A

area

B

width

C

carryover factor, torsional rigidity

c

distance from neutral axis to outer fiber

D

distribution factor, flexural rigidity of plate

[D]

elasticity matrix

d

diameter, distance

E

modulus of elasticity in tension or compression

E_s

modulus of plasticity or secant modulus

E_t

tangent modulus

e

dilatation, distance, eccentricity

{F}

nodal force matrix of bar and beam finite elements

F

body force per unit volume, concentrated force

f

coefficient of friction

{ f}

displacement function of finite element

G

modulus of elasticity in shear or modulus of rigidity

g

acceleration of gravity (≈9.81 m/s²)

h

depth of beam, height, membrane deflection, mesh width

I

moment of inertia of area, stress invariant

J

polar moment of inertia of area, strain invariant

K

bulk modulus, spring constant of an elastic support, stiffness factor, thermal conductivity, fatigue factor, strength coefficient, stress concentration factor

[K]

stiffness matrix of whole structure

k

constant, modulus of elastic foundation, spring constant

[k]

stiffness matrix of finite element

L

length, span

l, m, n

direction cosines

M

moment

M_xy

twisting moment in plates

m

moment caused by unit load

N

fatigue life (cycles), force

n

factor of safety, number, strain hardening index

P

concentrated force

p

distributed load per unit length or area, pressure, stress resultant

Q

first moment of area, heat flow per unit length, shearing force

{Q}

nodal force matrix of two-dimensional finite element

R

radius, reaction

r

radius, radius of gyration

r, θ

polar coordinates

S

elastic section modulus, shear center

s

distance along a line or a curve

T

temperature, twisting couple or torque

t

thickness

U

strain energy

U_o

strain energy per unit volume

U*

complementary energy

u, υ, w

components of displacement

V

shearing force, volume

υ

velocity

W

weight, work

x, y, z

rectangular coordinates

Z

plastic section modulus

α

angle, coefficient of thermal expansion, form factor for shear

b

numerical factor, angle

γ

shear strain, weight per unit volume or specific weight, angle

δ

deflection, finite difference operator, variational symbol, displacement

{δ}

nodal displacement matrix of finite element

∆

change of a function

ε

normal strain

θ

angle, angle of twist per unit length, slope

ν

Poisson’s ratio

λ

axial load factor, Lamé constant

Π

potential energy

ρ

density (mass per unit volume), radius

σ

normal stress

τ

shear stress

φ

total angle of twist

Φ

stress function

ω

angular velocity

ψ

stream function