This document discusses corrections for transverse sensitivity of strain gauges during measurement. It defines transverse sensitivity as a strain gauge's response to strains perpendicular to its primary sensing axis. It provides equations to correct for transverse sensitivity in 2-axis, rectangular, and delta rosette strain gauge configurations. It also discusses implementing these corrections in data acquisition software and post-processing analysis tools, including adding fields for input parameters and calculated channels for real-time monitoring of corrected strains.

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Corrections for Transverse Sensitivity
of Strain Gauges

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Computation of Equivalent Stress
 Prosig PIN:
– 167398
 Customer:
– Aeronautical Development Establishment (ADE), India
 Potential Sale Involved :
– Yes
 Tender Title:
– Universal Data Acquisition System for Vibration and Strain
Measurement
 Description as it is in Tender Document:
– Corrections for Bridge Non-linearity, Transverse
sensitivity of strain gages, gage factor (temperature
effects) and lead wire resistance error on gage factor)

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Objective
 Objective is to apply the corrections for transverse sensitivity of
strain gauges during measurement

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What is Transverse Sensitivity
 Transverse sensitivity in a strain gage refers to the behavior of
the gage in responding to strains which are perpendicular to
the primary sensing axis of the gage.

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Why
 Any gage which is:
– installed on a material with a different Poisson’s ratio other
than 0.285 or
– installed on steel, but subjected to other than a uniaxial
stress state or
– even installed on steel with a uniaxial stress state, but
aligned with other than the maximum principal stress,
exhibits a transverse-sensitivity error which may require
correction

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How
 How to correct the effects of Transverse sensitivity?
– By corrections equations
– 90ͦ (2-axes), Rectangular and Delta Rosettes have different
corrections equations
– Equations involve parameters v0 & Kt which can be obtained
from strain gauge datasheet

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Two-Gage, 90ͦ Rosette
 Corrected actual strain along gage axes 1 & 2 is
ε'1 , ε’2 = Strain from gage 1 & 2 uncorrected for transverse sensitivity
Kt1 , Kt2 = Transverse sensitivities of gage 1 & 2
𝜀1 =
𝜀′
1 1 − 𝑣0𝐾𝑡1 − 𝐾𝑡1𝜀′2(1 − 𝑣0𝐾𝑡2)
1 − 𝐾𝑡1𝐾𝑡2
𝜀2 =
𝜀′
2 1 − 𝑣0𝐾𝑡2 − 𝐾𝑡2𝜀′1(1 − 𝑣0𝐾𝑡1)
1 − 𝐾𝑡1𝐾𝑡2

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Three-Gage Rectangular, 45ͦ Rosette
 Corrected actual strain along gage axes 1,2 & 3 is
ε'1 , ε’2 , ε’2 = Strain from gage 1,2 & 3 uncorrected for transverse sensitivity
Kt1 , Kt2 , Kt3 = Transverse sensitivities of gage 1,2 & 3
𝜀1 =
𝜀′
1 1 − 𝑣0𝐾𝑡1 − 𝐾𝑡1𝜀′3(1 − 𝑣0𝐾𝑡3)
1 − 𝐾𝑡1𝐾𝑡3
𝜀3 =
𝜀′
3 1 − 𝑣0𝐾𝑡3 − 𝐾𝑡3𝜀′1(1 − 𝑣0𝐾𝑡1)
1 − 𝐾𝑡1𝐾𝑡3
𝜀2 =
𝜀′
2 1 − 𝑣0𝐾𝑡2
1 − 𝐾𝑡2
−
𝐾𝑡2[𝜀′
1 1 − 𝑣0𝐾𝑡1 1 − 𝐾𝑡3 + 𝜀′
3 1 − 𝑣0𝐾𝑡3 1 − 𝐾𝑡1 ]
(1 − 𝐾𝑡1𝐾𝑡3)(1 − 𝐾𝑡2)

