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mechanical stress …

Below, the principal directions are determined. First the tangent of an auxiliary angle ψ is calculated.For the 0/45/90rosette according to the formula:and for the 0/60/90rosette according to the formula: Note: The tangent of an angle in the right-angled triangle is the ratio of the oppositeside (numerator N) to the adjacent side (denominator D):This ambiguity of the tangent makes it necessary to determine the signs of the nume-rator (N) and the denominator (D) before carrying out the nal calculation of the two above mentioned quotients. Determining the signs is important because they aloneindicate the quadrant of the circular arc in which the angle

ND N D

ψ is located.From the numerical value of the tangent the size of the angle ψ should then be found:Then the angle ϕ should be determined using the below scheme: The angle opposite side

N D

adjacent side

N D

Ï• , found in this manner, should be applied from the axis of the referencemeasuring grid a in the mathematically positive direction (counterclockwise). The axisof measuring grid a forms one side of the angle Ï• , the second side gives prinicipaldirection 1.This is the direction of the principal normal stress

N D

σ

N D N D

1 which is identical to the directionof the principal strain ε
1 . The point of the angle is located at the intersection of theaxes of the measuring grids. The principal direction 2 (direction of the principal normalstress σ
2 ) has the angle Ï• +90. Strain Gages and Accessories19