Structural analysis methods and calculations

Force Method (Method of Displacements): A method based on calculating reactions and internal forces in a structure by first considering the displacements caused by loads. Often used for systems with redundancies or indeterminacies.
Displacement Method (Method of Stiffness): A method which involves determining displacements in a structure under given loads and then using these displacements to find reactions and internal forces.
Matrix Analysis: A computer-assisted method where matrix algebra is used to analyse complex structures. The entire structure is represented by a system of linear equations, and complex computations are used to find displacements and forces.

Dead and Live Loads: Use the provided unit weights and dimensions of the building components to calculate dead loads, and relevant codes or standards to estimate live loads on each element of the structure.
Wind Loads: Determine the pressure exerted by the wind on the building’s surface with local wind speeds, building height, exposure and shape. This includes lateral and uplift forces.
Snow Loads: Use local data on maximum snowfall and building dimensions to calculate the weight of accumulated snow on the roof.

Reaction Forces: Calculate the vertical and horizontal forces and moment reactions at the supports using equilibrium conditions. Sum of forces and moments in all directions should equal zero.

Strain and Stress: Use Hooke’s Law to connect stress (force over area) with strain (deformation due to stress). The constant of proportionality is called Young’s modulus, a material property.
Elastic and Plastic Deformation: Differentiate between deformations that are recoverable (elastic) and permanent (plastic). Distinguish which one dominates depends on the level of stress and the material properties.
Bending, Shear, and Torsional Stresses: For elements under complex loading, derive these stresses from the internal forces and moments using the pertinent formulas.

Failure Modes: Consider possible modes of failure such as instability (buckling), fracture, excessive deformation and yielding. The structure’s behaviour under extreme events should also be assessed.
Design Limit States: Check the elastic and plastic limit states for all critical sections and confirm the structure can safely support the intended loads. Ultimate and serviceability limit states should be verified.