# Different measured strain in beam experiencing pure bending

I have a beam experiencing a pure bending moment. The setup is similar to this image from these lecture notes (with different values).

Using the flexure formula, we can determine that the stress (and thus the strain) at any point along the top of the beam between C and D should be the same: $$\sigma_{max} = \frac{Mc}{I}$$ where $M$ is the moment, $c$ is the distance from the neutral axis, and $I$ is the area moment of inertia.

However, I've a couple of strain gauges along the top of the beam measuring strain in the axial direction. These gauges are reading different values at different locations between C and D.

Is this expected? Is it a limitation of the model or are the gauges malfunctioning (or laid up improperly)?

• besides other factors already mentioned , the experiment is sensitive to the precise positioning of the load/support points. Sep 28, 2016 at 0:24

What variation in value are you experiencing? Theoretically, the curvature or strain of the beam should be constant in between load points. Minor variation could be expected, but major probably indicates a problem. Assuming all strain gauges are calibrated thermo corrected etc then it could be a faulty strain gauge or poor adhesive/preparation.

• Thanks for the answer. The max applied force was ~20lb and difference in strain gauge readings in the area between the supports varied from 30-70µstrain. The gauges were balanced before the experiment, but the layup was performed eons ago by someone else. It looks like model inaccuracies might not be enough to explain the discrepancy, and that it might be worth it to redo the gauges :( Sep 28, 2016 at 23:22

If the loads you apply are too big, you can get local crushing of the beam, or plastic deformation of the beam at the loading points instead of uniform elastic bending.

But without more details of your experimental setup, it's a complete guess whether this is actually the cause.

A basic check is whether the beam returns to its original state when the loads are removed - i.e. it is still straight, and the gauges all read zero.

(Of course if this is a lab experiment and some previous student had permanently bent the beam before you used it, you won't get the expected results!)

• Thanks for the response. We're dealing with small enough forces to keep us well in the elastic region for our material. It could always be past students...now that's an error source I didn't consider! Sep 28, 2016 at 23:11

I would add to the above answers:

The beam could have sustained strain hardening from the manufacturing, cutting, preparation or any strain history that has left local changes in its elasticity modulus even if it has been straightened and looks within acceptable tolerances.

• That's a good theory. The flexure formula assumes homogeneity and isotropy, so doesn't account for local property changes. Sep 28, 2016 at 23:13

If the beam had previously been overloaded to point of plastic deformation then the strain readings will be incorrect. There is also the issue of repeated experiments causing permanent strain hardening in each successive iteration of the experiment. It is always worthwhile to understand why the experiment may not have modelled predictive calculations and discuss them in the assignment paper. Whilst this may not be the expected results and explain why is worth more to an examiner than just exact results because it demonstrates your knowledge and understanding of the issues at hand.