Short Notes: Strain Gages and Rosettes | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


Strain Gages and Rosettes  
Measurement of Strain
Strain measurement can be performed in two ways namely,
• Direct (electrical-type gauges based on Resistive, Capacitive, Inductive or 
Photoelectric principles)
• Indirect (optical methods, such as Photoelasticity, the Moire technique, or 
Holographic interferometry)
The majority of strain gauges are foil types, available in a wide choice of shapes 
and sizes to suit a variety of applications. They consist of a pattern of resistive foil 
which is mounted on a backing material. They operate on the principle that as the 
foil is subjected to stress, the resistance of the foil changes in a defined way.
The strain gauge is connected into a Wheatstone Bridge circuit with a combination 
of four active gauges (full bridge),two gauges (half bridge) or less commonly, a 
single gauge (quarter bridge). In the half and quarter circuits, the bridge is 
completed with precision resistors.
Page 2


Strain Gages and Rosettes  
Measurement of Strain
Strain measurement can be performed in two ways namely,
• Direct (electrical-type gauges based on Resistive, Capacitive, Inductive or 
Photoelectric principles)
• Indirect (optical methods, such as Photoelasticity, the Moire technique, or 
Holographic interferometry)
The majority of strain gauges are foil types, available in a wide choice of shapes 
and sizes to suit a variety of applications. They consist of a pattern of resistive foil 
which is mounted on a backing material. They operate on the principle that as the 
foil is subjected to stress, the resistance of the foil changes in a defined way.
The strain gauge is connected into a Wheatstone Bridge circuit with a combination 
of four active gauges (full bridge),two gauges (half bridge) or less commonly, a 
single gauge (quarter bridge). In the half and quarter circuits, the bridge is 
completed with precision resistors.
The complete Wheatstone Bridge is excited with a stabilised DC supply and with 
additional conditioning electronics, can be zeroed at the null point of measurement 
As stress is applied to the bonded strain gauge, a resistive change takes place and 
unbalances the Wheatstone Bridge.
This results in a signal output, related to the stress value. As the signal value is 
small, (typically a few millivolts) the signal conditioning electronics provides 
amplification to increase the signal level to 5 to 10 volts, a suitable level for 
application to external data collection systems such as recorders or PC Data 
Acquistion and Analysis Systems.
90° Rosette 45° Rosette 60° Rosette
Most manufacturers of strain gauges offer extensive ranges of differing patterns to 
suit a wide variety of applications in research and industrial projects.
They also supply all the necessary accessories including preparation materials, 
bonding adhesives, connections tags, cable, etc. The bonding of strain gauges is a 
skill and training courses are offered by some suppliers. There are also companies 
which offer bonding and calibration services, either as an in-house or on-site 
service. Rosette Strain Gage:
• A strain gage only measures strain in one direction, in order to get principal 
strains,it is necessary to use a strain rosette
• A strain rosette is a cluster of 3 strain gages oriented at different angles
A strain gage rosette is, by definition, an arrangement of two or more closely 
positioned gage grids, separately oriented to measure the normal strains along 
different directions in the underlying surface of the test part.
• Rosettes are designed to perform a very practical and important function in 
experimental stress analysis.
• Rosettes are manufactured from different combinations of grid alloy and 
backing material to meet varying application requirements.
• They are also offered in a number of gage lengths, noting that the gage length 
specified for a rosette refers to the active length of each individual grid within 
the rosette.
• To determine the three independent components of plane strain, three linearly 
independent strain measures are needed, i.e., three strain gages positioned in 
a rosette-like layout.
For example,Consider a strain rosette attached on the surface with an angle a from 
the x-axis. The rosette itself contains three strain gages with the internal angles b 
and g, as illustrated on the right.
Page 3


Strain Gages and Rosettes  
Measurement of Strain
Strain measurement can be performed in two ways namely,
• Direct (electrical-type gauges based on Resistive, Capacitive, Inductive or 
Photoelectric principles)
• Indirect (optical methods, such as Photoelasticity, the Moire technique, or 
Holographic interferometry)
The majority of strain gauges are foil types, available in a wide choice of shapes 
and sizes to suit a variety of applications. They consist of a pattern of resistive foil 
which is mounted on a backing material. They operate on the principle that as the 
foil is subjected to stress, the resistance of the foil changes in a defined way.
