A countershaft carrying two V-belt pullets is shown in the figure. Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side (T1) at B is 30% of the tension on the tight side (T2). (a) Determine the tension (i.e., T₂ and T₁) in the belt on pulley B, assuming the shaft is running at a constant speed. (b) Find the magnitudes of the bearing reaction forces, assuming the bearings act as simple supports. (c) Draw shear-force and bending moment diagrams for the shaft (in XZ and XY plane if needed). (d) Calculate the maximum moments at points A and B respectively and find the point of maximum bending moment (A or B). (e) Find maximum stresses (tensile, compressive, and shear stresses) at the identified point of maximum moment (hint: principal and max shear stresses) 8 dia. 9 400lbf 50lbf 45° 1.5 dia. T₂ B Units in inches T₁ 10 dia.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter11: Columns
Section: Chapter Questions
Problem 11.2.4P: Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.
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A countershaft carrying two V-belt pullets is shown in the figure. Pulley A receives power
from a motor through a belt with the belt tensions shown. The power is transmitted through
the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side
(T1) at B is 30% of the tension on the tight side (T2).
(a) Determine the tension (i.e., T₂ and T₁) in the belt on pulley B, assuming the shaft is
running at a constant speed.
(b) Find the magnitudes of the bearing reaction forces, assuming the bearings act as
simple supports.
(c) Draw shear-force and bending moment diagrams for the shaft (in XZ and XY plane
if needed).
(d) Calculate the maximum moments at points A and B respectively and find the point
of maximum bending moment (A or B).
(e) Find maximum stresses (tensile, compressive, and shear stresses) at the identified
point of maximum moment (hint: principal and max shear stresses)
8 dia.
9
400lbf
50lbf
45°
1.5 dia.
T₂
B
Units in inches
T₁
10 dia.
Transcribed Image Text:A countershaft carrying two V-belt pullets is shown in the figure. Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side (T1) at B is 30% of the tension on the tight side (T2). (a) Determine the tension (i.e., T₂ and T₁) in the belt on pulley B, assuming the shaft is running at a constant speed. (b) Find the magnitudes of the bearing reaction forces, assuming the bearings act as simple supports. (c) Draw shear-force and bending moment diagrams for the shaft (in XZ and XY plane if needed). (d) Calculate the maximum moments at points A and B respectively and find the point of maximum bending moment (A or B). (e) Find maximum stresses (tensile, compressive, and shear stresses) at the identified point of maximum moment (hint: principal and max shear stresses) 8 dia. 9 400lbf 50lbf 45° 1.5 dia. T₂ B Units in inches T₁ 10 dia.
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