Mechanics of Materials reminder stuff

Which way is tension and which is compression?

Tension = ← [object] → (think like a string)

Compression = → [obj] ←

Unit for stress?

Pascal (Pa)

What are the units of a Pa

N/m² = kg/(m*s²)

Factor of Safety? F.S.

permitted stress/actual stress
permitted stress = theoretical load. The amount that would cause our part to break
actual stress = actual load. The amount that we calculate/have rn.

What is a kip

1000 lb

What does negative stress mean in normal stress?

The part is under compression (compressive stress)
Positive stress number suggests tensile stress

Normal Stress

σ = P/A
σ = Normal stress, P = axial force, A = cross sectional area

Shearing Stress

T = P / A
T = shearing stress (supposed to be tau not t), P = shearing force, A = cross sectional area

Double shear?

When shear occurs in two spots. You multiply the area by 2 lol, but the force stays constant

Strain

ε = δ / L
ε = Strain, δ = deformation, L = initial length

Bearing Stress

σ = P/A
σ = Bearing stress, P = load force, A = projected area

What is young’s mod also called

Elastic modulus

Young’s mod

E = σ / ε
E = young’s mod, σ = stress, ε = strain

Deformation

δ = PL / (AE)
δ = deformation, P = force, L = Length, A = cross section area, E = young’s mod

Total deormation?

Sum of all section deformations

Poisson’s ratio

V = - lateral strain / axial strain
The V represents nu letter
ranges from 0.0 (cork) to 0.5 (rubber)

How will a cube deform under shearing stress?

Will deform into a rhomboid

Shear strain of a cube

T = GY
T = tau = shearing strain (tau is also used for shearing stress for like bolts and stuff idk why)
G = Modulus of rigidity or shear modulus
Y = gamma = angle (demonstrated in pic)

Modulus of rigidity?

G = E/2(1+V)
G = modulus of rigidity (shear mod), E = young’s mod, V = poisson’s ratio

Stress concentration factor?

K = σ_max / σ_avg

Shearing strain (for torsion) (for cylinder)?

Y = ρ Φ / L
Y = gamma = shearing strain, ρ = distance of point from axis (largest is r), Φ = angle of deformation (looking at the cross section), L = length

Second polar moment of area of circle?

J = π r⁴ / 2

What is second polar moment of area also called

second moment of inertia

Second polar moment of area of a hollow circle

J outer - J inner

Shear stress for elastic torsion

T₁ = T ρ / J
T₁ = tau = shear stress, T = torsion, ρ = distance from center of axis (max is r), J is second polar moment of area
called torsion stress on formula sheet

How do ductile materials generally fail in torsion

Shear

How do brittle materials generally fail in torsion

Tension

Hooke’s law

σ = E ε

σ = stress, E = youngs mod, ε = strain
(i assume this is axial stress)

What is it called when something fails after repeated loadings?

Fatigue. Usually fails in a brittle nature.

Endurance limit

Stress for which failure doesn’t occur over an indefinitely large number of cycles

Fatigue limit

Stress corresponding to failure after a specified number of loading cycles

Deformation of a non homogeneous rod

δ = (integral from 0 to L) P dx / (A E)
δ = deformation, P = axial force, dx = integral thing, A = cross sectional area, E = young’s mod.

Angle of twist for an object in torsion

Φ = T L / (G J)

Φ = angle (looking at cross section), T = torsion, L = length, G = shear mod, J = 2nd polar moment of area

Power?

P = T ω
P = power, T = torque, ω = angular speed (rad/sec)

Units for power?

SI = N m / sec.
American = ft lb / sec

Horsepower?

550 ft lb / sec

Horsepower to watts

1 hp = 745.7 watts

Linear thermal expansion

δ = α (ΔT) L
δ = expansion amount (not final length), α = thermal expansion coefficient, ΔT = change in temp (in C unless α is in F units), L = length

Thermal strain

ε = α (ΔT)
ε = thermal strain, α = thermal expansion coefficient, ΔT = change in temp (in C unless α is in F units).

Gear ratio information

Large gear / smaller gear = ratio
Smaller gear spins ratio times faster
Bigger gear spins with ratio amount more torque.