The main provisions of the hypothesis. The main provisions of the evolutionary hypothesis Z
1. What is life?
Answer. Life is a way of being of entities (living organisms) endowed with internal activity, the process of development of bodies organic structure with a stable predominance of synthesis processes over decay processes, a special state of matter achieved due to the following properties. Life is a way of existence of protein bodies and nucleic acids, the essential point of which is the constant exchange of substances with environment, and with the cessation of this exchange, life also ceases.
2. What hypotheses of the origin of life do you know?
Answer. Various ideas about the origin of life can be combined into five hypotheses:
1) creationism - Divine creation of living things;
2) spontaneous generation - living organisms arise spontaneously from nonliving matter;
3) steady state hypothesis - life has always existed;
4) panspermia hypothesis - life was brought to our planet from the outside;
5) the hypothesis of biochemical evolution - life arose as a result of processes that obey chemical and physical laws. Currently, most scientists support the idea of the abiogenic origin of life in the process of biochemical evolution.
3. What is the basic principle of the scientific method?
Answer. The scientific method is a set of techniques and operations used in constructing a system of scientific knowledge. The basic principle of the scientific method is to take nothing for granted. Any statement or refutation of something should be verified.
Questions after § 89
1. Why can the idea of the divine origin of life be neither confirmed nor refuted?
Answer. The process of the Divine creation of the world is conceived as having taken place only once and therefore inaccessible to research. Science deals only with those phenomena that are amenable to observation and experimental study. Consequently, from a scientific point of view, the hypothesis of the Divine origin of living things can neither be proven nor disproved. Main principle scientific method - “don’t take anything for granted.” Consequently, logically there can be no contradiction between the scientific and religious explanation of the origin of life, since these two spheres of thinking are mutually exclusive.
2. What are the main provisions of the Oparin–Haldane hypothesis?
Answer. IN modern conditions the emergence of living beings from inanimate nature impossible. Abiogenic (i.e., without the participation of living organisms) emergence of living matter was possible only under conditions of an ancient atmosphere and the absence of living organisms. The ancient atmosphere included methane, ammonia, carbon dioxide, hydrogen, water vapor and other non- organic compounds. Under the influence of powerful electrical discharges, ultraviolet radiation and high radiation, organic compounds could arise from these substances, which accumulated in the ocean, forming a “primary broth”. In the “primary broth” of biopolymers, multimolecular complexes - coacervates - were formed. into coacervate drops from external environment metal ions entered, acting as the first catalysts. From the huge number of chemical compounds present in the “primordial soup”, the most catalytically effective combinations of molecules were selected, which ultimately led to the emergence of enzymes. At the interface between the coacervates and the external environment, lipid molecules lined up, which led to the formation of a primitive cell membrane. At a certain stage, protein probionts included nucleic acids, creating unified complexes, which led to the emergence of such properties of living things as self-reproduction, preservation hereditary information and its transmission to subsequent generations. Probionts, whose metabolism was combined with the ability to reproduce themselves, can already be considered as primitive procells, the further development of which occurred according to the laws of the evolution of living matter.
3. What experimental evidence can be given in favor of this hypothesis?
Answer. In 1953, this hypothesis of A.I. Oparin was experimentally confirmed by the experiments of the American scientist S. Miller. In the installation he created, the conditions that supposedly existed in the primary atmosphere of the Earth were simulated. As a result of the experiments, amino acids were obtained. Similar experiments were repeated many times in various laboratories and made it possible to prove the fundamental possibility of synthesizing almost all monomers of the main biopolymers under such conditions. Subsequently, it was found that, under certain conditions, it is possible to synthesize more complex organic biopolymers from monomers: polypeptides, polynucleotides, polysaccharides and lipids.
4. What are the differences between A.I. Oparin’s hypothesis and J. Haldane’s hypothesis?
Answer. J. Haldane also put forward the hypothesis of the abiogenic origin of life, but, unlike A.I. Oparin, he gave primacy not to proteins - coacervate systems capable of metabolism, but to nucleic acids, that is, macromolecular systems capable of self-reproduction.
5. What arguments do opponents give when criticizing the Oparin–Haldane hypothesis?
Answer. The Oparin–Haldane hypothesis also has a weak side, which its opponents point out. Within the framework of this hypothesis, it is not possible to explain the main problem: how the qualitative leap from inanimate to living occurred. After all, for the self-reproduction of nucleic acids, enzyme proteins are needed, and for the synthesis of proteins, nucleic acids are needed.
Give possible arguments for and against the panspermia hypothesis.
Answer. Arguments for:
Life at the prokaryotic level appeared on Earth almost immediately after its formation, although the distance (in the sense of the difference in the level of complexity of organization) between prokaryotes and mammals is comparable to the distance from the primordial soup to pokaryotes;
In the event of the emergence of life on any planet of our galaxy, it, as shown, for example, by the estimates of A.D. Panov, can “infect” the entire galaxy over a period of just a few hundred million years;
Findings of artifacts in some meteorites that can be interpreted as the result of the activity of microorganisms (even before the meteorite hit Earth).
