# Convert Strain gauge readings to stress

In summary: The strain gauge readings were taken from an I-beam that was subjected to torsion. The Young's modulus and Poisson's ratio depend on the material (and to some degree the form e.g. cast, wrought, etc.). Assuming you have wrought mild steel (structural steel) your Poisson ratio is likely to be 0.295 to 0.3. The orientation of your strain gauge(s) on the I-Beam and was the beam subjected to strictly a torque?
Hello i am trying to convert the strain gauge readings i took in a lab from an I beam that was subjected to torsion. I am trying to convert the microstrain readings to stress and shear stress. I have the following information the Yield strength of the I beam and the youngs modulus but not the poissons ratio.

I thought the formula would be $$\tau$$= Tr/J but because it is an I beam i am unsure how to calculate the r and the J. also i know what the T (torsion) that the beam is subjected to.

any help would be very much appreciated.

Tr/J where J is polar moment of inertia only works for closed sections. Long explanation, but the most brief/clear I've seen is Omer Blodgett's in Design of Weldments (and repeated in other texts by the same author) available VERY inexpensively from the J.F. Lincoln Arc Welding Foundation.
(One quick visualization is in applying a torque to a tube, and measure the angular displacement. Then slit one side of the tube lengthwise, and apply the same torque. The displacement will be much larger in the 2nd instance even though the areas and polar moment of inertia will be essentially the same. This is because the torsional shear stress is the same on the plane normal to the axis of the tube as it is on the longitudinal. When you get to the slit, the shear stress has to be zero, because there's nothing there to resist it on the longitudinal plane.)

Young's Modulus and Poisson's ratio depend on the material (and to some degree the form e.g. cast, wrought, etc.). Assuming you have wrought mild steel (structural steel) your Poisson ratio is likely to be 0.295 to 0.3.

What is the orientation of your strain gauge(s) on the I-Beam and was the beam subjected to strictly a torque ?

## 1. What is a strain gauge and how does it measure stress?

A strain gauge is a device that measures the amount of strain or deformation on an object. It works by converting the change in length of an object into an electrical signal. When an object is under stress, it experiences a change in length, which is detected by the strain gauge and converted into a reading.

## 2. What is the relationship between strain and stress?

Strain and stress are closely related. Strain is the measure of deformation or change in length of an object, while stress is the force applied to the object that causes the deformation. The relationship between strain and stress is linear, meaning that as the stress increases, the strain also increases proportionally.

## 3. How do you convert strain gauge readings to stress?

To convert strain gauge readings to stress, you need to know the gauge factor of the strain gauge, which is a constant value provided by the manufacturer. The formula for converting strain gauge readings to stress is stress = (strain x gauge factor) / modulus of elasticity. The modulus of elasticity is a material property that represents the stiffness of the material being tested.

## 4. What are some common sources of error when converting strain gauge readings to stress?

There are several sources of error that can affect the accuracy of converting strain gauge readings to stress. These include improper installation of the strain gauge, temperature changes, electrical interference, and incorrect calibration of the equipment. It is important to carefully follow the manufacturer's instructions and regularly calibrate the equipment to minimize these errors.

## 5. How can the accuracy of strain gauge readings be improved?

The accuracy of strain gauge readings can be improved by using high-quality equipment, following proper installation techniques, and regularly calibrating the equipment. Additionally, it is important to carefully select the type and size of strain gauge for the specific application and to consider any potential sources of error. It may also be helpful to take multiple readings and average them to reduce the impact of any outliers.

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