# ENGINEERING MECHANICS FORMULAE

Mechanics

Oct 30, 2013 (4 years and 6 months ago)

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1

ME213 Mechanics of Materials Formula S
heet

Materials

Young’s modulus
, Shear modulus

where
ν
is Poissons ratio

Thermal expansion:

Composite M
aterials

(when loa
ded parallel to fibres)

Viscoelastic M
aterials

Stress at time t (

t
⤠楮⁡⁶楳捯污獴楣⁭l瑥t楡氠畮摥爠潮獴a湴⁳n牡楮

t

=

e
-

䕴E

, where

c

is stress at time t = 0, and

is a constant (
known as the time constant).

Bending and Torsion

Lateral strain:

Beam bending:

Second moment of area:

Parallel Axis Theorem:

Shear and torsion:

where
τ

is the shear stress produced by a torque
T

τ

= G
γ

where
γ

is the shear strain

Polar second moment of area:

Solid circular shaft:

Hollow circular shaft:

Power in shaft = torque

angular velocity (ra
d/sec) = 2
π
nT where n is the revolutions per second

Euler

s formula for the buckling of slender axially loaded pin
-
ended columns:

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2

Thin
-
Walled Pressure V
essels

Cylindrical :

hoop stress
,

longitudinal stress

Spherical :

B
iaxial Stress
(Plane S
tress)

Principal S
tresses

Mohr’
s
Circle For S
tress

Centre

Biaxial S
train

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3

Tan 2

p =

45

瑲慩a⁇慵来⁒

(

at 45

)

Stress/Strain T
ransformation

,

,

,

,

Von Mises Equivalent S
tress