Young's modulus of elasticity 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 using 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 is often paid attention to is the elastic modulus.

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

Modulus of elasticity - what is it?

The elastic modulus of any material is the totality physical quantities, which characterize the ability of a solid body to elastically deform under conditions of force applied 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 is impossible to say 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 tension or compression during elastic deformation. Young's version is determined by the ratio of stress to compressive strain. Usually it is simply called the modulus of elasticity.
Shear modulus (G), also called stiffness modulus. This method reveals the ability of a material to resist any change in shape, but while maintaining its norm. Shear modulus is expressed as the ratio of shear stress to shear strain, which is defined as the change in the right angle between existing planes subjected to shear stresses. The shear modulus, by the way, is one of the components of such a phenomenon as viscosity.
Bulk modulus (K), also called bulk modulus. This option denotes the ability of an object made of any material to change its volume in the event of a comprehensive impact on it. normal voltage, which is the same in all its directions. This option is expressed by the ratio of the magnitude of volumetric stress to the magnitude of relative volumetric compression.
There are also other indicators of elasticity, which are measured in other quantities and expressed in other ratios. Other very well-known and popular options for elasticity indicators are the Lamé parameters or Poisson's ratio.

Table of material elasticity indicators

Before moving directly to this characteristic of steel, let us first consider, as an example, 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, and the indicators also differ, if we take into account one or another option for calculating this indicator. Everyone is free to choose exactly the option for studying indicators that suits them best. It may be preferable to consider Young's modulus, since it is most often used specifically to characterize a particular material in this regard.

After we have briefly reviewed the data on this characteristic of other materials, we will move directly to the characteristics of steel separately.

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

Modulus of elasticity (E) for casting, hot-rolled reinforcement from steel grades called St.3 and St. 5 equals 2.1*106 kg/cm^2.
For steels such as 25G2S and 30KhG2S this value is 2*106 kg/cm^2.
For periodic wire and cold-drawn round wire, there is an elasticity value 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 cables 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 in accordance with all physical rules and taking into account all existing relationships that are used to derive the values of this characteristic.

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

Steel and several different grades

The elasticity values of steel vary, since there are several modules at once, which are calculated and calculated in different ways. You can notice the fact that, in principle, the indicators do not differ greatly, which indicates in favor of different studies of elasticity various materials. But it’s not worth going too deep into all the calculations, formulas and values, since it’s enough to choose a certain elasticity value in order to focus on it in the future.

By the way, if you do not express all the values in numerical ratios, but take it immediately and calculate it completely, then this characteristic of steel will be equal to: E = 200,000 MPa or E = 2,039,000 kg/cm^2.

This information will help you understand the very concept of modulus of elasticity, as well as become familiar with the main values of this characteristic for steel, steel products, and also 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. But even in such conditions, you can notice the fact that the indicators do not differ much. The elastic modulus of steel practically depends on the structure. and also on carbon content. The method of hot or cold processing of steel also cannot greatly affect this indicator.

stanok.guru

Table. Values of longitudinal elasticity modulus E, shear modulus G and Poisson's ratio µ (at a temperature of 20oC).

