Find the reaction forces of shaft AB

In summary: When you open your hand, the moment goes away and the object stays in the same place (unless you keep applying a moment). Similarly, when you have two moments, there is a resultant moment that combines the two individual moments.
  • #1
LT72884
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Homework Statement
find reaction forces of shaft AB
Relevant Equations
NA
1610405039013.png

Given: r1 = 0.75 r2 = 1.5
Ok, i have done statics and dynamics, but this book does things differently than the way i accomplished it in the previous classes. This is for mechanical engineering design class.

Here is my question. They take sum of the moments along X, which goes through the center of the rod, but i can't seem to see where they are taking the moment AT? Also where does (0.75) came from? I know its the radius of the gear on the shaft, but why are they using it for F? That is not even in the x direction. i do not see why and where they took the moment at.

thanks:)
 
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  • #2
spoto2 said:
Determine the reactions of simply supported, overhanging and cantilever beams; Calculate and draw the shearing force and bending moment diagrams of beams ... would be subjected to a torque, it would be called and treated as a shaft.
this doesn't seem to help me figure out where they are taking the moment at in the picture. They say the sum of the moments about x, but i don't see x and i don't see why they are bringing in the gear dimensions to anser the question
 
  • #3
LT72884 said:
this doesn't seem to help me figure out where they are taking the moment at in the picture. They say the sum of the moments about x, but i don't see x and i don't see why they are bringing in the gear dimensions to anser the question
Since they show the directions of axes y and z, we can assume that each axis x is colineal with the rotational axis of each of the shafts.

The book is trying to calculate the force on the contacting teeth of the gears from the value of the input moment trying to twist the input shaft, which acts about its axis.
That equation shows the balance (Mx=0) between reactive torque of F times r1 and input torque.

The problem is that something is not correct in the book, because shaft AB (linked to gear of r1=0.75 inch) is represented in figure c rather than d.

The torque exerted by each gear on its shaft is proportional to its radius (r1 for input shaft and r2 for output shaft).
The output torque should be greater than the input torque in the same proportion in which r1 and r2 are different (as F is the same for both).
 
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  • #4
im glad I am not the only one who noticed the issue with the book with the typo.

I thought when we took a moment, it was force(distance) why is it not force time the distance from the gear to the end of the shaft? why is it force time the distance of the gear, IE r1?

thanks
 
  • #5
LT72884 said:
... I thought when we took a moment, it was force(distance) why is it not force time the distance from the gear to the end of the shaft?
Please, note that you have force and distance(s) acting on the three planes.
Force F is trying to bend the shaft and induces both reaction forces at the bearings.
Same for force N.
As force F is the only acting off the axis of rotation of the shaft, it also induces a torsional moment.

Using force times distance, you can calculate any of the two bending moments and the torsional moment.
Each of those moments acts about a different axis of rotation.
 
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  • #6
The shafts are spinning at constant speeds so the sum of moments about their longitudinal axes must be =0 (no acceleration). This is stated in the problem. Summing the moments along this axis means accounting for all forces and moments that would act in such a direction as to cause the shaft to rotate (or prevent it from rotating - if counteracting another moment). Looking at shaft AB, there are two moments acting on it (along x-axis): (240in-lb) and (-F*r1) with r1=0.75 given. These must sum to 0.

You might need to familiarize yourself with how moments are specified. For example, with your fist closed and thumb up, a moment in the direction of your thumb corresponds to a rotation following the curl of your fingers.
 

Related to Find the reaction forces of shaft AB

1. What is the purpose of finding the reaction forces of shaft AB?

Finding the reaction forces of shaft AB is important in understanding the overall stability and equilibrium of the shaft. It allows us to determine how the shaft will react to external forces and loads, and helps in designing a safe and efficient structure.

2. How do you calculate the reaction forces of shaft AB?

The reaction forces of shaft AB can be calculated using the principles of statics. By taking into account the external forces and moments acting on the shaft, we can use equations of equilibrium to solve for the reaction forces at the supports.

3. What factors can affect the reaction forces of shaft AB?

The reaction forces of shaft AB can be influenced by various factors such as the magnitude and direction of external loads, the geometry and material properties of the shaft, and the type and location of supports. These factors must be carefully considered in order to accurately calculate the reaction forces.

4. Why is it important to consider the reaction forces in shaft AB design?

The reaction forces play a critical role in the design of shaft AB as they directly affect the structural integrity and stability of the shaft. Neglecting to consider these forces can lead to structural failure and potential safety hazards.

5. Can the reaction forces of shaft AB be negative?

Yes, the reaction forces of shaft AB can be negative if the direction of the external loads and the orientation of the supports result in a net force or moment in the opposite direction of the applied load. This can happen when the shaft is in an unstable state or when the supports are not properly designed.

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