After studying chapter 2, the bachelor should:


- basic definitions, hypotheses and assumptions;

- types of deformation of the body;

- the basis of the stress-strain state of the body;

- the basic formulas for determining stresses and strength reserves;

- methods and principles of calculation for strength, rigidity and stability of structural elements;

be able to

- apply the knowledge gained in practice;

- perform strength calculations for various types of body loading;

- choose different schemes for evaluating the strength of real parts and mechanisms;


- conceptual apparatus in the field of strength;

- methods of calculation for strength;

- the skills of applying the knowledge obtained to practical calculations.


Hypotheses and assumptions

The problem of material resistance (CM) is the development of fairly simple but effective methods for calculating the strength, stiffness and stability of structural elements.

We give the definitions of the basic concepts of resistance of materials.

A beam - a body , whose two dimensions are small compared to the third (length). The line connecting the centers of gravity of the sections of the beam is called its axis. Depending on the shape of the axis, straight and curved bars are distinguished. The bars are of constant and variable cross section, solid and non-continuous, with an open and closed cross-section profile.

Deformation - changing the shape, dimensions and individual parts of a solid.

Moving - changing the position of the body or its individual parts in space.

If, after lifting the load, the body takes its original shape and size, then this phenomenon is called elasticity . Deformations of the body, disappearing after the removal of the load, are called elastic . If, after removing the loads, the body does not fully assume the original shape and dimensions, i. E. gets residual deformations, then this phenomenon is called ductility .

Strength - The ability of a design or its elements to withstand external influences without breaking.

Stiffness - the ability of a structure or its elements to resist elastic deformations.

Sustainability - the ability of the structure and its elements to maintain a certain equilibrium shape.

The SM is based on a number of hypotheses and assumptions that make it possible to simplify the solution of the tasks posed.

1. It is assumed that the material of the deformed body before and after loading fills the entire volume, i.e. The body has no voids and cracks. This assumption makes it possible to apply methods of mathematical analysis to solving problems of material resistance.

2. The material of the deformable body is homogeneous; does not contain any inclusions that change its physical and mechanical properties in any arbitrarily small microvolume.

3. It is assumed that the material is isotropic, i.e. its physical and mechanical properties in all directions are the same in the process of loading. Materials that do not have this property are called anisotropic.

4. The material has an ideal elasticity, i.e. After de-stressing, deformations completely disappear. The property of ideal elasticity is determined by the physical law Hooke: the displacement of points of the elastic body within certain loading limits are directly proportional to the forces causing these movements.

For linearly deformed systems, i.e. in the framework of Hooke's law, the principle of superposition or independence of the action of forces : the result of the action of a group of forces does not depend on the sequence of loading of the structure and is equal to the sum of the results of the action of each of the forces separately.

5. The principle of Saint-Venant: in sections , sufficiently far from the place of application of the load , the stress-strain state does not depend on the way the load is applied. Based on this principle, the distributed load can be replaced by concentrated forces in calculations.

6. The principle of invariance of the initial dimensions: the change in linear dimensions under loading is much less than the initial dimensions, ie. the displacement of body points due to its elastic deformations is small in comparison with the size of the body.

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