Material	Modules, MPa		Poisson's ratio
Material			Poisson's ratio
Steel	(1.86÷2.1)*105	(7.8÷8.3)*104	0,25-0,33
Gray cast iron	(0.78÷1.47)*105	4,4*104	0,23-0,27
Gray modified cast iron	(1.2÷1.6)*105	(5÷6.9)*104	-
Technical copper	(1.08÷1.3)*105	4,8*104	-
Tin bronze	(0.74÷1.22)*105	-	0,32-0,35
Tin-free bronze	(1.02÷1.2)*105	-	-
Aluminum brass	(0.98÷1.08)*105	(3.6÷3.9)*104	0,32-0,34
Aluminum alloys	(0.69÷0.705)*105	2,6*104	0,33
Magnesium alloys	(0.4÷0.44)*105	-	0,34
Nickel technical	2,5*105	7,35*104	0,33
Technical lead	(0.15÷0.2)*105	0,7*104	0,42
Technical zinc	0,78*105	3,2*104	0,27
Brickwork	(0.24÷0.3)*104	-	-
Concrete (with temporary resistance) (1-2MPa)	(1.48÷2.25)*104	-	0,16-0,18
Conventional reinforced concrete: compressed elements	(1.8÷4.2)*104	-	-
Conventional reinforced concrete: bendable elements	(1.07÷2.64)*104	-	-
Wood of all species: along the grain	(8.8÷15.7)*104	(4.4÷6.4)*102	-
Wood of all species: across the grain	(3.9÷9.8)*104	(4.4÷6.4)*102	-
1st grade aviation plywood: along the grain	12,7*103	-	-
1st grade aviation plywood: across the grain	6,4*103	-	-
Textolite (PT, PTK, PT-1)	(5.9÷9.8)*103	-	-
Getinax	(9.8÷17.1)*103	-	-
Viniplast sheet	3,9*103	-	-
Glass	(4.9÷5.9)*104	(2.05÷2.25)*103	0,24-0,27
Organic glass	(2.8÷4.9)*103	-	0,35-0,38
Bakelite without fillers	(1.96÷5.9)*103	(6.86÷20.5)*102	0,35-0,38
Celluloid	(1.47÷2.45)*103	(6.86÷9.8)*102	0,4
Rubber	0,07*104	2*103	-
Fiberglass	3,4*104	(3.5÷3.9)*103	-
Capron	(1.37÷1.96)*103	-	-
Fluoroplast F-4	(4.6÷8.3)*102	-	-

tehtab.ru

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

Elastic properties of bodies

Below are reference 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 longitudinal elasticity in dyn/cm2.

Shear modulus or torsional modulus G in dyn/cm2.

Compressive modulus or bulk modulus K in dynes/cm2.

Compressibility volume k=1/K/.

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

For a homogeneous isotropic solid material, the following relationships between these constants hold:

G = E / 2(1 + μ) - (α)

μ = (E / 2G) - 1 - (b)

K = E / 3(1 - 2μ) - (c)

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

Tables of Young's Modulus of Elasticity, Shear Modulus and Poisson's Ratio

Values calculated from relations (a), (b), (c) are given in italics.

Material at 18°C	Young's modulus E, 1011 dynes/cm2.	Poisson's ratio µ
Aluminum











Steel (1% C) 1)

Constantan 2)
Manganin
1) For steel containing about 1% C, elastic constants are known to change during heat treatment. 2) 60% Cu, 40% Ni.

The experimental results given below are for common laboratory materials, mainly wires.

Substance	Young's modulus E, 1011 dynes/cm2.	Shear modulus G, 1011 dynes/cm2.	Poisson's ratio µ	Modulus of bulk elasticity K, 1011 dynes/cm2.
Bronze (66% Cu)

Nickel silver1)

Glass yen crowns
Jena flint glass
Welding iron


Phosphor bronze2)
Platinoid3)
Quartz threads (floating)
Soft vulcanized rubber


1) 60% Cu, 15% Ni, 25% Zn 2) 92.5% Cu, 7% Sn, 0.5% P 3) Nickel silver with a small amount of tungsten.

Substance	Young's modulus E, 1011 dynes/cm2.	Substance	Young's modulus E, 1011 dynes/cm2.
Zinc (pure)

		Mahogany
		Zirconium

Alloy 90% Pt, 10% Ir
Duralumin
Silk threads1		Teak

		Plastics:
		Thermoplastic
		Thermoset
		Tungsten
1) Rapidly decreases with increasing load 2) Detects noticeable elastic fatigue

Temperature coefficient (at 150C) Et=E11 (1-ɑ (t-15)), Gt=G11 (1-ɑ (t-15))			Compressibility k, bar-1 (at 7-110С)

