Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Fundamental Mechanics
of Materials Equations
APPENDIXE
Common Greek letters
α Alpha µ
β
γ
Beta
Gamma
Mu
Nu
Pi
∆, δ Delta ρ Rho
ε
θ
κ
λ
Epsilon Σ, σ Sigma
Theta
Kappa
Lambda
ν
π
τ
φ
ω
Tau
Phi
Omega
Basic definitions
Average normal stress in an axial member
F
σ avg =
A
Average direct shear stress
V
τ avg =
A V
Average bearing stress
F
σ b =
A
b
Average normal strain in an axial member
L δ
εlong
= ∆ =
L L
d
t
h
εlat
= ∆ or
∆ or
∆
d
t
h
Average normal strain caused by temperature change
εT
= α ∆T
Average shear strain
π
γ = change in angle from rad 2
Hooke’s law (one-dimensional)
σ = Eε
and τ = Gγ
Poisson’s ratio
εlat
ν =−
ε
long
Relationship between E, G, and ν
E
G =
2(1 + ν)
Definition of allowable stress
σ failure
τ
σ allow = or τ allow =
FS
FS
Factor of safety
σ failure
τ
FS = or FS =
σ
τ
actual
Axial deformation
Deformation in axial members
failure
actual
failure
FL
FL i i
δ = or δ = ∑
AE
i
AE i i
Force-temperature-deformation relationship
FL
δ = + α∆TL
AE
Torsion
Maximum torsion shear stress in a circular shaft
Tc
τ max =
J
where the polar moment of inertia J is defined as:
π π J = [ R
4 − r
4 ] = [ D
4 − d
4 ]
2 32
Angle of twist in a circular shaft
TL
TL i i
φ = or φ = ∑
JG
JG
Power transmission in a shaft
P = Tω
Power units and conversion factors
1W
1N ⋅ m
550 lb⋅ft
6,600 lb⋅in.
=
1hp = =
s
s
s
1rev
1Hz = 1rev = 2π
rad
s
1rpm 2 π
=
rad
60 s
i
i
i
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