Modulus of elasticity of aluminum kg cm2. Calculated resistances and moduli of elasticity for various building materials

Young's modulus and shear, Poisson's ratio values ​​(Table). Table modulus of elasticity of materials table

Modulus of elasticity for steel as well as for other materials

Before you use any material in construction work, you should familiarize yourself with its physical characteristics in order to know how to handle it, what mechanical impact will be acceptable for it, and so on. One of the important characteristics that are often paid attention to is the modulus of elasticity.

Below we consider the concept itself, as well as this value in relation to one of the most popular materials in construction and repair work - steel. These indicators will also be considered for other materials, for the sake of an example.

Modulus of elasticity - what is it?

The elastic modulus of a material is a set of physical quantities that characterize the ability of a solid body to deform elastically under conditions of application of force to it. It is expressed by the letter E. So it will be mentioned in all the tables that will go further in the article.

It cannot be argued that there is only one way to determine the value of elasticity. Different approaches to the study of this quantity have led to the fact that there are several different approaches at once. Below are three main ways to calculate the indicators of this characteristic for different materials:

• Young's modulus (E) describes the resistance of a material to any stretch or compression under elastic deformation. The Young variant is determined by the ratio of stress to compressive strain. It is usually referred to simply as the modulus of elasticity.
• Shear modulus (G), also called stiffness modulus. This method reveals the ability of the material to resist any change in shape, but under the conditions of maintaining its norm. The shear modulus is expressed as the ratio of the shear stress to the shear strain, which is defined as the change in right angle between the available planes subjected to shear stresses. The shear modulus, by the way, is one of the components of such a phenomenon as viscosity.
• The bulk modulus (K), which is also referred to as the bulk modulus. This variant denotes the ability of an object made of any material to change its volume if it is subjected to an all-round normal stress, which is the same in all its directions. This variant is expressed by the ratio of the volumetric stress to the relative volumetric compression.
• There are also other indicators of elasticity, which are measured in other quantities and are expressed in other ratios. Other still very well-known and popular options for elasticity indicators are Lame parameters or Poisson's ratio.

Table of indicators of elasticity of materials

Before proceeding directly to this characteristic of steel, let us first consider, as an example and additional information, a table containing data on this value in relation to other materials. Data is measured in MPa.

Modulus of elasticity of various materials

As you can see from the table above, this value is different for different materials, moreover, the indicators differ if one or another option for calculating this indicator is taken into account. Everyone is free to choose exactly the option of studying indicators that suits him best. It may be preferable to consider Young's modulus, since it is more often used specifically to characterize a particular material in this regard.

After we briefly got acquainted with the data of this characteristic of other materials, we will proceed directly to the characteristic of steel separately.

To begin with, let's turn to dry numbers and derive various indicators of this characteristic for different types of steels and steel structures:

• Modulus of elasticity (E) for casting, hot-rolled reinforcement from steel grades referred to as St.3 and St. 5 equals 2.1*106 kg/cm^2.
• For such steels as 25G2S and 30KhG2S, this value is 2 * 106 kg / cm ^ 2.
• For a wire of a periodic profile and a cold-drawn round wire, there is such a value of elasticity equal to 1.8 * 106 kg / cm ^ 2. For cold-flattened reinforcement, the indicators are similar.
• For strands and bundles of high-strength wire, the value is 2 10 6 kg / cm ^ 2
• For steel spiral ropes and ropes with a metal core, the value is 1.5·10 4 kg/cm^2, while for ropes with an organic core, this value does not exceed 1.3·10 6 kg/cm^2.
• The shear modulus (G) for rolled steel is 8.4·10 6 kg/cm^2.
• And finally, Poisson's ratio for steel is equal to 0.3

These are general data given for types of steel and steel products. Each value was calculated according to all physical rules and taking into account all the available relationships that are used to derive the values ​​of this characteristic.

All general information about this characteristic of steel will be given below. Values ​​will be given both in Young's modulus and in shear modulus, both in one unit of measure (MPa) and in another (kg/cm2, newton*m2).

Steel and several different grades

The values ​​of the elasticity indices of steel vary, since there are several modules at once, which are calculated and calculated in different ways. One can notice the fact that, in principle, the indicators do not differ much, which testifies in favor of different studies of the elasticity of various materials. But it is not worth going deep into all calculations, formulas and values, since it is enough to choose a certain value of elasticity in order to be guided by it in the future.

By the way, if you do not express all the values ​​​​by numerical ratios, but take it immediately and calculate it completely, then this steel characteristic will be equal to: E \u003d 200000 MPa or E \u003d 2,039,000 kg / cm ^ 2.

This information will help you understand the very concept of the modulus of elasticity, as well as get acquainted with the main values ​​\u200b\u200bof this characteristic for steel, steel products, as well as for several other materials.

It should be remembered that the elastic modulus indicators are different for different steel alloys and for different steel structures that contain other compounds in their composition. But even in such conditions, one can notice the fact that the indicators do not differ much. The value of the modulus of elasticity of steel practically depends on the structure. as well as carbon content. The method of hot or cold processing of steel also cannot greatly affect this indicator.

stanok.guru

tehtab.ru

Young's modulus and shear, Poisson's ratio values ​​(Table)

Elastic properties of bodies

The following are lookup tables for commonly used constants; if two of them are known, then this is quite sufficient to determine the elastic properties of a homogeneous isotropic solid.

Young's modulus or modulus of elasticity in dynes/cm2.

Shear modulus or torsion modulus G in dyne/cm2.

Compressive modulus or bulk modulus K in dyne/cm2.

Volume of compressibility k=1/K/.

Poisson's ratio µ is equal to the ratio of the transverse relative compression to the longitudinal relative tension.

For a homogeneous isotropic solid material, the following relations between these constants take place:

G = E / 2(1 + μ) - (α)

μ = (E / 2G) - 1 - (b)

K = E / 3(1 - 2μ) - (c)

Poisson's ratio is positive, and its value is usually in the range from 0.25 to 0.5, but in some cases it may go beyond these limits. The degree of agreement between the observed values ​​of µ and those calculated by formula (b) is an indicator of the isotropy of the material.