The panspermia hypothesis (life brought to our planet from outside) does not answer main question how life arose, but transfers this problem to some other place in the Universe;
Complete radio silence of the Universe;
Since it turned out that our entire Universe is only 13 billion years old (i.e., our entire Universe is only 3 times older (!) than planet Earth), then there is very little time left for the origin of life somewhere in the distance... The distance to the nearest star to us is a-centauri - 4 light years. of the year. A modern fighter (4 speeds of sound) will fly to this star ~ 800,000 years.
Charles Darwin wrote in 1871: “But if now... in some warm body of water containing all the necessary salts of ammonium and phosphorus and accessible to the influence of light, heat, electricity, etc., a protein was chemically formed, capable of further , increasingly complex transformations, then this substance would immediately be destroyed or absorbed, which was impossible in the period before the emergence of living beings.”
Confirm or refute this statement by Charles Darwin.
Answer. The process of the emergence of living organisms from simple organic compounds was extremely long. For life to arise on Earth, it took an evolutionary process that lasted many millions of years, during which complex molecular structures, primarily nucleic acids and proteins, were selected for stability, for the ability to reproduce their own kind.
If today on Earth, somewhere in areas of intense volcanic activity, quite complex organic compounds can arise, then the likelihood of these compounds existing for any length of time is negligible. The possibility of life re-emerging on Earth is excluded. Now living beings appear only through reproduction.
Question 1. List the main provisions of A.I. Oparin’s hypothesis.
In modern conditions, the emergence of living beings from inanimate nature is impossible. Abiogenic (i.e., without the participation of living organisms) emergence of living matter was possible only under conditions of an ancient atmosphere and the absence of living organisms. The ancient atmosphere included methane, ammonia, carbon dioxide, hydrogen, water vapor and other inorganic compounds. Under the influence of powerful electrical discharges, ultraviolet radiation and high radiation, organic compounds could arise from these substances, which accumulated in the ocean, forming a “primary broth”.
In the “primary broth” of biopolymers, multimolecular complexes—coacervates—were formed. Metal ions, which acted as the first catalysts, entered the coacervate droplets from the external environment. From the huge number of chemical compounds present in the "primordial soup", the most catalytically effective combinations of molecules were selected, which ultimately led to the appearance of enzymes. At the interface between the coacervates and the external environment, lipid molecules lined up, which led to the formation of a primitive cell membrane.
At a certain stage, protein probionts incorporated nucleic acids, creating unified complexes, which led to the emergence of such properties of living things as self-reproduction, preservation of hereditary information and its transmission to subsequent generations.
Probionts, whose metabolism was combined with the ability to reproduce themselves, can already be considered as primitive procells, the further development of which occurred according to the laws of the evolution of living matter.
Question 2. What experimental evidence can be given in favor of this hypothesis?
In 1953, this hypothesis of A.I. Oparin was experimentally confirmed by the experiments of the American scientist S. Miller. In the installation he created, the conditions that supposedly existed in the primary atmosphere of the Earth were simulated. As a result of the experiments, amino acids were obtained. Similar experiments were repeated many times in various laboratories and made it possible to prove the fundamental possibility of synthesizing almost all monomers of the main biopolymers under such conditions. Subsequently, it was found that, under certain conditions, it is possible to synthesize more complex organic biopolymers from monomers: polypeptides, polynucleotides, polysaccharides and lipids.
Question 3. What are the differences between A.I. Oparin’s hypothesis and J. Haldane’s hypothesis?
J. Haldane also put forward the hypothesis of the abiogenic origin of life, but, unlike A.I. Oparin, he gave primacy not to proteins - coacervate systems capable of metabolism, but to nucleic acids, i.e. macromolecular systems capable of self-reproduction.
Question 4. What arguments do opponents give when criticizing the hypothesis of A.I. Oparin?
Unfortunately, within the framework of the hypothesis of A.I. Oparin (and J. Haldane too) it is not possible to explain the main problem: how the qualitative leap from inanimate to living occurred.
1. All living organisms evolve.
2. The driving forces of evolution and the mechanism of changes in organisms are:
■ direct influence of environmental conditions , which change;
■ inner desire for progress and the influence of conditions determine the appearance of useful traits;
■ exercises or organ misalignment leads to the development of these signs;
■ inheritance by organisms only useful signs .
3. Evolution is a continuous process of acquiring useful characteristics.
4. The result of evolution is not only the occurrence of useful changes, but also gradation organisms - stepwise complications of the organic world.
5. Life is constantly self-generating, so there are species that are at different levels of the ladder.
6. Live nature- a series of individuals that are constantly changing and which a person unites into species only in the imagination.
