On the free surface of a steel machine element E 210 Gpa v

On the free surface of a steel machine element (E = 210 Gpa, v = 0.31), strain rosette configuration shown in the figure measures the following values: epsilon_a = -115 mu epsilon epsilon_b = 750 mu epsilon epsilon_c = -15 mu epsilon. Determine the strain components epsilon_x, epsilon_y and gamma_xy at this point Determine the principal strains and the principle angles. Pair up & clearly state the associated strains & angles Determine the maximum in-plane shear strain Determine the \"out of plane\" principal strain, i.e. epsilon_z or epsilon_p3 and clearly state the criterion for your decision Determine the absolute maximum shear strain Sketch deformations & distortions, i.e., plot the principal strains and the maximum in plane shear strain on an appropriate strain element to also indicate the rotation of axes Making use of the results you have found from part (b), determine the principal stresses Determine the shear modulus G for the steel material making use of the result you have found from part (c) & (h), determine the maximum in plane shear stress Making use of the results you have found from part (g), determine the average normal stress Sketch the principal stresses, maximum in plane shear stress & the average normal stress on an appropriate stress element(s) to also indicate the orientation of principal planes and maximum shear plane Making use of the results you have found from part (e) & (h), determine the absolute maximum shear stress.

Solution

taking angle 1 =0, angle 2-= 120, angle 3 -60

Measured strain-1

E/(2(1+v))

Modulus of rigidity

Obtain   strain components

ex=-115, ey = 528.33, gxy = =883.35

Principal strains e1 750.06, e2 -115.06, gamma 865.13, angle 0.497

Measred strain 1	1	x(cos1)2+y(sin1)2+xysin1cos1
Measured strain-2	2	x(cos2)2+y(sin2)2+xysin2cos2
Measured strain-3	3	x(cos3)2+y(sin3)2+xysin3cos3
Normal strain	x	(x/E-vy/E-vz/E)
Normal strain	y	(y/E-vz/E-vx/E)
Normal strain	z	(z/E-vx/E-vy/E)
Shear strain	xy	xy/G
Shear strain	yz	yz/G
Shear strain	zx	zx/G
	G	E/(2(1+v)) Modulus of rigidity Obtain   strain components ex=-115, ey = 528.33, gxy = =883.35 Principal strains e1 750.06, e2 -115.06, gamma 865.13, angle 0.497