In practical problems, an element may be subjected to stresses in any direction and hence it is not possible to locate the direction of principle stress. Therefore, it is not possible to orient the strain, gauges along the direction of principle stress. Hence, there is a nIn practical problems, an element may be subjected to stresses in any direction and hence it is not possible to locate the direction of principle stress. Therefore, it is not possible to orient the strain, gauges along the direction of principle stress. Hence, there is a necessity to evolve a strain gauge measurement system which measures the values of principle strains & stresses without actually knowing their direction. The solution to the problem lies in using three strain gauges to form a unit called a ‘Rosette’. Rosettes are of many types: (1) Two gauge rosette for simple tension and compression -> Two element Rosette Type Load cells

The two strain gauges are mounted at 90˚ to each other. Principal strain = ϵ1 or ϵ2 Principal stresses, S1 = E/(1-v^2 )(ϵ1+vϵ2) S2 = E/(1-v^2 )(ϵ2+vϵ1) Maximum shear stress τmax = E/(2(1-v))(ϵ1 - ϵ2)

(2) Rectangular Rosette

The three strain gauges are oriented as shown in fig. The strains measured by the three strain gauges are ϵ1, ϵ2 and ϵ3. The maximum & minimum principle strains are given below: ϵmax, ϵmin = (∈1+∈3)/2 ± 1/√2 〖[(〖ϵ1-ϵ2)〗^2+ (〖ϵ2-ϵ3)〗^2]〗^(1/2) Smax, Smin = (E(∈1+∈3))/(2(1-v)) ± E/((1+v)√2) 〖[(〖ϵ1-ϵ2)〗^2+ (〖ϵ2-ϵ3)〗^2]〗^(1/2) The maximum sheer stress is, τmax = E/((1+v)√2) 〖[(〖ϵ1-ϵ2)〗^2+ (〖ϵ2-ϵ3)〗^2]〗^(1/2) The orientation θ of principal stress is given by: tan 2θ = (2ϵ2- ϵ1- ϵ3)/(ϵ1- ϵ2) This is the axis at which the maximum stress Smax occurs. Angle θ may be in the first quadrant or the second quadrant. Angle θ is in the first quadrant or 0<θ<π/2 when ϵ2 > (ϵ1 + ϵ3)/2 If ϵ2 is less than (ϵ1 + ϵ3)/2, angle θ is in second quadrant.

(3) Delta Rosette

The arrangement for this rosette is shown in the fig, three strain gauges are mounted as shown. The principal strains are, ϵmax, ϵmin = (ϵ1+ ϵ2+ϵ3)/3±√2/3 〖[(〖ϵ1-ϵ2)〗^2 + (〖ϵ2-ϵ3)〗^2 + (〖ϵ3-ϵ1)〗^2]〗^(1/2) The maximum shear stress is, τmax = (√2E)/(3(1+v)) 〖[(〖ϵ1-ϵ2)〗^2+ (〖ϵ2-ϵ3)〗^2+ (〖ϵ3-ϵ1)〗^2]〗^(1/2) The orientation of the principal stress is tan 2θ = (√3(ϵ3- ϵ2))/(2ϵ1- ϵ2-ϵ3) Angle θ is in first quadrant where ϵ3 >ϵ2 and in the second quadrant when ϵ2>ϵ3.