# Fracture point formula?

1. Mar 13, 2009

### peleus

Hi all,

I'm a 1st year (first 2 weeks) engineering student, with a quick question in regards to fracture points of materials.

We're currently going through the elastic modulus and the deflection formula, which is pretty handy and I think I've got a decent (basic) grasp on it now.

Thinking though, it's all well and good seeing my material would deflect 100mm over the 400mm span, but obviously it would have snapped well before that. I'm assuming that the deflection forumla has no way of knowing this point.

My question is then, how do I determine the point my material is going to fracture, to make sure I'm not trying to deflect it to far?

(Full story - Balsa wood beam, spanning 400mm using minimum of materials, has to hold 2.5kg. Must deflect between 1 - 6.5mm. I've worked out it will deflect 5.5 mm but I don't know if it would have snapped beforehand).

Cheers.

2. Mar 13, 2009

### ank_gl

The section will snap at the point where the local stresses exceed the ultimate tensile stress value(in case bending moment is applied).
Are you familiar with an equation relating the stress to applied moment or force & geometry of the cross section?

More practically speaking, it may snap at the points of high local stress concentration, cropping up due to some notch, crack, shoulder etc. Nonetheless, that point can be calculated accurately.

Last edited: Mar 13, 2009
3. Mar 13, 2009

### peleus

Two weeks into uni I'm smart enough to know I know nothing :)

Formula's I know are things such as

Strain = (l -l0) / l0

Deflection formula

Can calculate the second moment of area of it.

Can probably look up information about the material for other things (such as tensile strength etc)

That's about it, what else do I need to learn, or can you point me in the direction of some reading?

Cheers.

4. Mar 13, 2009

### PhanthomJay

What did you use for your deflection formula? The equations you listed are for axial load only (tension or compression along the longitudinal beam axis). You are intersted in bending stresses and deflection, as ank gl has noted above. Are you familiar with the bending stresses caused by bending moments in the beam?

5. Mar 14, 2009

### ank_gl

peleus, if its an activity, start breaking a few beams, run through some tests & estimate the relations between the geometry, material & stress(try to include applied moment or torque).

Practically speaking, deflection isn't generally a design parameter for beams, force is(it is so, for example, in case of springs, but that too, indirectly). I mean, you don't design a beam to deflect 3 mm at the end, but to take 5000N at the end. You have your requirements, 2.5 kgs, beam span = 400mm, material properties known, location of load known(i assume it is), bending moments along the length can be calculated, your design objective is to minimize the material, maximum stress at any X section = Moment / section modulus, here you have to play with the section modulus to minimize the volume of the material used.

You can also go for variable cross section along the length to save weight, but that depends upon the manufacturing process &  you are ready to put in

6. Mar 29, 2009

### peleus

Hey all,

Back looking at this problem again.

I've developed it a little further, and now I have the maximum stress being 67.44 and the maximum bending moment of 2452.5.

It's two parallel beams 1cm apart taking a force of 24.5N in the centre of a 400mm span. Total second moment of area is 2662mm^4. Youngs modulus is 4000MPa.

Can anyone tell me if this beam will fail? Unfortunately testing isn't an option.

7. Mar 29, 2009

### nvn

peleus: (1) What are the current cross-sectional dimensions of your beam? (2) Do you want to load this beam almost to the point of rupture, with no factor of safety? (3) What bending ultimate strength (Sbu) are you using for this material? Isn't Sbu = 21.60 MPa for balsa? Or do you have a different value for the material bending strength? (4) I thought E = 3400 MPa for balsa. Is your E value fairly accurate? (5) What are the units on the numbers you listed? By the way, there should always be a space between the numeric value and its following unit symbol. See international standard for writing units; i.e., ISO 31-0.

8. Mar 29, 2009

### peleus

Hi NVN, thank's for your response.

1) The current cross sectional dimensions are 25 mm (h) x 1.5 mm (w),
2) I want to load it almost to the point of rupture, or more importaintly, know HOW to figure out the point of rupture.
3) I have no idea, I haven't got access to material to test or find out, even if I knew how to find that out :) I would have to use a literary figure.
4) It's the result of student experementation of a class, so I'd say it's wildley inaccurate :) However it's the value we've decided to use as it was the average of results. We are also aiming for the mid point deflection criteria (has to deflect between 1.5 and 6mm) so we can be a little above / over with it.
5) I appologise but I don't know. It's the result of Stressmax = Maximum moment of bending * height/ (2 * Second moment of area). Maximum moment of bending is Max = Load * Span / 4.

Height = 25mm
Span = 400mm
SMOA = 1953 mm^4

Sorry in the current configuration the stress is actually 15.696 Units, not the value I listed previous. Maximum bending moment is 2452.

If you can tell me how to figure out if these units are Pa, MPa or what it would be greatly appreciated.

Again more importaintly is I have no idea what I'm ment to be comparing. I'm more interested in the PROCESS than the result. What value am I comparing it to? Is it a simple comparision to the bending ultimate strength? Do I need to factor this SBu into a formula?

Again I just don't know the process of HOW I do it, rather than if this particular configuration would break or not.

9. Mar 29, 2009

### nvn

The value I have for balsa bending ultimate strength is Sbu = 21.60 MPa, but it's better if you pretend it is 19.63 MPa. Let's call your beam width b. If you are using just a rectangular cross section, I would set h such that it does not exceed h = 1.50*b, or I would make the cross section square (h = b), to try to avoid stability problems. Find in your text book the formula for deflection of a simply-supported beam, then use it to compute the required cross-sectional dimensions to give a deflection of, say, delta = 5.6 mm. Afterwards, compute the bending stress (your formulas in post 8 are correct), and you will see that the stress does not exceed Sbu; therefore it will not rupture.

The units of your listed moment and stress are N*mm and MPa, respectively. 1 MPa = 1 N/mm^2. Just plug the units of each parameter into your stress formula, and you will see it is (N*mm)(mm)/mm^4 = N/mm^2 = MPa. As mentioned in item 5 in post 7, there should always be a space between the numeric value and its following unit symbol. E.g., 400 mm, not 400mm.