What is the relationship between normal and shear forces in structural analysis?

[savva]

Homework Statement

Given in uploaded file View attachment Q8.37.pdf

Homework Equations

σallow=$\frac{P}{A}$
τallow=$\frac{V}{A}$

The Attempt at a Solution

Given in uploaded file View attachment Q8.37 WORKING.pdf

Answers are d=16mm, h=10mm
I tried using methods used in previous questions but it didn't work out for me here, if anyone could give a hand, would be greatly appreciated.

I would also like to clarify a couple of other things related to the theory that I'm not sure about.
- I'm not sure what the relationship is between normal force (P) and shear force (V), particularly if given a normal force (P) for example and the question asks to find shear stress. Would Shear force (V) = P/2. I have basically used this principle and it has been generally successful but I am not sure if I'm getting answers correct because double shear applies.

-Secondly, I was doing a question that involved a couple of beams that had pin-joints on each side. Subsequently, I found the external force applied on each pin joint. I have attached a file and drawn an arrow on the diagram. I would like to verify if the arrow acting on the member is a normal force. Because that's what I assumed and when solving the normal stress it gave me the correct answer. The attachment of the problem is below
View attachment Q8.44.pdf

 

[PhanthomJay]

Homework Statement

Given in uploaded file View attachment 47970

Homework Equations

σallow=$\frac{P}{A}$
τallow=$\frac{V}{A}$

The Attempt at a Solution

Given in uploaded file View attachment 47971

Answers are d=16mm, h=10mm
I tried using methods used in previous questions but it didn't work out for me here, if anyone could give a hand, would be greatly appreciated.

The area of a circle is pi d^2/4. You forgot the 4. Otherwise your calcs look good for tensile stress in the rod and 'punching' shear stress in the supporting material.

I would also like to clarify a couple of other things related to the theory that I'm not sure about.
- I'm not sure what the relationship is between normal force (P) and shear force (V), particularly if given a normal force (P) for example and the question asks to find shear stress. Would Shear force (V) = P/2. I have basically used this principle and it has been generally successful but I am not sure if I'm getting answers correct because double shear applies.

Well, as in your example at the eye, 25 kN vert load is 12.5 kN shear load in the curved rod either side of the load (double shear).

-Secondly, I was doing a question that involved a couple of beams that had pin-joints on each side. Subsequently, I found the external force applied on each pin joint. I have attached a file and drawn an arrow on the diagram. I would like to verify if the arrow acting on the member is a normal force. Because that's what I assumed and when solving the normal stress it gave me the correct answer. The attachment of the problem is below
View attachment 47972

Yes it is the normal axial force in the member, causing shear stress in the bolt (double shear). At the left support, however, you have both axial and shear forces in the member. Their resultant is the shear force on the pin...single shear.