Mechanical Engineering Principles

A list of formulae

Formula Formula symbols Units

Stress =

applied force

cross-sectional area

σ=

F

A

Pa

Strain =

change in length

original length

ε=

x

L

Young’s modulus of elasticity =

stress

strain

E=

σ

ε

Pa

Stiffness =

force

extension

k=Fδ N/m

Modulus of rigidity =

shear stress

shear strain

G=

τ

γ

Pa

Thermal strain

=coefficient of linear expansion×temperature rise

ε=αT

Thermal stress in compound bar σ 1 =

(α 1 −α 2 )E 1 E 2 A 2 T

(A 1 E 1 +A 2 E 2 )

Pa

Ultimate tensile strength=

maximum load

original cross-sectional area

Pa

Moment = force×perpendicular distance M=Fd Nm

stress

distance from neutral axis

=

bending moment

second moment of area

=

Young’s modulus

radius of curvature

σ

y

=

M

I

=

E

R

N/m^3

Torque = force×perpendicular distance T=Fd Nm

Power = torque×angular velocity P=Tω= 2 πnT W

Horsepower 1 hp= 745 .7W

Torque=moment of inertia×angular acceleration T=Iα Nm

shear stress

radius

=

torque

polar second moment of area

=

(rigidity)(angle of twist)

length

τ

r

=

T

J

=

Gθ

L

N/m^3

Average velocity =

distance travelled

time taken

v=

s

t

m/s

Acceleration =

change in velocity

time taken

a=

v−u

t

m/s^2

Linear velocity v=ωr m/s

(Continued)