Aluminum			Aluminum





			Flint glass
			German glass

Nickel silver
Phosphor bronze
Quartz threads

infotables.ru

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

Modulus of elasticity

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

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

Modulus of elasticity (Young's modulus) Material Ekgf/mm2 107 N/m2 MPa

Metals
Aluminum	6300-7500	6180-7360	61800-73600
Annealed aluminum	6980	6850	68500
Beryllium	30050	29500	295000
Bronze	10600	10400	104000
Aluminum bronze, casting	10500	10300	103000
Rolled phosphor bronze	11520	11300	113000
Vanadium	13500	13250	132500
Vanadium annealed	15080	14800	148000
Bismuth	3200	3140	31400
Bismuth cast	3250	3190	31900
Tungsten	38100	37400	374000
Tungsten annealed	38800-40800	34200-40000	342000-400000
Hafnium	14150	13900	139000
Duralumin	7000	6870	68700
Rolled duralumin	7140	7000	70000
Wrought iron	20000-22000	19620-21580	196200-215800
Cast iron	10200-13250	10000-13000	100000-130000
Gold	7000-8500	6870-8340	68700-83400
Annealed gold	8200	8060	80600
Invar	14000	13730	137300
Indium	5300	5200	52000
Iridium	5300	5200	52000
Cadmium	5300	5200	52000
Cadmium cast	5090	4990	49900
Cobalt annealed	19980-21000	19600-20600	196000-206000
Constantan	16600	16300	163000
Brass	8000-10000	7850-9810	78500-98100
Rolled ship brass	10000	9800	98000
Cold drawn brass	9100-9890	8900-9700	89000-97000
Magnesium	4360	4280	42800
Manganin	12600	12360	123600
Copper	13120	12870	128700
Deformed copper	11420	11200	112000
Cast copper	8360	8200	82000
Rolled copper	11000	10800	108000
Cold drawn copper	12950	12700	127000
Molybdenum	29150	28600	286000
Nickel silver	11000	10790	107900
Nickel	20000-22000	19620-21580	196200-215800
Nickel annealed	20600	20200	202000
Niobium	9080	8910	89100
Tin	4000-5400	3920-5300	39200-53000
Tin cast	4140-5980	4060-5860	40600-58600
Osmium	56570	55500	555000
Palladium	10000-14000	9810-13730	98100-137300
Palladium cast	11520	11300	113000
Platinum	17230	16900	169000
Platinum annealed	14980	14700	147000
Rhodium annealed	28030	27500	275000
Ruthenium annealed	43000	42200	422000
Lead	1600	1570	15700
Cast lead	1650	1620	16200
Silver	8430	8270	82700
Annealed silver	8200	8050	80500
Tool steel	21000-22000	20600-21580	206000-215800
Alloy steel	21000	20600	206000
Special steel	22000-24000	21580-23540	215800-235400
Carbon steel	19880-20900	19500-20500	195000-205000
Steel casting	17330	17000	170000
Tantalum	19000	18640	186400
Tantalum annealed	18960	18600	186000
Titanium	11000	10800	108000
Chromium	25000	24500	245000
Zinc	8000-10000	7850-9810	78500-98100
Rolled zinc	8360	8200	82000
Cast zinc	12950	12700	127000
Zirconium	8950	8780	87800
Cast iron	7500-8500	7360-8340	73600-83400
Cast iron white, gray	11520-11830	11300-11600	113000-116000
Malleable cast iron	15290	15000	150000
Plastics
Plexiglass	535	525	5250
Celluloid	173-194	170-190	1700-1900
Organic glass	300	295	2950
Rubbers
Rubber	0,80	0,79	7,9
Soft vulcanized rubber	0,15-0,51	0,15-0,50	1,5-5,0
Tree
Bamboo	2000	1960	19600
Birch	1500	1470	14700
Beech	1600	1630	16300
Oak	1600	1630	16300
Spruce	900	880	8800
iron tree	2400	2350	32500
Pine	900	880	8800
Minerals
Quartz	6800	6670	66700
Various materials
Concrete	1530-4100	1500-4000	15000-40000
Granite	3570-5100	3500-5000	35000-50000
Limestone is dense	3570	3500	35000
Quartz thread (fused)	7440	7300	73000
Catgut	300	295	2950
Ice (at -2 °C)	300	295	2950
Marble	3570-5100	3500-5000	35000-50000
Glass	5000-7950	4900-7800	49000-78000
Glass crowns	7200	7060	70600
Flint glass	5500	5400	70600

