3.1. Introduction

In the analysis of structures (hand calculations), it is often easier (but not always necessary) to start by determining the reactions. Once the reactions are determined, internal forces are determined next; finally, deformations (deflections and rotations) are determined last.

When analyzing a structure, it is common to start by calculating the reactions of the structure at its supports. These reactions are the forces that the supports exert back to maintain balance. After figuring out these reactions, the next step is to analyze the internal forces within the structure, which will help in understanding how the structure carries loads. The final step involves looking at how the structure deforms, such as bending or twisting, under the applied loads.

Imagine the process of holding a long plank on your shoulders. First, you need to balance the plank (establish reactions) by adjusting your hold. Once you have it balanced, you can then think about how it feels as you walk (internal forces), and finally, how it bends slightly due to the weight or wind (deformations).

Reactions are necessary to determine foundation load. Depending on the type of structures, there can be different types of support conditions.

The reactions at the supports of a structure are crucial because they allow engineers to calculate the total load that the structure needs to support. Each type of support (like rollers, hinges, and fixed supports) has unique characteristics that affect how loads are transmitted and distributed within the structure. Understanding these reactions helps in ensuring that the foundation will properly support the entire structure without failure.

Think of a seesaw in a playground. The reactions at each end where children sit help determine how much weight each side can hold before it tips over. If one side is much heavier, the reactions change, and it’s crucial to know how to balance that load.

Roller: provides a restraint in only one direction in a 2D structure; in 3D structures, a roller may provide restraint in one or two directions. A roller will allow rotation. Hinge: allows rotation but no displacements. Fixed Support: will prevent rotation and displacements in all directions.

Different support conditions influence how forces are managed in a structure. A roller allows for some rotation-such as a wheel rolling on a surface- but restricts movement in other directions. A hinge acts like a door that can swing open but doesn't move away from its frame (no displacements). A fixed support, on the other hand, holds the structure firmly in place, preventing any rotation or movement. These distinctions are critical for engineers in designing stable structures.

Consider the legs of a table. The legs can be thought of as fixed supports, preventing the tabletop from moving. If the legs were replaced with wheels (rollers), the table could roll away but remain stable while sitting still. And if the table had a pivoting leg (hinge), it could tilt but wouldn't slide away from its designated spot.

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