This course focuses on teaching you how to determine the internal forces (axial, shear, and bending moment) and external reactions of both statically determinate and indeterminate structures under various types of loading conditions.

Structural analysis serves as the essential bridge between the basic principles learned in mechanics (Statics and Strength of Materials) and the practical application of designing structural elements (like beams, columns, and slabs) using concrete, steel, or timber. You cannot design a structure safely without first knowing the forces it must withstand.

While this course focuses on fundamental manual techniques, these principles are the foundation for modern Finite Element Analysis (FEA) software. Understanding classical methods allows engineers to verify software results, a critical step to prevent catastrophic failures caused by "black box" reliance.

Most classical methods taught in this course assume that structures behave linearly and elastically. This means that deformations are directly proportional to the applied loads (Hooke's Law), and the structure will return to its original shape once the loads are removed. Material properties, such as the Modulus of Elasticity ($E$), are assumed constant.

In contrast, non-linear analysis accounts for changes in geometry as the structure deforms (geometric non-linearity) or changes in material properties beyond the elastic limit, such as yielding or cracking (material non-linearity). While advanced, non-linear analysis is crucial for evaluating structures under extreme events like severe earthquakes or for determining ultimate collapse loads.

For a linearly elastic structure, the total response (deflection, internal force, or reaction) caused by a combination of multiple loads acting simultaneously is equal to the algebraic sum of the responses caused by each individual load acting alone. This principle is extremely powerful because it allows complex loading scenarios to be broken down into simpler, solvable parts.

Also known as geometric compatibility. This principle states that the deformed shape of a structure must be continuous and physically possible. Members that are connected together must deform together at the connection points without tearing apart or overlapping. This concept is vital for solving indeterminate structures.

The most fundamental principle used in structural analysis is that a structure must be in a state of static equilibrium under the action of applied loads. For a planar (2D) structure, this requires that the sum of all forces in the x and y directions is zero, and the sum of all moments about any point is zero: $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M = 0$.

Classical methods assume that the deflections of a structure under load are very small compared to its overall dimensions. Because the displacements are negligible, the equations of equilibrium can be formulated based on the original, undeformed geometry of the structure rather than its final deformed shape.

A core concept throughout this course is the difference between static determinacy and indeterminacy: