Flexural Modulus of a Test Specimen (3-point bending)

[BenjineerM]

Hello everyone,

I need to work out the flexural modulus (E_f) of a test specimen that is subjected to a 3-point bend test. I know that: E_f = L³m/4bd³. I have:

Support Span(L)= 0.1m
width(b)= 0.01m
depth(d) = 0.01m
Max normal stress σ_f= 98.1 MPa
Strain (ε_f) = 0.0525
Max force (applied to the center of the beam) = 656 N
Max deflection = 0.0089m
Specimen length = 0.14m

My question is, how do I work out 'm'? m is defined as "The gradient (i.e., slope) of the initial straight-line portion of the load deflection"

Thanks in advance.

 

[Achy47]

To work out the value of 'm' in your equation, you will need to plot a load-deflection curve for your test specimen. This curve will show the relationship between the applied load and the resulting deflection of the specimen. The initial straight-line portion of this curve will represent the elastic region of the material, where Hooke's Law applies.

To determine the slope of this initial straight-line portion, you can choose two points on the curve and calculate the rise over the run (change in load over change in deflection). The value of 'm' will be the average of these slopes. Alternatively, you can use a graphing program to automatically calculate the slope for you.

Once you have the value of 'm', you can plug it into your equation (Ef = L3m/4bd3) along with the other given values to calculate the flexural modulus of your test specimen. I hope this helps. Good luck with your experiment!