Literature

Brief physical and technical reference book. T.1 / Ed. ed. K.P. Yakovleva. M.: FIZMATGIZ. 1960. – 446 p.
Handbook on welding of non-ferrous metals / S.M. Gurevich. Kyiv: Naukova Dumka. 1981. 680 p.
Handbook of elementary physics / N.N. Koshkin, M.G. Shirkevich. M., Science. 1976. 256 p.
Tables of physical quantities. Handbook / Ed. I.K. Kikoina. M., Atomizdat. 1976, 1008 pp.

weldworld.ru

METALS MECHANICAL PROPERTIES | Encyclopedia Around the World

Contents of the article

METALS MECHANICAL PROPERTIES. When a force or system of forces is applied to a metal sample, it reacts by changing its shape (deforming). Various characteristics, which 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 over which it acts. Deformation refers to the relative change in sample dimensions caused by applied stresses.

ELASTIC AND PLASTIC DEFORMATION, DESTRUCTION

If the stress applied to the metal sample is not too great, 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. Thus, 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 sum of forces acting on it. This is expressed by Hooke's law, which states that stress is equal to elastic strain multiplied by a constant coefficient of proportionality called the modulus of elasticity: s = eY, where s is stress, e is elastic strain, and Y is the modulus of elasticity (Young's modulus). The elastic moduli of a number of metals are presented in Table. 1.

Using the data from this table, you can calculate, for example, the force required to stretch a steel rod of 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 in excess of its elastic limit are applied to a metal specimen, they cause plastic (irreversible) deformation, resulting in a permanent 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 construction steels, but spring steels are able to withstand much greater stresses, and therefore much greater elastic deformations without plastic deformation, because they have a higher yield strength.

The plastic properties of a metallic material (as opposed to the elastic properties) can be changed by alloying and heat treatment. Thus, the yield strength of iron can be increased 50 times using similar methods. Pure iron goes 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 several percent of chromium and nickel, after heating to 950 ° C and hardening, can reach 2000 MPa.

When metal material loaded beyond the yield strength, it continues to deform plastically, but during the deformation process it becomes harder, so that to further increase the deformation it is necessary to increase the stress more and more. This phenomenon is called deformation or mechanical hardening (as well as work hardening). It can be demonstrated by twisting or repeatedly bending a metal wire. Strain 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 level of hardness required in the final product.

Stretching.

The relationship between stress and strain for materials is often examined by carrying out tensile tests, and in this case a tensile diagram is obtained - a graph in which strain is plotted along the horizontal axis and stress is plotted along the vertical axis (Fig. 1). Although tension reduces the cross-section of the specimen (and increases its length), the stress is usually calculated by relating the force to the original cross-sectional area rather than to the reduced cross-sectional area, which would give the true stress. For small deformations this does not matter much, but for large ones it can lead to a noticeable difference. In Fig. Figure 1 shows stress-strain curves for two materials with unequal ductility. (Plasticity is the ability of a material to elongate without destruction, but also without returning to its original shape after removing the load.) The initial linear section of both curves ends at the point of the yield stress, where plastic flow begins. For a less ductile material, the highest point on the diagram, its tensile strength, corresponds to failure. For a more ductile material, the ultimate tensile strength is achieved when the rate of decrease in cross-section during deformation becomes greater than the rate of strain hardening. At this stage during the test, necking begins (local accelerated reduction in cross-section). Although the specimen's ability to withstand the load decreases, the material in the neck continues to strengthen. The test ends with a cervical rupture.

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.

Table 2

Table 2
Metals and alloys	State	Yield strength, MPa	Tensile strength, MPa	Elongation, %
Mild steel (0.2% C)	Hot rolled	300	450	35
Medium carbon steel (0.4% C, 0.5% Mn)	Hardened and tempered	450	700	21
High strength steel (0.4% C, 1.0% Mn, 1.5% Si, 2.0% Cr, 0.5% Mo)	Hardened and tempered	1750	2300	11
Gray cast iron	After casting	–	175–300	0,4
Aluminum is technically pure	Annealed	35	90	45
Aluminum is technically pure	Strain-hardened	150	170	15
Aluminum alloy (4.5% Cu, 1.5% Mg,0.6% Mn)	Aging hardened	360	500	13
	Fully Annealed	80	300	66
Sheet brass (70% Cu, 30% Zn)	Strain-hardened	500	530	8
Tungsten, wire	Drawn to 0.63mm diameter	2200	2300	2,5
Lead	After casting	0,006	12	30

Compression.