The strain gauge is connected into a Wheatstone Bridge circuit with a combination 
of four active gauges (full bridge),two gauges (half bridge) or less commonly, a 
single gauge (quarter bridge). In the half and quarter circuits, the bridge is 
completed with precision resistors.
The complete Wheatstone Bridge is excited with a stabilised DC supply and with 
additional conditioning electronics, can be zeroed at the null point of measurement 
As stress is applied to the bonded strain gauge, a resistive change takes place and 
unbalances the Wheatstone Bridge.
This results in a signal output, related to the stress value. As the signal value is 
small, (typically a few millivolts) the signal conditioning electronics provides 
amplification to increase the signal level to 5 to 10 volts, a suitable level for 
application to external data collection systems such as recorders or PC Data 
Acquistion and Analysis Systems.
90° Rosette 45° Rosette 60° Rosette
Most manufacturers of strain gauges offer extensive ranges of differing patterns to 
suit a wide variety of applications in research and industrial projects.
They also supply all the necessary accessories including preparation materials, 
bonding adhesives, connections tags, cable, etc. The bonding of strain gauges is a 
skill and training courses are offered by some suppliers. There are also companies 
which offer bonding and calibration services, either as an in-house or on-site 
service. Rosette Strain Gage:
• A strain gage only measures strain in one direction, in order to get principal 
strains,it is necessary to use a strain rosette
• A strain rosette is a cluster of 3 strain gages oriented at different angles
A strain gage rosette is, by definition, an arrangement of two or more closely 
positioned gage grids, separately oriented to measure the normal strains along 
different directions in the underlying surface of the test part.
• Rosettes are designed to perform a very practical and important function in 
experimental stress analysis.
• Rosettes are manufactured from different combinations of grid alloy and 
backing material to meet varying application requirements.
• They are also offered in a number of gage lengths, noting that the gage length 
specified for a rosette refers to the active length of each individual grid within 
the rosette.
• To determine the three independent components of plane strain, three linearly 
independent strain measures are needed, i.e., three strain gages positioned in 
a rosette-like layout.
For example,Consider a strain rosette attached on the surface with an angle a from 
the x-axis. The rosette itself contains three strain gages with the internal angles b 
and g, as illustrated on the right.
respectively.
The following coordinate transformation equation is used to convert the 
longitudinal strain from each strain gage into strain expressed in the x-y 
coordinates,
~x y i " y __~
£vr = ------------- H ---------------cos 26/-I- £rr sin 26/
Applying this equation to each of the three strain gages results in the following 
system of equations,
e x “I” €y € y
e„ = -------— H ------- — cos2a + £vv sin 2a
2 2 ¥
£r”t"£v .
¦ = — 1 — H ----- cos 2 (a +/S) sin 2 (a + /?)
ec = r ^ ^ + * 2 ^ C °S ^(a + y) sin 2 (a +/? + ?)
These equations are then used to solve for the three unknowns, ex, ey, and exy. 
Note:
1. The above formulas use the strain measure exy as opposed to the engineering 
shear strain gxy,
V = - + £ = 2-
-IJ “J X —X V
. To use gxy, the above equations should be adjusted accordingly
2. The free surface on which the strain rosette is attached is actually in a state 
of plane stress, while the formulas used above are for plane strain. However, 
the normal direction of the free surface is indeed a principal axis for strain. 
Therefore, the strain transform in the free surface plane can be applied.
Special Cases of Strain Rosette Layouts:
Case 1: 45° strain rosette aligned with the x-y axes, i.e., a = 0°, p = y = 45°.
I Y
X
Page 4


Strain Gages and Rosettes  
Measurement of Strain
Strain measurement can be performed in two ways namely,
• Direct (electrical-type gauges based on Resistive, Capacitive, Inductive or 
Photoelectric principles)
• Indirect (optical methods, such as Photoelasticity, the Moire technique, or 
Holographic interferometry)
The majority of strain gauges are foil types, available in a wide choice of shapes 
and sizes to suit a variety of applications. They consist of a pattern of resistive foil 
which is mounted on a backing material. They operate on the principle that as the 
foil is subjected to stress, the resistance of the foil changes in a defined way.
