Bone
Stress in bones: Internal distribution of external loads.
Strength in bones: material property of the bone and can change over time.
U = displacement
F = Force
L0 = begin length
LΔ = elongation (=u)
Force-displacement plot / stress-strain plot
Plastic part: permanent deformation, even after load removal.
Linear part: deformation disappears after load removal.
Linear relation between load and deformation.
F = K * u (K=spring constant, slope straight curve)
σ = E * ε (E=modulus of elasticity or ‘Young’s modulus’)
Yield point: between linear elastic to plastic part, after yield point, permanent
strain occurs.
Mostly, deformation is too small to be seen with the naked eye.
More Force increases elongation.
Smaller cross sectional area increases
elongation.
Further away from neutral line, higher stress.
(inhomogeneous stress distribution)
σ = M * y/I
y = distance from neutral line to the stress location
I = area moment of inertia (resistance against bending)
, Binding stress due to shear force: σ = (F*x*y)/I
This means stress is maximal at x = max and y = max.
Principle of superposition: eccentric force
An eccentric force can be divided into bending and
compression.
This results in a shift of the neutral zone.
Finite element analysis: Method to calculate internal loads (stresses) and deformations (strains) of a
certain object using a computational model.
Useful equations
Calculating compressive (or tensile) stress:
F
σ compr. (or tens. )=
A
in which: σ = compressive or tensile stress [N/m2]
F = force [N]
A = cross-sectional area [m2]
Calculating shear stress:
F
τ=
A
in which: τ = shear stress [N/m2]
F = force [N]
A = cross-sectional area [m2]
Calculating bending stress:
M⋅y
σ bending =
I
in which: M = moment of force [Nm]
y = (maximal) distance to the neutral layer
I = moment of inertia
Moment of inertia of a hollow pipe:
1
I = 4⋅π⋅( R 4− R 4 )
out in
Hooke’s law:
σ =E⋅ε
Stress in bones: Internal distribution of external loads.
Strength in bones: material property of the bone and can change over time.
U = displacement
F = Force
L0 = begin length
LΔ = elongation (=u)
Force-displacement plot / stress-strain plot
Plastic part: permanent deformation, even after load removal.
Linear part: deformation disappears after load removal.
Linear relation between load and deformation.
F = K * u (K=spring constant, slope straight curve)
σ = E * ε (E=modulus of elasticity or ‘Young’s modulus’)
Yield point: between linear elastic to plastic part, after yield point, permanent
strain occurs.
Mostly, deformation is too small to be seen with the naked eye.
More Force increases elongation.
Smaller cross sectional area increases
elongation.
Further away from neutral line, higher stress.
(inhomogeneous stress distribution)
σ = M * y/I
y = distance from neutral line to the stress location
I = area moment of inertia (resistance against bending)
, Binding stress due to shear force: σ = (F*x*y)/I
This means stress is maximal at x = max and y = max.
Principle of superposition: eccentric force
An eccentric force can be divided into bending and
compression.
This results in a shift of the neutral zone.
Finite element analysis: Method to calculate internal loads (stresses) and deformations (strains) of a
certain object using a computational model.
Useful equations
Calculating compressive (or tensile) stress:
F
σ compr. (or tens. )=
A
in which: σ = compressive or tensile stress [N/m2]
F = force [N]
A = cross-sectional area [m2]
Calculating shear stress:
F
τ=
A
in which: τ = shear stress [N/m2]
F = force [N]
A = cross-sectional area [m2]
Calculating bending stress:
M⋅y
σ bending =
I
in which: M = moment of force [Nm]
y = (maximal) distance to the neutral layer
I = moment of inertia
Moment of inertia of a hollow pipe:
1
I = 4⋅π⋅( R 4− R 4 )
out in
Hooke’s law:
σ =E⋅ε