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

Hardness.

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

It may seem that in metallic materials maximum yield strength and hardness are always desirable. 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 processed at 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 cutting tools wear out quickly. This kind of difficulty can be reduced by processing metals at elevated temperatures, when they become softer. If hot processing is not possible, then metal annealing (slow heating and cooling) is used.

Second, as a metal material gets 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 failure. 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 destruction by absorbing impact energy. For example, glass is brittle because it cannot absorb energy through plastic deformation. With an equally sharp blow 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 testing metals for impact strength. When using the Charpy method, a prismatic sample of metal with a notch is subjected to the impact of a retracted pendulum. The work expended on the destruction of the sample is determined by the distance by which the pendulum deviates after the impact. Such tests show that steels and many metals behave as brittle when low temperatures, but as viscous - at elevated levels. The transition from brittle to ductile behavior often occurs over a fairly 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 specimen, and the method and speed of impact loading. Since no single type of test reproduces the full range of operating conditions, impact tests are valuable only in that they allow comparison. different materials. However, they provided much important information about the effects of alloying, fabrication techniques, and heat treatment on the susceptibility to brittle failure. The transition temperature for steels, measured using the Charpy V-notch method, can reach +90°C, but with appropriate alloying additives and heat treatment it can be lowered to -130°C.

The brittle fracture of steel has been the cause of numerous accidents, such as unexpected pipeline breaks, explosions of pressure vessels and storage tanks, and bridge collapses. Among the most famous examples – large number maritime ships of the "Liberty" type, the hull of which unexpectedly came apart during voyage. As the investigation showed, the failure of the Liberty ships was due, in particular, to wrong technology welding that left internal stresses, poor control over weld composition and design defects. Information obtained from laboratory tests has significantly reduced the likelihood of such accidents. The brittle-ductile transition temperature of some materials, such as tungsten, silicon and chromium, under normal conditions is much higher than room temperature. Such materials are usually considered brittle, and they can be given the desired shape through plastic deformation only by heating. At the same time, copper, aluminum, lead, nickel, some grades of stainless steel and other metals and alloys do not become brittle at all when the temperature drops. Although much is already known about brittle fracture, this phenomenon is not yet fully understood.

Fatigue.

Fatigue is the failure of a structure under the influence 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, fracture can be caused by stresses that are significantly lower than those at which failure occurs in the case of a single loading. Alternating stresses cause localized plastic deformation and strain hardening of the material, as a result of which small cracks appear over time. The concentration of stress near the ends of such cracks causes them to grow. At first, cracks grow slowly, but as the cross-section bearing the load decreases, the stresses at the ends of the cracks increase. In this case, the cracks grow faster and faster and, finally, instantly spread to the entire cross-section of the part. See also DESTRUCTION MECHANISMS.

Fatigue is undoubtedly the most common cause of structural failure under operating conditions. Machine parts operating under cyclic loading conditions are especially susceptible to this. In the aircraft industry, fatigue turns out to be a very important problem due to vibration. Airplane and helicopter parts must be inspected and replaced frequently to avoid fatigue failure.

Creep.

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

At normal temperatures, plastic deformation is established almost instantly as soon as the appropriate stress is applied, and subsequently increases little. At elevated temperatures, metals not only become softer, but also deform so that the deformation continues to increase over 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 speed decreases and becomes almost constant. Before failure, the creep rate increases again. The temperature at which creep becomes critical is not the same for different metals. Telephone companies are concerned about creep in lead-sheathed overhead cables operating at normal temperatures. environment; at the same time, some special alloys can operate at 800 ° C without exhibiting excessive creep.