The strain gauge is connected into a Wheatstone Bridge circuit with a combination 
of four active gauges (full bridge),two gauges (half bridge) or less commonly, a 
single gauge (quarter bridge). In the half and quarter circuits, the bridge is 
completed with precision resistors.
The complete Wheatstone Bridge is excited with a stabilised DC supply and with 
additional conditioning electronics, can be zeroed at the null point of measurement 
As stress is applied to the bonded strain gauge, a resistive change takes place and 
unbalances the Wheatstone Bridge.
This results in a signal output, related to the stress value. As the signal value is 
small, (typically a few millivolts) the signal conditioning electronics provides 
amplification to increase the signal level to 5 to 10 volts, a suitable level for 
application to external data collection systems such as recorders or PC Data 
Acquistion and Analysis Systems.
90° Rosette 45° Rosette 60° Rosette
Most manufacturers of strain gauges offer extensive ranges of differing patterns to 
suit a wide variety of applications in research and industrial projects.
They also supply all the necessary accessories including preparation materials, 
bonding adhesives, connections tags, cable, etc. The bonding of strain gauges is a 
skill and training courses are offered by some suppliers. There are also companies 
which offer bonding and calibration services, either as an in-house or on-site 
service. Rosette Strain Gage:
• A strain gage only measures strain in one direction, in order to get principal 
strains,it is necessary to use a strain rosette
• A strain rosette is a cluster of 3 strain gages oriented at different angles
A strain gage rosette is, by definition, an arrangement of two or more closely 
positioned gage grids, separately oriented to measure the normal strains along 
different directions in the underlying surface of the test part.
• Rosettes are designed to perform a very practical and important function in 
experimental stress analysis.
• Rosettes are manufactured from different combinations of grid alloy and 
backing material to meet varying application requirements.
• They are also offered in a number of gage lengths, noting that the gage length 
specified for a rosette refers to the active length of each individual grid within 
the rosette.
• To determine the three independent components of plane strain, three linearly 
independent strain measures are needed, i.e., three strain gages positioned in 
a rosette-like layout.
For example,Consider a strain rosette attached on the surface with an angle a from 
the x-axis. The rosette itself contains three strain gages with the internal angles b 
and g, as illustrated on the right.
respectively.
The following coordinate transformation equation is used to convert the 
longitudinal strain from each strain gage into strain expressed in the x-y 
coordinates,
~x y i " y __~
£vr = ------------- H ---------------cos 26/-I- £rr sin 26/
Applying this equation to each of the three strain gages results in the following 
system of equations,
e x “I” €y € y
e„ = -------— H ------- — cos2a + £vv sin 2a
2 2 ¥
£r”t"£v .
¦ = — 1 — H ----- cos 2 (a +/S) sin 2 (a + /?)
ec = r ^ ^ + * 2 ^ C °S ^(a + y) sin 2 (a +/? + ?)
These equations are then used to solve for the three unknowns, ex, ey, and exy. 
Note:
1. The above formulas use the strain measure exy as opposed to the engineering 
shear strain gxy,
V = - + £ = 2-
-IJ “J X —X V
. To use gxy, the above equations should be adjusted accordingly
2. The free surface on which the strain rosette is attached is actually in a state 
of plane stress, while the formulas used above are for plane strain. However, 
the normal direction of the free surface is indeed a principal axis for strain. 
Therefore, the strain transform in the free surface plane can be applied.
Special Cases of Strain Rosette Layouts:
Case 1: 45° strain rosette aligned with the x-y axes, i.e., a = 0°, p = y = 45°.
I Y
X
ery — £b '
£ a "I" £ c
Y
_ 2 ( 1 , 1
ex— +«c
£ y = £},
sxy = - ^ { ea ~ ec)
Uses of Strain Gages:
• Strain gages attached to Wheatstone bridges can be used for measurement of 
tension, bending, and torsion.
• In biomedical applications, strain gages can be used for determining forces in 
bones
• Slightly modified strain gages can be used for muscle contraction and blood 
pressure measurement.