# Introduction to Statics

What conditions must be created so that the structure is in equilibrium? The roof didn't fall on your head, did the chair fail under us, and the elevator did not fail from the passenger's entry? These questions can be answered after studying the course of statics: statics studies the state of equilibrium and uses as a tool for describing the concepts of force and moment, which we will talk about further.

Even stationary bodies can have micro-displacements or deform: movement caused by the forces that we unable to measure/account for /calculate, for example, a change in the magnetic field or gravitational waves. They exist, but in statics we study processes for which such movements can be considered an error. The deformation of bodies is studied by other sciences: materials science and the resistance of materials, and within the framework of statics, deformation we we simply ignore it.

Everything is in constant motion. Even if we look at the pen that is lying on the table - it is now moving around the sun, and its speed is slightly different from the speed of the table. Since in our understanding bodies are stationary (and in fact they are moving), we will introduce the concept of a reference frame - a coordinate system in which the studied objects will be stationary relative to each other.

The termframe of referencehas a different meaning, described above applies only in this article

We will use a Cartesian coordinate system: three axes perpendicular to each other intersect at one point, which will be the starting point - that is, zero. All three axes will be in the same proportions, then the position we we will be able to count in the metric system familiar to us, the distance to the point to count in projections on the coordinate axis:

**Graph 1.**Linear scale, each axis has the same segment, graph z = log_{2}x

**Graph 2.**Here the X-axis is made in a logarithmic scale, so that the row 1,2,3,4 ... the values correspond to 1,2,4,8,... . Thus, the graph z = log_{2}x looks straight## Power

Force is a measure of interaction, we put pressure on the table - we apply force, the table presses on us in response, the table does not have enough strength - he presses on the supports, the supports do not have enough strength - they press on the ground, so the force is transferred between the bodies. If the body is motionless, and when we pressed on the table - everything remained motionless, then we say that the forces balanced, we apply force to the table - we get force in return. Ultimately, we are pressing down on the ground that we consider it stationary, so we will continue to designate the earth as a fixed support. Developing this idea, if we are indoors, the floor transfers the load to the walls, those to the foundation, which in turn to the ground, if our loads incommensurable with the calculation of load-bearing walls, then we consider our floor to be a fixed support, if we want to put it on the floor a fireplace weighing a ton - we will consider whether the floor will withstand and the ground will again be a fixed support.

Thus, a fixed support is something that in the problem being solved does not change its position from the applied force and can be considered stationary.

---------- designation of a fixed support

## Moment

Moment is the force causing rotation, the moment is determined by the lever and the applied force. The lever at one end is on the axis of rotation, and the other end is the point of application of force. Under the influence of the moment , the body will not necessarily move, it can also be in equilibrium, this will mean that there is the moment opposite to the one described.

For a better understanding, imagine a wheel that is located on an axis: you are standing on one side, your friend on the other. You push the wheel down - a moment is created relative to the axis, the wheel began to move, then your friend delays the wheel on its side and the wheel stops is a balancing moment: it exists as before, but now it is compensated and there is no movement.

---------- image of the moment

## Supports

Depending on the transmitted forces and moment, there are three types of supports. Reactions in the supports are transmitted in those directions, in which moving is not possible:

- Fixed support - the body transmits vertical, horizontal force and moment
- Movable support - the body transmits vertical force and moment, since it has the ability to move horizontally
- Pivotally movable support - horizontal force and moment are not transmitted, since horizontal movement and rotation are possible

Let's look at examples of how to schematically depict the existing situation:

The bracket that holds the TV and consists of two parts connected by a hinge and two hinge mounts - allows you to move the TV horizontally and rotate it. The place of attachment to the wall will be a fixed support: forces and moments will be transmitted in all directions. The hinge joint will be rotatable by horizontally, so the moment of rotation along the Z axis will not be transmitted. The junction of the two parts will not transmit the moment relative to the Z axis; the hinge of the attachment to the TV will not transmit the moment along the axes, but will transmit loads.For analysis, three-dimensional systems are quite complex, because it is necessary to write down a large number of equations (and also solve them), so a simplification is used - projection onto a two-dimensional space. In two-dimensional space the moment and movement along one of the axes are excluded and, in most cases, this simplification allows you to calculate the necessary forces.