The service life of parts under creep conditions can be determined either by the maximum permissible deformation or by destruction, and the designer must always keep these two in mind possible options. 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 for a duration equal to the expected service life is often impractical, and the results of short-term (accelerated) tests are not easily extrapolated to longer periods, since the failure pattern may change. Although the mechanical properties of high-temperature alloys are constantly improving, metal physicists and materials scientists will always be faced with the challenge of creating materials that can withstand even more high temperatures. See also PHYSICAL METAL SCIENCE.

CRYSTAL STRUCTURE

Above we talked about general patterns behavior of metals under 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 crystalline structure of a metal can be thought of as consisting of atomic planes, or layers. When shear stress (a force that causes two adjacent planes of a metal specimen to slide against each other in opposite directions) is applied, a single 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, 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 the microscope and are called slip lines.

Common metal objects that we encounter every day 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 atomic planes in each crystal. Noticeable sliding of entire crystals along their boundaries is observed only under conditions of creep at elevated temperatures. The average size of one crystal, or grain, can range from several thousandths to several tenths of a centimeter. A finer grain size is desirable because the mechanical properties of a fine-grained metal are better than those of a coarse-grained metal. In addition, fine-grained metals are less brittle.

Slip and dislocations.

Sliding processes were studied in more detail on single crystals of metals grown in the laboratory. It turned out not only that sliding occurs in certain specific directions and usually along very specific planes, but also that single crystals are deformed at very low stresses. The transition of single crystals to the fluid state 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 idea 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 throughout the crystal. The boundary between the shifted and non-shifted regions (Fig. 4) is a linear defect in the crystal structure, called a dislocation (in the figure, this line extends into the crystal perpendicular to the plane of the figure). When a shear stress is applied to a crystal, the dislocation moves, causing it to slide along the plane in which it is located. Once dislocations have formed, they move very easily throughout the crystal, which explains the “softness” of single crystals.

Metal crystals usually contain many dislocations (the total length of dislocations in one cubic centimeter of annealed metal crystal can be more than 10 km). But in 1952, scientists at the Bell Telephone Corporation laboratories, testing the bending of very thin whisker crystals (whiskers) of tin, discovered, to their surprise, that the bending strength of such crystals was close to the theoretical value for perfect crystals. Later, extremely strong whiskers of many other metals were discovered. It is believed that such 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 based on ideas about 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 heats up, the atoms become mobile and rearrange into new, more perfect crystals containing fewer dislocations. Such recrystallization is associated with the softening that is observed during the annealing of metals.

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Young's modulus table. Modulus of elasticity. Definition of Young's Modulus.

PROBLEM BOOK ONL@YN LIBRARY 1 LIBRARY 2

Note. The value of the elastic modulus depends on the structure, chemical composition and the method of processing the material. Therefore, E values may differ from the average values given in the table.

Young's modulus table. Modulus of elasticity. Definition of Young's modulus. Safety factor.

Young's modulus table

Material			Material
Material			Material
Aluminum	70	7000	Alloy steels	210-220	21000-22000
Concrete	3000		Carbon steels	200-210	20000-2100
Wood (along the grain)	10-12	1000-1200	Glass	56	5600
Wood (across the grain)	0,5-1,0	50-100	Organic glass	2,9	290
Iron	200	2000	Titanium	112	11200
Gold	79	7900	Chromium	240-250	24000-25000
Magnesium	44	4400	Zinc	80	8000
Copper	110	11000	Gray cast iron	115-150	11500-15000
Lead	17	1700

Material tensile strength

Allowable mechanical stress in some materials (tensile)

Safety factor

To be continued...

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Elastic moduli and Poisson's ratios for some materials 013

Mobile concrete plant on chassis

To what depth should the foundation be poured for a house?