Tables of values ​​for Young's Modulus, Shear Modulus and Poisson's Ratio

The values ​​calculated from relations (a), (b), (c) are given in italics.

The experimental results given below refer to common laboratory materials, mainly wires.

infotables.ru

Modulus of elasticity (Young's modulus) | world of welding

Elastic modulus

Modulus of elasticity (Young's modulus) E - characterizes the resistance of a material to tension / compression under elastic deformation, or the property of an object to deform along an axis when a force is applied along this axis; defined as the ratio of stress to elongation. Young's modulus is often referred to simply as the modulus of elasticity.

1 kgf/mm2 = 10-6 kgf/m2 = 9.8 106 N/m2 = 9.8 107 dynes/cm2 = 9.81 106 Pa = 9.81 MPa

Literature

1. Brief physical and technical reference book. T.1 / Under the general. ed. K.P. Yakovlev. Moscow: FIZMATGIZ. 1960. - 446 p.
2. Reference book on welding of non-ferrous metals / S.M. Gurevich. Kyiv: Naukova Dumka. 1981. 680 p.
3. Handbook of elementary physics / N.N. Koshkin, M.G. Shirkevich. M., Science. 1976. 256 p.
4. Tables of physical quantities. Handbook / Ed. I.K. Kikoin. M., Atomizdat. 1976, 1008 p.

weldworld.com

METAL MECHANICAL PROPERTIES | Encyclopedia Around the World

METAL MECHANICAL PROPERTIES. When a force or a system of forces acts on a metal sample, it reacts to this by changing its shape (deforms). Various characteristics that determine the behavior and final state of a metal sample, depending on the type and intensity of forces, are called the mechanical properties of the metal.

The intensity of the force acting on the sample is called stress and is measured as the total force divided by the area on which it acts. Deformation is understood as a relative change in the dimensions of the sample caused by applied stresses.

ELASTIC AND PLASTIC DEFORMATION, DESTRUCTION

If the stress applied to the metal sample is not too high, then its deformation turns out to be elastic - as soon as the stress is removed, its shape is restored. Some metal structures are deliberately designed to deform elastically. So, springs usually require a fairly large elastic deformation. In other cases, elastic deformation is minimized. Bridges, beams, mechanisms, devices are made as rigid as possible. The elastic deformation of a metal sample is proportional to the force or the sum of the forces acting on it. This is expressed by Hooke's law, according to which the stress is equal to the elastic strain multiplied by a constant proportionality factor called the modulus of elasticity: s = eY, where s is the stress, e is the elastic strain, and Y is the modulus of elasticity (Young's modulus). The elastic moduli of a number of metals are presented in Table. one.

Using the data in this table, you can calculate, for example, the force required to stretch a steel rod with a square cross section with a side of 1 cm by 0.1% of its length:

F = YґAґDL/L = 200,000 MPa ґ 1 cm2ґ0.001 = 20,000 N (= 20 kN)

When stresses are applied to a metal sample that exceed its elastic limit, they cause plastic (irreversible) deformation, leading to an irreversible change in its shape. Higher stresses can cause material failure.

The most important criterion when choosing a metal material that requires high elasticity is the yield strength. The best spring steels have almost the same modulus of elasticity as the cheapest building steels, but spring steels are able to withstand much greater stresses, and therefore much greater elastic deformations without plastic deformation, since they have a higher yield strength.

The plastic properties of a metallic material (as opposed to elastic) can be changed by fusion and heat treatment. Thus, the yield strength of iron by similar methods can be increased 50 times. Pure iron passes into a state of fluidity already at stresses of the order of 40 MPa, while the yield strength of steels containing 0.5% carbon and a few percent chromium and nickel, after heating to 950 ° C and hardening, can reach 2000 MPa.

When a metallic material is loaded beyond its yield strength, it continues to deform plastically, but becomes harder as the deformation progresses, so that more and more stress is required to further increase the deformation. This phenomenon is called deformation or mechanical hardening (and hardening). It can be demonstrated by twisting or repeatedly bending a metal wire. Work hardening of metal products is often carried out in factories. Sheet brass, copper wire, aluminum rods can be cold rolled or cold drawn to the hardness required for the final product.

Stretching.

The relationship between stress and strain for materials is often investigated by conducting tensile tests, and in doing so, a strain diagram is obtained - a graph with strain plotted along the horizontal axis and stress plotted along the vertical axis (Fig. 1). Although the cross-section of the specimen decreases (and the length increases) in tension, the stress is usually calculated by referring the force to the original cross-sectional area, and not to the reduced one that would give the true stress. At small strains, this does not matter much, but at large strains, it can lead to a noticeable difference. On fig. Figure 1 shows strain-stress curves for two materials with different ductility. (Plasticity is the ability of a material to elongate without breaking, but also without returning to its original shape after the load is removed.) The initial linear section of both curves ends at the yield point, where plastic flow begins. For a less ductile material, the highest point on the diagram, its ultimate tensile strength, corresponds to failure. For a more ductile material, the ultimate tensile strength is reached when the rate of reduction in cross-section during deformation becomes greater than the strain hardening rate. At this stage, during the test, the formation of a "neck" (local accelerated reduction in the cross section) begins. Although the load bearing capacity of the specimen is reduced, the material in the neck continues to harden. The test ends with a rupture of the neck.

Typical values ​​of quantities characterizing the tensile strength of a number of metals and alloys are presented in table. 2. It is easy to see that these values ​​for the same material can vary greatly depending on the processing.

Compression.

Elastic and plastic properties under compression are usually very similar to those observed under tension (Fig. 2). The curve of the relationship between the nominal stress and the nominal strain in compression passes above the corresponding curve for tension only because the cross section of the sample does not decrease, but increases during compression. If, however, the true stress and true strain are plotted along the axes of the graph, then the curves practically coincide, although fracture occurs earlier in tension.

Hardness.

