# Bending of beams

Help needed In my course paperwork I cant seem to find the relevant equations needed to complete the following in if someone could help point me in the right direction of equations needed I would be very grateful

1. Homework Statement

A rectangular hollow beam length of 3m is simply supported at its ends it has width of 10 mm and depth of 200 mm the beam is subjected to a uniformly disturbed load of 2 tonnes/m and a point load of 200N at its centre position
I) determine the maximum stress due to bending (occurring at the centre point)
ii) determine the value of the radius of the curvature of the neutral layer
iii) the factor of safety if the maximum allowable stress of the material is 100MPa

## Answers and Replies

SteamKing
Staff Emeritus
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If the beam is hollow, what are the dimensions of the interior portion? That's kinda necessary to work this problem.

Also, I can't believe that you have allowed your notes to become so disorganized that you can't write down anything pertaining to solving this problem. No textbook? Google? Bueller?

SteamKing thanks for your reply this is the problem all the info on dimensions is as above this is why I am struggling with this I do have text books etc but cannot find anything relevant to solve the above is this possible with the above information?

SteamKing
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Science Advisor
Homework Helper
SteamKing thanks for your reply this is the problem all the info on dimensions is as above this is why I am struggling with this I do have text books etc but cannot find anything relevant to solve the above is this possible with the above information?

If the beam is hollow and the internal dimensions are not provided, then you're stuck. A clarification from the instructor of the course is in order.

It's not clear what text books you have, but searching for 'bending of beams', 'bending stress', or 'radius of curvature' would be a good place to start, if you have a text book on strength of materials. Even if your notes and books have been eaten by zombies, you can Google these terms and come up with something.

thanks very much I have been told to treat it as a solid so from that do I first calculate the second moment area then (stress/y=M/I)?

SteamKing
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thanks very much I have been told to treat it as a solid so from that do I first calculate the second moment area then (stress/y=M/I)?
Yes, but only after you have determined the bending moment at the center of the beam.

how do I calculate the bending moment in the centre of the beam?

Can anyone help I am struggling as the point load in the centre of the beam keeps throwing me can any one help point me in the right direction

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
Have you calculated the support reactions for the beam? Can you draw the shear force curve for this beam?

Simply saying 'I don't know.' or 'I lost all of my notes.' is not sufficient to receive help at PF. You must show some effort, either at working your problem directly or at least researching how to solve it.

You were given some search terms in Post #4. Did you try them?

Chestermiller
Mentor
hi andrewh21.

You have so far shown no effort on this problem. SteamKing has been trying to elicit some response from you, but none has been forthcoming, other than "I don't have a clue." This is unacceptable. We are not here to do your homework for you or to teach you the entire subject. I have given you a 1 point warning.

The least you could have done was to articulate how you would begin to approach a problem like this. Tell us your thinking. What do you think is happening physically?

At one point, you indicated that you could handle the case of a distributed load, but not the point load case. OK. Tell us what you would do if you had a distributed load.

What text book are you using?

I am about to close this thread if I don't see some effort on your part.

Chet

Chestermiller
Mentor
As a first step, calculate the reaction forces at the supports. That is just a statics problem, and has nothing to do with beam bending. What do you get for the reaction forces?

Chet

Ra=Rb
Ra*3m=200tonnes/m*3*1.5
=900Tonnes/m
from which Ra=900/3=300 tonnes/m =Rb

anywhere near?

SteamKing
Staff Emeritus
Science Advisor
Homework Helper

## Homework Statement

A rectangular hollow beam length of 3m is simply supported at its ends [and] ... is subjected to a uniformly disturbed load of 2 tonnes/m and a point load of 200N at its centre position

Ra=Rb
Ra*3m=200tonnes/m*3*1.5
=900Tonnes/m
from which Ra=900/3=300 tonnes/m =Rb

anywhere near?

Where do you get 200 tonnes and 300 tonnes from?

Chestermiller
Mentor
What is the total of the distributed and the point load on the beam?

Chet

sorry should have been
Ra=Rb
Ra*3m=19613nm/m*3*1.5
=88258.5nm/m
from which Ra=88258.5/3=29419.5Nm/m =Rb

any better?

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
sorry should have been
Ra=Rb
Ra*3m=19613nm/m*3*1.5
=88258.5nm/m
from which Ra=88258.5/3=29419.5Nm/m =Rb

any better?

And what is a N-m/m ?

Nm

Chestermiller
Mentor
Nm
Since when are the units of force Nm?

Chet

this is where I am falling down odiously I have UDL of 2 tonnes/m but also this point load I have viewed dozens of worked examples trying to find something similar but nothing I have looked at contains a UDL and a point load it seems to be one or the other any advice on where to look etc would be greatly appreciated

Andrew

Chestermiller
Mentor
this is where I am falling down odiously I have UDL of 2 tonnes/m but also this point load I have viewed dozens of worked examples trying to find something similar but nothing I have looked at contains a UDL and a point load it seems to be one or the other any advice on where to look etc would be greatly appreciated

Andrew
What if the distributed load wasn't there? Would you then be able to determine the reaction forces at the two ends resulting from the point load? This is a simple freshman physics problem involving static equilibrium.

Chet

so Ra=Rb
Ra*3=200N*3*1.5=
=900N
from which Ra=900/3=300N=Rb

Is this more like it?

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
so Ra=Rb
Ra*3=200N*3*1.5=
=900N
from which Ra=900/3=300N=Rb

Is this more like it?

If you have a 200 N point load in the center of the beam, how can the sum of the reactions be greater than the magnitude of the load?

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
If you have units of newtons multiplied by meters, making N-m, then dividing by meters gives what units? [N*m/m = ?]

guys thanks for bearing with me I know I am a total newbie
W=2*3=6
W= 6 tones
so the reaction forces at each support would be 3 tonnes

an for the point load
W=200N
as this is central the reaction forces at the supports would be 100N
assuming this is correct and it is as simple as combining both of the forces would I be correct in assuming that
the reaction forces at each support would be 29.15KN

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
guys thanks for bearing with me I know I am a total newbie
W=2*3=6
W= 6 tones
so the reaction forces at each support would be 3 tonnes

an for the point load
W=200N
as this is central the reaction forces at the supports would be 100N
assuming this is correct and it is as simple as combining both of the forces would I be correct in assuming that
the reaction forces at each support would be 29.15KN

Yes.