# Help with a three point bending test

1. Nov 4, 2015

### musacci

Hello everyone,

I am trying to evaluate the spring constant of a coaxial polymer cylindrical fiber. This fiber has a stiff core and a more soft sheath.

I know the geometry of the system and I know the Young's moduli of both components. I can find separate models for the core or for the sheath where using the area moment of inertia I can extract the spring constant. My problem is that I don't know how to extract the spring constant of the whole object.

I need this to have a theoretical value to compare it with the results of three point bending experiments in which I directly measure the spring constant and extract the bending modulus of the whole structure.

Any help would be great!

2. Nov 4, 2015

### JBA

One trial and error method is to individually measure the deflection of each component using the same trial load. Then iterate that load by transferring increments of the load on the largest deflecting element to the stiffer element until their deflections match. At that point you will then be able to calculate their composite spring constant using the that original load and new matching deflection value.

3. Nov 4, 2015

### musacci

thank you for your suggestion JBA, that would indeed be a good strategy, but unfortunately I cannot perform such experiment due to the impossibility of separating the sheath and core of my rods.

I thought of the possibility of calculating an equivalent sheath thickness as if it was made of the same material as the core. That would give me an equivalent radius which I could use in my data analysis. This is similar to what is done to study composite beams of different materials.

I'm not sure if I am allowed to link other websites but here is an explanation of the equivalent area method: http://web.mst.edu/~mecmovie/chap08/m08_16_steel_alum.swf

4. Nov 4, 2015

### JBA

What I am proposing is a calculation using a trial load value and calculated deflections, not an actual load test.

I can understand the alternative method for a rectangular bar but I am not sure how it could be duplicated for your cylindrical composite.

5. Nov 5, 2015

### JBA

One solution might be to use the ratio of the material elastic modulus' as an equalizer to adjust the wall thickness of the sleeve to an equivalent added diameter of your core.

6. Nov 9, 2015

### musacci

Hi JBA,

I thought of calculating an equivalent diameter for the core. In order to estimate this correctly I would need to calculate the spring constant of the softer material sheath and extrapolate the radius of a sheath of the harder material but with the same spring constant. Is this correct?

7. Nov 9, 2015

### Nidum

Is the core bonded to the sheath or can core slide relative to sheath - makes big difference to calculation .

8. Nov 9, 2015

### musacci

Hi Nidum,

the core and sheath are bonded together

9. Nov 9, 2015

### JBA

The elastic modulus ratio is the equavlent of the spring constant ratio.