In the hypothesis of J.-B. Lamarck has serious shortcomings: he incorrectly explained the driving forces of evolution, did not recognize species as really existing categories, and recognized the emergence and inheritance of only useful characters.
Advances in biology in the first half of the 19th century as a prerequisite further development evolutionary doctrine
The first half of the 19th century was marked by many discoveries in various fields of biology.
Advances in biology in the first half of the 19th century
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the science |
names of scientists |
advances in science |
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cytology |
M. Schleiden, T. Schwann, K. Baer, R. Virchow and others. |
Creation of cell theory |
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embryology |
Discovery of germ layers and study of the main stages of embryogenesis in vertebrates |
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paleontology |
Established that each geological era corresponds to a certain set of fossil species |
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biogeography |
A. Humboldt, P. S. Pallas |
It has been established that the differences in the population of different continents and islands are greater, the more they are isolated from each other |
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biochemistry |
Established the participation of living beings in the cycle of substances |
So, successes natural sciences, and geographical discoveries, agricultural practices became prerequisites for the further development of evolutionary teaching, since a lot of new data appeared on the structure and vital activity of living organisms, on the variability of living nature, which required systematization and theoretical explanation. There was a need in society for a theory that could explain how and why organisms change.
The main provisions of the evolutionary teachings of Charles Darwin English scientist Charles Darwin(1809-1882) - one of the world's best biologists. His evolutionary hypothesis, known as Darwinism, was used for more than 100 years
theoretical basis of biology. Main scientific works Darwin is “The Origin of Species by Means of Natural Selection” (1859), “Change in Domestic Animals and Cultivated Plants” (1868), “The Descent of Man and Sexual Selection” (1871), “Self-Pollination and Cross-Pollination” (1876), etc.
Darwin believed that the driving forces of evolution were hereditary variability and natural selection. Darwin collected numerous evidence of the variability of organisms living in humans and organisms different types in nature. Under conditions of domestication based hereditary variability organisms through artificial selection, man has created numerous breeds of domestic animals and varieties of cultivated plants.
Similarly, Darwin came to the conclusion that in natural conditions there is a factor that directs the evolution of organisms - natural selection. Darwin showed that in nature, organisms of any species are characterized by a constant struggle for existence, consisting of their interactions with environmental factors and intra- and interspecific competition. The result of hereditary variability of organisms and the struggle for existence is natural selection - the preferential survival and participation in reproduction of the most adapted individuals of each species. The consequence of natural selection is adaptation, speciation and progressive evolution of living nature. A special case of natural selection is sexual, which ensures the development of traits associated with the reproductive function.
Basic principles of Darwin's theory of evolution
1. Evolution consists of continuous adaptive changes in species.
2. Each species is capable of unlimited reproduction.
3. The driving forces of evolution and the mechanism of changes in organisms:
The basis for evolution is uncertain (hereditary ) variability : changes in organisms can be beneficial, harmful, or neutral;
Unlimited reproduction is hampered by limited life resources and most of the individuals die in struggle for existence,
selective survival and reproduction of the fittest individuals
Charles Darwin named natural selection .
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Driving forces of evolution according to Darwin |
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Uncertain (hereditary) variability |
Changes that occur individually in each organism, regardless of environmental influences, and can be transmitted to descendants |
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Struggle for existence |
The entire set of relationships between organisms and environmental factors. There are three forms of struggle for existence: intraspecific, interspecific interaction with the forces of inanimate nature |
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natural selection |
A process that manifests itself in the predominant survival and reproduction of organisms of a probable species that are most adapted to the conditions of existence and the death of those less adapted |
4. Under the influence of natural selection, groups of individuals of the same species accumulate various adaptive characteristics from generation to generation and transform into new species.
5. New breeds of animals and varieties of plants are formed under the influence artificial selection .
The importance of Darwin's theory of evolution for the development of natural science was very great: a) was revealed scientific basis the driving forces of evolution and this established the historical method of knowledge, which oriented researchers not only to describe natural phenomena, but also to explain their essence, to establish the causes of phenomena, stages of development; b) It has been proven that the driving forces for the development of nature are contained in nature itself.
At the same time, taking into account the then level of development of biology, Charles Darwin’s teachings had a number of shortcomings: the nature of hereditary variability remained unclear, the elementary unit of evolution was considered to be an individual on which natural selection acts, the concept of “species” remained the same as it was proposed by K. Linnaeus.
Do you know the origins of life?
3. What is the basic principle of the scientific method?
The problem of the origin of life on our planet is one of the central ones in modern natural science. Since ancient times, people have tried to find the answer to this question.
Creationism (Latin, creatio - creation).
IN different times at different nations had their own ideas about the origin of life. They are reflected in the sacred books of various religions, which explain the emergence of life as an act of the Creator (the will of God). The hypothesis of the divine origin of living things can only be taken on faith, since it cannot be experimentally verified or refuted. Therefore, it cannot be considered with scientific points of view.
