Branches of Solid Mechanics

Definitions and principles of statics, dynamics, and kinematics, the branches of the mechanics of solids.

STATICS

Statics is a very old branch of mechanics, and its earliest principles were used in ancient Egypt and Babylon in the construction of pyramids and temples.
The first written principles of statics were established by Archimedes (287–212 BC) for the equilibrium conditions of forces acting on beams, and have come down to us today. Statics saw its major development in the 17th century, led by scientists such as Stevinus, Varignon, and Newton.
In statics, the changes in shape that can occur in a body under the effect of force (torsion, fracture, deflection, etc.) are not taken into account.
When and at what point a body will fracture is not a subject of statics.

What is the subject of statics?

Statics studies the equilibrium conditions of bodies acted on by forces.
We noted earlier that not all bodies can generally be considered solid bodies. Bodies loaded with forces undergo some degree of deformation, small or large. If this deformation is very small, it can be disregarded, and the system’s equilibrium condition can be studied as though no deformation had occurred at all.

In statics, we won’t take into account, in any way, the changes in shape that occur on a body under the effect of forces, and we’ll treat the body as perfectly rigid under the effect of a system of forces. Studying the shape changes that occur on a body falls more into the subject of strength of materials.
In the study of strength of materials, the relative motion of a body’s molecules or crystals under the effect of force is taken into account. This kind of motion is what produces the deformation in the body.

KINEMATICS

Kinematics, a subject within physics, is a science that studies the motion of bodies. Without considering the causes of motion, kinematics studies the relationships between distance, time, speed, and acceleration in the motion of solid bodies.

Compared to statics, kinematics is a fairly recent subject. The first principles of motion were established scientifically by Galileo (1564–1642). The natural philosophy established by Aristotle around 2000 BC was still accepted, even in Galileo’s time, as never being in error.

Galileo, at just 26 years old, began to reject the principles of natural philosophy, which showed no experimental basis at all. For example, he rejected the claim that “if two objects of different weights are dropped from the same height, they will hit the ground at different times.” By dropping two stones of quite different masses from the Tower of Pisa, from the same height and at the same time, he showed that there was no relationship between mass and time of fall.

Through his experiments sliding objects down an inclined plane, Galileo concluded that there was some kind of relationship between force and acceleration. However, because a clock of the required precision for measuring time hadn’t yet been built, he wasn’t able to give a full experimental explanation. He could only offer a limited explanation.

Later, the relationships between force and acceleration were studied analytically and experimentally by the English scientist Newton and formulated into a set of principles. Today these are known as “Newton’s laws.”

The purpose of kinematics is to study motion both graphically and analytically. Depending on the nature of the motion, the method of study is chosen to be either graphical or analytical.

Industrial kinematics problems are mostly solved using the graphical method. The reason is that it doesn’t require extensive mathematical knowledge, and the results obtained through graphical solutions are sufficiently precise.

In this subject, the material on kinematics has been simplified. However, enough information has been given at this level to recognize and study motion.

Kinematics, one of the subtopics of the mechanics course, is the geometry of motion. It studies the motion of a material point without considering the effect of force.

DYNAMICS

While statics considers solid bodies in equilibrium and the systems of forces acting on them, and kinematics studies the motion of bodies without considering their weight or the forces acting on them.

What is the subject of dynamics?

Dynamics, one of the subjects of the mechanics course, studies the motion of bodies acted on by forces, along with the related phenomena and laws.

Although statics has a fairly ancient history, dynamics is a fairly recent subject. Its origin goes back to the time of Galileo. Generally, the second half of the 16th century marks the birth years of dynamics. The reason dynamics developed so late is that experimental physics had not yet taken its place as a scientific field.

For dynamic phenomena to be studied experimentally, force, length, and time need to be precisely measurable. Since measuring force and length is fairly simple, these were discovered and developed in the earliest ages of history.

The measurement of time, however, didn’t reach the necessary quality until the middle of the 17th century. As a result, once small time intervals could begin to be measured, dynamics found the environment it needed to develop.

In dynamics, the type of motion a body or any system undergoes, or will undergo, under applied forces is studied, along with what character the system of forces needs to have in order to achieve the desired motion.

For a body to go from a resting state to a moving state, or to change its state of motion, an external force must act on that body.

The motion that results from a force acting on any body depends on the fundamental characteristics of the force, such as its magnitude, line of action, direction, and point of application, as well as on the material properties of the body.