Concept explainers
The slope of the shaft at each bearing.
Answer to Problem 32P
The slope of the shaft at bearing point O is
Explanation of Solution
The figure below shows the free body diagram of pulley A.
Figure (1)
The figure below shows the free body diagram of pulley B.
Figure (2)
The given assumption is that the belt tension on the loose side is
Write the expression for the tensions on the loose side in terms of tension on the tight side.
Here, the tension on the tight side is
Write the equation to balance the tension on the counter shaft.
Here, the tension on the tight side of pulley
Substitute
Write the expression for net applied load at point A.
Here, the tension force exerted by the pulley at each side at point A are
Write the expression for net applied load at point B.
Here, the tension force exerted by the pulley at each side at point B are
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 (3)
Write the equation for force component along y-axis.
Here, the net force at point A is
Write the equation for force component along z-axis.
Write the deflection equation for portion OA using Table A-9 for beam 6.
Here, Young’s modulus of the shaft material is
Substitute
Write the expression for net slope of the shaft at point O along z-axis.
Substitute
The free body diagram of the beam in the direction of z-axis is shown below.
Figure (4)
Write the deflection equation along z-axis using Table A-9 for beam 6.
Here, the force component along z-axis is
Write the expression for net slope of the shaft at point O along y-axis.
Substitute
Substitute
Write the expression for net slope at point O.
Write the deflection equation for portion BC using Table A-9 for beam 6.
Here, the location of applied point load at point A from left end bearing point O is
Write the expression for net slope of the shaft at point C along z-axis.
Substitute
Substitute
Write the deflection equation for portion BC using Table A-9 for beam 6.
Here, the location of applied point load at point B from left end bearing point O is
Write the expression for net slope of the shaft at point C along y-axis.
Substitute the value of
Substitute
Write the expression for net slope at point C.
Conclusion:
Substitute
Substitute
Substitute
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 C along y-axis is
Substitute
Thus, the net slope of the shaft at bearing point C is
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Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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