Biomechanics Exam 3

stress

external applied load

strain

deformation caused

mechanical stress

how an applied force is distributed over the body it acts on

mecahnical stress equation

σ = 𝑭/A

three principal stresses

tension

compression

shear

axial stress

external forces act perpendicular (normal) to the analysis plane

aka normal or longitudinal stress

uniaxial load

external forces are colinear

tensile stress

an axial or normal stress

occurs at the analysis plane as a resulr of a force or load pulling the molecules apart at that plane

causes body to deform by stretching (elongating)

larger cross-sectional area

lower stress

smaller cross-sectional area

higher stress

compressive stress

an axial or normal stress

occurs at the analysis plane as a result of a load squeezing the molecules together at that plane

causes body to deform by shortening

shear stress

a transverse stress

acts paralleled to the analysis plane as a result of non-colineaer forces sliding molecules at that plane

causes body to deform by skewing (changes orientation of the sides of the object

tension injuries

sprains (rupture) ligament and tendon

strains (tear) muscle and cartilage

compression injuries

bruises soft tissue

crushing fracture of bone

shear injuries

blister on skin

dislocation of a joint

complex loading (not uniaxial)

bending

torsion

combined loads

complexity of loading reflects

number, direction and location of external forces imposed

shape of the object itself

bending load

nonaxial loading

tension and compression produced at the analysis plane from 3 or more forces creating force couples at opposite ends of the object

tends to rotate ends of the body in opposite directions at the analysis plane

torion load

nonaxial loading

shear stress acts parallel to the analysis plane as a result of opposing torques applied about the long axis of the body

causes body to deform by twisting (shear stress increases with greater distance from axis

torsion resistance

tubular and hollow cross-section of bones

combined loading

human bones under complex loading from gravity, tendons, ligaments, other bones, contact forces

sustained loading a combination of

tension

compression

simple shear loads

bending

torsion

strain

quantifies the material’s deformation

linear strain

change in an object’s length

deformation produced by tensile or compressive stress

linear strain reported in absolute terms

describing the change in length

intervertebral disc compressed 2mm

linear strain reported in relative terms

as a proportional length change

(deformed length — undeformed length) / undeformed length

linear stress equation

ε = (ℓ – ℓo ) / ℓ

linear stress units

dimensionless

ε is a ratio

often reported as a percentage: ε x 100

shear strain

change in orientation of an object’s adjacent molecules

deformation produced by shear stress

shear strain math

△⍬

reported as the change in angle of a perpendicular plane

shear strain units

radians

poisson’s ratio

width of an object also changes as it lengthens or shortens

transverse strain

object lengthens: object gets wider

object shortens: object gets narrower

poisson’s ratio equation

(axial strain) / (transverse strain)

poisson’s ratio range

0.1 to 0.5 (dimensionless)

typically 0.25 to 0.35

stress-strain relationship

describes the behavior of a material under load

elastic behavior

material deforms and returns to original length when unloaded

elastic behavior equation

E = △σ / △ε

elastic modulus (E)

slope of the stress-strain curve

aka Young’s modulus

bulk modulus

slope describing compressive loading

shear modulus

slope describing shear loading

stiff material

less strain per unit of stress (large E)

pilant material

more strain per unit of stress (low E)

plastic behavior

material deforms but doesn’t return to original length

permanent deformation (disruption of internal structure)

elastic limit

the yield point for a material on the σ/ε curve

stress beyond this point causes permanent deformation of material

mechanical strength of a material

maximum stress a material can withstand before failure

yield strength

stress at the elastic limit

disruption of internal organization, material does not regain shape

ultimate strength

maximum stress material can withstand

material starts to give way

failure strength

stress level where total failure occurs

breakage or complete rupture of the material occurs

failure strain

strain exhibited when a total failure occurs

ductile material

exhibits a large failure strain

deforms a lot before giving way (ligament)

brittle material

exhibits low failure strain

deforms minimally before giving way (bone)

toughness

ability of a material to absorb energy before failure

active element of connective tissue

muscle

passive elements of connective tissue

bone

cartilage

ligament

tendon

collagen

a fibrous protein

very stiff

elastin

a fibrous protein

very pilant

isotropic

stiffness similar in different directions

anisotropic

stiffness dependent on load direction

mechanical properties of bone

strongest and stiffest material in musculoskeletal system

compression > tension > shear

strength affected by rate of loading

mechanical properties of cartilage

hyaline (articular): covers bone ends at joints

fibrous: specialized in joints (intervertebral disks, menisci)

mechanical properties of tenons and ligaments

ligaments have more elastin that tendons

collagen fibers in bundles aligned with functional axis

high stiffness to tensile loading

mechanical properties of muscle

active component (sarcomere) determines muscle stiffness

passive component (connective tissue sheaths) create high failure strain

skeletal system components

bones

joints

cartilage

ligaments

axial skeleton

skull

vertebral column

rib cage (74 bones)

appendicular skeleton

upper and lower extremities (126 bones)

basic skeletal mechanics

bones constitute rigid links

they are connected at joints (articulation)

they are acted on by muscles

support soft tissue

provide protection to vital organs

provide sites for metabolic function

skull and vertebrae protect

brain and spinal cord

ribs and sternum protect

heart, lungs, major blood vessels, liver, spleen

pelvis protects

reproductive organs, bladder

skeletal metabolic function

store calcium and phosphorous

red marrow produces blood cells and platelets

cortical (compact) bone tissue

dense and compact

cancellous (spongy, trabecular)

porous and spongy

bone ____ to mechanical loading

responds (adapts)

long bones

humerus

radius

ulna

metacarpals

phalanges

clavicle

short bones

carpals

tarsals

flat bones

ribs

skull bones

scapula

sternum

pelvic bones

irregular bones

vertebrae

facial bones

long bone anatomy: outer shell composed of ____

cortical bone

long bone anatomy: long shaft covered by_____

periosteum

hollow core (medullary cavity) filled with red marrow

hollow core keeps bones light but strong

long bone anatomy: expanded ends covered with ______

articular cartilage at joints

composed of cancellous bone below cortical shell

condyle

rounded projection for joint articulation

epicondyle

rounded projection for muscle attachment

facet

a small, smooth, and usually flat articular surface

foramen

a hole, usually for nerves or vessels passage

fossa

a hollow depression or pit

fovea

a smaller hollow depression or pit

head

spherical articular end of a long bone

line

a raised line or small ridge

neck

part of a bone joining the head to the shaft

notch

an indentation on the border or edge of a bone

process

a projecting part of bone

spine

a sharp projecting part of bone

trochanter

a large, knobby projection

tubercle

a small, knobby projection

tuberosity

a knobby projection

endochondral ossification

bone development

cartilage is replaced by bone

epiphyseal plate (growth plate)

responsible for longitudinal growth

most close during puberty; some open until age 25

circumferential growth (bone diameter)

bone deposited under periosteum, bone absorbed at medullary

continues throughout life

joint

where two bones meet

mechanical function of joints

join bones while controlling motion

transfer force between bones