Mechanics of materials-homework

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Discussion Overview

The discussion revolves around a homework problem related to the mechanics of materials, specifically focusing on determining the maximum axial force that can be applied to a thrust bearing without exceeding a specified shear stress limit. Participants explore the application of free body diagrams (FBDs) and the relationship between shear forces and axial forces in this context.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant presents a problem statement involving a thrust bearing and the need to calculate the maximum axial force while adhering to a shear stress limit of 170 MPa.
  • Participants discuss the application of free body diagrams and the summation of forces, with one participant expressing confusion over whether the shear forces should equal the maximum axial force.
  • Another participant suggests that the free body diagram should include the shaft and collar, questioning the exclusion of the surfaces where shear occurs.
  • There is a mention of the normal force exerted by the collar as a reaction to the applied thrust force.
  • Participants note that the shear areas for the collar and thrust bearing are different, which affects the maximum allowable axial force.

Areas of Agreement / Disagreement

Participants generally agree on the need to consider both the collar and the shaft in the free body diagram, but there is some confusion regarding the relationship between the shear forces and the maximum axial force. The discussion remains unresolved regarding the correct approach to calculating the forces involved.

Contextual Notes

Participants express uncertainty about the necessity of including certain forces in their diagrams and the implications of different shear areas on the calculations. There are unresolved questions about the correct interpretation of the problem statement and the application of shear stress limits.

Hellohi
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Homework Statement



1–80. The thrust bearing consists of a circular collar A fixed to the shaft B.Determine the maximum axial force P that can be applied to the shaft so that it does not cause the shear stress along a cylindrical surface a or b to exceed an allowable shear stress of 170 MPa.

upload_2016-2-6_10-10-50.png
[/B]

Homework Equations



T=V/A or T = P/A[/B]

The Attempt at a Solution


This is how I thought I would draw my FBD

upload_2016-2-6_10-10-28.png


therefore I thought that if I did the summation of all forces in the x direction, P = Va+Vb
However, the solution takes it individually, like this:

T = P/A for a and T = P/A for b and calculates each P. This is confusnig me because, shouldn't the two V (shear forces) equal to the Maximum axial force?

thanks for any help, Id really like to understand this.
 

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I forgot to mention that for my FBD I did two cuts just so I can have a and b in there but I believed that we didnt need the rest.

I don't want any answers I just need some help with this, thank you!
 
Hellohi said:

Homework Statement



1–80. The thrust bearing consists of a circular collar A fixed to the shaft B.Determine the maximum axial force P that can be applied to the shaft so that it does not cause the shear stress along a cylindrical surface a or b to exceed an allowable shear stress of 170 MPa.

View attachment 95393[/B]

Homework Equations



T=V/A or T = P/A[/B]

The Attempt at a Solution


This is how I thought I would draw my FBD

View attachment 95392

therefore I thought that if I did the summation of all forces in the x direction, P = Va+Vb
However, the solution takes it individually, like this:

T = P/A for a and T = P/A for b and calculates each P. This is confusnig me because, shouldn't the two V (shear forces) equal to the Maximum axial force?

thanks for any help, Id really like to understand this.

If you draw a free body diagram of the shaft and the collar attached to it, how many forces will this diagram show? Which is the applied force and which is the reaction?
 
Do you mean just of the shaft and collar excluding the a and b surfaces?
 
Hellohi said:
Do you mean just of the shaft and collar excluding the a and b surfaces?
The collar is rigidly attached to the shaft, so you can't exclude it.

You have a thrust P applied to one end of the shaft. What keeps the shaft from accelerating in the direction opposite of P?
 
Oh! It should be the normal force correct?
 
the normal force that A exerts
 
Hellohi said:
the normal force that A exerts
Correct.

The shear area for the collar and the shear area for the thrust bearing are two different values. One of these surface areas will limit how large P can be, subject to the shear stress limit.
 
Thank you!
 

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