Structural engineering theory is the application of physics and mathematics to analyze and design structures to ensure they can withstand loads. 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. To apply the knowledge successfully structural engineers will need a detailed knowledge of mathematics and of relevant empirical and theoretical design codes. They will also need to know about the corrosion resistance of the materials and structures, especially when those structures are exposed to the external environment. The criteria which govern the design of a structure are either serviceability (criteria which define whether the structure is able to adequately fulfill its function) or strength (criteria which define whether a structure is able to safely support and resist its design loads). A structural engineer designs a structure to have sufficient strength and stiffness to meet these criteria. Loads imposed on structures are supported by means of forces transmitted through structural elements. These forces can manifest themselves as tension (axial force), compression (axial force), shear, and bending, or flexure (a bending moment is a force multiplied by a distance, or lever arm, hence producing a turning effect or torque).
Strength Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion. The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States customary units system). 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). See also:
Stiffness Stiffness depends upon material properties and geometry. The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. 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. The deflection of a structure under loading is dependent on its stiffness. The dynamic response of a structure to dynamic loads (the natural frequency of a structure) is also dependent on its stiffness. In a structure made up of multiple structural elements where the surface distributing the forces to the elements is rigid, the elements will carry loads in proportion to their relative stiffness - the stiffer an element, the more load it will attract. This means that load/stiffness ratio, which is deflection, remains same in two connected (jointed) elements. In a structure where the surface distributing the forces to the elements is flexible (like a wood-framed structure), the elements will carry loads in proportion to their relative tributary areas. 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. The inverse of stiffness is flexibility.
Safety factors The safe design of structures requires a design approach which takes account of the statistical likelihood of the failure of the structure. Structural design codes are based upon the assumption that both the loads and the material strengths vary with a normal distribution. The job of the structural engineer is to ensure that the chance of overlap between the distribution of loads on a structure and the distribution of material strength of a structure is acceptably small (it is impossible to reduce that chance to zero). 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). The safety factor applied to the load will typically ensure that in 95% of times the actual load will be smaller than the design load, while the factor applied to the strength ensures that 95% of times the actual strength will be higher than the design strength. The safety factors for material strength vary depending on the material and the use it is being put to and on the design codes applicable in the country or region. A more sophisticated approach of modeling structural safety is to rely on structural reliability, in which both loads and resistances are modeled as probabilistic variables. However, using this approach requires detailed modeling of the distribution of loads and resistances. Furthermore, its calculations are more computation intensive.
Load cases
A load case is a combination of different types of loads with safety factors applied to them. A structure is checked for strength and serviceability against all the load cases it is likely to experience during its lifetime. Typical load cases for design for strength (ultimate load cases; ULS) are:
1.2 x Dead Load + 1.6 x Live Load 1.2 x Dead Load + 1.2 x Live Load + 1.2 x Wind Load A typical load case for design for serviceability (characteristic load cases; SLS) is:
1.0 x Dead Load + 1.0 x Live Load Different load cases would be used for different loading conditions. For example, in the case of design for fire a load case of 1.0 x Dead Load + 0.8 x Live Load may be used, as it is reasonable to assume everyone has left the building if there is a fire. 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.
Newton's laws of motion
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