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- Thread starter randall016
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In summary: No, I think you can just do it once and then use the calculated deflection for the rest of the application.

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At the same time, at very low loads or deflections, the accuracy of the associated load and deflection measurement instrumentation/systems and the possible external effects of operating temperature variations upon the beam material and/or instrumentation accuracy must also be taken into consideration.

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I think a deflection of 2% of the length is probably more than you should look for.randall016 said:

In structural applications, a max. deflection of L/360 is generally the limit for most beams. This works out to about 0.28% L, rather than 2% L.

With such large deflections in such simple beam geometries, I would also be concerned that the bending stress in the beam has exceeded the yield stress of the material, and a permanent set has been created.

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randall016,

(Edited post)

What is your calculated maximum stress for the beam at this deflection?

I have run the calculation in my US units for your 10% deflection and seen that the stress is about 46,000 psi, which, if correct, is acceptable if you are using spring steel or alloy. So 2% is very safe and your 10% is acceptable for these kinds of applications as opposed to civil structural standards.

(Edited post)

What is your calculated maximum stress for the beam at this deflection?

I have run the calculation in my US units for your 10% deflection and seen that the stress is about 46,000 psi, which, if correct, is acceptable if you are using spring steel or alloy. So 2% is very safe and your 10% is acceptable for these kinds of applications as opposed to civil structural standards.

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I guess my question is to see if it is appropriate to use euler-bernoulli beam theory when it assumes small deflections or should I use another beam theory such as Timoshenko that would account for shear? I would assume that the strain would end up being less using Timoshenko beam theory so Euler-Bernoulli may be a more conservative estimate of the strain.

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Assuming you are using foil adhesive mounted gages, I will leave all of the factors related to gage factor, gain and instrumentation accuracy to you; but, just to be safe, I do want to mention two items, of which you are most likely already aware. One is that preflexing is to a significant strain to address adhesive bonding relaxation and slip is important for these applications; and the second, particularly critical for your low strain application is accurate temperature compensation either by foil to base material thermal coefficient matching or by including a static (unloaded) gage mount in your measuring circuit.

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The preflexing is only required for initial "break in".

After break in you should run a repeatability cycling test to check the percent of error at your required deflection. The amount of scatter during that test will tell you whether or not the gage output and your measurement system at that deflection is repeatable and within your % of error requirements.

When I was working with foil strain gages, even after break in there was a "rule of thumb" minimum percent of strain for reliable gage readings; unfortunately, I no longer remember what that value was.

I recommend you contact your strain gage manufacturer/supplier for any technical documents or input they have regarding their gage applications.

Also, for a reference on all elements of foil strain gage application see:

http://www.omega.com/techref/pdf/StrainGage_Measurement.pdf

After break in you should run a repeatability cycling test to check the percent of error at your required deflection. The amount of scatter during that test will tell you whether or not the gage output and your measurement system at that deflection is repeatable and within your % of error requirements.

When I was working with foil strain gages, even after break in there was a "rule of thumb" minimum percent of strain for reliable gage readings; unfortunately, I no longer remember what that value was.

I recommend you contact your strain gage manufacturer/supplier for any technical documents or input they have regarding their gage applications.

Also, for a reference on all elements of foil strain gage application see:

http://www.omega.com/techref/pdf/StrainGage_Measurement.pdf

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How are you going to mount a strain gauge to work on such a tiny sensing area ?

The Cantilever Beam Small Deflection Approximation is a simplification technique used in structural engineering to estimate the deflection of a cantilever beam under a load. It assumes that the deflection of the beam is small compared to its length, and neglects higher-order terms in the equations of motion.

This approximation is applicable when the deflection of the beam is less than 1/10th of its length, and the material is linearly elastic. It is commonly used in the design of simple structures such as bridges, balconies, and shelves.

The deflection of a cantilever beam under a load can be calculated using the following equation:

δ = (FL^3)/(3EI)

Where δ is the deflection, F is the applied load, L is the length of the beam, E is the Young's modulus of the material, and I is the moment of inertia of the cross-section of the beam.

While this approximation is useful for simple structures, it has some limitations. It does not take into account the effect of shear forces, and it assumes that the material is linearly elastic. It also becomes less accurate as the deflection becomes larger, and is not suitable for highly curved or irregularly shaped beams.

The accuracy of this approximation depends on the assumptions made and the conditions of the beam. In general, it provides a good estimate for small deflections and can be improved by using more refined methods, such as finite element analysis, for more complex or critical structures.

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