Perform free body diagram analysis to get reaction force at bearings
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
Perform free body diagram analysis to get reaction force at bearings
![A double reduction gearbox design has developed to the point that the general
layout and axial dimensions of the countershaft carrying two spur gears has been
proposed, as shown in Fig. 7-10. The gears and bearings are located and supported
by shoulders, and held in place by retaining rings. The gears transmit torque
through keys. Gears have been specified as shown, allowing the tangential and
radial forces transmitted through the gears to the shaft to be determined as
follows.
Bearing A
where the superscripts tand rrepresent tangential and radial directions,
respectively; and, the subscripts 23 and 54 represent the forces exerted
by gears 2 and 5 (not shown) on gears 3 and 4, respectively.
Proceed with the next phase of the design, in which a suitable material
is selected, and appropriate diameters for each section of the shaft are
estimated, based on providing sufficient fatigue and static stress capacity
for infinite life of the shaft, with minimum safety factors of 1.5.
D₁ D₂
Datum
0.25
0.75
1.25
1.75
2.0
W
480 lbf
W₂₁3 = 197 lbf
CADEF
Gear 3
d; = 12.5 in
-0
2.75
OS
G H
D₁
W$4 = 2099 lbf
W54 = 885 lbf
Figure 7-10
Shaft layout for Ex. 7-2. Dimensions in inches.
7.50
I
Gear 4
d₂ = 2.7 in
8.50
J
9.50
9.75
Bearing B
D₁ D₂
10.25
10.75
11.25
11.50
K L M B N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4000e28a-5cf8-47ab-bb9c-d9b564c038d2%2F667c69da-19f4-40e0-a3b8-21ba8e2d26dd%2Fbwko86c_processed.png&w=3840&q=75)
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