2.17 For the 0-45°-90° strain rosette of Example 2.6, find...

2.17 For the 0-45°-90° strain rosette of Example 2.6, find general expressions for the principal strains and maximum shear strains in terms of the measurable values $\epsilon_0$, $\epsilon_{45^\circ}$, and $\epsilon_{90^\circ}$. 2.18 Whereas Eqs. (2.69), (2.75), and (2.77) are called strain-stress relations,

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00:01 Here given, epsilon a is equal to minus 150 micro epsilon, epsilon b is equal to minus 190 micro epsilon and epsilon c is equal to 65 micro epsilon and e is equal to 10500 kilo pounds per square inch and v is equal to 0 .33 from the given figure, theta a is equal to 45 degree theta b is equal to 90 degree and theta c is equal to 135 degree therefore, epsilon a is equal to epsilon x cos square theta a plus epsilon y sin square theta a plus rxy sin theta a cos theta a by substituting the values we will get minus 150 micro epsilon is equal to epsilon x cos square 45 degree plus epsilon y sin square 45 degree plus rxy sin 45 degree multiplied by cos 45 degree therefore, it is equal to epsilon x multiplied by 0 .5 plus epsilon y multiplied by 0 .5 plus rxy multiplied by 0 .5 which is equal to minus 300 micro epsilon is equal to epsilon x plus epsilon y plus rxy this is equation number 1 and epsilon b is equal to epsilon x cos square theta b plus epsilon y sin square theta b plus rxy sin theta b cos theta b therefore, by substituting we will get minus 190 micro epsilon is equal to epsilon x cos square 90 degree plus epsilon y sin square 90 degree plus rxy sin 90 degree multiplied by cos 90 degree since cos 90 degree is equal to 0 minus 190 micro epsilon is equal to epsilon y and epsilon c is equal to epsilon x cos square theta c plus epsilon y sin square theta c plus rxy sin theta c multiplied by cos theta c by substituting the values we will get 65 micro epsilon is equal to epsilon s cos square 135 degree plus epsilon y multiplied by sin square 135 degree plus rxy multiplied by sin 135 degree multiplied by cos 135 degree it is equal to 0 .5 epsilon x plus 0 .5 epsilon y minus 0 .5 rxy therefore, 130 micro epsilon is equal to epsilon x plus epsilon y minus rxy this is equation number 2 then by adding equation 1 and equation 2 implies minus 300 micro epsilon is equal to epsilon x plus epsilon y plus rxy plus 130 micro epsilon is equal to epsilon x plus epsilon y minus rxy by adding these two we will get minus 170 micro epsilon is equal to 2 epsilon x plus 2 epsilon y therefore, epsilon x plus epsilon y is equal to minus 85 micro epsilon or epsilon x is equal to minus 85 micro epsilon minus epsilon y that is equal to minus 85 micro epsilon plus 190 micro epsilon that is equal to 105 micro epsilon and equation 1 minus equation 2 implies minus 300 micro epsilon is equal to epsilon x plus epsilon y plus r x y minus 130 micro epsilon is equal to epsilon x plus epsilon y minus r x y...

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