Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 2.2, Problem 2.11P
Determine the shear strain γxy at corners D and C if the plastic distorts as shown by the dashed lines.
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The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle.
The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear
5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft?
TS
I
y
18T
32T
This
a
12
x
18T
C
48T
5
Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth
should be drawn near the pressure line so that the teeth from the pinion should
mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or
CAD drawing is acceptable. Draw all the trajectories of the involute lines and the
circles.
Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch.
Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet,
c=b-a.
5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces.
The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2)
is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this
gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2.
(a) Find the revolution speed of gear 5.
(b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue.
(c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress).
(d) According to the computation results of the questions (b) and (c), explain the possible failure
mechanisms for each gear.
N4=28
800rpm
N₁=43
N5=34
N₂=14
P(diameteral pitch)=8 for all gears
Coupled to 2.5hp motor
Chapter 2 Solutions
Mechanics of Materials (10th Edition)
Ch. 2.2 - A loading causes the member to deform into the...Ch. 2.2 - A loading causes the mamber to deform into the...Ch. 2.2 - A loading causes the wires to elongate into the...Ch. 2.2 - A loading causes the block to deform into the...Ch. 2.2 - A loading causes the block to deform into the...Ch. 2.2 - When force P is applied to the rigid arm ABC,...Ch. 2.2 - If the force P causes the rigid arm ABC to rotate...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The triangular plate is deformed into the shape...Ch. 2.2 - The square plate is deformed into the shape shown...
Ch. 2.2 - The square deforms into the position shown by the...Ch. 2.2 - The pin-connected rigid rods AB and BC are...Ch. 2.2 - The wire AB is unstretched when = 45. If a load...Ch. 2.2 - If a horizontal load applied to the bar AC causes...Ch. 2.2 - Determine the shear strain xy at corners A and B...Ch. 2.2 - Determine the shear strain xy at corners D and C...Ch. 2.2 - The material distorts into the dashed position...Ch. 2.2 - The material distorts into the dashed position...Ch. 2.2 - Part of a control linkage for an airplane consists...Ch. 2.2 - Part of a control linkage for an airplane consists...Ch. 2.2 - The nylon cord has an original length L and is...Ch. 2.2 - A thin wire, lying along the x axis, is strained...Ch. 2.2 - Determine the shear strain xy at corners A and B...Ch. 2.2 - Determine the shear strain xy at corners D and C...Ch. 2.2 - Determine the average normal strain that occurs...Ch. 2.2 - The corners of the square plate are given the...Ch. 2.2 - The triangular plate is fixed at its base, and its...Ch. 2.2 - The triangular plate is fixed at its base, and its...Ch. 2.2 - The triangular plate is fixed at its base, and its...Ch. 2.2 - The polysulfone block is glued at its top and...Ch. 2.2 - The corners of the square plate are given the...Ch. 2.2 - The corners of the square plate are given the...Ch. 2.2 - The block is deformed into the position shown by...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The nonuniform loading causes a normal strain in...Ch. 2.2 - The rectangular plate undergoes a deformation...Ch. 2.2 - The fiber AB has a length L and orientation . If...Ch. 2.2 - If the normal strain is defined in reference to...
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- 1. The rotating steel shaft is simply supported by bearings at points of B and C, and is driven by a spur gear at D, which has a 6-in pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA =3000 lbĘ in. The shaft is machined from steel with Sy=60kpsi and Sut=80 kpsi. (1) Draw a shear force diagram and a bending moment diagram by F. According to your analysis, where is the point of interest to evaluate the safety factor among A, B, C, and D? Describe the reason. (Hint: To find F, the torque Tд is generated by the tangential force of F (i.e. Ftangential-Fcos20°) When n=2.5, K=1.8, and K₁ =1.3, determine the diameter of the shaft based on (2) static analysis using DE theory (note that fatigue stress concentration factors need to be used for this question because the loading condition is fatigue) and (3) a fatigue analysis using modified Goodman. Note) A standard diameter is not required for the questions. 10 in Darrow_forward3 N2=28 P(diametral pitch)=8 for all gears Coupled to 25 hp motor N3=34 Full depth spur gears with pressure angle=20° N₂=2000 rpm (1) Compute the circular pitch, the center-to-center distance, and base circle radii. (2) Draw the free body diagram of gear 3 and show all the forces and the torque. (3) In mounting gears, the center-to-center distance was reduced by 0.1 inch. Calculate the new values of center-to-center distance, pressure angle, base circle radii, and pitch circle diameters. (4)What is the new tangential and radial forces for gear 3? (5) Under the new center to center distance, is the contact ratio (mc) increasing or decreasing?arrow_forward2. A flat belt drive consists of two 4-ft diameter cast-iron pulleys spaced 16 ft apart. A power of 60 hp is transmitted by a pulley whose speed is 380 rev/min. Use a service factor (Ks) pf 1.1 and a design factor 1.0. The width of the polyamide A-3 belt is 6 in. Use CD=1. Answer the following questions. (1) What is the total length of the belt according to the given geometry? (2) Find the centrifugal force (Fc) applied to the belt. (3) What is the transmitted torque through the pulley system given 60hp? (4) Using the allowable tension, find the force (F₁) on the tight side. What is the tension at the loose side (F2) and the initial tension (F.)? (5) Using the forces, estimate the developed friction coefficient (f) (6) Based on the forces and the given rotational speed, rate the pulley set. In other words, what is the horse power that can be transmitted by the pulley system? (7) To reduce the applied tension on the tight side, the friction coefficient is increased to 0.75. Find out the…arrow_forward
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