4.9 through 4.11 Two vertical forces are applied to a beam of the cross section shown. Determine the maximum tensile and compressive stresses in portion BC of the beam.
Fig. P4.11
Find the maximum tensile and compressive stresses in portion BC of the beam.
Answer to Problem 11P
The maximum compressive and tensile stress in the in the section BC are
Explanation of Solution
Given information:
Calculation:
Show the cross-section of the beam as shown in figure 1.
Refer to Figure 1.
Calculate the value of
Substitute
Calculate the moment of inertia
Substitute
The moment of inertia of rectangle 2 is same as the moment of inertia of rectangle 1. Then,
Calculate the moment of inertia
Substitute
Calculate the total moment of inertia (I) of the cross-section as follows:
Substitute
Refer Figure 1.
Consider the distance between the neutral axis and the top fiber and bottom fiber of the beam is
Calculate
Show the section of the beam left of C as shown in Figure 2.
Refer to Figure 2.
Calculate the moment M using the relation:
Substitute
Calculate the value of stress
Substitute
Calculate the value of stress
Substitute
Thus, the maximum compressive and tensile stress in the in the section BC are
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Mechanics of Materials, 7th Edition
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