Abstract
The paper describes a reusable biaxial-strain transducer consisting of a delta-shaped element in the form of a hollow equilateral traingle, with legs mounted perpendicular to its plane at the apices. The legs terminate in hard styli which are impressed into a test surface by axial forces acting on the legs. When the surface is strained, the displacements of the styli induce bending and torsional strains in the arms of the delta element. Strain gages mounted longitudinally on the arms detect the bending strains. It is shown that the strain in any arm is proportional to the strain in the test surface in the direction parallel to the arm. An instrument with a gage length of one inch is described and experimental results show that it has an accuracy of better than one percent.
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Abbreviations
- A, B :
-
constants
- b :
-
width of arm
- E :
-
Young's modulus for material of arm
- E ℓ :
-
Young's modulus for material of leg
- f :
-
\(\frac{{E_\ell }}{E}\) (factor necessary if leg material is different from arm material)
- f′, f″, f′″ :
-
constants
- G :
-
shear modulus
- I :
-
second moment of area of leg cross section, or gage current
- I z :
-
second moment of area of arm cross section in the flexible direction
- J :
-
torsional property of arm cross section =Nbt 3 for a rectangular cross section
- K :
-
gage factor
- K, K′, K″ :
-
constants
- L :
-
length of arm, or gage length
- l :
-
length of leg
- M b ,M c ,M f-g :
-
moments in armsb, c andf-g, respectively
- M 1,M 2,M 3 :
-
redundant moments
- N :
-
torsional constant for rectangular cross section
- P x ,P z :
-
transverse forces on stylus
- Q :
-
generalized force
- R :
-
gage resistance
- t :
-
thickness of arm
- V 0 :
-
voltage output from strain gage
- X 1,X 2,X 3,Z :
-
redundant forces
- X, Y, Z :
-
global coordinates
- x, y, z :
-
local coordinates
- Δ x , Δ z :
-
transverse deflections of stylus
- ∈ I , ∈ II :
-
principal strains in test surface
- ∈ x , ∈ z :
-
components of strain in test surface
References
Leahy, T.F., “A Reusable Biaxial Strain Transducer,”Experimental Mechanics,14 (1),111–117 (March 1974).
Timoshenko, S.P. and Goodier, J., “Theory of Elasticity,” 3rd ed., (1970).
Brewer, G.A., “The Equilateral Fleximeter,” Proc. SESA (1948).
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Leahy, T.F. The delta-element reusable strain transducer. Experimental Mechanics 24, 191–202 (1984). https://doi.org/10.1007/BF02323165
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DOI: https://doi.org/10.1007/BF02323165