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 Engineering Formulae
Strength of Materials

 Stress Pure Shear Strain Torsion Formula for Thin Walled Tubes Hooke's Law Torsion Formula for Circular Shaft Piosson's Ratio Flexure Formula Unit Volume Change Shear Stress in Bending Elongation due to its Weight Thin Walled Hollow Members (Tubes) Thin Rings Stress Concentration Strain Energy Curved Beam in Pure Bending Thin-walled Pressure vessels Bending of a Beam Mohr's Circle for Biaxial Stress

Stress where,       σ=normal stress, or tensile stress, pa

P=force applied, N

A=cross-sectional area of the bar, m2

=shearing stress, Pa

As=total area in shear, m2

Strain where,

=tensile or compressive strain, m/m

=total elongation in a bar, m

=original length of the bar, m

Hooke's Law

Stress is proportional to strain where,

E=proportionality constant called the elastic modulus or modulus of elasticity or Youngs modulus, Pa

Piosson's Ratio where,

v=Poissons ratio

=lateral strain

=axial strain

Unit Volume Change where,

=change in volume

=original volume

=strain

=Poissons ratio

Elongation due to its weight where,

=total elongation in a material which hangs vertically under its own weight

W=weight of the material

Thin Rings where,

=Circumferential or hoop Stress

S=Circumferential or hoop tension

A=Cross-sectional area

=Circumferential strain

E=Youngs modulus

Strain Energy where,

U=total energy stored in the bar or strain energy

P=tensile load

=total elongation in the bar

L=original length of the bar

A=cross-sectional area of the bar

E=Youngs modulus

U=strain energy per unit volume Thin Walled Pressure vessels where,

=normal or circumferential or hoop stress in cylindrical vessel, Pa

=normal or circumferential or hoop stress in spherical vessel,  Pa  and longitudinal stress around the circumference

P=internal pressure of cylinder, Pa

r=internal radius, m

t=thickness of wall, m

Mohr's Circle for Biaxial Stress Pure Shear where,

=Shearing Stress, Pa

=Shearing Strain or angular deformation

G=Shear modulus, Pa

E=Youngs modulus, Pa

V=Poissons ratio

Torsion formula for Thin walled tubes where,

=maximum shearing stress, Pa =Shearing stress at any point a distance x from the centre of a                           section

r=radius of the section, m

d=diameter of a solid circular shaft, m

=polar moment of inertia of a cross-sectional area, m4

T=resisting torque, N-m

N= rpm of shaft

P=power, kW =angle of twist, radian

L=length of shaft, m

G=shear modulus, Pa

do=outer diameter of hollow shaft, m

di=inner diameter of hollow shaft, m

and Torsion formula for Circular Shafts where,

=Ip, polar moment of inertia for thin-walled tubes

r=mean radius

t=wall thickness

Flexure Formula where,

=Stress on any point of cross-section at distance y from the                        neutral axis

=stress at outer fibre of the beam

c=distance measured from the neutral axis to the most remote fibre of the beam

I=moment of inertia of the cross-sectional area about the centroidal axis

Shear Stress In Bending where,

F=Shear force

Q=statistical moment about the neutral axis of the cross-section

b=width

I=moment of inertia of the cross-sectional area about the Centroidal axis.

Thin-Walled Hollow Members (Tubes) where,      =shearing stress at any point of a blue

t=thickness of tube

q=shear flow

T=applied torque

R=distance between a reference point and segment ds

Π=angle of twist of a hollow tube

Stress Concentration Curved Beam in Pure Bending where,     =normal stress

M=bending moment

dA=cross-sectional area of an element

r=distance of curved surface from the centre of curvature

A=cross-sectional area of beam

R=distance of neutral axis from the centre of curvature

R1=distance of centroidal axis from the centre of curvature

Bending of a Beam

(a) Bending of a Beam Supported at Both Ends (b) Bending of a Beam Fixed at one end where,     d= bending displacement, m

F=force applied, N

I=length of the beam, m

a=width of beam, m

b=thickness of beam, m

Y=Youngs modulus, N/m2  All Rights Reserved. eformulae 2005.