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

33.Strength consideration of self weight in compression ( self weight, specific weight, stress, deformation, critical length, strength condition, three types of problem)
In some cases, the self-weight of the constructions creates such large stresses and deformations that it is necessary to take into account their influence.
We will see the effect of the weight of the bar with a constant cross-sectional area (Fig. 7.1). We find the stresses in the arbitrary section of the brush by the cutting method. We check the balance of the removed lower part.
Z=0; _Z FR-FZ =0
The normal stress on an arbitrary section
(3.39)
Here is the specific gravity of the material.
Normal stress under the effect of the bruce's own weight
_z = Z . (3.40)
When this stress reaches the stress value corresponding to the time resistance (strength limit) of the grinding material, the grinding is broken under the influence of its own weight. The length at which the beam breaks under its own weight is called the critical length :
_k = _v /  (3.41)
A condition of strength of a sturgeon under its own weight
(3.42)
Safer load size than this

the required size of the cross section

dz due to its own weight :

Let's integrate
(3.43)
Here the own weight of the bruce is Q=F l
The normal force under the influence of the bruce's own weight is at the lower end (Z=0) N _z =0; in the upper fixed section N _z =Q=Fl ; and the average normal force is equal to On the other hand, in calculations, it is possible to consider that the bruce's own weight is placed in the center of gravity of the bruce, that is, in the middle of its length. In this case, it can be considered that only the upper part of the beam with length /2 is stretched. The physical meaning of "2" in the denominator of formula (3.43) can be explained from these points of view.
Deformation under the influence of external force and own weight according to the principle of independence of forces