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

6.-30-54Calculation of strength of beams under normal stress. (Stress: maximum, allowable, type of material, symmetrical section, three types of Problem).

Beam strong to be for his Dangerous in the section harvest divider maximum normal voltages beam material for permission done from tension increased don't go need .

8. 4 - fig

If the beam is made of materials with uniform resistance to stretching and compression, and the cross-section is symmetrical about the neutral axis (as in Fig. 8.4, a), then the strength condition of the beam is based on the formula (1 8. 6 ) is written:
( 8 . 1 1 )
in this - bending moment in the dangerous section of the beam; [ ] is the permissible stress for the material of the beam.
If the material of the beam is made of brittle materials with different resistance to stretching and compression, for example, and the shape of the section is symmetrical about the neutral axis (Fig . 8.4 , b), the beam For elastic and compressive zones, it should be checked separately:
( 8 . 1 2 )
in this _ч - normal tensile stress; _s is the normal stress in compression.
of resistance given in the formula (8.12 ) are determined using the following formulas (8.4 - fig . b ):
and
the strength condition of the beam (8.4 ) , the following three problems can be solved :
1. If the forces applied to the beam and the cross-sectional dimensions of the beam are known, the greatest stresses of the dangerous sections are found and the strength of the beam is checked:
( 8.13 ) _ _
by 5% from the allowable stress for the material of the beam, otherwise the strength of the beam or the economy of the material will not be ensured.
2. If the material of the beam and the cross-sectional dimensions are known , it is possible to find the force that the beam can carry. (8 . 11 ) should be calculated based on the formula :
( 8.11 ) _ _
The external forces that can be applied are determined by dividing the bending moment of the critical section by the forces applied to the beam .
3. If the material of the beam and the forces applied to it are known, in order to choose the cross section that ensures the strength of the beam and find its dimensions, it is necessary to determine the moment of resistance from the formula (8 . 11 ):
( 8.15 ) _ _
Depending on the shape of the cross-section according to the found moment of resistance, the geometric expression of the moment of resistance of this shape is put into the above formula, and the required dimensions are determined from it. If the beam is made of rolled steel (8 . 1 5) according to the value of the moment of resistance W _{x from the formula} , the cross-sectional dimensions of the beam are taken from the GOST table