1-98 Section 1 Gage Sensitivities and Gage Factor The electrical-resistance strain gage has a sensitivity to both axial and transverse strain. The magnitude of the transverse strain transmitted to the grid depends on a number of factors, including the thickness and elastic modulus of the adhesive, the carrier material, the grid material, and the width-to-thickness ratio of the axial segments of the grid. Sometimes it is necessary to calculate the true value of strain that includes all contributions, from (1.5.62) where ε a is the normal strain along the axial direction of the gage, ε t is the normal strain along the transverse direction of the gage, v 0 = 0.285 is Poisson’s ratio for the calibration beam, and K t is the transverse-sensitivity factor of the gage. The strain gage sensitivity factor, S g , is a calibration constant provided by the manufacturer. By using Equations 1.5.61 and 1.5.62 the percent error involved in neglecting the transverse sensitivity can be calculated. These errors can be significant for large values of both K t and ε t /ε a , so it may be necessary to correct for the transverse sensitivity of the gage (Figure 1.5.40). Strain Analysis Methods Electrical-resistance strain gages are normally employed on the free surface of a specimen to establish the stress at a particular point on this surface. In general it is necessary to measure three strains at a point to completely define either the stress or the strain field. For this general case, where nothing is known about the stress field or its directions before experimental analysis, three-element rosettes are required to establish the stress field. This is accomplished by using the three-element gage with orien- tations at arbitrary angles, as shown in Figure 1.5.41. Using this setup, the strains ε x , ε y , and γ xy can be determined. These values can be used to determine the principal strains and principal directions, (1.5.63) where φ is the angle between the principal axis (σ 1 ) and the x axis. The principal stresses can be computed using the principal strains, FIGURE 1.5.40Error as a function of transverse-sensitivity factor with the biaxial strain ratio as a parameter. ε εε a g t tta RR S vK K = () − + () ∆ 1 1 0 εεε εεγ εεε εεγ φ γ εε 1 2 2 2 2 2 1 2 1 2 1 2 1 2 2 =+ () +− () + =+ () −− () + = − xx yy xx yy xy xx yy xx yy xy xy xx yy tan . on a number of factors, including the thickness and elastic modulus of the adhesive, the carrier material, the grid material, and the width-to-thickness ratio of the axial segments of the grid value of strain that includes all contributions, from (1.5.62) where ε a is the normal strain along the axial direction of the gage, ε t is the normal strain along the transverse direction of. 1- 98 Section 1 Gage Sensitivities and Gage Factor The electrical-resistance strain gage has a sensitivity to both axial and transverse strain. The magnitude of the transverse strain