The hypothesis of the spontaneous origin of life.
From ancient times to the middle of the 17th century. scientists had no doubt about the possibility of the spontaneous origin of life. It was believed that living creatures could appear from inanimate matter, for example, fish from silt, worms from soil, mice from rags, flies from rotten meat, and also that some forms could give rise to others, for example, animals could be formed from fruits (see, p. 343).
Thus, the great Aristotle, studying eels, found that among them there are no individuals with caviar or milt. Based on this, he suggested that eels are born from “sausages” of silt, formed from the friction of adult fish on the bottom.
The first blow to the idea of spontaneous generation came from the experiments of the Italian scientist Francesc Redi, who in 1668 proved the impossibility of spontaneous generation of flies in rotting meat.
Despite this, the ideas of spontaneous generation of life persisted until the middle of the 19th century. Only in 1862 did the French scientist Louis Pasteur finally refute the hypothesis of the spontaneous generation of life.
The Master’s works made it possible to assert that the principle “Every living thing is from living things” is true for all known organisms on our planet, but they did not resolve the question of the origin of life.
Panspermia hypothesis.
The proof of the impossibility of spontaneous generation of life gave rise to another problem. If another living organism is necessary for the emergence of a living organism, then where did the first living organism come from? This gave impetus to the emergence of the panspermia hypothesis, which had and still has many supporters, including among prominent scientists. They believe that for the first time life did not arise on Earth, but was somehow brought to our planet.
However, the panspermia hypothesis only attempts to explain the emergence of life on Earth. It does not answer the question of how life originated.
Denial of the fact of the spontaneous generation of life at the present time does not contradict the ideas about the fundamental possibility of the development of life in the past from inorganic matter.
Hypothesis of biochemical evolution.
In the 20s of the XX century, the Russian scientist A. I. Oparin and the Englishman J. Haldane expressed a hypothesis about the emergence of life in the process of biochemical evolution carbon compounds, which formed the basis of modern ideas.
In 1924, A.I. Oparin published the main provisions of his hypothesis of the origin of life on Earth. He proceeded from the fact that in modern conditions the emergence of living beings from inanimate nature is impossible. Abiogenic (i.e., without the participation of living organisms) emergence of living matter was possible only under conditions of an ancient atmosphere and the absence of living organisms.
According to A.I. Oparin, in the primary atmosphere of the planet, saturated with various gases, under powerful electrical discharges, as well as under the influence of ultraviolet radiation (there was no oxygen in the atmosphere and, therefore, there was no protective ozone screen, the atmosphere was reducing) and high radiation Organic compounds could have been formed and accumulated in the ocean, forming a “primordial soup.”
It is known that in concentrated solutions organic matter(proteins, nucleic acids, lipids) under certain conditions, clumps called coacervate droplets, or coacervates, can form. Coacervates were not destroyed under reducing atmosphere conditions. From the solution they received chemical substances, new compounds were synthesized in them, as a result of which they grew and became more complex.
Coacervates already resembled living organisms, but they were not yet such, since they did not have an ordered internal structure, inherent in living organisms, and were not able to reproduce. Protein coacervates were considered by A.I. Oparin as probionts - the predecessors of a living organism. He assumed that at a certain stage, protein probionts incorporated nucleic acids, creating single complexes.
The interaction of proteins and nucleic acids has led to the emergence of such properties of living things as self-reproduction, preservation of hereditary information and its transmission to subsequent generations.
Probionts, in which metabolism was combined with the ability to reproduce themselves, can already be considered as primitive procells.
In 1929, the English scientist J. Haldane also put forward a hypothesis of the abiogenic origin of life, but according to his views, the primary one was not a coarcerate system capable of exchanging substances with the environment, but a macromolecular system capable of self-reproduction. In other words, A.I. Oparin gave primacy to proteins, and J. Haldane - to nucleic acids.
The Oparin-Haldane hypothesis won many supporters, as it received experimental confirmation of the possibility of abiogenic synthesis of organic biopolymers.
In 1953, the American scientist Stanley Miller, in the installation he created (Fig. 141), simulated the conditions that supposedly existed in the primary atmosphere of the Earth. As a result of the experiments, amino acids were obtained. Similar experiments were repeated many times in various laboratories and made it possible to prove the fundamental possibility of synthesizing almost all monomers of the main biopolymers under such conditions. Subsequently, it was found that, under certain conditions, it is possible to synthesize more complex organic biopolymers from monomers: polypeptides, polynucleotides, polysaccharides and lipids.
But the Oparin-Haldane hypothesis also has a weak side, which its opponents point out. Within the framework of this hypothesis, it is not possible to explain the main problem: how the qualitative leap from inanimate to living occurred. After all, for the self-reproduction of nucleic acids, enzyme proteins are needed, and for the synthesis of proteins, nucleic acids are needed.
