4.19 and 4.20 Knowing that for the extruded beam shown the allowable stress is 120 Mpa in tension and 150 Mpa in compression, determine the largest couple M that can be applied.
Fig. P4.19
Find the largest couple moment (M) that can be applied to the beam.
Answer to Problem 19P
The largest couple moment (M) applied to the beam is
Explanation of Solution
Given information:
The allowable stress in tension is
The allowable stress in compression is
Calculation:
Show the cross-section of the material as shown in figure 1.
Refer Figure 1.
Calculate the value of
Substitute
Calculate the moment of inertia
Substitute
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
Calculate the maximum moment
Substitute
Calculate the value of stress
Substitute
Compare
Get the largest moment applied on the beam as
Thus, the largest couple moment (M) applied to the beam is
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Chapter 4 Solutions
Mechanics of Materials - With Access
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