Material	Elastic modulus, MPa		Poisson's ratio
Material	Young's modulus E	Shear modulusG	Poisson's ratio
White cast iron, gray malleable cast iron	(1.15...1.60) 105 1.55 105	4.5·104 -	0,23...0,27 -
Carbon steel Alloy steel	(2.0...2.1) 105 (2.1...2.2) 105	(8.0...8.1) 104 (8.0...8.1) 104	0,24...0,28 0,25...0,30
Rolled copper Cold drawn copper Cast copper	1.1 105 1.3 105 0.84 105	4.0 104 4.9 104 -	0,31...0,34 - -
Rolled phosphor bronze Rolled manganese bronze Cast aluminum bronze	1.15 105 1.1 105 1.05 105	4.2 104 4.0 104 4.2 104	0,32...0,35 0,35 -
Cold drawn brass Rolled ship brass	(0.91...0.99) 105 1.0 105	(3.5...3.7) 104 -	0,32...0,42 0,36
Rolled aluminum Drawn aluminum wire Rolled duralumin	0.69 105 0.7 105 0.71 105	(2.6...2.7) 104 - 2.7 104	0,32...0,36 - -
Rolled zinc	0.84 105	3.2·104	0,27
Lead	0.17 105	0.7 104	0,42
Ice	0.1 105	(0.28...0.3) 104	-
Glass	0.56 105	0.22 104	0,25
Granite	0.49 105	-	-
Limestone	0.42 105	-	-
Marble	0.56 105	-	-
Sandstone	0.18 105	-	-
Granite masonry Limestone masonry Brick masonry	(0.09...0.1) 105 0.06 105 (0.027...0.030) 105	- - -	- - -
Concrete at ultimate strength, MPa: 10 15 20	(0.146...0.196) 105 (0.164...0.214) 105 (0.182...0.232) 105	- - -	0,16...0,18 0,16...0,18 0,16...0,18
Wood along the grain Wood across the grain

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Additional information from the DPVA Engineering Handbook, namely other subsections of this section:

External link: Theoretical mechanics. Strength of materials. Theory of mechanisms and machines. Machine parts and design fundamentals. Lectures, theory and examples of problem solving. Problem solving - theoretical mechanics, strength of materials, technical and applied mechanics, TMM and DetMash

Table. Values of longitudinal elasticity modulus E, shear modulus G and Poisson's ratio µ (at a temperature of 20 o C). Table of strength of metals and alloys.

Table. Bend. Axial moments of inertia of sections (static moments of sections), axial moments of resistance and radii of inertia of plane figures.

Table. Torsion. Geometric characteristics of rigidity and strength for running sections during torsion of a straight beam. Axial moments of inertia of sections (static moments of sections), axial moments of resistance during torsion. The point of greatest tension.

You are here now: Conversion of units of elastic modulus, Young's modulus (E), tensile strength, shear modulus (G), yield strength.

Table. Calculation data for typical beams of constant cross-section. Reactions of the left and right support, expression of the bending moment (and the largest), equation of the elastic line; values of the largest and rotation angles of the extreme left and right sections.

Radii of inertia of the main combinations of sections of channels, angles, I-beams, pipes, circles... Approximate values.

Geometric characteristics and weight of the pipe and water in the pipe. Outer diameter 50-1420 mm, wall thickness 1-30 mm, Sectional area, axial moment of inertia, polar moment of inertia, axial moment of resistance, polar moment of resistance, radius of inertia

Rolled steel range. I-beams GOST 8239-72, Channels GOST 8240-72, Equal angles GOST 8509-72. Unequal angles GOST 8510-72. Moments of inertia, moments of resistance, radii of gyration, static half-section moments...

Tables for determining the load-bearing capacity of brick walls and pillars

Tables - Guide to the selection of sections of elements of building steel structures 6.8 MB. TSNIIPROEKTSTALKONSTRUCTION, Moscow, 1991, Part 1, Part 2, Part 3, Part 4

Selection tables for lintels, purlins and base plates. VMK-41-87. ALTAIGRAZHDANPROEKT. Barnaul. 1987 / 2006. 0.27 MB

Tables for selecting sections of reinforced concrete structures with non-prestressing reinforcement. Kharkov PROMSTROYNIIPROEKT. 1964. Issue 1. 5.07 MB

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

For example, what number of steel I-beam should be used as a span beam for a structure? If we take a profile with dimensions smaller than required, we are guaranteed to get the destruction of the structure. If it is more, then this leads to irrational use of metal, and, consequently, heavier construction, more complicated installation, and increased financial costs. Knowledge of such a concept as the modulus of elasticity of steel will answer the above question and will allow you to avoid the occurrence of these problems at a very early stage of production.

