Sample Problem : Principal Stress Calculation with Strain Gage Rosette Measurements

On the foot of a machine, strain measurement has been done with 45° strain gage rosette as shown in the figure. Measurement results recorded from the strain gages 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 gage 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 defined in sample example


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

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


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 Gage Rosette Results" page to calculate principal stresses.


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 fully solved with calculators which are summarized as follows.



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