Creationism. Spontaneous generation. Panspermia hypothesis. Hypothesis of biochemical evolution. Coacervates. Probionts.
1. Why can the idea of the divine origin of life be neither confirmed nor refuted?
2. What are the main provisions of the Oparin-Haldane hypothesis?
3. What experimental evidence can be given in favor of this hypothesis?
4. What are the differences between A.I. Oparin’s hypothesis and J. Haldane’s hypothesis?
5. What arguments do opponents give when criticizing the Oparin-Haldane hypothesis?
Give possible arguments for and against the panspermia hypothesis.
Charles Darwin wrote in 1871: “But if now... in some warm body of water containing all the necessary ammonium and phosphorus salts and accessible to the influence of light, heat, electricity, etc., a protein was chemically formed that could to further, increasingly complex transformations, then this substance would immediately be destroyed or absorbed, which was impossible in the period before the emergence of living beings.”
Confirm or refute this statement by Charles Darwin.
In understanding the essence of life and its origin in the culture of human civilization, two ideas have long existed - biogenesis and abiogenesis. The idea of biogenesis (the origin of living things from living things) comes from ancient Eastern religious constructions, for which the idea of the absence of beginning and end was common. natural phenomena. Reality eternal life For these cultures, the eternity of matter and the Cosmos is logically acceptable, just like the eternity of matter.
An alternative idea - abiogenesis (the origin of living things from non-living things) dates back to civilizations that existed long before our era in the valleys of the Tigris and Euphrates rivers. This area was subject to constant flooding, and it is not surprising that it became the birthplace of catastrophism, which influenced European civilization through Judaism and Christianity. Catastrophes seem to interrupt the connection, the chain of generations, suggesting its creation, its emergence anew. In this regard, the belief in the periodic spontaneous generation of the organism under the influence of natural or supernatural causes was widespread in European culture.
Kamensky A. A., Kriksunov E. V., Pasechnik V. V. Biology 10th grade
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SECTION “Strength of materials”
Basic provisions. Main hypotheses and assumptions.
Types of loads and basic deformations. Strength of materials – is the science of the strength and deformation of bodies, machine elements and structures. Durability – is called the ability of the material of structures and their elements to resist the action of external forces without collapsing. WITH Opromat considers methods for calculating structural elements for strength, rigidity and stability. R Strength calculations make it possible to determine the dimensions and shapes of parts that can withstand a given load with the least amount of material. Under rigidity refers to the ability of a body or structure to resist the formation of deformation. Calculations for rigidity ensure that changes in the shape and dimensions of the structure and their elements do not exceed permissible standards. Under stability refers to the ability of a structure to resist forces that try to throw it out of equilibrium. Stability calculations prevent the possibility of sudden loss of stability and bending of part lengths. In practice, in most cases you have to deal with structures of complex shape, but they can be imagined as consisting of individual simple elements (beams, arrays). The main design material of the strength of material is timber, that is, a body whose transverse dimensions are small compared to its length. The ability of a material to eliminate deformation after the cessation of external forces is called. elasticity Main hypotheses and assumptions: 1) hypothesis about the absence of initial internal forces - assume that if there are no reasons causing deformation of the body (load), then at all its points all its forces are equal to 0, thus the interaction forces between the parts and the loaded body are not taken into account. 2) assumption of one-sidedness of the material, physics – bodies may not be the same at different points. 3) the assumption of continuity of material, the material of any body has a continuous structure and represents a continuous medium. 4) assumption of isotropy of the material, assume that the material of the body has the same properties in all directions. A material that does not have the same properties in different directions is called anisotropic (wood). 5) assumption of ideal elasticity, let us assume that, within certain limits, the loading of the material has ideal elasticity, that is, after removing the load, the deformation completely disappears.
A change in the linear and angular dimensions of a body is called linear and angular deformation, respectively. 1) the assumption of small displacement or the principle of initial dimensions. 2) the assumption of linear deformation of bodies, the movement of points and sections of an elastic body within certain limits, loaded in proportion to the forces caused by these movements. 3) hypothesis of plane sections. Types of loads and main deformations: Surface loads can be concentrated or distributed, depending on the nature of the action of the load, divided into statistical and dynamic. Statistical Loads are called numerical values, the direction and location of which remains constant or changes slowly and not significantly. Dynamic loads characterized by rapid coupling in the time of their direction or location are called. Main types of deformations: 1) tension – chains; 2) compression – columns; 3) shift - seals, dowels. Shear deformation brought to the point of destruction of the material is called shear. 4) Torsion 5) bending – beams, axes.
Section method.
Voltage.
The method of sections is that the body is mentally cut by a plane into 2 parts, any of which is discarded and in its place the forces acting before the cut are applied to the remaining section, the remaining part is considered as an independent body that is in equilibrium under the influence of external and internal forces applied to the section . According to Newton’s 3rd law, the internal forces acting in the section of the remaining and discarded parts of the body are equal in magnitude, but opposite; therefore, when we consider the equilibrium of any of the 2 parts of the dissected body, we get the same value of the internal forces. Figure page 8 in lectures.