The hardness of a material is its ability to resist plastic deformation. Since tensile tests require expensive equipment and are time consuming, simpler hardness tests are often resorted to. When testing according to the Brinell and Rockwell methods, an “indenter” (a tip having the shape of a ball or pyramid) is pressed into the metal surface at a given load and loading speed. The size of the print is then measured (often done automatically) and the hardness index (number) is determined from it. The smaller the print, the greater the hardness. Hardness and yield strength are to some extent comparable characteristics: usually, when one of them increases, the other also increases.

One might get the impression that maximum yield strength and hardness are always desirable in metallic materials. In fact, this is not the case, and not only for economic reasons (hardening processes require additional costs).

First, materials need to be shaped into various products, and this is usually done using processes (rolling, stamping, pressing) in which plastic deformation plays an important role. Even when machining on a metal-cutting machine, plastic deformation is very significant. If the hardness of the material is too great, then too much force is required to give it the desired shape, as a result of which the cutting tools wear out quickly. Difficulties of this kind can be reduced by working metals at elevated temperatures when they become softer. If hot working is not possible, then metal annealing is used (slow heating and cooling).

Second, as the metal material becomes harder, it usually loses its ductility. In other words, a material becomes brittle if its yield strength is so high that plastic deformation does not occur up to those stresses that immediately cause fracture. The designer usually has to choose some intermediate levels of hardness and ductility.

Impact strength and brittleness.

Toughness is the opposite of brittleness. This is the ability of a material to resist fracture by absorbing impact energy. For example, glass is brittle because it is unable to absorb energy through plastic deformation. With an equally sharp impact on a sheet of soft aluminum, large stresses do not arise, since aluminum is capable of plastic deformation, which absorbs the impact energy.

There are many different methods for testing metals for impact strength. When using the Charpy method, a notched prismatic metal sample is substituted for the impact of a retracted pendulum. The work expended on the destruction of the sample is determined by the distance that the pendulum deflects after impact. Such tests show that steels and many metals behave as brittle at low temperatures, but as ductile at elevated temperatures. The transition from brittle to ductile behavior often occurs in a rather narrow temperature range, the midpoint of which is called the brittle-ductile transition temperature. Other impact tests also indicate the presence of such a transition, but the measured transition temperature varies from test to test depending on the depth of the notch, the size and shape of the sample, and the method and speed of impact loading. Because no test type covers the full range of operating conditions, impact testing is only valuable because it allows comparison of different materials. However, they provided a lot of important information about the effect of alloying, fabrication technology and heat treatment on brittle fracture propensity. The transition temperature for steels, measured using the V-notch Charpy method, can reach +90°C, but with appropriate alloying additions and heat treatment, it can be reduced to -130°C.

The brittle fracture of steel has been the cause of numerous accidents, such as unexpected bursts of pipelines, explosions of pressure vessels and storage tanks, and collapses of bridges. Among the best-known examples is the large number of Liberty-class ships whose hulls unexpectedly came apart while sailing. As the investigation showed, the failure of the Liberty ships was due, in particular, to improper welding technology that left internal stresses, poor control of the composition of the weld, and structural defects. The information obtained as a result of laboratory tests made it possible to significantly reduce the likelihood of such accidents. The brittle-ductile transition temperature of some materials, such as tungsten, silicon and chromium, is under normal conditions much higher than room temperature. Such materials are usually considered brittle, and they can be shaped by plastic deformation only when heated. At the same time, copper, aluminium, lead, nickel, some grades of stainless steels and other metals and alloys do not become brittle at all when the temperature is lowered. Although much is already known about brittle fracture, this phenomenon cannot yet be considered fully understood.

Fatigue.

Fatigue is the destruction of a structure under the action of cyclic loads. When a part is bent in one direction or the other, its surfaces are alternately subjected to compression and tension. With a sufficiently large number of loading cycles, failure can cause stresses that are much lower than those at which failure occurs in the case of a single loading. The alternating stresses cause localized plastic deformation and work hardening of the material, resulting in small cracks occurring over time. The stress concentration near the ends of such cracks causes them to grow. At first, the cracks grow slowly, but as the load cross section decreases, the stresses at the ends of the cracks increase. In this case, cracks grow faster and faster and, finally, instantly spread to the entire section of the part. See also DESTRUCTION MECHANISMS.

Fatigue is by far the most common cause of structural failure under operating conditions. Particularly susceptible to this are machine parts operating under cyclic loading conditions. In the aircraft industry, fatigue turns out to be a very important issue due to vibration. In order to avoid fatigue failure, it is necessary to frequently check and replace parts of aircraft and helicopters.

Creep.

Creep (or creep) is a slow increase in the plastic deformation of a metal under a constant load. With the advent of jet engines, gas turbines and rockets, the properties of materials at elevated temperatures have become increasingly important. In many areas of technology, further development is constrained by limitations associated with the high-temperature mechanical properties of materials.

At normal temperatures, plastic deformation sets in almost instantaneously as soon as an appropriate stress is applied, and increases little thereafter. At elevated temperatures, metals not only become softer, but also deform in such a way that the deformation continues to grow with time. This time-dependent deformation, or creep, can limit the life of structures that must operate at elevated temperatures for long periods of time.

The greater the stress and the higher the temperature, the greater the creep rate. Typical creep curves are shown in fig. 3. After the initial stage of rapid (unsteady) creep, this velocity decreases and becomes almost constant. Before destruction, the creep rate increases again. The temperature at which creep becomes critical varies for different metals. Telephone companies are concerned about the creep of overhead lead-sheathed cables operating at normal ambient temperatures; while some special alloys can work at 800°C without exhibiting excessive creep.

The service life of parts under creep conditions can be determined by either maximum allowable deformation or failure, and the designer must always keep these two options in mind. The suitability of materials for the manufacture of products designed for long-term operation at elevated temperatures, such as turbine blades, is difficult to assess in advance. Testing over time equal to the expected service life is often practically impossible, and the results of short-term (accelerated) tests are not so easy to extrapolate to longer periods, since the nature of the destruction may change. Although the mechanical properties of superalloys are constantly improving, the challenge for metal physicists and materials scientists will always be to create materials that can withstand even higher temperatures. See also PHYSICAL METAL SCIENCE.

