(Solved): Part C - Calculate stress A point in a material experiences strain \epsi lon_(x)=195(10^(-6)). The ...
Part C - Calculate stress A point in a material experiences strain
\epsi lon_(x)=195(10^(-6)). The strains along the other two axes are zero. What is the stress in the
z-direction? Use
E=200GPa and
u =0.26. Express your answer with appropriate units to three significant figures. View Available Hint(s)
\sigma _(z)=Part A - Calculate strain Learning Goal: A material is homogenous and isotropic when it has a modulus of elasticity that does not vary with direction and it has uniform properties throughout. When a point in a material is subjected to only normal stresses in three dimensions, but they are not necessarily equal, the state is called triaxial stress. When the response of the material is linear elastic, the strains along the three axes can be calculated using a generalized form of Hooke's law. Each strain depends on all three stresses because of the Poisson effect.
\epsi lon_(x)=(1)/(E)[\sigma _(x)-
u (\sigma _(y)+\sigma _(z))]
\epsi lon_(y)=(1)/(E)[\sigma _(y)-
u (\sigma _(x)+\sigma _(z))]
\epsi lon_(z)=(1)/(E)[\sigma _(z)-
u (\sigma _(x)+\sigma _(y))]Figure A cube is subjected to stresses with magnitudes
a=15MPa,b=23MPa, and
c=8MPa(Figure 1). What is the strain in the
y-direction? Let
E=200GPa and
u =0.26. Express your answer to three significant figures. View Available Hint(s)
\epsi lon_(y)=Previous Answers Incorrect; Try Again; 4 attempts remaining Part B - Change in volume The cube from Part A originally has side length 4.7 cm . What is the change in volume of the cube under the given stresses? Express your answer with appropriate units to three significant figures. View Available Hint(s)