Types of deformations. Hooke's law in tension and compression.
1) in the section only longitudinal force N occurs, in this case this deformation is tensile if the force is directed from the section. 2) in the cross section only transverse force Q occurs, in this case this is a shear deformation. 3) in the section only torque T occurs in this In this case, this is a torsional deformation. 4) a bending moment M occurs in the section; in this case, this is a pure bending deformation; if both M and Q occur simultaneously in the section, then the bending is transverse.
Hooke's law is valid only within certain load limits. Normal stress is directly proportional to the relative elongation or shortening. E – coefficient of proportionality (modulus of longitudinal elasticity) characterizes the stiffness of the material, i.e. the ability to resist elastic deformations of tension or compression.
Stress and longitudinal strain in tension and compression. Calculations of tensile and compressive strength.
As a result of mechanical tests, the limiting stress was established at which malfunction or destruction of the material of a structural part occurs. To ensure the strength of a part, it is necessary that the stresses arising in them during operation be less than the maximum. 
safety factor. 
;S – is called the permissible strength coefficient. It depends on the properties, quality and uniformity of the material. For fragile S=2 – 5, for wood 8 – 12. 
permissible voltage. 
condition of tensile and compressive strength.
Tension or compression is a type of deformation in which only longitudinal force occurs in any section of the beam. Bars with a straight axis (straight bars) working in tension or compression are called rods. When stretching, the hypothesis of flat sections is true, that is, all the fibers of the beam elongate by the same amount. When stretched and compressed in cross sections beam, only normal stresses arise, uniformly distributed over the section. 
The cross-sectional shape does not affect the stress. In all sections of the beam, the stress is distributed evenly and in the section where a concentrated force is applied to the beam along the axis, the value of the longitudinal force and stress changes abruptly. 
relative extension.
Physical basis of strength. Tensile diagram of mild steel.
Graph... page 14 in lectures. Describe: 3 straight lines parallel to each other with a dotted line at an angle of 30 degrees. The triangle is small near the origin. Tell me where the points are.
they call the maximum stress up to which the deformation increases in proportion to the load, that is, Hooke’s law is valid. Point A corresponds to another limit, which is called the elastic limit.
Elastic stress is the stress up to which deformations practically remain elastic.
C-yield strength is the stress at which a noticeable elongation appears in the sample without increasing the load. B – temporary resistance or tensile strength. temporary resistance is called a conditional stress equal to the ratio of the maximum force that the sample can withstand to the original cross-sectional area; when the temporary resistance is reached, a narrowing is formed on the tensile sample - a neck, that is, the destruction of the sample begins. We talk about conditional stress because in the section of the neck the stress will be large. M - corresponding to the voltage arose. In the smallest cross section at the moment of rupture - the rupture stress. 
.
Statically indeterminate rod systems.
Equation of displacement compatibility. Statically indeterminate systems
– these are elastic rod systems (structures) in which the number of unknown internal forces and reactions of supports is greater than the number of static equations possible for this system.
In addition to the static equations, to calculate such systems (structures), it is necessary to involve additional conditions that describe the deformation of the elements of a given system. They are conventionally called displacement equations or deformation compatibility equations (and the solution method itself is sometimes called the deformation comparison method). Degree of static indetermination
system is the difference between the number of unknowns and the number of independent equilibrium equations that can be compiled for a given system.
The number of additional displacement equations required to reveal static indetermination must be equal to the degree of static indetermination of the system. Compatibility equations
displacements are called canonical equations of the force method, since they are written according to a certain law (canon). These equations, the number of which is equal to the number of extra unknowns, together with the equilibrium equations make it possible to reveal the static indetermination of the system, i.e., to determine the values of the extra unknowns.
Torsion is a type of deformation in which only one force factor appears in the cross section of the rod - torque Mz. Torque by definition equal to the sum moments of internal forces relative to the longitudinal axis of the rod Oz. Normal forces parallel to the Oz axis do not contribute to the torque.
As can be seen from the formula, shears and shear stresses are proportional to the distances from the axis of the rod. Let us pay attention to the structural analogies of the formulas for normal stresses of pure bending and tangential torsion stresses. Hypotheses taken when calculating torsion:
1) sections that are flat before deformation remain flat after deformation (Bernoulli hypothesis, hypothesis of plane sections);
2) all radii of a given section remain straight (not curved) and rotate through the same angle ϕ, that is, each section rotates relative to the x axis like a hard thin disk;
3) the distances between sections do not change during deformation.
