Mechanics of materials-homework

[Hellohi]

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.

[/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

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.

 

[Hellohi]

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!

 

[SteamKing]

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?

 

[Hellohi]

Do you mean just of the shaft and collar excluding the a and b surfaces?

 

[SteamKing]

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?

 

[Hellohi]

Oh! It should be the normal force correct?

 

[Hellohi]

the normal force that A exerts

 

[SteamKing]

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.

 

[Hellohi]

Thank you!