CRYSTAL STRUCTURE

Above, we talked about the general laws of the behavior of metals under the action of mechanical loads. To better understand the corresponding phenomena, it is necessary to consider the atomic structure of metals. All solid metals are crystalline substances. They consist of crystals, or grains, the arrangement of atoms in which corresponds to a regular three-dimensional lattice. The crystal structure of a metal can be thought of as consisting of atomic planes, or layers. When a shear stress (a force that causes two adjacent planes of a metal sample to slide over each other in opposite directions) is applied, one layer of atoms can move an entire interatomic distance. Such a shift will affect the shape of the surface, but not the crystal structure. If one layer moves many interatomic distances, then a "step" is formed on the surface. Although individual atoms are too small to be seen under a microscope, the steps formed by sliding are clearly visible under a microscope and are called slip lines.

Ordinary metal objects that we encounter daily are polycrystalline, i.e. consist of a large number of crystals, each of which has its own orientation of atomic planes. The deformation of an ordinary polycrystalline metal has in common with the deformation of a single crystal that it occurs due to sliding along the atomic planes in each crystal. A noticeable sliding of whole crystals along their boundaries is observed only under creep conditions at elevated temperatures. The average size of one crystal, or grain, can be from several thousandths to several tenths of a centimeter. A finer grit is desirable, since the mechanical characteristics of a fine-grained metal are better than those of a coarse-grained one. In addition, fine-grained metals are less brittle.

Slip and dislocation.

The sliding processes were studied in more detail on single crystals of metals grown in the laboratory. It became clear not only that slip occurs in certain definite directions and usually along well-defined planes, but also that single crystals are deformed at very low stresses. The transition of single crystals to the state of fluidity begins for aluminum at 1, and for iron, at 15–25 MPa. Theoretically, this transition in both cases should occur at voltages of approx. 10,000 MPa. This discrepancy between experimental data and theoretical calculations has remained an important problem for many years. In 1934, Taylor, Polanyi and Orowan proposed an explanation based on the concept of defects in the crystal structure. They suggested that during sliding, a displacement first occurs at some point in the atomic plane, which then propagates through the crystal. The boundary between the displaced and non-displaced regions (Fig. 4) is a linear defect in the crystal structure, called a dislocation (in the figure, this line goes into the crystal perpendicular to the plane of the figure). When a shear stress is applied to the crystal, the dislocation moves, causing it to slip along the plane it is in. After the dislocations have formed, they move very easily through the crystal, which explains the "softness" of single crystals.

In metal crystals, there are usually many dislocations (the total length of dislocations in one cubic centimeter of an annealed metal crystal can be more than 10 km). But in 1952, scientists from the laboratories of the Bell Telephone Corporation, testing very thin whiskers of tin for bending, discovered, to their surprise, that the bending strength of such crystals was close to the theoretical value for perfect crystals. Later, extremely strong whiskers and many other metals were discovered. It is assumed that such a high strength is due to the fact that in such crystals there are either no dislocations at all, or there is one that runs along the entire length of the crystal.

temperature effects.

The effect of elevated temperatures can be explained in terms of dislocations and grain structure. Numerous dislocations in crystals of a strain-hardened metal distort the crystal lattice and increase the energy of the crystal. When the metal is heated, the atoms become mobile and rearrange into new, more perfect crystals containing fewer dislocations. This recrystallization is associated with softening, which is observed during annealing of metals.

www.krugosvet.ru

Table Young's modulus. Elastic modulus. Definition of Young's Modulus.

www.kilomol.ru

Elastic moduli and Poisson's ratios for some materials 013

How deep to fill the foundation under the house

One of the main tasks of engineering design is the choice of construction material and the optimal section of the profile. It is necessary to find the size that, with the minimum possible mass, will ensure the preservation of the shape of the system under the influence of the load.

For example, what number of steel I-beam should be used as the span beam of the structure? If we take a profile with dimensions below the required one, then we are guaranteed to get the destruction of the structure. If more, then this leads to an inefficient use of metal, and, consequently, to a heavier structure, more difficult installation, and an increase in financial costs. Knowledge of such a concept as the modulus of elasticity of steel will give an answer to the above question, and will avoid the appearance of these problems at the earliest stage of production.

General concept

Modulus of elasticity (also known as Young's modulus) is one of the indicators of the mechanical properties of a material, which characterizes its resistance to tensile deformation. In other words, its value indicates the plasticity of the material. The greater the modulus of elasticity, the less any rod will stretch, all other things being equal (load value, cross-sectional area, etc.).

In the theory of elasticity, Young's modulus is denoted by the letter E. It is an integral part of Hooke's law (the law on the deformation of elastic bodies). It relates the stress that occurs in the material and its deformation.

According to the international standard system of units, it is measured in MPa. But in practice, engineers prefer to use the dimension kgf / cm2.

The determination of the modulus of elasticity is carried out empirically in scientific laboratories. The essence of this method lies in the rupture of dumbbell-shaped material samples on special equipment. Having learned the stress and elongation at which the sample was destroyed, these variables are divided by each other, thereby obtaining the Young's modulus.

We note right away that this method determines the elastic moduli of plastic materials: steel, copper, and so on. Brittle materials - cast iron, concrete - are compressed until cracks appear.

