Chapter 7, Problem 32P

Delta rosette is a set of three strain gages oriented at 120° relative to each other. The strain measured with each of the strain gages is e_A, e_B, and e_C. The principal strains e₁ and e₂ can be calculated from the strains measured with the rosette by:

${ϵ}_{1.2}=\frac{{ϵ}_A+{ϵ}_B+{ϵ}_C}{3}\pm \frac{\sqrt{2}}{3}\sqrt{{({ϵ}_A-{ϵ}_B)}^2+{({ϵ}_B-{ϵ}_C)}^2+{({ϵ}_C-{ϵ}_A)}^2}$

Write a user-defined MATLAB function that determines the principal strains given the strains e_A, e_B. and e_C. For the function name and arguments, use [P1, P2]=DeltaRos (A, B, C). The input arguments A. B, and C are the values of the three strains measured by the rosette. The output arguments P1 and P2 are the values of the principal strains.

Use the function to determine the principal strains for the following cases:

(a)ϵ_A=42µ, ϵ_B=970µ, ϵ_C=340µ.

(b) ϵ_A=110µ, ϵ_B=80µ, ϵ_C=-60µ.