Strain gage transverse corrections for rosette legs

A rosette leg is supposed to produce a change in electrical resistance that is proportional to the longitudinal strain in the leg. However the gage response is sensitive to the strain component transverse to the leg. The true leg strains εa, εb, εc must be determined from the measured leg strains ε’a, ε’b, ε’c by eliminating the effect of the parasitic normal strains εnorm,a, εnorm,b, εnorm,c.

For all rosette types, the measured leg strains are related to the true leg strains and the parasitic normal strains by NOTE:

	(1)

where:

• ν0 is the Poisson’s ratio for the strain gage rosette.

• Ka, Kb, Kc are the transverse sensitivities of the gage legs.

If transverse sensitivities are not known, you can ignore them by setting the transverse sensitivities to zero. When transverse sensitivities are zero, the measured and true leg strains are identical.

For a stacked rosette: Ka = Kb = Kc.

For a planar rosette: Ka = Kc ≠ Kb

For a user-defined rosette: Ka ≠ Kb ≠ Kc.

True leg strain for a delta rosette

A delta strain gage rosette has the leg a along the X-direction.

Thus, εa = εx and εnorm,a = εy.

Using the double angle transformation formula, the strains in legs b and c can be written as:

	(2)

Solving equation (2) for εy gives:

	(3)

From the first strain invariant and equation (3), you get the expressions for εnorm,b and εnorm,c:

	(4)

Plugging in the expressions from equations (3) and (4) into equation (1), you get the true leg strains from the measured leg strains:

	(5)

True leg strain for a rectangular rosette

A rectangular strain gage rosette has the leg a along the X-direction and leg c along the Y-direction.

Thus, by construction:

εnorm,a = εc	(6)
εnorm,c = εa	(7)

From the first strain invariant

εnorm,b = εa + εc – εb	(8)

Plugging in the expressions from equations (6), (7) and (8) into equation (1), you get the true leg strains from the measured leg strains:

	(9)

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Analyzing strain gage rosette data

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Strain gage transverse corrections for rosette legs, Simcenter 3D 2021.1 Series

© 2020 Siemens

Murray, W.W. and Miller, W.R., “The Bonded Electrical Resistance Strain Gage”, Chapters 8 and 9, Oxford University Press, 1992.

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