *FC* is

**Calculation:**

Find the loading at the center of the beam *AB*

Substitute *AB* and 12 ft for the length of beam *AB*.

Convert the unit from lb to kip.

Sketch the Free Body Diagram of the beam *AB* shown in Figure 1.

Refer to Figure 1.

Find the angle of cable *BC* to the horizontal

Find the tension in cable *BC* as shown below.

Take moment about *A* is Equal to zero.

Find the support reaction at *A* as shown below.

Apply the Equations of Equilibrium as shown below.

Summation of forces along horizontal direction is Equal to zero.

Summation of forces along vertical direction is Equal to zero.

Find the loading at the center of the beam *AD*

Substitute *AD* and 6 ft for the length of beam *AD*.

Convert the unit from lb to kip.

Sketch the Free Body Diagram of the section for point *D* as shown in Figure 2.

Refer to Figure 2.

Find the internal loadings as shown below.

Apply the Equations of Equilibrium as shown below.

Summation of forces along horizontal direction is Equal to zero.

Summation of forces along vertical direction is Equal to zero.

Take moment about *D* is Equal to zero.

Hence, the resultant internal loadings at cross section at *D* are

Find the loading at the center of the column *FC*

Substitute *FC* and 16 ft for the length of column *FC*.

Convert the unit from lb to kip.

Sketch the Free Body Diagram of the beam *FC* shown in Figure 3.

Refer to Figure 3.

Find the angle of cable *CG* to the horizontal.

Find the tension in cable *CG* as shown below.

Summation of forces along horizontal direction is Equal to zero.

Find the loading at the center of the column *FE*

Substitute *FE* and 4 ft for the length of column *FC*.

Convert the unit from lb to kip.

Sketch the Free Body Diagram of the section for point *E* as shown in Figure 4.

Refer to Figure 4.

Find the internal loadings as shown below.

Apply the Equations of Equilibrium as shown below.

Summation of forces along horizontal direction is Equal to zero.

Summation of forces along vertical direction is Equal to zero.

Take moment about *E* is Equal to zero.

Therefore, the resultant internal loadings at cross section at *E* are

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