Principal Stress Calculation Example with Strain Gauge Rosette Measurements

On the foot of a machine, strain measurement has been done with 45° strain gauge rosette (rectangular rosette) as shown in the figure. Measurement results recorded from the strain gauges are ε1=65 μin/in, ε2= 700 μin/in and ε3= 150 μin/in. (Use E=205 GPa and v=0.29)

Using the measurement results of strain gauge rosette, calculate:

a) Strain components εxyxy.

b) The principal stresses (in XY plane) at the measurement point.

Principal Stress Calculation with Strain Results

Solution:


Step 1 : Write down input parameters which are given.


INPUT PROPERTIES SUMMARY
Parameter Value Unit
Measured strain-1 (ε1) 65 μin/in
Measured strain-2 (ε2) 700 μin/in
Measured strain-1 ( ε3) 150 μin/in
Strain gauge rosette angles (θ) 0-45-90 deg
Elastic Modulus (E) 205 GPa
Poisson's Ratio (v) 0.29 ---

Step 2 : Go to "Strain Calculation with Strain Rosette Measurement" page to calculate strain components εxyxy by using the values summarized in step 1.


RESULTS
Parameter Value Unit
Normal strain in x-direction (εx) 65 μm/m (μin/in)
Normal strain in y-direction (εy) 150
Shear strain in xy-direction (γxy) 1185

Strain components are calculated as εx=65, εy=150,γxy=1185. This is the answer of clause a) of the problem.


Step 3 : Since the measurement has been recorded from the free surface of the machine,  it can be assumed that the situation is plane stress state. For the calculation of principal stresses, go to " Calculation of Plane Stress State With Strain Gauge Rosette Results" page to calculate principal stresses by using the values summarized in step 1.


RESULTS
Parameter Value Unit
STRAINS ON REFERENCE AXIS (X-Y)
Normal strain in x-direction (εx) 65 μm/m (μin/in)
Normal strain in y-direction (εy) 150
Shear strain in xy-direction (γxy) 1185
PLANE STRESSES
Normal stress in x-direction (σx) 24.3 MPa
Normal stress in y-direction (σy) 37.8
Shear stress in xy plane (τxy) 94.2
PRINCIPAL STRESSES
Maximum principal stress (σmax) 125.4 MPa
Minimum principal stress (σmin) -63.4
Maximum shear stress (τmax) 94.4
Average principal stress (σavg) 31
Von Mises stress (σmises) 166.4

Principal stresses are calculated as 125.4 MPa and -63.4 MPa . This is the answer of clause b) of the problem.

Summary

The problem is completely solved with calculators which are summarized as follows.


Calculator Usage
Calculation of Plane Stress State With Strain Gauge Rosette Results To calculate principal stresses for plane stress state with the usage of strain gauge rosette measurement.
Strain Calculation with Strain Rosette Measurement To calculate normal and shear strain by using the measurement results of strain gauge rosette.