Additional characteristics of mechanical properties

The modulus of elasticity makes it possible to predict the behavior of the material only when working in compression or tension. In the presence of such types of loads as crushing, shearing, bending, etc., additional parameters will need to be introduced:

• Rigidity is the product of the modulus of elasticity and the cross-sectional area of ​​the profile. By the magnitude of the rigidity, one can judge the plasticity of not the material, but the structure assembly as a whole. Measured in kilograms of force.
• The relative longitudinal elongation shows the ratio of the absolute elongation of the sample to the total length of the sample. For example, a certain force is applied to a rod 100 mm long. As a result, it decreased in size by 5 mm. Dividing its elongation (5 mm) by the original length (100 mm) we obtain a relative elongation of 0.05. The variable is a dimensionless quantity. In some cases, for convenience of perception, it is translated into percentages.
• The relative transverse elongation is calculated similarly to the above paragraph, but instead of the length, the diameter of the rod is considered here. Experiments show that for most materials the transverse elongation is 3-4 times less than the longitudinal one.
• The Punch ratio is the ratio of relative longitudinal strain to relative transverse strain. This parameter allows you to fully describe the change in shape under the influence of a load.
• The shear modulus characterizes the elastic properties when the sample is subjected to tangential stresses, i.e., in the case when the force vector is directed at 90 degrees to the body surface. Examples of such loads are the work of rivets in shear, nails in crushing, and so on. By and large, the shear modulus is associated with such a concept as the viscosity of the material.
• The modulus of bulk elasticity is characterized by a change in the volume of the material for a uniform, versatile application of the load. It is the ratio of volumetric pressure to volumetric compressive strain. An example of such work is a sample lowered into water, which is affected by liquid pressure over its entire area.

In addition to the above, it should be mentioned that some types of materials have different mechanical properties depending on the direction of the load. Such materials are characterized as anisotropic. Vivid examples are wood, laminated plastics, some types of stone, fabrics, and so on.

Isotropic materials have the same mechanical properties and elastic deformation in any direction. These include metals (steel, cast iron, copper, aluminum, etc.), non-layered plastics, natural stones, concrete, rubber.

The value of the modulus of elasticity

It should be noted that Young's modulus is not a constant value. Even for the same material, it can fluctuate depending on the points of application of the force.

Some elastic-plastic materials have a more or less constant modulus of elasticity when working both in compression and in tension: copper, aluminum, steel. In other cases, the elasticity may vary based on the shape of the profile.

Here are examples of Young's modulus values ​​(in millions of kgf/cm2) for some materials:

• Brass - 1.01.
• Bronze - 1.00.
• Brick masonry - 0.03.
• Granite masonry - 0.09.
• Concrete - 0.02.
• Wood along the fibers - 0.1.
• Wood across the fibers - 0.005.
• Aluminum - 0.7.

Consider the difference in readings between the moduli of elasticity for steels, depending on the grade.

Before you use any material in construction work, you should familiarize yourself with its physical characteristics in order to know how to handle it, what mechanical impact will be acceptable for it, and so on. One of the important characteristics that are often paid attention to is the modulus of elasticity.

Below we consider the concept itself, as well as this value in relation to one of the most popular materials in construction and repair work - steel. These indicators will also be considered for other materials, for the sake of an example.

Modulus of elasticity - what is it?

The modulus of elasticity of a material is called set of physical quantities, which characterize the ability of a solid body to deform elastically under conditions of application of a force to it. It is expressed by the letter E. So it will be mentioned in all the tables that will go further in the article.

It cannot be argued that there is only one way to determine the value of elasticity. Different approaches to the study of this quantity have led to the fact that there are several different approaches at once. Below are three main ways to calculate the indicators of this characteristic for different materials:

Table of indicators of elasticity of materials

Before proceeding directly to this characteristic of steel, let us first consider, as an example and additional information, a table containing data on this value in relation to other materials. Data is measured in MPa.

Modulus of elasticity of various materials

As you can see from the table above, this value is different for different materials, moreover, the indicators differ if one or another option for calculating this indicator is taken into account. Everyone is free to choose exactly the option of studying indicators that suits him best. It may be preferable to consider Young's modulus, since it is more often used specifically to characterize a particular material in this regard.

After we briefly got acquainted with the data of this characteristic of other materials, we will proceed directly to the characteristic of steel separately.

To start let's look at dry numbers and derive various indicators of this characteristic for different types of steels and steel structures:

• Modulus of elasticity (E) for casting, hot-rolled reinforcement from steel grades referred to as St.3 and St. 5 equals 2.1*106 kg/cm^2.
• For such steels as 25G2S and 30KhG2S, this value is 2 * 106 kg / cm ^ 2.
• For a wire of a periodic profile and a cold-drawn round wire, there is such a value of elasticity equal to 1.8 * 106 kg / cm ^ 2. For cold-flattened reinforcement, the indicators are similar.
• For strands and bundles of high-strength wire, the value is 2 10 6 kg / cm ^ 2
• For steel spiral ropes and ropes with a metal core, the value is 1.5·10 4 kg/cm^2, while for ropes with an organic core, this value does not exceed 1.3·10 6 kg/cm^2.
• The shear modulus (G) for rolled steel is 8.4·10 6 kg/cm^2.
• And finally, Poisson's ratio for steel is equal to 0.3

These are general data given for types of steel and steel products. Each value was calculated according to all physical rules and taking into account all the available relationships that are used to derive the values ​​of this characteristic.

All general information about this characteristic of steel will be given below. Values ​​will be given as n about Young's modulus, and according to the shear modulus, both in one unit of measurement (MPa) and in others (kg / cm2, newton * m2).

Steel and several different grades

The values ​​of the elasticity indices of steel differ, since there are multiple modules, which are calculated and calculated differently. One can notice the fact that, in principle, the indicators do not differ much, which testifies in favor of different studies of the elasticity of various materials. But it is not worth going deep into all calculations, formulas and values, since it is enough to choose a certain value of elasticity in order to be guided by it in the future.

By the way, if you do not express all the values ​​​​by numerical ratios, but take it immediately and calculate it completely, then this characteristic of the steel will be equal to: Е=200000 MPa or Е=2,039,000 kg/cm^2.

This information will help you understand the very concept of the modulus of elasticity, as well as get acquainted with the main values ​​\u200b\u200bof this characteristic for steel, steel products, as well as for several other materials.

It should be remembered that the elastic modulus indicators are different for different steel alloys and for different steel structures that contain other compounds in their composition. But even in such conditions, one can notice the fact that the indicators do not differ much. The value of the modulus of elasticity of steel practically depends on the structure. as well as carbon content. The method of hot or cold processing of steel also cannot greatly affect this indicator.

stanok.guru

Calculated resistances and moduli of elasticity of heavy concrete, MPa

table 2

Note.
Estimated
concrete resistance for limit
states of the 2nd group are equal to the normative:
R b , ser
= R b , n ;
R bt , ser
= R
bt , n .

