How Do You Calculate Maximum Flexural Stress in a Cast Iron Pipe?

[samuelvil]

Homework Statement

so the question I got from my teacher is:
A cast iron pipe of external diameter 60mm and 10 mm thickness and 5 m long is supported at its ends. The pipe carries a point load of 100N at its centre. Calculate the maximun flexural stress induced?

Homework Equations

I think that the relevant eqn to be used should be
M/I=σ/y=ε/r

The Attempt at a Solution

I have the equation but don't really know how to solve it as I was not able to get any example...please help

 

[SteamKing]

How hard did you look?

If you are taking a structural analysis course, you should have a textbook or some notes. Did you do any work at all besides log onto PF?

 

[samuelvil]

yes I did, we don't use any specific textbook, and if you do have some references it will be welcome,it is the first time I use such websites. I tried to watch some videos on youtube, and tried to have some information on google, but the explanation are so vast that I am not able to find out how to apply it to the question I have. I don't want you to do all the work...I just want an advice or a website where I can understand how flexural stress is calculated.

 

[SteamKing]

For basic flexure theory, try this ref.:

http://www.freestudy.co.uk/d209/t2.pdf

If you don't know how to calculate the bending moment, more research will be required.

 

[rezeew]

I would first clarify any assumptions or missing information with the teacher or in the problem statement. Assuming the pipe is cylindrical and the load is applied at the center, I would use the following equation to calculate flexural stress:

σ = (M*c)/I

Where:
σ = flexural stress (Pa)
M = bending moment (Nm)
c = distance from neutral axis to the outermost fiber (m)
I = moment of inertia (m^4)

To find the bending moment, I would use the equation:

M = PL/4

Where:
P = point load (N)
L = length of pipe (m)

To calculate the distance from the neutral axis to the outermost fiber, I would use the equation:

c = d/2

Where:
d = external diameter of pipe (m)

To find the moment of inertia, I would use the equation for a solid cylindrical beam:

I = π*d^4/64

Where:
d = external diameter of pipe (m)

Plugging in the given values, I would get:

M = (100 N)(5 m)/4 = 125 Nm
c = (0.06 m)/2 = 0.03 m
I = (π*(0.06 m)^4)/64 = 1.415x10^-7 m^4

Substituting these values into the flexural stress equation, I would get:

σ = (125 Nm * 0.03 m)/(1.415x10^-7 m^4) = 2.64x10^10 Pa

Therefore, the maximum flexural stress induced in the cast iron pipe would be 2.64x10^10 Pa.