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The content of the original site is very big so I pick up what structural engineer needs.
Copying the content for educational reasons. All rights belongs to the original owner.
Poisson's ratio is the ratio of the relative contraction strain, or transverse strain normal to the applied load, to the relative extension strain, or axial strain in the direction of the applied load.
Can be expressed as υ = - εt / εl (m/m) (1)
Where: υ = Poisson's ratio
εt = transverse strain
εl = longitudinal or axial strain
Strain can be expressed as ε = dl/L (2)
Where: dl = change in length
L = initial length
For most common materials the Poisson's ratio is in the range 0 - 0.5.
| Material | Poisson's Ratio |
| Upper limit | 0.5 |
| Aluminum | 0.334 |
| Aluminum, 6061-T6 | 0.35 |
| Aluminum, 2024-T4 | 0.32 |
| Glass | 0.24 |
| Stainless Steel 18-8 | 0.305 |
| Steel, cast | 0.265 |
| Steel, Cold-rolled | 0.287 |
| Steel, high carbon | 0.295 |
| Steel, mild | 0.303 |
| Concrete | 0.2 |
Stress can be expressed as stress = F / A (2)
Stress = (N/m2) (lb/in2, psi)
F = force (N) (lb)
A = area of object (m2) (in2)
Young's Modulus (Tensile Modulus)
Young's modulus or Tensile modulus can be expressed as
E = stress / strain = (F / A) / (dL / L) (3)
Where
E = Young's modulus (N/m2) (lb/in2, psi)
Hooke's Law
One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law which can be expressed as
Fs = -k dL (4)
Where
Fs = force in the spring (N)
k = spring constant (N/m)
dL = elongation of the spring (m)
Yield strength
Yield strength, or the yield point, is defined in engineering as the amount of strain that a material can undergo before moving from elastic deformation into plastic deformation.
Ultimate Tensile Strength
The Ultimate Tensile Strength - UTS - of a material is the limit stress at which the material actually breaks, with sudden release of the stored elastic energy.
1 N/m2 = 1x10-6 N/mm2 = 1 Pa = 1.4504x10-4 psi
1 psi (lb/in2) = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895x10-3 N/mm2
Modulus of Rigidity (or Shear Modulus) is the coefficient of elasticity for a shearing force. It is defined as "the ratio of shear stress to the displacement per unit sample length".
Modulus of Rigidity can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material.
Definition of Modulus of Rigidity:
The ratio of shear stress to the displacement per unit sample length
1 GPa = 0.145x106 psi (lbf/in2)
1 x 106 psi = 6.9 GPa
The Bulk Modulus Elasticity can be expressed as
E = - dp / (dV / V) (1)
Where E = bulk modulus elasticity
dp = differential change in pressure on the object
dV = differential change in volume of the object
V = initial volume of the object
The Bulk Modulus Elasticity can be alternatively expressed as E = dp / (dρ / ρ) (2)
Where: dρ = differential change in density of the object
ρ = initial density of the object
An increase in the pressure will decrease the volume (1). A decrease in the volume will increase the density (2).
The SI unit of the bulk modulus elasticity is N/m2 (Pa)
The imperial (BG) unit is lbf/in2 (psi)
1 lbf/in2 (psi) = 6.894 103 N/m2 (Pa)
A large Bulk Modulus indicates a relative incompressible fluid.
Bulk Modulus for some common fluids can be found in the table below:
| Material | Shear Modulus | |
| (106 psi) | (GPa) | |
| Aluminum Alloys | 3.9 | 27 |
| Aluminum, 6061-T6 | 3.8 | 24 |
| Aluminum, 2024-T4 | 4 | 28 |
| Carbon Steel | 11.2 | 77 |
| Concrete | 3 | 21 |
| Glass, 96% silica | 2.8 | 19 |
| Plywood | 0.09 | 0.62 |
| Structural Steel | 11.5 | 79.3 |
| Stainless Steel | 11.2 | 77.2 |
| Steel, Cast | 11.3 | 78 |
| Steel, Cold-rolled | 10.9 | 75 |
Mass and Weight - the difference! - What is weight and what is mass? An explanation of the difference between weight and mass.
Specific Weight can be expressed as
γ = ρ g (2)
where
γ = specific weight (N/m3)
ρ = density (kg/m3)
g = acceleration of gravity (m/s2)
The SI-units of specific weight are N/m3. The imperial units are lb/ft3. The local acceleration g is under normal conditions 9.807 m/s2 in SI-units and 32.174 ft/s2 in imperial units.
Example - Specific Weight Water
Specific weight for water at 39 oF (4 oC) is 62.4 lb/ft3 (9.81 kN/m3) in imperial units. Specific weight in SI units can be calculated like
γ = (1000 kg/m3) (9.81 m/s2)
= 9810 N/m3
= 9.81 kN/m3
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