Distance Between Points Before
and After Loading

The distance between points A, B, C and O are measured using a laser device before and after the bracket is loaded. The results are listed in the table below.

		Distance (cm)
Pt 1	Pt 2	Initial	Final
O	A	1.0	1.00150
O	B	1.41421	1.41775
O	C	1.0	1.00200

These displacements can be used to find the normal strain in the direction of OA, OB, and OC. Then, the strains can be analyzed using the strain transformation equations. Finally, the maximum shear strain can be determined.

Since the distance before and after loading are known, the normal strains can be determined as

The ε_OA and ε_OC are in the direction of the y-axis and x-axis, respectively. Also, the strain ε_OB is in the direction of the new rotated coordinate x´. This gives

      ε_OA = ε_y = 0.00150 = 1,500 μ

      ε_OB = ε_x´ = 0.00250 = 2,500 μ

      ε_OC = ε_x = 0.00200 = 2,000 μ

Since strain is generally a very small number, the symbol μ "micro-strain" is commonly used to represent 10^-6. This symbol does not represent units, and strain is still unit-less.

The stress element needs to be rotated 45^o in the positive direction. Using the stress transformation equations, the stresses in the new x'-y' coordinate system will be,

     2,500 μ = 1,750 μ + 0 + γ_xy/2

     γ_xy = 750 μ = 0.000750

The maximum shear strain can be found by

     γ_max = 450.7μ = 0.0004507

The maximum shear strain will on a plane that is rotated θ_γ-max. That angle is,

     θ_γ-max = -16.85^o