ENGG1700: Statics and Materials

how do you draw a tension force?

as an arrow away from the connection → always assume tension at the connection

how to find the proportion of the forces (aka Δx , y or z)?

for a change in x: cos θ = Δx/L → same for y and z

how to determine what coordinates go in what order for L?

tip-to-tail: if arrow is pointing a direction, start at coordinates closest to tip of arrow and subtract the tail (e.g. if F_AB, then B - A)

how to find total force in certain direction using tension force and length?

F_x = F_T x L

what is a moment?

when a force is applied to an object and the object’s body rotates (aka torque)

what is the magnitude of a moment at a point?

force x perpendicular distance

→ if force is in x-y plane, then it’s a moment around z-axis and vice versa (a moment perpendicular to where force is between)

what is a force couple?

two forces equal in magnitude that are parallel but opposite in direction

what is a moment centre?

a moment of force creates a tendency of that force to rotate a body about a selected point or axis

how to find moments using x-y components?

1. separate original force into its x and y components

2. find if the moments are positive or negative

3. for x: multiply the x component value by the distance perpendicular to x axis (and do the same for y)

4. add up the values in step 4 to find total moment

how to find moments using the principle of transmissibility?

move the force point along its line of action until it hits the y-axis where the y-component’s p.d is 0 (applies no moment) and you can only use x

when is no moment applied?

when a force is parallel to corresponding axis or intersects it

what are properties of metals?

good heat and electrical conductors and is strong, deformable and good machinability

what are properties of ceramics?

are electrical and thermal conductors that are resistant to high temperature and harsh environments, are hard and brittle

what are properties of polymers?

primarily consisted of hydrogen and carbon, large molecules, have low densities and are flexible

what are properties of composites?

achieves a perfect combination of properties or combination of best characteristics of each materials e.g. wood, fibreglass

what is primary bonding?

tendency of atoms to obtain stable electrons through valence electrons e.g. ionic, covalent and metallic bonding

what is ionic bonding?

a valence electron in outer shell from one atom will be given to another to form two ions with complete shells → has strong bonds that are complex and electrically neutral

what is covalent bonding?

the sharing of electrons between two atoms → is a strong bond such as C-H bond

what is secondary bonding/van der Waals bonding?

weaker than primary bonds and are between molecules due to moving electrons

induced dipoles and polar molecules (permanent dipoles)

very weak and dependent on distance

what is hydrogen bonding?

very strong bonding between hydrogen and fluorine, nitrogen, oxygen, etc

what is the formula for net force in interatomic forces?

F_N = F_A + F_R (attraction + repulsion)

what is the formula for net energy in interatomic forces?

integral between infinity and r of F_N (r is distance between 2 atoms)

what is a face-centred cubic crystal structure?

• common in materials such as silver and gold

• closely packed and has 4 atoms per unit cell (per face of structure)

• coordination number 12

• APF (volume of atoms in unit cell) = 0.74

what is a body-centred cubic crystal structure?

• less closely-packed than FCC

• common materials include iron and chromium

• 2 atoms per unit cell

• coordination number 8

• APF = 0.68

what is a hexagonal close-packed crystal structure?

• as closely-packed as FCC

• common materials include zinc and cobalt

• 6 atoms per unit cell

• coordination number 12

• APF = 0.74

what is a polycrystalline structure?

a solid material made up of many small, distinct crystal regions called grains, where different grains face different directions and cause grain boundaries

what is an amorphous structure?

an arrangement of atoms or molecules in a solid that lacks a long-range repeating pattern

what is equilibirum?

when an object is at rest, it is in static equilibrium meaning the resultant forces acting on objects must be 0

what are free-body diagrams?

shows the applied forces and moments on a body

what is a concurrent coplanar system?

a group of forces that are in the same 2D plane and meet at the same common point

what are collinear systems?

a group of forces whose lines of action or paths lie precisely along a single, shared straight line

what is the density of water?

1000kg/m³

what is the formula for buoyancy?

B = vpg where p is density

what is deformation?

when a material carries a load, solids can change shape by contracting or stretching when a mechanical force is applied to it

what is stress?

force or load which happens to be acting in that direction at the point divided by the area on which the force acts (F/A₀ N/m²) aka how hard atoms at any point are being pulled apart

what is the conversion from N/m² to Pa?

