ENGINEERING MECHANICS FORMULAE

ducktowndivergentMechanics

Oct 30, 2013 (3 years and 9 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)


(when loaded perpendicular 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


Axial loading:

Lateral strain:

Beam bending:

Second moment of area:




Rectangle about N.A.:




Circle about diameter:





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

Radius =


Biaxial S
train





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3


Tan 2

p =



45


瑲慩a⁇慵来⁒
潳o瑴e



(

at 45

)


Stress/Strain T
ransformation



,



,




,


,



Von Mises Equivalent S
tress