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The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W = 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The force Q acting in the +x direction, represents the traction force between the tire and the ground. The wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis with coordinate yD = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point G lies in the xy plane. Questions & Analysis: (a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and the bearing at A is a thrust bearing. Label all unknowns. (b) Is the assembly statically determinate or statically indeterminate? Explain. (c) Repeat Parts (a) and (b) if the bearings at A and B are self-aligning and the bearing at A is still a thrust bearing. (c) Invoke the free-body diagram from Part (c), and determine force Q and the reactions at the bearings. F = 5000 lb E X 4 in. C 24 in. w=1000 lb Z gear radius = 3 in. 18 in. y

The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W = 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The force Q acting in the +x direction, represents the traction force between the tire and the ground. The wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis with coordinate yD = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point G lies in the xy plane. Questions & Analysis: (a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and the bearing at A is a thrust bearing. Label all unknowns. (b) Is the assembly statically determinate or statically indeterminate? Explain. (c) Repeat Parts (a) and (b) if the bearings at A and B are self-aligning and the bearing at A is still a thrust bearing. (c) Invoke the free-body diagram from Part (c), and determine force Q and the reactions at the bearings. F = 5000 lb E X 4 in. C 24 in. w=1000 lb Z gear radius = 3 in. 18 in. y

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter1: Tension, Compression, And Shear
Section: Chapter Questions
Problem 1.8.22P: A cargo ship is tied down to marine boll arts at a number of points along its length while its cargo...
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The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W = 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The force Q acting in the +x direction, represents the traction force between the tire and the ground. The wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis with coordinate yp = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point G lies in the xy plane. Questions & Analysis: (a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and the bearing at A is a thrust bearing. Label all unknowns. (b) Is the assembly statically determinate or statically indeterminate? Explain. (c) Repeat Parts (a) and (b) if the bearings at A and B are self-aligning and the bearing at A is still a thrust bearing. (c) Invoke the free-body diagram from Part (c), and determine force Q and the reactions at the bearings. F = 5000 lb E X 4 in. 24 in.- W=1000 lb G gear radius = 3 in. 18 in. y
Transcribed Image Text:The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W = 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The force Q acting in the +x direction, represents the traction force between the tire and the ground. The wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis with coordinate yp = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point G lies in the xy plane. Questions & Analysis: (a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and the bearing at A is a thrust bearing. Label all unknowns. (b) Is the assembly statically determinate or statically indeterminate? Explain. (c) Repeat Parts (a) and (b) if the bearings at A and B are self-aligning and the bearing at A is still a thrust bearing. (c) Invoke the free-body diagram from Part (c), and determine force Q and the reactions at the bearings. F = 5000 lb E X 4 in. 24 in.- W=1000 lb G gear radius = 3 in. 18 in. y
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