1. Concepts about the science of "Strength of Materials" tasks, consistency, uniformity, priority, brief history

21 -43Stretching is the potential energy of deformation during compression (elastic deformation, work, potential energy
External forces do work in the migration process. In this case, their potential energy decreases, and according to the law of conservation of energy, it becomes the potential energy of deformation. Since the value of the reduced amount of the potential energy of the external force is equal to the work done by the external force during the deformation process, the problem of determining the potential energy of the deformation is reduced to the problem of calculating the work done by the external force, i.e. U=A.
The energy accumulated in the material as a result of elastic deformation caused by external forces is called potential energy of deformation. When an external force is removed from the stern, the dimensions and shape of the stern are restored under its influence. Consequently, the deformable elastic body becomes a "battery" that is a source of energy (for example, the spring of a gramophone and a mechanical watch).
Since it is necessary to determine the work under the influence of a static variable force, it is convenient to use the P- graph (Fig. 3.23).
Let P be the force value at some point in the deformation process, and be the corresponding displacement of the bottom section of the boom. In the next infinitesimally small moment, the force value dR increases, and the cross-section moves correspondingly to d increment. It is elementary work performed by an external force
dA=(R+dR)d =Rd +dR d
If we drop the infinitesimal value of the second order,
if we integrate both sides of the equation over P
22-46.Geometric characteristics of plane sections. Static and inertial moments (surface, center of gravity, axis, pole, relation, centrifugal).
We have seen above that in calculating the strength and stifness of straight bars to tensile and compressive deformation, the resistance of bars is directly proportional to its cross-sectional area.
It is known from the following formulas that the larger the cross-sectional surface is, the stronger the rod that works for stretching and compression is.
σ =
That is, the greater F is, the smaller the stress and deformation.
Let's conduct the following experiment to study the resistance of bar with F=const in bending to an external force:
It can be seen from the experiment that the cross-section shows different resistance to the influence of the external force if it is placed in different situations with F=const. Based on this experience, it is concluded that the cross-sectional surface of the rod cannot fully express its resistance to the influence of external forces.
In this regard, the issue of studying the geometrical characteristics of various flat cross-sectional surfaces arises.
It is necessary to know how to calculate the quality of the material of the structural elements, the shape and condition of the cross-sectional surfaces in order for the structural elements to fulfill the conditions of strength, stiffness and sustainability.
In addition, it is necessary to use more complex forms of cross-sectional surfaces in torsion bending and other complex deformations.
These geometrical characteristics depend on the size and shape of the cross-section and form them as cross-sectional surfaces, static moments, moments of inertia, moments of resistance and radius of inertia. (F,S,J,W,i)