Calculated resistances and moduli of elasticity of some reinforcing steels, MPa

table
3

Note.
Estimated
steel resistance for ultimate
states of the 2nd group are equal
normative: R s , ser
= R s , n .

studfiles.net

Example 3.5. Checking the section of an I-beam column for compression

It is necessary to check the section of a column made of an I-beam 20K1 according to STO ASChM 20-93 from steel C235.

Compressive force: N=600kN.

Column height: L=4.5m.

Effective length factor: μ x =1.0; μy=1.0.

Solution.
Design resistance of steel C235: R y \u003d 230N / mm 2 \u003d 23.0 kN / cm 2.
Modulus of elasticity of steel C235: E \u003d 2.06x10 5 N / mm 2.
Coefficient of working conditions for columns of public buildings at a constant load γ c = 0.95.
The sectional area of ​​the element is found according to the assortment for an I-beam 20K1: A \u003d 52.69 cm 2.
The radius of gyration of the section relative to the x-axis, also according to the assortment: i x \u003d 4.99 cm.
The radius of gyration of the section relative to the y-axis, also according to the assortment: i y \u003d 8.54 cm.
The estimated length of the column is determined by the formula:
l ef,x \u003d μ x l x \u003d 1.0 * 4.5 \u003d 4.5 m;
l ef,y \u003d μ y l y \u003d 1.0 * 4.5 \u003d 4.5 m.
Flexibility of the section about the x-axis: λ x \u003d l x / i x \u003d 450 / 4.99 \u003d 90.18.
Flexibility of the section about the y-axis: λ y \u003d l y /i y \u003d 450 / 8.54 \u003d 52.69.
Maximum allowable flexibility for compressed elements (chords, support braces and posts transmitting support reactions: spatial structures from single corners, spatial structures from pipes and paired corners over 50m) λu = 120.
Checking conditions : x< λ u ; λ y < λ u:
90,18 < 120; 52,69 < 120 - the conditions are met.
The stability of the section is checked for the greatest flexibility. In this example, λ max = 90.18.
The conditions for the flexibility of an element are determined by the formula:
λ’ = λ√(R y /E) = 90.18√(230/2.06*10 5) = 3.01.
The coefficient α and β is taken according to the type of section, for an I-beam α = 0.04; β = 0.09.
Coefficient δ \u003d 9.87 (1-α + β * λ ') + λ ' 2 \u003d 9.87 (1-0.04 + 0.09 * 3.01) + 3.01 2 \u003d 21.2.
The stability coefficient is determined by the formula:
φ \u003d 0.5 (δ-√ (δ 2 -39.48λ' 2) / λ' 2 \u003d 0.5 (21.2-√ (21.2 2 -39.48 * 3.01 2) / 3 .01 2 = 0.643.
The coefficient φ can also be taken from the table according to the type of section and λ'.
Condition check: N/φAR y γ c ≤ 1,
600,0/(0,643*52,69*23,0*0,95) = 0,81 ≤ 1.
Since the calculation was made for maximum flexibility about the x-axis, there is no need to check about the y-axis.

Examples:

spravkidoc.ru

The modulus of elasticity of steel in kgf \ cm2, examples

One of the main tasks of engineering design is the choice of construction material and the optimal section of the profile. It is necessary to find the size that, with the minimum possible mass, will ensure the preservation of the shape of the system under the influence of the load.

For example, what number of steel I-beam should be used as the span beam of the structure? If we take a profile with dimensions below the required one, then we are guaranteed to get the destruction of the structure. If more, then this leads to an inefficient use of metal, and, consequently, to a heavier structure, more difficult installation, and an increase in financial costs. Knowledge of such a concept as the modulus of elasticity of steel will give an answer to the above question, and will avoid the appearance of these problems at the earliest stage of production.

General concept

Modulus of elasticity (also known as Young's modulus) is one of the indicators of the mechanical properties of a material, which characterizes its resistance to tensile deformation. In other words, its value indicates the plasticity of the material. The greater the modulus of elasticity, the less any rod will stretch, all other things being equal (load value, cross-sectional area, etc.).

In the theory of elasticity, Young's modulus is denoted by the letter E. It is an integral part of Hooke's law (the law on the deformation of elastic bodies). It relates the stress that occurs in the material and its deformation.

According to the international standard system of units, it is measured in MPa. But in practice, engineers prefer to use the dimension kgf / cm2.

The determination of the modulus of elasticity is carried out empirically in scientific laboratories. The essence of this method lies in the rupture of dumbbell-shaped material samples on special equipment. Having learned the stress and elongation at which the sample was destroyed, these variables are divided by each other, thereby obtaining the Young's modulus.

We note right away that this method determines the elastic moduli of plastic materials: steel, copper, and so on. Brittle materials - cast iron, concrete - are compressed until cracks appear.

Additional characteristics of mechanical properties

The modulus of elasticity makes it possible to predict the behavior of the material only when working in compression or tension. In the presence of such types of loads as crushing, shearing, bending, etc., additional parameters will need to be introduced:

• Rigidity is the product of the modulus of elasticity and the cross-sectional area of ​​the profile. By the magnitude of the rigidity, one can judge the plasticity of not the material, but the structure assembly as a whole. Measured in kilograms of force.
• The relative longitudinal elongation shows the ratio of the absolute elongation of the sample to the total length of the sample. For example, a certain force is applied to a rod 100 mm long. As a result, it decreased in size by 5 mm. Dividing its elongation (5 mm) by the original length (100 mm) we obtain a relative elongation of 0.05. The variable is a dimensionless quantity. In some cases, for convenience of perception, it is translated into percentages.
• The relative transverse elongation is calculated similarly to the above paragraph, but instead of the length, the diameter of the rod is considered here. Experiments show that for most materials the transverse elongation is 3-4 times less than the longitudinal one.
• The Punch ratio is the ratio of relative longitudinal strain to relative transverse strain. This parameter allows you to fully describe the change in shape under the influence of a load.
• The shear modulus characterizes the elastic properties when the sample is subjected to tangential stresses, i.e., in the case when the force vector is directed at 90 degrees to the body surface. Examples of such loads are the work of rivets in shear, nails in crushing, and so on. By and large, the shear modulus is associated with such a concept as the viscosity of the material.
• The modulus of bulk elasticity is characterized by a change in the volume of the material for a uniform, versatile application of the load. It is the ratio of volumetric pressure to volumetric compressive strain. An example of such work is a sample lowered into water, which is affected by liquid pressure over its entire area.

