Stress and Strain

Stress

Stress is the ratio of applied force F to a cross section area - defined as "force per unit area".

                                                          

• 
  tensile stress - stress that tends to stretch or lengthen the material - acts normal to the stressed area
• compressive stress - stress that tends to compress or shorten the material - acts normal to the stressed area
• shearing stress - stress that tends to shear the material - acts in plane to the stressed area at right-angles to compressive or tensile stress

Tensile or Compressive Stress - Normal Stress

Tensile or compressive stress normal to the plane is usually denoted "normal stress" or "direct stress" and can be expressed as

σ = F_n / A                                    

where

σ = normal stress (Pa (N/m²), psi (lb_f/in²))

F_n = normal force acting perpendicular to the area (N, lb_f)

A = area (m², in²)

• a kip is an imperial unit of force - it equals 1000 lb_f (pounds-force)
• 1 kip = 4448.2216 Newtons (N) = 4.4482216 kilo Newtons (kN)

A normal force acts perpendicular to area and is developed whenever external loads tends to push or pull the two segments of a body.

Shear Stress

Stress parallel to a plane is usually denoted as "shear stress" and can be expressed as

τ = F_p / A                              

where

τ = shear stress (Pa (N/m²), psi (lb_f/in²))

F_p = shear force in the plane of the area (N, lb_f)

A = area (m², in²)

A shear force lies in the plane of an area and is developed when external loads tend to cause the two segments of a body to slide over one another.

Strain (Deformation)

Strain is defined as "deformation of a solid due to stress". 

• Normal strain - elongation or contraction of a line segment
• Shear strain - change in angle between two line segments originally perpendicular

Normal strain and can be expressed as

ε = dl / l_o

   = σ / E                             

where

dl = change of length (m, in)

l_o = initial length (m, in)

ε = strain - unit-less

E = Youngs Modulus (Modulus of Elasticity) (Pa , (N/m²), psi (lb_f/in²))

• Young's modulus can be used to predict the elongation or compression of an object when exposed to a force

Note that strain is a dimensionless unit since it is the ratio of two lengths. But it also common practice to state it as the ratio of two length units - like m/m or in/in.

• Poisson's ratio is the ratio of relative contraction strain

Strain Energy

Stressing an object stores energy in it. For an axial load the energy stored can be expressed as

U = 1/2 F_n dl

where

U = deformation energy (J (N m), ft lb)

 

Deflection 

Deflection is the degree to which a structural element is displaced under a load (due to its deformation). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations. Otherwise methods such as virtual work, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method are used. The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications.

The deformation of a beam

The deformation of a beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam

Thermal Stress and strain

Thermal stress is mechanical stress created by any change in temperature of a material. These stresses can lead to fracturing or plastic deformation depending on the other variables of heating, which include material types and constraints.[1] Temperature gradients, thermal expansion or contraction and thermal shocks are things that can lead to thermal stress. This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general, the greater the temperature change, the higher the level of stress that can occur. Thermal shock can result from a rapid change in temperature, resulting in cracking or shattering.

 

Thermal strains are strains that develop when a material is heated or cooled, they can be the bane of an engineer’s existence if they are not considered Materials that fit perfectly at one temperature can rupture or fall out when their environmental temperature changes.