Biomechanics Exam 2

Stresses straight down down the diagonal

Principal stresses

Stresses in the upper right and lower left corners

Shear stresses

Stresses in 2D equilibrium

2 normal, 1 shear

Stresses in 3D principal equilibrium 

3 normal, 3 shear 

Special case stresses in equilibrium 

xy = yx , zx = xz , yx = zy 

Angle of rotation of principle stress

xy’ = 0

Angle of rotation of shear stress

xx’ = yy’

angle of rotation of principle compared to rotation of shear

always 45 degrees apart

e

Linearized strain, simplified solution

E

green strain, nonlinear most accurate

What material characteristics can be used to identify the framework for deterring a constitutive equation 

Elastic vs nonelastic, linear vs nonlinear, homogenous vs heterogenous, Isotropic vs Anisotropic 

Equations for LEHI

poisson’s ration (v) , elastic modulus (E) , shear modulus G

transverse isotropic

one direction has different mechanical properties

Orthotropic

different mechanical properties in all three axes

Displacement equation

u(x) = integral (0 to L) F/EA dx = Fx/EA or u(x=l) = FL/EA

Where do you make a cut for bending

For any changes in length, force or modulus

V

Internal shear force 

M

Internal moment

Bending shear stress xy

proportional to v(x), depends on cross sectional area, depends on y but opposite for normal stress 

bending normal stress

0 at the center, highest at the edges

bending shear stress

0 at the edges, highest in the center

distributed load constant load equations

qa,

distributed load decreasing load

inegral (0 to L) qa +(qb-qa/L)x