Concept explainers
The deflection of the shaft at point
The slope of the shaft at point
Answer to Problem 28P
The deflection of the shaft at point
The slope of the shaft at point
Explanation of Solution
Write the expression for the moment of inertia of the shaft.
Here, the diameter of the shaft is
Draw the free body diagram of the beam.
Figure (1)
The free body diagram of the beam in the direction of y-axis is shown in figure (1).
Write the deflection equation along y-axis for beam 6 using Table A-9.
Here, the force component at point
Write the force component at point
Here, the force component at
Write the force component at point
Here, the force component at
The free body diagram of the beam in the direction of z-axis is shown below.
Figure (2)
Write the deflection equation along z-axis for beam 6 using Table A-9.
Here, the force component at point
Write the force component at point A along z-axis.
Here, the force component at
Write the force component at point B along z-axis.
Here, the force component at
Write the expression for net displacement at point
Here, the net deflection at point
Write the slope equation at along z-axis at point
Here, the slope along z-axis at point is
Write the slope equation at along y-axis at point
Here, the slope along z-axis at point is
Write the expression for the net slope at point
Here, the net slope is
Conclusion:
Substitute
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Thus, the net displacement of the shaft at point
Substitute
Substitute
Substitute
Thus, the net slope of the shaft at point
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Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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