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Stress Formulas

PROPERTY

Formula

Units

Example

DENSITY: Mass per unit volume 

= Mass (kg)  /  Volume (m3)

kg / m3

Steel = 7800

STRENGTH: How much Stress it can 'take'
Ultimate Strength (max stress before breaking)
Yield Strength (max stress before plastic)
Stresses: Tensile & Compression (Axial),  Shear
Fatigue: Max stress under millions of reps
Working/Allowable; 'Safe' stress, design value

= Force (N)  /  Area (mm2)

MPa

 
1020 Steel UTS = 400MPa
1020 Steel YS = 200MPa
1020 Steel SS = MPa
Steel Grade 250 FS = 207MPa
1020 ATS = 120MPa

HARDNESS: Resistance to indentation or abrasion

Size or depth of indent 

varies

HRC55  (Rockwell) etc

STIFFNESS: How much Stress for a certain Strain
Young's Modulus, Elastic Modulus

= Stress (MPa)  /  Strain

MPa

1020 Steel E = 205GPa

TOUGHNESS: Energy to break

= Area under Stress-Strain curve

J / m2

Charpy Test (Joules)

ELASTICITY: Ability to Stretch with plasticity

= Strain at yield

%

1020 Steel: 0.01% @ yield

PLASTICITY: Permanent deformation:
Ductility = tensile plasticity
Malleablility = compressive plasticity

= (L2 - L1) / L1

%

1020 Steel:  25%

POISSON'S RATIO: side strain to axial strain

v = ex / ey

-

1020 Steel v = 0.29


Stress-Strain Diagram

   

DEFINE >

Formula>

Units>

Diagram>

Axial Stress (Tension or Compression) 

Stress = Force / Area

MPa


Axial Strain (Tension or Compression) 

Strain = extension / original Length

-


Shear Stress

Stress = Force / Area

MPa


Modulus of Elasticity (Young's Mod)

E = Stress / Strain

GPa

Slope of Stress:Strain diagram

Modulus of Rigidity (Shear Mod.) =~ 0.4E

G = S. Stress / S. Strain

GPa

Slope of S.Stress:S.Strain diagram

Shear Strain

Strain = movement / original Depth

-


Shear in Detail:

Shear Strain is usually small enough to ignore the changes in L with angle. 

Angle is in radians.

Area is the zone that would slide apart  assuming it broke in shear.





Bolted Joints

Find Force for the 3 modes of failure - lowest force is critical


Welds

Typically, electrode 41** are 410MPa. Take 410 / 3 = 136.7MPa



Pressure Vessels

Hint: Pipes are simply cylinders with pure hoop stress.


Beam Bending

Find M and I, the rest is a simple equation...


Torsion