In torsion, strength calculations are also divided into design and verification. The calculations are based on the strength condition where τmax is the maximum shear stress in the beam, determined from the above equations depending on the shape of the section; [τ] - permissible shear stress, equal to part of the limiting stress for the material of the part - tensile strength τv or yield strength τt. The safety factor is set based on the same considerations as for tension. For example, for a shaft of hollow circular cross-section, with outer diameter D and inner diameter d, we have 
where α=d/D is the section cavity coefficient.
The torsional rigidity condition for such a shaft is as follows: 
where [φo] is the permissible relative angle of twist
Statically indeterminate problems in torsion
In torsion, as in tension, statically indeterminate problems may arise, for the solution of which equations for the compatibility of displacements must be added to the static equilibrium equations.
It is easy to show that the method for solving these problems in torsion and tension is the same. Let us consider, as an example, a beam embedded at both ends in absolutely rigid walls (Fig. 7.21). Let's discard the terminations, replacing their action with the unknown moments M1 and M2. We obtain the deformation compatibility equation from the condition that the angle of torsion in the right embedment is equal to zero:
Where Ip1=πd14/32, Ip2=πd24/32.
Torque moments in beam sections are related by the following equation:
.
Solving the above equations together for unknown moments, we obtain:
The twist angle of the section C is determined from the equation
Diagrams of torques and twist angles are presented in Fig. 7.21.
Straight transverse bending of beams. Pure bending diagram of internal forces during bending of beams.
Pure bending is a type of deformation in which only a bending moment occurs in any cross section of the beam; pure bending deformation will occur if 2 equal but opposite in sign pairs of forces are applied to the beam, a plane passing through the axis. Beams, axles, and shafts work for bending. We will consider such beams that have at least 1 plane of symmetry and the plane of load action coincides with it; in this case, bending deformation occurs in the plane of deformation of external forces and bending is called direct. Transverse bend– bending, in which in the sections of the rod, in addition to the internal bending moment, a transverse force also arises. For pure bending, the hypothesis of flat sections is valid. Fibers lying on the convex side are stretched, those lying on the concave side are compressed at the boundary. Between them lies a central layer of fibers that only bends without changing its length. With pure bending, normal tensile and compressive stresses arise in the cross sections of the beam, unevenly distributed over the section.
Analysis of the above differential dependencies during bending allows us to establish some features (rules) for constructing diagrams of bending moments and transverse forces:
A - in areas where there is no distributed load q, diagrams Q are limited to straight lines parallel to the base, and diagrams M– inclined straight lines;
b – in areas where a distributed load is applied to the beam q, diagrams Q are limited by inclined straight lines, and diagrams M– quadratic parabolas. Moreover, if the diagram M if we build “on a stretched fiber”, then the convexity of the rabola will be directed in the direction of action q, and the extremum will be located in the section where the diagram Q crosses the baseline;
V - in sections where a concentrated force is applied to the beam in the diagram Q there will be jumps by the magnitude and in the direction of a given force, and on the diagram M– kinks, the tip directed in the direction of action of this force;
G - in sections where a concentrated moment is applied to the beam in the diagram Q there will be no changes, but on the diagram M– jumps by the magnitude of this moment;
d – in areas where Q>0, moment M increases, and in areas where Q M decreases (see figures a–d).
Bending hypotheses. Formula for normal stresses
There are three such hypotheses for bending:
a – hypothesis of flat sections (Bernoulli hypothesis) – flat sections before deformation remain flat after deformation, but only rotate relative to a certain line, which is called the neutral axis of the beam section. In this case, the fibers of the beam lying on one side of the neutral axis will stretch, and on the other, compress; fibers lying on the neutral axis do not change their length; 
b – hypothesis about the constancy of normal stresses – stresses acting at the same distance y from the neutral axis, constant across the width of the beam;
c – hypothesis about the absence of lateral pressures – adjacent longitudinal fibers do not press on each other.
Maximum normal bending stresses we find it using the formula: 
Where W z– axial moment of resistance
During tension and compression in the cross sections of a beam, only normal stresses arise, uniformly distributed over the section. The shape of the section does not affect the stress. In all sections of the beam, the stress is distributed evenly and in the section where a concentrated force is applied to the beam along the axis, the value of the longitudinal force and stress changes abruptly. relative extension.
Differential dependencies during bending
Let us establish some relationships between internal forces and external loads during bending, as well as characteristic features of the diagrams Q And M, knowledge of which will facilitate the construction of diagrams and allow you to control their correctness. For convenience of notation, we will denote: M≡M z , Q≡Q y .
Let us select a small element on a section of a beam with an arbitrary load in a place where there are no concentrated forces and moments dx. Since the entire beam is in equilibrium, the element dx will be in equilibrium under the action of transverse forces applied to it, bending moments and external load. Because the Q And M in the general case change along the axis of the beam, then in the sections of the element dx shear forces will occur Q And Q+dQ, as well as bending moments M And M+dM. From the equilibrium condition of the selected element we obtain 
The first of the two equations written gives the condition
From the second equation, neglecting the term q· dx·( dx/2) as an infinitely small quantity of the second order, we find
Considering expressions (10.1) and (10.2) together we can obtain
Relations (10.1), (10.2) and (10.3) are called differential dependences of D.I. Zhuravsky during bending.
