Definitions & Terms Flashcards
statically intedeterminate
– over-stiff
– too many unknowns to find a solutions
statically determinate
– just stiff
– you have the same number of equilibrium equations as unknown forces
mechanism
–more equilibrium equations than unknowns
ties
tension only structures
truss
– tie when tension–only
–strut when compression only
formula for pin jointed structures
number of members (ties/struts) + number of reactions(depends on the supports at the bottom) ~ 2 x number of joints (pins, rollers, etc. at bottom)
statically determinate
nm + nr = 2nj
statically indeterminate
nm + nr > 2nj
mechanism
nm + nr
beam
laterally loaded structural member where the cross sectional area is significantly less than its length
Young’s Modulus
– a measure of elasticity, equal to the ratio of the stress acting on a substance to the strain produced.
– represents the straight line portion of a stress strain diagram
Tangent Modulus
– general term defined as the local gradient of the stress-strain curve
–same as Young’s Modulus in the linear elastic region
–unique at other points
elastic modulus
–same as Young’s Modulus
– shear and tensile Young’s moduli
elastic behaviour
–deformation that is fully recoverable when stress is removed
– if behaviour is Hookean, then elastic response is linear
Hooke’s Law
– extension is directly proportional to the load applied
material yield
– material yields and maintains structural integrity (no failure) but it does not recover to the initial state on unloading
tensile strength
– maximum stress a material withstands before failing is its ultimate tensile strength
is stress x strain work?
yes! internal work done!
hysteresis loop
– strain energy dissipated as heat to deform the body beyond the elastic limit in tension and compression
strain hardening
– change of yield point after plastic deformation
toughness
– large area under stress strain curve
brittle materials
– small region under stress strain curve
ducility
– ability of a metal to be stretched into a wire
– measure of toughness
small strain
– bulk and shear modulus
– poisson’s ratio
large strain
–yield stress
–tensile strength
isotropy
– properties of material are independent of direction or orientation
homogeneity
properties do not vary from location to location in material
incompressibility
– constant density (no volume changes)
creep
– keep the applied stress constant
– strain of the material changes (goes up and curves over and down)
stress relaxation
–keep strain constant
–stress needed to keep the material at that strain value lowers
hardness
– resistantce to point loading (indentation damage)
normal stress formula
stress = force/area
normal strain formula
strain = change in length/length
rigidity
– Relative stiffness of a material that allows it to resist bending
ashby chart
– young’s modulus vs density
hydrostatic stress
– stress is equal in all directions
shear modulus symbol and alternate name?
–modulus of rigidity (G)
bulk modulus symbol?
K
poisson’s ratio
–normal stress results in normal and lateral strains
–within the elastic limit the ratios of these are:
v = -(lateral strain)/(normal stress)
anisotropic
–21 independent elastic constants
–different behaviour in all orientations and directions
orthotropic
– 9 independent elastic constants
–material symmetry in three mutually perpendicular planes
transversely isotropic
– 5 independent elastic constants
–material symmetry in one plane
isotropic
– 2 independent elastic constants
– same behaviour in all orientations and directions
plane stress
stress whereby one normal stress and associated shear stresses are 0
plane strain
strain whereby one normal strain and associated shear strains are assumed to be zero
Tresca Failure Theory
– used to predict yielding and is applicable to ductile materials
–max shear stress in a material reaches a value of max shear stress that would be observed when yielding occurs
–hexagon
– static loading
von Mieses Failure Theory
– used to predict yielding and is applicable for ductile materials
–occurs when the root mean square of the difference between the principal stresses is equal to the yield of the material established by a simple tension test
–ellipse
–static loading
Rankine’s failure theory
– used for brittle materials
–static loading
safety factor
SF = ultimate stress/permitted stress
–safety factor of a hip implant is 1
–safety factor of a car is 3
static strength
ability to resist a short term steady load at normal room temperature
fatigue strength
ability to resist a fluctuating/time variable load
creep strength
ability to resist a load at temperatures high enough for the load to produce a progressive change in dimensions over an extended period of time
toughness
resistance to brittle fracture
brittle fracture
fast, low-energy, occurs at a stress level below that required to produce yielding across the whole cross-section
tough fracture
slow, high-energy, occurs at a stress level equal to that required to produce yielding across the whole cross section
stiffness
ability of a structure to maintain its shape when loaded
fatigue strength
the amplitude (or range) of cyclic stress that can be applied to the material without causing fatigue failure.
endurance/fatigue limit
same as fatigue strength
assumptions for a uniformly loaded thin shell
–thin (diameter less than thickness)
–uniform pressure loading
–no resistance in bending
pure bending
constant bending moment along the length
stable equilibrium
– a small disturbance is applied, the mechanical system has the tendency to restore its initial position
restoring moment>displacing moment
unstable equilibrium
– small disturbance is applied the mechanical system has the tendency to move/accelerate towards the same direction as the disturbance
restoring moment
critical condition
restoring moment ≠ displacing moment
the load is the critical load
