Structural engineering theory
Structural engineering depends upon a detailed knowledge of loads, physics and materials to understand and predict how structures support and resist self-weight and imposed loads.
A structure fails the strength criterion when the stress (force divided by area of material) induced by the loading is greater than the capacity of the structural material to resist the load without breaking, or when the strain (percentage extension) is so great that the element no longer fulfills its function (yield).
Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law.
This means that load/stiffness ratio, which is deflection, remains same in two connected (jointed) elements.
A structure is considered to fail the chosen serviceability criteria if it is insufficiently stiff to have acceptably small deflection or dynamic response under loading.
Structural design codes are based upon the assumption that both the loads and the material strengths vary with a normal distribution.
It is normal to apply a partial safety factor to the loads and to the material strengths, to design using 95th percentiles (two standard deviations from the mean).
[1][2] However, using this approach requires detailed modeling of the distribution of loads and resistances.
A structure is checked for strength and serviceability against all the load cases it is likely to experience during its lifetime.
In multi-story buildings it is normal to reduce the total live load depending on the number of stories being supported, as the probability of maximum load being applied to all floors simultaneously is negligibly small.
It is not uncommon for large buildings to require hundreds of different load cases to be considered in the design.
The Third Law requires that for a structure to be stable all the internal and external forces must be in equilibrium.
A statically determinate structure can be fully analysed using only consideration of equilibrium, from Newton's Laws of Motion.
[3] Much engineering design is based on the assumption that materials behave elastically.
Materials that are elastic obey Hooke's Law, and plasticity does not occur.
For systems that obey Hooke's Law, the extension produced is directly proportional to the load: where Some design is based on the assumption that materials will behave plastically.
[4] A plastic material is one which does not obey Hooke's Law, and therefore deformation is not proportional to the applied load.
[5] Plasticity theory depends upon a correct understanding of when yield will occur.
is the second moment of area, the product of these giving the flexural rigidity of the beam.
This equation is very common in engineering practice: it describes the deflection of a uniform, static beam.
When subjected to compressive forces it is possible for structural elements to deform significantly due to the destabilising effect of that load.
