# Material shear and normal stress question

1. Oct 9, 2012

### Redoctober

1. The problem statement, all variables and given/known data

Everything needed is written in the question ( Open the attached image )
Nyhow the required is to find the value of P.

2. Relevant equations

$$Shear stress = \frac{ \Delta V }{\Delta A}$$ eq 1
$$normal stress = \frac{ \Delta N }{\Delta A}$$ eq 2

3. The attempt at a solution

For the coned part,

I know that

$$r = (h + 25)/1000 meters$$ so is substute in

$$A = 2 \pi r h$$ to get

$$A = 2 \pi \frac{(h^2 + 25h)}{1000}$$ therefore taking the derivative DA/DH give

$$dA = \frac{4 \pi h + 50 \pi}{1000} .dh$$ substute to derivative of eq 2 and then integrate wiith respect to h for the boundries 0 < h < 50*10^-3 m and then multiplying by sin (45) to get sum of vertical force.

For the cylindrical part,

Just multiply A = 2*pie*r*30*10^(-3) to shear stress to get the force.
suming up the two force should equal P. however i got it wrong :/ !

So any ideas of how to solve this beast ??

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