How to calculate stress from strain gauge

Introduction

In the lab our objective was to experimentally measure strains in order to calculate the stresses at a particular point. The sensor used was a 45-degree strain gage rosette that was mounted to our cantilever beam specimen. The sensor ‘stretches’ as the part is loaded due to the strains developed. Due to this stretch, the sensor’s electrical resistance is altered. Using a computer machine from Vishay the strains can be recorded. The machine was tared to zero strain just before the weight was applied. It is necessary to measure the strain value between the longitudinal and transverse strain in order to calculate shear strain, since it is impossible to be measured directly. Experimental strains will then be converted into stresses and compared to hand calculations and finite element analysis results. A percent error analysis will be completed to compare results.

Methods

A 45-degree strain gage rosette was mounted on the cylindrical cantilever beam (See Figure A). Dimensions of the beam were recorded as well as the distance from the applied load to the strain gages. The beam was loaded with 4.5 pounds at the unfixed end of the pipe. A low weight was chosen due to the size of the structure and to avoid yielding of it. The Vishay machine was wired to the schematic and the three wires leading to the strain gages. The strain gage rosette measures longitudinal strain, transverse strain, and strain at a 45-degree angle. Using the strains measured through experimentation (ϵx , ϵy , and ϵ45) and by applying transformation equations the stresses can be calculated (σx , σy , and τxy).

The second method involved hand calculations by taking a cut at the element of interest (where the strain gage was applied). A moment and torque resulted due to the loading and were used to calculate the stresses. The calculated stresses were then converted into strains for comparison.

The third method involved computer simulation. By creating the part in Solidworks and transferring it to Mechanical Simulation the stresses could be analyzed as well as the strains in the longitudinal and transverse directions. The node was carefully selected and results were pulled from the FEA analysis.

Results

Data Comparison

(Stress in units of PSI)

Experimental

Hand Calculations

FEA

σ x

434

466

488

σ y

43

0

15

τ xy

399

466

416

Micro Strain-(Strain in units of in/in)*(10-6)

Experimental

Hand Calculations

FEA

ϵ x

42

46

46

ϵ y

-10

0

-14

γ xy

106

91

74

Percent Error to Actual Results (FEA)

Experimental Method

Calculation Method

σ x

11.10%

4.50%

σ y

187%

100%

τ xy

4.10%

4.08%

ϵ x

8.70%

0%

ϵ y

28.57%

100%

γ xy

43.24%

22.97%

*Reference the appendix for the hand calculations*

Discussion

Finite element analysis provides the most accurate solution, so calculation and experimental methods were compared to those values for the percent error. For σx, the percent error was low for calculations but more error was in the experimental method. Hand Calculations give no stress or strain in the y-direction but FEA and experimental methods prove to show low strains, so the percent error for the stress and strains in the y-direction were 100%. Both the experimental and calculations had very low percent of error for the shear stress at the element. High percent error was found in the experimental and calculation methods for the shear strain.

Causes for high percentages in error: Hand calculations disregard the weight of the actual specimen during static loading. Experimental specimen has pipe fittings around the bends whereas the model created in FEA consists of a smooth bent pipe. Imperfections in the test specimen and human error (such as measurements and placement of strain gage rosette) affect the experimental method. The hand calculations are more closely related to the FEA results compared to the experimental method.

Appendix

Figure (A) – Strain Gage Rosette on Specimen

E:\Stress & Strain Lab\Lab #4\SpecimenPIC.png

Figure (B) – Stress tensor at element

Strain Gage Location of Element

Force = 4.5 lb

Figure (C) – Strain tensor at element

Node of Interest