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

17 -39Stretching and compression of the right stern. Stresses in the cross section (longitudinal tensile strength, hypothesis of flat sections, Hooke's law, modulus of elasticity).
Let's move on to determining the deformation of the stern. Relative elongation from:

Multiplier E in the denominator is defined as the stiffness of the cross-section of the stern in tension and compression, and has a measure of strength. The quantity C=E/ is called the stiffness of the stern.
T he sum of the relative deformations of elementary lengths distributed over the entire length of the stern constitutes the absolute deformation of the stern:

here:
the formula represents Hooke's law (second law) for absolute deformation. According to it, the absolute elongation or compression is directly proportional to the longitudinal force, the length of the mast and inversely proportional to the stiffness of the mast.
The known relation (3.3) above is called Hooke's law, according to which the normal stress is directly proportional to the relative strain. The formula can be obtained by expressing the left and right sides of this connection:
, from this
connection can be represented by a straight line in the system of coordinate axes
The tangent of the angle between the straight line and the abscissa axis indicates the amount of the modulus of elasticity E=tg 
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19.Stretching - longitudinal deformation in compression. Hooke's law. Displacements (longitudinal, transverse, uniform, Hooke's law, modulus of elasticity, relative, absolute, displacement of physical and geometrical texts).
Hooke's law is a law that expresses the linear relationship between the elastic deformation of a rigid body and the mechanical stress applied to it. Discovered by Robert Hooke (1660). An object can be stretched or compressed under the influence of tension. For example, if a rod with length and cross-sectional area S is stretched by a force G', its elongation will be Al=Fl/ES, where: D is the absolute (absolute) elongation (shortening), Ye is the modulus of elasticity (Yung's modulus). For relative elongation, o"=£e, where o is the normal stress, ye is the relative elongation. For shear, x=Su, where: u is the angle of shear, x is the tensile stress, G is the modulus of elasticity in shear, and G=0 for most materials. ,4E.For example, £=2-106 kg-k/cm2 for steel, £'=1-106 kg-k/cm2 for cast iron or copper, etc.

Consider a wire of length l and cross-sectional area A fixed at one end. When other end of the wire is pulled with a force F, the wire gets slightly elongated by ΔlΔ and the external force gets balanced by the internal forces. The internal forces in a wire are along its length i.e., normal to cross-sectional plane. The internal force per unit area is called longitudinal stressσ=F/ASince the wire is under tension, the stress is called tensile stress. The unit of stress is N/m² or Pascal.

The increase in length per unit orginal length is called strain i.e.,Longitudinal strain=ΔllLongitudinal strain=The strain is a dimesnionless quantity. It is usually expressed as percentage increase in length.
If a rod is compressed then the stress in it is compressive stress, and the strain is compressive strain.
The tangential force per unit area is called shear stress i.e.,σs=Fs/A

The shearing strain is defined as i.e.,Shearing strain=xl=tanθ≈θShearing strain=x/l=tan⁡0≈0