# How to calculate elastic modulus

1. Aug 10, 2015

### John54321

1. The problem statement, all variables and given/known data
I am struggling with a part of the question. Please see diagram in the attached.

Calculate the relevant Elastic Modulus and select the lightest suitable beam section assuming a maximum allowable bending stress of 120 Mpa ?

2. Relevant equations

3. The attempt at a solution

To find the stress
the formula is stress = force / area
Force = 140KN
Area = 10m x 10m =100m2
Therefore 100 / 100 = 1 KN/m2

To find the strain
The formula is: strain change in length / original length
Change in length = 10.1m - 10.0 = 0.1m
Original length = 10m
Therefore strain = 0.1 / 10 = 0.01m

young modulus = strain / stress
Using the values from the stress and strain above
Elastic modulus =
1 / 0.01 =100Kn/m2

Im not sure if these calcs are correct would be greatful of any help thanks

#### Attached Files:

• ###### Beam Diagram.jpg
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Last edited: Aug 10, 2015
2. Aug 10, 2015

### SteamKing

Staff Emeritus
You have provided only a portion of a much longer problem statement. PF Rules for the HW forums ask that you provide a complete statement of the problem, so that helpers have as much information to work with as possible.

The snippet of problem statement you provided along with the brief attempt at solution does not appear to make much sense, even with the attached diagram.

You state "Force = 140 KN". What force is this?

You have a calculation "Area = 10m x 10m = 100 m2" What area is this?

You state "Original length = 10m" Original length of what?

It doesn't appear that the attached diagram even goes with this problem.

3. Aug 10, 2015

### John54321

10m being the total length of the beam in diagram and 140 KN being the total load I have worked out Ra and Rb if these are needed Ra = 95KN Rb = 165KN

The full question is below for some reason it wouldn't allow me to upload the 2 files

Calculate the relevant elastic modulus and select the lightest suitable beam from the attached table 3.1 universal beams (based on Bs5950) assuming a maximum allowable bending stress of 120Mpa

#### Attached Files:

• ###### Beam selection.jpg
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4. Aug 10, 2015

### SteamKing

Staff Emeritus
What happened to the UDL of 12 kN/m?

{Edit: I see now. The load on the beam is not 140 kN. That's the sum of the concentrated loads. The load on the beam should be the sum of the concentrated loads and the UDL.}

The first part of this question doesn't make sense.

UB's are made from steel, so the elastic modulus of that material should already be known. What is unknown is the second moment of area I which will ensure that the maximum bending stress is below 120 MPa. That's what must be selected from the table of beam properties, with the further condition that the beam have the lowest total mass.

Is it possible that the question is asking you to determine the "elastic section modulus" of the beam?

You haven't provided any calculations for determining the maximum bending moment of this beam under the loading as shown.

Last edited: Aug 10, 2015
5. Aug 10, 2015

### John54321

Hi Steam King

In the attached is the maximum bending moment measured at Ra

#### Attached Files:

• ###### Max bend Moment.jpg
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6. Aug 10, 2015

### Staff: Mentor

Hi SteamKing,

You are giving the OP more credit for knowledge on beams than he deserves. The only thing he has demonstrated so far is his ability to determine the reaction forces.

John54321: Have you drawn any shear and moment diagrams? Have you calculated the shear force and the bending moment distribution in the various sections of the beam. Do you know how the bending moment distribution is related to the shear force distribution? Once you know the bending moment distribution, you will be much closer to having a solution to your problem.

Chet

7. Aug 10, 2015

### John54321

I have the shear force diagram in the attached I hope is correct? I have 4 parts left to answer for this question then the assignment is finished im just struggling with these last few bits

#### Attached Files:

• ###### Shear force diagram.jpg
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8. Aug 10, 2015

### SteamKing

Staff Emeritus
I appreciate the comment Chet. I'm just trying to make sense out of a confusing and incomplete problem statement which was originally posted.

9. Aug 10, 2015

### SteamKing

Staff Emeritus
If you have calculated the shear force diagram for this beam, then you should be able to calculate the bending moment diagram as well.

If you can't post the diagrams, then post the values for SF and BM at different locations along the beam.

10. Aug 10, 2015

### John54321

Shear force diagram in attached

#### Attached Files:

• ###### Shear force diagram.jpg
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11. Aug 10, 2015

### John54321

Bending moments in attached again not sure if im correct !!

#### Attached Files:

• ###### Bending moment diagram.jpg
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12. Aug 10, 2015

### SteamKing

Staff Emeritus
The shear forces and the bending moments appear to be correct.

Now, use this information to solve the rest of the problem.

13. Aug 10, 2015

### John54321

That's good then. That's the problem im struggling on how to work out that question and 3 other parts ?

14. Aug 10, 2015

### SteamKing

Staff Emeritus

Given the bending moment, how do you calculate the bending stress in the beam?

15. Aug 10, 2015

### John54321

would this be the flexure formula ?

16. Aug 10, 2015

### SteamKing

Staff Emeritus
Yes.

17. Aug 10, 2015

### John54321

So the formula I need to use is 0 = m y / l

or is this wrong ?

bending moment maximum = 3.75m

to find modulus = strain/ stress

As this is a self study course its hard going thanks for helping.

18. Aug 10, 2015

### SteamKing

Staff Emeritus
Ah, another piece of the puzzle falls into place.

The bending stress σ = M y / I. It is also written as σ = M / SM, where SM is called the elastic section modulus of the beam, which I think you are confusing with the elastic modulus of the material, which is denoted by E. E does not figure into the calculation of the bending stress of the beam.

Note, SM = I / y, where I is the moment of inertia (or second moment of area) of the beam cross section, and y is the distance to the outer fiber of the beam, measured from the neutral axis.

You have determined the maximum bending moment from your calculations of the beam.

You are given a maximum bending stress σ = 120 MPa.

What you want to do is to calculate the SM of the beam such that the bending stress is less than this maximum stress.

Once you have determined the minimum SM of the beam which produces bending stresses less than 120 MPa, then you can use the table of UB properties to find which section can be used to make the beam which has the least total mass.

19. Aug 10, 2015

### John54321

Sorry what do you mean by the outer fibre of the beam ? this has to be explained in laymans terms I do apologise.

20. Aug 10, 2015

### SteamKing

Staff Emeritus
That's what you should have learned when studying about calculating the bending stress in a beam.

The outer fiber is that part of the beam which is furthest from the neutral axis. The bending stress is greater at locations further away from the neutral axis, as seen here:

For the UB sections, y = d/2.