SS - Deformation

Deformations can be the trickiest calculations for an architect/engineer to calculate. In nature, they are clear to the human eye. Deformations include any change in shape or size of an object, and generally are the result of an applied force (although chemical forces also can cause deformation on more microscopic scales). It is typically measured as strain, which is a unitless quantity, helpful in calculating the rate of elongation or contraction a member might undergo.

Internally, inter-molecular forces arise that act in an equal but opposite direction of the force applied onto the member. If a force isn't large enough, these internal stresses are enough to withstand permanent deformation (or plastic failure), and allow the member to completely resist the force. However, if the force is large enough, a new equilibrium stage will be reached via plastic failure, which allows the member to bend into a new geometric shape in order to compensate for a deficiency in internal strength. If an excessively large force is imposed on the structural shape, no matter what the material may be, structural failure will occur.

Stress-strain curves are the best way to plot this relationship. Although strain is actually the dependent variable we're talking about here, for engineering purposes, it is typically conveyed along the abscissa for relative ease. The linear portion of the curve is considered the elastic region, where Hooke's Law pertains most fiercely (and members retain their original form after being subjected to loads). It is followed by the plastic region (the curvilinear portion) and ultimately the finite fracture limit where the member fails to retain any structural integrity.

The above chart shows the particular strengths of utmost importance. Such quantities like Young's Modulus, the yield strength, strain hardening, ultimate strength, and necking vary for different materials. Concrete and steel, for instance, vary widely in every one of these quantities. And yet they both remain two of the most commonly used materials in construction. This is one fascinating example depicting the variety and versatility in modern day construction. Engineering properties can be worlds apart for our materials and manufactured products today, and yet still both be of great usage.

Four kinds of deformation: 1) Elastic, 2) Plastic and 3) Fatigue and 4) Failure

1. Elastic Deformation - The following is Hooke's Law. It pertains to elastic deformation:

Where σ is the applied stress, E is a material constant called Young's modulus, and ε is the resulting strain. This deformation is reversible and depends primarily on elastomers and shape memory in the construction materials used. Because of these stretching properties, engineers primarily calculate this region via the use of tensile tests (where a yield strength can quickly and methodically be obtained). At the yield strength, the element will follow the trajectory of the stress-strain curve and proceed into plastic deformation.

2. Plastic Deformation - Not reversible. But the element under stress will return to part of it's shape. Ductile metals, such as copper, silver and gold, will bend for an extended amount of time in the plastic range before failure, as will steel. But other elements, such as cast iron, will not. It all depends on the carbon content of a material and whether it the metallic bonds are enough to give way to internal stresses or are enough to hold firm. Carbon bonds stabilize a metallic element best with their versatility of valences.

Also of importance is the fact that the plastic region of a stress-strain curve has two portions: one, a strain hardening phase, where the material becomes stronger by a new movement of atoms to a stronger equilibrium state, and two, a necking region which holds off, but leads to the eventual failure of a member in structural loading. Necking usually results in a smaller cross-section in the member, which in turn results in the member stresses overcoming the internal axial stability of the member.

3. Fatigue - Happens most in ductile materials. Fatigue is the process of microscopic faults and molecular cracks compiling up over a period of time which eventually lead to the elimination of plastic deformation and results in fracture. An approximation of the number of deformations needed to result in fracture is somewhere between a thousand and a trillion depending on the structural members used. When compared to the short periods of impact loading in an earthquake, this concatenation of events truly conveys the power of the natural elements upon those built by man.

4. Fracture - Essentially, the breaking point in a structural member. All forces accumulate and overcome the internal forces of the beam, column, truss chord, etc. Fracture is, best put, the resultant death of a structure. Members should be either recycled or cast away after this point is attained as they are of no structural use.