curved beam

[logistic_guy]

here is the question

The curved beam is subjected to a bending moment of \(\displaystyle M = 85\) N \(\displaystyle \cdot\) m as shown. Determine the stress at points \(\displaystyle A\) and \(\displaystyle B\) and show the stress on a volume element located at these points.




my attemb
i'll start with the area of the cross section
\(\displaystyle 20*100 + 15*150 + 20*100 = 2000 + 2250 + 2000 = 4000 + 2250 = 6250\)
the stress at point \(\displaystyle A\)
\(\displaystyle \sigma_{A} = \frac{M(R - r_{A})}{Ar_{A}(\bar{r}-R)}\)
i've \(\displaystyle M\) and \(\displaystyle r_{A}\) and \(\displaystyle A\)
what is \(\displaystyle R\) and \(\displaystyle \bar{r}\)? how to find it?
i'm think \(\displaystyle \bar{r}\) is average radius. i'm not sure
is it corect to say \(\displaystyle \bar{r} = \frac{r_{A} + r_{B}}{2}\)?

 

[khansaheb]

here is the question

The curved beam is subjected to a bending moment of \(\displaystyle M = 85\) N \(\displaystyle \cdot\) m as shown. Determine the stress at points \(\displaystyle A\) and \(\displaystyle B\) and show the stress on a volume element located at these points.

View attachment 38885


my attemb
i'll start with the area of the cross section
\(\displaystyle 20*100 + 15*150 + 20*100 = 2000 + 2250 + 2000 = 4000 + 2250 = 6250\)
the stress at point \(\displaystyle A\)
\(\displaystyle \sigma_{A} = \frac{M(R - r_{A})}{Ar_{A}(\bar{r}-R)}\)
i've \(\displaystyle M\) and \(\displaystyle r_{A}\) and \(\displaystyle A\)
what is \(\displaystyle R\) and \(\displaystyle \bar{r}\)? how to find it?
i'm think \(\displaystyle \bar{r}\) is average radius. i'm not sure
is it corect to say \(\displaystyle \bar{r} = \frac{r_{A} + r_{B}}{2}\)?

Where did you find the equation of stress?
That is where you'll find the definition of \(\displaystyle \bar{r}\)

Look at the given sketch and analyze

 

[logistic_guy]

thank

Where did you find the equation of stress?

in wikideia under the section of curved beams

That is where you'll find the definition of \(\displaystyle \bar{r}\)

it don't explain anything about it

Look at the given sketch and analyze

i look but i can't figure its meaning
can you show me how to solve it from the given information? appreciate it

 

[khansaheb]

thank


in wikideia under the section of curved beams


it don't explain anything about it


i look but i can't figure its meaning
can you show me how to solve it from the given information? appreciate it

I added some extra features in the original drawing:

Here point of interest is P
Point O is center of the circular beam
rˉ is the distance OP

Now does it make more sense?

 

[logistic_guy]

thank very much khan

Now does it make more sense?

yes. i can calculate

\(\displaystyle \bar{r} = 400 + 20 + 75 = 495\)

what about \(\displaystyle R\)

i hope there's no calculus in this question

 

[khansaheb]

what about R\displaystyle RR

R = (r_A + r_B)/2

 

[logistic_guy]

R = (r_A + r_B)/2

so \(\displaystyle R = \frac{590 + 400}{2} = \frac{990}{2} = 495\)

this same as \(\displaystyle \bar{r}\)

\(\displaystyle \bar{r} - R = 495 - 495 = 0\)

it can't be

 

[Dr.Peterson]

in wikideia under the section of curved beams

Please give a link to your source. (Do you mean Wikipedia? What article? What language?)

 

[logistic_guy]

Please give a link to your source. (Do you mean Wikipedia? What article? What language?)

wikideia isn;t a link. it's something like a table contain formulas. you mean i take a picture of the formula? it's useless, there's no exlanation for the parameters

 

[Dr.Peterson]

wikideia isn;t a link. it's something like a table contain formulas. you mean i take a picture of the formula? it's useless, there's no exlanation for the parameters

Please make some attempt to tell us exactly where you found your formula.

If you do mean Wikipedia, it is a website that contains pages you can link to, like this; surely you know that. If you mean something else, then tell us more about it.

And any source for formulas will explain the meaning of the variables. A formula is nothing otherwise.

 

[logistic_guy]

Please make some attempt to tell us exactly where you found your formula.

If you do mean Wikipedia, it is a website that contains pages you can link to, like this; surely you know that. If you mean something else, then tell us more about it.

And any source for formulas will explain the meaning of the variables. A formula is nothing otherwise.

when i say it's useless and you don;t trust me it's mean the trust between the student and the teacher is lost
the teacher have doubts and the student have more doubts
my doubts is khan and you don't understnd curve beams because you don't understand and trust the formula i write

thank

 

[Dr.Peterson]

when i say it's useless and you don;t trust me it's mean the trust between the student and the teacher is lost
the teacher have doubts and the student have more doubts
my doubts is khan and you don't understnd curve beams because you don't understand and trust the formula i write

thank

Maybe a teacher knows when things are not useless, though the student thinks they are. The student needs to do what he's asked.

If you won't, then there's nothing more I can do.

By the way, I never said I know anything at all about stress problems, much less curved beams. I'm just trying to help you provide the necessary information (or discover it for yourself by looking in the right places), because I know that where there is a formula, there is a definition of terms. If your source, whatever it is, doesn't, then just find a better source.

 

[khansaheb]

this same as rˉ\displaystyle \bar{r}rˉ

No .... look at the drawing again carefully. How do you locate the point at which you need to calculate the stress?