3. EQUILIBRIUM AND REACTIONS

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

In structural analysis, before we can find out how much a structure deforms under load, we first need to know the reactions at the supports. The reactions are forces that counteract the loads acting on a structure. After determining these reactions, we can analyze the internal forces within the structure, and lastly, figure out how much the structure bends or rotates when loads are applied.

Imagine a seesaw. Before you can calculate how much it tilts when you sit on one end, you first need to understand the reactions at the supports (pivots). The weight of each person on the seesaw creates a reaction force at the pivot to keep it balanced.

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.

There are three main types of supports in structural analysis:

1. Roller support allows movement in one direction while preventing movement in the other, meaning it can rotate.
2. Hinge support allows for rotation but does not allow the structure to move vertically or horizontally.
3. Fixed support stops both rotations and movements entirely. Understanding these supports is crucial, as they dictate how the structure responds to loads.

Think of a door: the door hinges allow it to rotate but not move inwards or outwards, which is like a hinge support in structures. A roller support is like a ping-pong ball that rolls on a flat surface in only one direction but can still spin.

Reactions are determined from the appropriate equations of static equilibrium. Summation of forces and moments, in a static system must be equal to zero.

To ensure that a structure is in equilibrium, the sum of all forces acting on it must equal zero, as well as the sum of all moments (torques). This means that all the forces pushing, pulling, and turning the structure must perfectly balance each other out.

Think of balancing on a seesaw: to maintain balance, the force exerted by the weight of each side must equal, and the moment created by that weight around the pivot must also be equal. If you add a heavier person to one side without adjusting positions on the other side, the seesaw will tip, showing that equilibrium is lost.

In statically determinate structures, reactions depend only on the geometry, boundary conditions and loads. If the reactions can not be determined simply from the equations of static equilibrium (and equations of conditions if present), then the reactions of the structure are said to be statically indeterminate.

A structure is considered statically determinate if you can figure out the reactions using just the rules of equilibrium based on the structure's shape and support configurations. If it cannot be determined using these rules, the structure is statically indeterminate, meaning it has more unknowns than equations available to solve for them.

Imagine a simple bridge supported by two piers. If you can calculate the forces using the known loads and the shape of the bridge easily, it’s statically determinate. But if you added an extra support or a complex shape that made calculations difficult without extra information, it would be statically indeterminate, making things more complicated!

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