4. It's as simple as this:

Stress can be defined as force per unit area. When an object is pulled apart by a force it will cause elongation which is also known as deformation, like the stretching of an elastic band, and is sometimes referred to as tensile stress. When the forces result in the compression of an object it is called compressive stress. This happens when forces like tension or compression act on a body, such as a train rolling over a track on a bridge. The greater this force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Therefore, stress is measured in newton per square meter (N/m2) or pascal (Pa), and can be expressed thusly: σ = F/A.

Strain, on the other-hand, is inside a material (and also, bizarrely, around a material) and may arise by various mechanisms, such as stress applied by external forces to the bulk material (like gravity) or to its surface (like contact forces, external pressure, or friction, once again: think about the train on the tracks here). Strain is associated with deformation in terms of relative particle displacement in the body, excluding rigid-body movements. Depending on whether the strain field is defined with regard to the initial or final configuration of the body, and whether the metric tensor or its dual is considered, several equivalent options for the formulation of the strain field may be made, but mostly can be expressed as ε = Δx/x where, Δx is the change in dimension and x is original dimension.

Finally, because most metals deforms proportional to imposed load over a range of loads, the ratio of stress (force per unit area) along an axis to strain (ratio of deformation over initial length) along that axis can be expressed using Young's Modulus. That is to say:

E = stress / strain

   = σ / ε

   = (F_n / A) / (dl / l_o)                                    

where

E = Young's Modulus (N/m²) (lb/in², psi)

It should be noted that Modulus of Elasticity, or Young's Modulus, is commonly used for metals and metal alloys and expressed in terms 10⁶ lb_f/in², N/m² or Pa.

When Alvie's increasingly jealous colleagues ran the numbers through their equations, they realized the monkey engineer had made a terrible blunder indeed: numbers just don't lie.