In addition to the above, it should be mentioned that some types of materials have different mechanical properties depending on the direction of the load. Such materials are characterized as anisotropic. Vivid examples are wood, laminated plastics, some types of stone, fabrics, and so on.

Isotropic materials have the same mechanical properties and elastic deformation in any direction. These include metals (steel, cast iron, copper, aluminum, etc.), non-layered plastics, natural stones, concrete, rubber.

The value of the modulus of elasticity

It should be noted that Young's modulus is not a constant value. Even for the same material, it can fluctuate depending on the points of application of the force.

Some elastic-plastic materials have a more or less constant modulus of elasticity when working both in compression and in tension: copper, aluminum, steel. In other cases, the elasticity may vary based on the shape of the profile.

Here are examples of Young's modulus values ​​(in millions of kgf/cm2) for some materials:

• Cast iron white - 1.15.
• Cast iron gray -1.16.
• Brass - 1.01.
• Bronze - 1.00.
• Brick masonry - 0.03.
• Granite masonry - 0.09.
• Concrete - 0.02.
• Wood along the fibers - 0.1.
• Wood across the fibers - 0.005.
• Aluminum - 0.7.

Consider the difference in readings between the moduli of elasticity for steels, depending on the grade:

• High quality structural steels (20, 45) - 2.01.
• Steel of ordinary quality (Art. 3, Art. 6) - 2.00.
• Low-alloy steels (30KhGSA, 40X) - 2.05.
• Stainless steel (12X18H10T) - 2.1.
• Die steels (9KhMF) - 2.03.
• Spring steel (60С2) - 2.03.
• Bearing steels (ШХ15) - 2.1.

Also, the value of the modulus of elasticity for steels varies depending on the type of rolled products:

• High strength wire - 2.1.
• Braided rope - 1.9.
• Cable with a metal core - 1.95.

As you can see, the deviations between the steels in the values ​​of the moduli of elastic deformation are small. Therefore, in most engineering calculations, errors can be neglected and the value E = 2.0 can be taken.

prompriem.ru

Elastic moduli and Poisson's ratios for some materials 013

www.sopromat.info

Steel load limit index - Young's modulus

Before taking any building material into work, it is necessary to study its strength data and possible interaction with other substances and materials, their compatibility in terms of adequate behavior under the same loads on the structure. The decisive role for solving this problem is assigned to the elastic modulus - it is also called the Young's modulus.

The high strength of steel allows it to be used in the construction of high-rise buildings and openwork structures of stadiums and bridges. Additives to steel of certain substances that affect its quality, called doping, and these additives can double the strength of steel. The modulus of elasticity of alloyed steel is much higher than that of conventional steel. Strength in construction, as a rule, is achieved by selecting the cross-sectional area of ​​​​the profile due to economic reasons: high-alloy steels have a higher cost.

physical meaning

The designation of the modulus of elasticity as a physical quantity is (E), this indicator characterizes the elastic resistance of the material of the product to the deforming loads applied to it:

• longitudinal - tensile and compressive;
• transverse - bending or made in the form of a shift;
• voluminous - twisting.

The higher the value (E), the higher , the stronger the product from this material will be and the higher the fracture limit will be. For example, for aluminum this value is 70 GPa, for cast iron - 120, for iron - 190, and for steel up to 220 GPa.

Definition

The modulus of elasticity is a summary term that has absorbed other physical indicators of the elasticity properties of solid materials - under the influence of a force, change and acquire its former shape after its termination, that is, elastically deform. This is the ratio of the stress in the product - the pressure of the force per unit area, to the elastic deformation (a dimensionless value determined by the ratio of the size of the product to its original size). Hence its dimension, like that of stress - the ratio of force to unit area. Since the voltage in the metric SI is usually measured in Pascals, then the strength indicator is also.

There is another, not very correct definition: modulus of elasticity is the pressure, capable of doubling the product. But the yield strength of a large number of materials is well below the applied pressure.

Elastic moduli, their types

There are many ways to change the conditions for applying force and the resulting deformations, and this also implies a large number of types of elastic moduli, but in practice, in accordance with the deforming loads there are three main ones:

The elasticity characteristics are not limited to these indicators, there are others that carry other information, have different dimension and meaning. These are also widely known among specialists, the Lame elasticity index and Poisson's ratio.

How to determine the modulus of elasticity of steel

To determine the parameters of various steel grades, there are special tables as part of regulatory documents in the field of construction - in building codes and regulations (SNiP) and state standards (GOST). So, modulus of elasticity (E) or Young, for white and gray cast iron from 115 to 160 GPa, malleable - 155. As for steel, the modulus of elasticity of carbon steel C245 has values ​​from 200 to 210 GPa. Alloy steel has slightly higher performance - from 210 to 220 GPa.

The same characteristic for ordinary steel grades St.3 and St.5 has the same value - 210 GPa, and for steel St.45, 25G2S and 30KhGS - 200 GPa. As you can see, the variability (E) for different grades of steel is insignificant, but in products, for example, in ropes, the picture is different:

• for strands and strands of high-strength wire 200 GPa;
• steel cables with a metal core 150 GPa;
• steel ropes with organic core 130 GPa.

As you can see, the difference is significant.

The values ​​of the shear modulus or stiffness (G) can be seen in the same tables, they have smaller values, for rolled steel - 84 GPa, carbon and alloyed - from 80 to 81 hPa, and for steels St.3 and St.45–80 GPa. The reason for the difference in the values ​​of the elasticity parameter is the simultaneous action of three main modules at once, calculated by different methods. However, the difference between them is small, which indicates sufficient accuracy of the study of elasticity. Therefore, you should not get hung up on calculations and formulas, but you should take a specific value of elasticity and use it as a constant. If you do not make calculations for individual modules, but make a complex calculation, the value (E) will be 200 GPa.