1 N/m² = 1 Pa

what is conversion from kPa to MPa?

1 kPa = 0.001 MPa (divide by 1000, multiply by 1000)

what is strain?

how far apart atoms are being pulled (what proportion the bonds between atoms are stretched) - has no units

what is the formula for strain?

strain = (length after load is applied - original load)/original load

strain = ΔL/L₀

what is young’s modulus?

a mechanical property that measures the stiffness of a solid material

E = stress/strain

what is yield strength?

the stress at which plastic deformation begins (break/permanently deform a piece of material) → on y-axis

what is ultimate tensile strength (UTS)?

maximum stress that can be sustained by a material in tension

what is a stress-strain diagram?

• elastic region: obeys hooke’s law, elastic deformation when stress > yield strength (elastic region ends at yield strength)

• UTS: highest point

• plastic region: material does not obey hooke’s law

what is % elongation?

how much a material stretches before it breaks:

%EL = (l_f - l₀)/l₀ × 100%

what is percent reduction in area?

measures how much cross-sectional area shrink:

%EL = (A₀ - A_f)/A₀ × 100%

what is an equivalent force system?

is an equivalent force system if the external effects are the same as the original force system

what is a support?

means of preventing translation of an object in a specific direction by exerting a force on the object in the opposite direction or the means of preventing the rotation of an object by exerting either a force couple or moment on object in opposite direction

how does plastic deformation occur?

through the motion of dislocations (crystalline defect) which include edge dislocation and screw dislocations

what is a slip dislocation motion?

deformation occurs as a collective effect of the motion of a large quantity of dislocation where the extra half length of atom traverses across the entire crystal (driven by sheer stress) and dislocation lines propagate toward direction until reaches other side of lattice

what is dislocation-lattice strain?

the presence of a dislocation generates a lattice strain/stress where atoms are subjected to compressive stress in top half of lattice and tension in bottom half

strain fields interact

what are the 3 mechanisms of strengthening metals?

1. grain refinement

2. solid solution/alloying

3. strain hardening

what is grain refinement?

by introducing grain boundaries (by making crystals smaller), it is more difficult for a dislocation passing from grain A to B as it must change its direction of motion (extra energy)

what is the grain size and yield strength graph?

• yield strength increases with a decrease in grain size

• to find constants in hall-petch equation, pick two points from graph and put into equation

what is hall-petch equation?

σ_y = σ_o + k_y x d^-1/2

what is solid-solution/alloying?

incorporating impurity atoms into materials to make it harder to deform (making it less ductile) as they travel to where dislocations are to stop them and restrict dislocation movement

• adding atom of different element that is bigger = compression

• adding atom of different element that is smaller = tension

what is strain hardening?

a ductile metal becomes harder and stronger after it is plastically deformed, the motion of a dislocation is hindered by the presence of other dislocations

what is cold-working?

strain hardening is done at a temperature much lower than room temperature e.g. cold rolling (thicker metal place between two rollers makes plate into elongated structure which introduces microscopical anisotropy)

what is the reverse of strain hardening?

annealing → subjecting to a particular temperature for a particular amount of time

what is the formula for % of cold work?

%CW = (A₀ - A_D/A₀) x 100%

what happens when we strengthen a material?

stiffness increases, ductility and flexibility reduces

what is the order of polymer molecular structure based on resistance to deformation?

1. linear: flexible and soft

2. branched

3. crosslinked

4. network: stiffest and strongest

what is the crystallinity of polymers?

crystalline polymers are stronger and more resistant to dissolution and softening by heat

what are the reactions in a smooth-contacting surface?

normal force (vertical)

what are the reactions in a rough-contacting surface?

normal force (vertical) and friction (horizontal)

what are the reactions in a pinned support?

vertical and horizontal

what are the reactions in a roller support?

vertical

what are the reactions in a fixed support (cantilever)?

around, vertical and horizontal

what is a point load?

3 points of reaction forces

what is a uniformly-distributed load?

self-weight of structural elements e.g. in a line

force per metre = force per person/separation per person

what is a uniformly varying load?

the weight of the soil creates a pressure against retaining wall where P increases with depth H

what is equivalent point load?

equal to area under varying load and applies to centroid of shape (triangle = 1m up)

what is hooke’s law?

yield strength = E x strain_max