# Calculation of strength. Margin of safety. Allowable stresses...

## Strength calculation. Margin of safety. Allowable Voltage

Strength and stiffness calculations are performed using two methods: allowable stresses and strains and allowable loads .

Stresses in which a specimen from a given material is destroyed or under which significant plastic deformations develop are called marginal . These stresses depend on the properties of the material and the type of deformation.

The voltage, the magnitude of which is governed by the technical conditions, is called acceptable .

The permissible stresses are set taking into account the material of the structure and the variability of its mechanical properties during operation, the degree of structural responsibility, the accuracy of the loads, the service life of the structure, the accuracy of calculations for static and dynamic strength.

For plastic materials, the permissible stresses are chosen so that, for any inaccuracies in the calculation or unforeseen operating conditions, there are no residual deformations in the material, i.e. (2.23)

Here is the safety factor in relation to σt.

For brittle materials, the permissible stresses are assigned from the condition that the material does not collapse. In this case Thus, the safety factor has a complex structure and is intended to guarantee the strength of the structure against any accidents and inaccuracies that arise during the design and operation of the structure.

Tolerable is the load that can not exceed the internal forces that occur in the most dangerous sections of the structure during its operation: where - the destructive load obtained as a result of calculations or experiments taking into account the experience of manufacture and operation; - factor of safety.

When calculating the allowable stresses, the strength conditions have the form In the future we will use the method of allowable stresses (strains) adopted in general engineering. The strength condition for allowed voltages has the form where - the voltage acting in this section.

Stiffness conditions where and are the allowed values ​​for the displacements and deformations, respectively.

There are the following types of calculations for strength:

design, for which the specified dimensions of the part for the given loads N imax and known material characteristics . For example, for a rod, the cross-sectional area is found from the condition ;

verification, which is used to evaluate the strength of a real design. In this case, for known design sizes and specified loads, determine the maximum stresses and compare them with the permissible . For example, for a rod The actual margin of safety is determined by the ratio where and are the limiting stresses for plastic and brittle materials, respectively.

## The work of external forces and the potential energy of deformation under tension (compression)

The work of deformation or the work of external forces is the work performed by external forces in deformation of the body. The work of external forces is performed on the movements that receive the points of application of forces to the body as a result of deformation. If the deformations of the body are perfectly elastic, then after removing the load, the energy expended is returned by the body in the form of mechanical energy.

The potential energy of deformation (PED) is the energy that accumulates in the deformed volume in the process of imposing the load system.

Consider the SED within the framework of Hooke's law. In the region of elastic deformations, we can assume that the work of external forces A completely passes into the potential energy of deformation U. In the case of uniaxial tension of a straight rod under static loading, the work of external forces A can be calculated according to Clapeyron's theorem on the elastic region of the tension diagram (Figure 2.10) as the area bounded by this section: For a uniform rod ', then . Since according to Hooke's law , In the general case  Fig. 2.10

Neglecting the scattering of energy, it is believed that Specific potential energy of deformation 'where V - the volume of the bar. Then Potential energy is widely used in computational practice.

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