1. Basic concepts and principles

1. Tasks, main hypothesis and assumptions of the strength of materials

Practice shows that all construction parts are deformed by the load actions i.e. they change their shape and dimensions and in some cases the construction rupture takes place.

The science of the strength and deformation of the machines and construction materials elements is the strength of materials.

The capability of the construction materials and their elements to resist the external forces without breaking is called the strength.

The calculation methods for the strength, stiffness and buckling of construction elements are considered by the strength of materials science.

The strength calculations make it possible to determine the dimensions and shapes of the elements bearing the load under the minimum material expenditure.

Stiffness is the capability of a body or a construction to resist the deformation arising.

The shape and constructions dimentions changes being within the admitted limits are guaranteed by the stiffness calculation.

The stability is the capability of a construction to resist the actions intendiny to move it into a new equilibrium position.

The appearance of large deformations causing a sudden system transition into a new equilibrium shape or a rupture is prevented by stability calculations.

A sudden curvature of a long rectilineal bar compressed along the axis can be an example of buckling.

In practice we deal in most cases with constructions of a complicated shape but they can be presented as consisting of separate simple elements, such as bars, plates, shells.

The basic calculation element in the strength of materials is the bar i.e. a body whose transverse sizes are much lesser compared to its length. The bars can have a straight or curved axis, be of a constant or variable section.

The plane section perpendicular to the bar axis is called the cross section while that parallel to the bar axis is called longitudinal.

Besides the bar calculation the strength of materials considers the calculation of plates and shells i.e. the bodies having smaller thickness compared to other sizes (for example, reservoirs, pipes, ship and plane sheaths). The bodies whose three basic sizes are of commensurable quantities are called massive bodies (e.g. foundations, lathe beds).

The elastic force arising in the body due to its deformation under external force actions resists a deformation and tends to return the body particles to the initial position. The internal force molecule interactions cause the elastic forces.

The strength of materials studies body deformations and internal forces arising under these deformations.

The deformation caused by external force actions can completely or partially disappear when the forces are removed. The capability of materials to eliminate the deformation after the external force actions removal is called elasticity. The deformation disappearing after the external force action removal is called elastic; the deformation not disappearing after the external force action is called residual or plastic. Plasticity is the capability of the material to have a considerable deformation without breaking and the materials are called plastical. Low - carbon steel, aluminum, copper, brass and others are referred to the materials in question.

It should be noted that the rise of considerable residual deformations in many cases brings to the disturbance of the construction normal work and therefore it is inadmissible.

The materials having very small elastity are called brittle. The brittle materials unlike plastical break under the visible residual deformation. Cast iron, hard facing alloys, glass, brick and some others are examples of brittle materials.

The science of the strength of materials is based on the theoretical mechanics laws. The principle of solidification in the strength of materials considered by the theoretical mechanics in the strength of materials will be applied to compose the static equations of equilibrium of the deformed bodies so as to determine the connection reactions and the internal forces in details sections.

Hypotheses and assumptions in the subject of the strength of materials. All real bodies have the complicated pattern construction, hollownesses, heterogeneous inclusions which have the dimensions much lesser than the dimensions of the bodies. The mentioned peculiarities of the materials are impossible to take into account because of their chaotic nature and volume distribution, therefore a number of the hypotheses and assumptions are accepted. These are:

1. The material is to be as follows

• solid (we ignore the atom structure, hollownesses and inclusions);

• homogeneous (a material has the same properties in all volume points);

• isotropic (a material has the same properties in all directions).

2. The body does not have any internal forces before the external forces are applied.

3. All materials are ideal elastic ones (bodies take their initial shape and dimensions when the external load is entirely removed).

4. The change values of the dimensions and shape depend on the external load linear and are small compared to the body dimensions.

5. The plane body section before and after the deformation remains the same.

The mentioned conditions allow one to receive the principle of the superposition i.e. the result of the system forces action is equal to the sum of the action results of each force of this system when the force is applied in turns and in any order possible.