Concept explainers
For the steel countershaft specified in the table, find the slope of the shaft at each bearing. Use superposition with the deflection equations in Table A–9. Assume the bearings constitute simple supports.
The slope of the shaft at each bearing.
Answer to Problem 33P
The slope of the shaft at bearing point O is
Explanation of Solution
Calculate the force
Here, the force acting on pulley
Write the equation for moment of inertia of the shaft.
Here, the diameter of the shaft is
The free body diagram of the beam in the direction of y-axis is shown below.
Figure (1)
Write the force component at point A along y-axis.
Write the force component at point B along y-axis.
Write the deflection equation along y-axis for beam 6 and beam 10 using Table A-9.
Here, the force component at point A along y-axis is
Write the expression for net slope of the shaft along z-axis at point O.
Substitute
Substitute
The free body diagram of the beam in the direction of z-axis is shown below.
Figure (2)
Write the force component at point A along z-axis.
Write the force component at point B along z-axis.
Write the deflection equation along z-axis for beam 6 and beam 10 using Table A-9.
Here, the force component at point A along z-axis is
Write the expression for net slope of the shaft along y-axis at point O.
Substitute
Substitute
Write the expression for the net slope at point O.
Write the deflection equation along y-axis for section AC for beam 6 and beam 10 using Table A-9.
Here, the location of point A from point O is
Write the expression for net slope of the shaft along z-axis at point C.
Substitute
Substitute
Write the deflection equation along z-axis for section AC for beam 6 and beam 10 using Table A-9.
Write the expression for net slope of the shaft along z-axis at point C.
Substitute
Substitute
Write the expression for the net slope at point C.
Conclusion:
Substitute
Substitute
Substitute
Thus, the slope of the shaft at bearing point O along z-axis is
Substitute
Thus, the slope of the shaft at bearing point O along y-axis is
Substitute
Thus, the net slope of the shaft at bearing point O is
Substitute
Thus, the slope of the shaft at bearing point C along z-axis is
Substitute
Thus, the slope of the shaft at bearing point O along y-axis is
Substitute
Thus, the net slope of the shaft at bearing point C is
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Chapter 4 Solutions
Connect 1-semester Access Card For Shigley's Mechanical Engineering Design
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