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MECH 3230 Name: Problem 1 (10 Points) Consider the gear and shaft assembly below, which are made of AISI 4130 Annealed Steel (Table A-21 in the textbook). The gear at A has a diameter of 20in, and the shaft has a diameter of 1.25in. Motion is transmitted to the shaft when the gear at A receives power from another gear (not drawn) with a transmitted force of 900 lbf at a pressure angle 30°. (a) Assuming the end bearings act as simple supports, determine the reaction forces. (b) Identify the critical location along the shaft. (c) Calculate the maximum bending stress and maximum torsional shear stress at the critical location on the shaft. (d) Determine the factor of safety using a less conservative failure theory. 16 in 14 in 1.25-in dia. Gear A 20-in dia. A F$_A$ = 900 lbf 30° Page 2 of 7

          MECH 3230
Name:
Problem 1 (10 Points)
Consider the gear and shaft assembly below, which are made of AISI 4130 Annealed Steel (Table
A-21 in the textbook). The gear at A has a diameter of 20in, and the shaft has a diameter of
1.25in. Motion is transmitted to the shaft when the gear at A receives power from another gear
(not drawn) with a transmitted force of 900 lbf at a pressure angle 30°.
(a) Assuming the end bearings act as simple supports, determine the reaction forces.
(b) Identify the critical location along the shaft.
(c) Calculate the maximum bending stress and maximum torsional shear stress at the critical
location on the shaft.
(d) Determine the factor of safety using a less conservative failure theory.
16 in
14 in
1.25-in dia.
Gear A
20-in dia.
A
F$_A$ = 900 lbf
30°
Page 2 of 7

MECH 3230
Name:
Problem 1 (10 Points)
Consider the gear and shaft assembly below, which are made of AISI 4130 Annealed Steel (Table
A-21 in the textbook). The gear at A has a diameter of 20in, and the shaft has a diameter of
1.25in. Motion is transmitted to the shaft when the gear at A receives power from another gear
(not drawn) with a transmitted force of 900 lbf at a pressure angle 30°.
(a) Assuming the end bearings act as simple supports, determine the reaction forces.
(b) Identify the critical location along the shaft.
(c) Calculate the maximum bending stress and maximum torsional shear stress at the critical
location on the shaft.
(d) Determine the factor of safety using a less conservative failure theory.
16 in
14 in
1.25-in dia.
Gear A
20-in dia.
A
FA = 900 lbf
30°
Page 2 of 7

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