Geometric characteristics of flat sections.
The static moment of the area of a flat figure relative to an axis lying in the same plane is the sum of the products of the areas of elementary areas at a distance from them to this axis, taken over the entire area, and the static moments about the axes. Can be greater than zero or less.
The polar moment of inertia of a flat figure relative to a pole lying over the entire area is the sum of the products of the areas of elementary areas by the squares of their distances to the pole. 
The polar moment of inertia is always greater than 0.
The moment of inertia of a mechanical system relative to a fixed axis (“axial moment of inertia”) is called physical quantity Ja, equal to the sum of the products of the masses of all n material points of the system by the squares of their distances to the axis: 
Where:
mi- i-th mass points,
ri - distance from i-th point to the axis.
The axial moment of inertia of a body Ja is a measure of the inertia of a body in rotational motion around an axis, just as the mass of a body is a measure of its inertia in translational motion. Where:
dm = ρdV - mass of a small element of body volume dV,
ρ - density,
r is the distance from element dV to axis a.
If the body is homogeneous, that is, its density is the same everywhere, then 
The axes about which the centrifugal moment of inertia of the section becomes zero are called the main axes, and the main axes passing through the center of gravity of the section are called the main central axes of inertia of the section.
The moments of inertia relative to the main axes of inertia of the section are called the main moments of inertia of the section and are denoted by I1 and I2, with I1>I2. Usually, when talking about main moments, they mean axial moments of inertia about the main central axes of inertia.
Let's assume that the u and v axes are principal. Then 
From here 
THIS Equation determines the position of the main axes of inertia of the section at a given point relative to the original coordinate axes. When rotating the coordinate axes, the axial moments of inertia also change. Let us find the position of the axes relative to which the axial moments of inertia reach extreme values. To do this, we take the first derivative of Iu with respect to α and equate it to zero: hence, if the moments of inertia of the section about the main axes are the same, then all axes passing through the same point of the section are the main ones and the axial moments of inertia about all these axes are the same: Iu=Iv =Iy=Iz. This property is possessed, for example, by square, round, and annular sections.
Statically indeterminate beams and frames. Method of forces for revealing the static indetermination of beams and frames.
Statically indeterminate is a system that cannot be calculated using static equations alone, since it has unnecessary connections. To calculate such systems, additional equations are compiled that take into account the deformations of the system.
Statically indeterminate systems have a number of characteristic features:
Statically indeterminate system- this is a design power factors in the elements of which it is impossible to determine only from the equilibrium equations (static equations).
Static indetermination arises in the case when the number of connections imposed on a system turns out to be greater than is necessary to ensure its equilibrium. At the same time, some of these connections become, as it were, “superfluous”, and the efforts in them become unnecessary unknowns. Based on the number of extra unknowns, the degree of static indetermination of the system is determined. Note that the term “extra” connections is conditional, since these connections are necessary to ensure the strength and rigidity of the system, although they are “redundant” from the point of view of its equilibrium. 
Frame– a structure consisting of rods of arbitrary configuration and having one or more rigid (not hinged) nodes. 
To reveal static indetermination, it is necessary, in addition to the static side of the problem, to analyze the deformations of the system and, in addition to the equilibrium equations, to compile equations of compatibility of deformations, from the solution of which the “extra” unknowns are found. In this case, the number of such equations must be equal to the degree of static indetermination of the system.
Method of forces. The main idea of the method
In order to convert a given statically indeterminate system into a statically determinate one, the method of forces uses the following technique. All “extra” connections imposed on the structure are discarded, and their action is replaced by corresponding reactions - forces or moments. At the same time, in order to maintain the specified conditions of fastening and loading, the reactions of the discarded bonds must have such values that the displacements in the direction of these reactions would be equal to zero (or the specified values). Thus, when revealing static indetermination by this method, what is sought is not the deformations, but the corresponding forces—reactions of bonds (hence the name “method of forces”).
Let us write down the main stages of revealing static indetermination using the method of forces:
1) we determine the degree of static indetermination of the system, that is, the number of unnecessary unknowns;
2) we remove unnecessary connections and thus replace the original statically indeterminate system with a statically definable one. This new system, freed from unnecessary connections, is called basic Note that the choice of extra connections can be quite arbitrary and depends only on the desire of the designer, so that for the same initial statically indeterminate system, different versions of the main systems are possible. However, care must be taken to ensure that the main system remains geometrically unchanged - that is, its elements, after removing unnecessary connections, should not be able to move freely in space. 3) we compose equations for deformations at the points of application of extra unknowns. Since in the original system these deformations are equal to zero, then the indicated equations must also be equated to zero. Then from the resulting equations we find the value of the extra unknowns. 
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