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Delta Rosette
 Corrected actual strain along gage axes 1,2 & 3 is
ε'1 , ε’2 , ε’2 = Strain from gage 1,2 & 3 uncorrected for transverse sensitivity
Kt1 , Kt2 , Kt3 = Transverse sensitivities of gage 1,2 & 3
𝜀1 =
𝜀′
1 1 − 𝑣0𝐾𝑡1 3 − 𝐾𝑡2 − 𝐾𝑡3 − 𝐾𝑡2𝐾𝑡3 − 2𝐾𝑡1[𝜀′
2 1 − 𝑣0𝐾𝑡2 1 − 𝐾𝑡3 + 𝜀′
3 1 − 𝑣0𝐾𝑡3 1 − 𝐾𝑡2 ]
3𝐾𝑡1𝐾𝑡2𝐾𝑡3 − 𝐾𝑡1𝐾𝑡2 − 𝐾𝑡2𝐾𝑡3 − 𝐾𝑡1𝐾𝑡3 − 𝐾𝑡1 − 𝐾𝑡2 − 𝐾𝑡3 + 3
𝜀2 =
𝜀′
2 1 − 𝑣0𝐾𝑡2 3 − 𝐾𝑡3 − 𝐾𝑡1 − 𝐾𝑡3𝐾𝑡1 − 2𝐾𝑡2[𝜀′
3 1 − 𝑣0𝐾𝑡3 1 − 𝐾𝑡1 + 𝜀′
1 1 − 𝑣0𝐾𝑡1 1 − 𝐾𝑡3 ]
3𝐾𝑡1𝐾𝑡2𝐾𝑡3 − 𝐾𝑡1𝐾𝑡2 − 𝐾𝑡2𝐾𝑡3 − 𝐾𝑡1𝐾𝑡3 − 𝐾𝑡1 − 𝐾𝑡2 − 𝐾𝑡3 + 3
𝜀3 =
𝜀′
3 1 − 𝑣0𝐾𝑡3 3 − 𝐾𝑡1 − 𝐾𝑡2 − 𝐾𝑡1𝐾𝑡2 − 2𝐾𝑡3[𝜀′
1 1 − 𝑣0𝐾𝑡1 1 − 𝐾𝑡2 + 𝜀′
2 1 − 𝑣0𝐾𝑡2 1 − 𝐾𝑡1 ]
3𝐾𝑡1𝐾𝑡2𝐾𝑡3 − 𝐾𝑡1𝐾𝑡2 − 𝐾𝑡2𝐾𝑡3 − 𝐾𝑡1𝐾𝑡3 − 𝐾𝑡1 − 𝐾𝑡2 − 𝐾𝑡3 + 3

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Correction of Principal Strains
 Corrected principal strain is
ε‘q , ε’p = Principal Strain from gage uncorrected for transverse sensitivity
Kt = Nominal Transverse sensitivities of gage
𝜀𝑝 =
1 − 𝜐0𝐾𝑡
1 − 𝐾𝑡
2 (𝜀′
𝑝 − 𝐾𝑡𝜀′
𝑞)
𝜀𝑞 =
1 − 𝜐0𝐾𝑡
1 − 𝐾𝑡
2 (𝜀′
𝑞 − 𝐾𝑡𝜀′
𝑝)

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Implementation in Acquisition
 Availability in Existing Acquisition – No
 Separate field to define the type of rosettes must be created
 Separate input field must be created for v0 , Kt1 , Kt2 , Kt3
 From the inputs defined above a calculated channels can be
added with appropriate corrections equations
 This method allows the user to monitor the corrected strain
levels in real time
 Please check for any error in the correction equations before
implementing
 This method can be implemented without calculated channels
by adding some new features
Note: The same equations can also be implemented in DATS
Analysis as a post processing Algorithm

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Implementation in DATS Analysis
 Availability in Existing DATS – No
 Fatigue Analysis – Principal Strain calculates maximum and
minimum Principal strain from which Transverse sensitivity
corrections can be implemented
 Please include an analysis menu separately to calculate only
Transverse Sensitivity Corrected Strain inside Fatigue Analysis
 Prototype script which works as a menu inside DATS user
analysis is attached. Please refer my mail
 The attached script should be refined
 Also please check for any error in the correction equations
before implementing

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Sample - Requirement
Acquisition
Analysis

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