Question

A rectangular plate ABCD with base a = 654 mm and height b = 574 mm experiences the deformation illustrated below, resulting in the deformed plate AB*C*D*. Determine the normal strain of the side BC and the shear strain gamma at the corner B when delta_Bx = 2 mm delta_Cx = 3 mm, delta_Cy = 2 mm, delta_Dx = 2 mm and delta_Dy = 3 mm. Assume small deformations. Matlab input: a = 654: b = 574: dbx = 2: dcx = 3: dcy = 2: ddx = 2: ddy = 3: epsilon = ___________ middot 10⁻³

Answer 1

The calculation involves determining the normal strain on side BC, which is 0.00153, and shear strain (γ) at corner B, which is 0.00348, assuming small deformations.

Step-by-step explanation:

The student is asking about the normal strain and shear strain for a deformed rectangular plate. To calculate the normal strain (ε) on side BC, the change in length (δL) needs to be divided by the original length (L). In this case, δL is the difference in displacement between points B and C in the x-direction, which is (δ_Cx - δ_Bx). The original length L is the base 'a' of the rectangular plate. Therefore, the normal strain on side BC is:

ε = (δ_Cx - δ_Bx) / a

Substituting numbers:

ε = (3 mm - 2 mm) / 654 mm = 0.00153

Similarly, for the shear strain (γ) at the corner B, it is measured as the change in the original right angle between sides AB and BC. Since we assume small deformations, shear strain can be approximated using changes in displacement over the height 'b':

γ = (δ_Cy - δ_Bx) / b

γ = (2 mm - 0 mm) / 574 mm = 0.00348

Therefore, the normal strain (ε) in the material is 0.00153 (or 1.53 x 10⁻³ when expressed as a multiple of 10 to the power of minus three) and the shear strain (γ) is 0.00348.