It must be understood that these values ​​differ for steels with different additives and steel products that include parts from other substances, but these values ​​differ slightly. The main influence on the elasticity index is exerted by the carbon content, but the method of processing steel - hot rolling or cold stamping, does not have a significant effect.

When choosing steel products, they also use another indicator, which is regulated in the same way as the modulus of elasticity in the tables of GOST and SNiP publications is the design resistance to tensile, compressive and bending loads. The dimension of this indicator is the same as that of the modulus of elasticity, but the values ​​are three orders of magnitude smaller. This indicator has two purposes: standard and design resistance, the names speak for themselves - design resistance is used when performing structural strength calculations. So, the calculated resistance of steel C255 with a rolled thickness of 10 to 20 mm is 240 MPa, with a standard 245 MPa. The calculated resistance of rolled products from 20 to 30 mm is slightly lower and amounts to 230 MPa.

instrument.guru

| world of welding

Elastic modulus

Modulus of elasticity (Young's modulus) E - characterizes the resistance of the material to tension / compression under elastic deformation, or the property of the object to deform along the axis when a force is applied along this axis; defined as the ratio of stress to elongation. Young's modulus is often referred to simply as the modulus of elasticity.

1 kgf / mm 2 \u003d 10 -6 kgf / m 2 \u003d 9.8 10 6 N / m 2 \u003d 9.8 10 7 dynes / cm 2 \u003d 9.81 10 6 Pa \u003d 9.81 MPa

Literature

1. Brief physical and technical reference book. T.1 / Under the general. ed. K.P. Yakovlev. Moscow: FIZMATGIZ. 1960. - 446 p.
2. Reference book on welding of non-ferrous metals / S.M. Gurevich. Kyiv: Naukova Dumka. 1981. 680 p.
3. Handbook of elementary physics / N.N. Koshkin, M.G. Shirkevich. M., Science. 1976. 256 p.
4. Tables of physical quantities. Handbook / Ed. I.K. Kikoin. M., Atomizdat. 1976, 1008 p.

Before you use any material in construction work, you should familiarize yourself with its physical characteristics in order to know how to handle it, what mechanical impact will be acceptable for it, and so on. One of the important characteristics that are often paid attention to is the modulus of elasticity.

Below we consider the concept itself, as well as this value in relation to one of the most popular materials in construction and repair work - steel. These indicators will also be considered for other materials, for the sake of an example.

Modulus of elasticity - what is it?

The modulus of elasticity of a material is called set of physical quantities, which characterize the ability of a solid body to deform elastically under conditions of application of a force to it. It is expressed by the letter E. So it will be mentioned in all the tables that will go further in the article.

It cannot be argued that there is only one way to determine the value of elasticity. Different approaches to the study of this quantity have led to the fact that there are several different approaches at once. Below are three main ways to calculate the indicators of this characteristic for different materials:

Table of indicators of elasticity of materials

Before proceeding directly to this steel characteristic, let's first consider, as an example and additional information, a table containing data on this value in relation to other materials. Data is measured in MPa.

As you can see from the table above, this value is different for different materials, moreover, the indicators differ if one or another option for calculating this indicator is taken into account. Everyone is free to choose exactly the option of studying indicators that suits him best. It may be preferable to consider Young's modulus, since it is more often used specifically to characterize a particular material in this regard.

After we briefly got acquainted with the data of this characteristic of other materials, we will proceed directly to the characteristic of steel separately.

To start let's look at dry numbers and derive various indicators of this characteristic for different types of steels and steel structures:

• Modulus of elasticity (E) for casting, hot-rolled reinforcement from steel grades referred to as St.3 and St. 5 equals 2.1*106 kg/cm^2.
• For such steels as 25G2S and 30KhG2S, this value is 2 * 106 kg / cm ^ 2.
• For a wire of a periodic profile and a cold-drawn round wire, there is such a value of elasticity equal to 1.8 * 106 kg / cm ^ 2. For cold-flattened reinforcement, the indicators are similar.
• For strands and bundles of high-strength wire, the value is 2 10 6 kg / cm ^ 2
• For steel spiral ropes and ropes with a metal core, the value is 1.5·10 4 kg/cm^2, while for ropes with an organic core, this value does not exceed 1.3·10 6 kg/cm^2.
• The shear modulus (G) for rolled steel is 8.4·10 6 kg/cm^2.
• And finally, Poisson's ratio for steel is equal to 0.3

These are general data given for types of steel and steel products. Each value was calculated according to all physical rules and taking into account all the available relationships that are used to derive the values ​​of this characteristic.

All general information about this characteristic of steel will be given below. Values ​​will be given as n about Young's modulus, and according to the shear modulus, both in one unit of measurement (MPa) and in others (kg / cm2, newton * m2).

Steel and several different grades

The values ​​of the elasticity indices of steel differ, since there are multiple modules, which are calculated and calculated differently. One can notice the fact that, in principle, the indicators do not differ much, which testifies in favor of different studies of the elasticity of various materials. But it is not worth going deep into all calculations, formulas and values, since it is enough to choose a certain value of elasticity in order to be guided by it in the future.

By the way, if you do not express all the values ​​​​by numerical ratios, but take it immediately and calculate it completely, then this characteristic of the steel will be equal to: Е=200000 MPa or Е=2,039,000 kg/cm^2.

This information will help you understand the very concept of the modulus of elasticity, as well as get acquainted with the main values ​​\u200b\u200bof this characteristic for steel, steel products, as well as for several other materials.

It should be remembered that the elastic modulus indicators are different for different steel alloys and for different steel structures that contain other compounds in their composition. But even in such conditions, one can notice the fact that the indicators do not differ much. The value of the modulus of elasticity of steel practically depends on the structure. as well as carbon content. The method of hot or cold processing of steel also cannot greatly affect this indicator.