General concept

The 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 shows the ductility of the material. The greater the elastic modulus, the less any rod will stretch, all other things being equal (load magnitude, cross-sectional area, etc.).

In the theory of elasticity, Young's modulus is denoted by the letter E. It is integral part Hooke's law (law on the deformation of elastic bodies). Connects the stress arising 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 elastic modulus is determined experimentally in scientific laboratories. The essence of this method is to break into special equipment dumbbell-shaped samples of material. Having found out the stress and elongation at which the sample failed, divide these variables by each other, thereby obtaining Young's modulus.

Let us note right away that this method is used to determine the elastic moduli of plastic materials: steel, copper, etc. 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 a material only when working in compression or tension. In the presence of such types of loads as crushing, shear, bending, etc., additional parameters will need to be introduced:

Stiffness is the product of the elastic modulus and the cross-sectional area of the profile. By the value of rigidity, one can judge the plasticity not of the material, but of the structure as a whole. Measured in kilograms of force.
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 was 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. A variable is a dimensionless quantity. In some cases, for ease of perception, it is converted to percentages.
Relative transverse elongation is calculated similarly to the point above, but instead of length, the diameter of the rod is considered here. Experiments show that for most materials, transverse elongation is 3-4 times less than longitudinal elongation.
The Punch ratio is the ratio of the relative longitudinal deformation to relative transverse deformation. This parameter allows you to fully describe the change in shape under the influence of load.
The shear modulus characterizes the elastic properties when the sample is exposed to tangential stresses, i.e., in the case when the force vector is directed at 90 degrees to the surface of the body. Examples of such loads are the work of rivets in shear, nails in crushing, etc. By and large, the shear modulus is associated with such a concept as the viscosity of the material.
The bulk modulus of elasticity is characterized by a change in the volume of the material for uniform, versatile application of 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 subject to 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 loading. Such materials are characterized as anisotropic. Vivid examples are wood, laminated plastics, some types of stone, fabrics, etc.

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

Elastic modulus value

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 at which the force is applied.

Some elastic-plastic materials have a more or less constant modulus of elasticity when working in both compression and 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 kgscm2) of some materials:

White cast iron – 1.15.
Gray cast iron -1.16.
Brass – 1.01.
Bronze - 1.00.
Brick masonry - 0.03.
Granite stonework - 0.09.
Concrete – 0.02.
Wood along the grain – 0.1.
Wood across the grain – 0.005.
Aluminum – 0.7.

Let's consider the difference in readings between elastic moduli for steels depending on the grade:

Structural steel high quality (20, 45) – 2,01.
Standard quality steel (St. 3, St. 6) - 2.00.
Low alloy steels (30ХГСА, 40Х) – 2.05.
Stainless steel (12Х18Н10Т) – 2.1.
Die steel (9ХМФ) – 2.03.
Spring steel (60С2) – 2.03.
Bearing steel (ШХ15) – 2.1.

Also, the value of the elastic modulus for steels varies depending on the type of rolled product:

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

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

Material	Modulus of elasticity E, MPa
Cast iron white, gray	(1.15. 1.60) 10 5
Malleable cast iron	1.55 10 5
Carbon steel	(2.0. 2.1) 10 5
Alloy steel	(2.1. 2.2) 10 5
Rolled copper	1.1 10 5
Cold drawn copper	1.3 10 3
Cast copper	0.84 10 5
Rolled phosphor bronze	1.15 10 5
Rolled manganese bronze	1.1 10 5
Cast aluminum bronze	1.05 10 5
Cold drawn brass	(0.91. 0.99) 10 5
Rolled ship brass	1.0 10 5
Rolled aluminum	0.69 10 5
Aluminum wire drawn	0.7 10 5
Rolled duralumin	0.71 10 5
Rolled zinc	0.84 10 5
Lead	0.17 10 5
Ice	0.1 10 5
Glass	0.56 10 5
Granite	0.49 10 5
Lime	0.42 10 5
Marble	0.56 10 5
Sandstone	0.18 10 5
Granite masonry	(0.09. 0.1) 10 5
Brick masonry	(0.027. 0.030) 10 5
Concrete (see table 2)
Wood along the grain	(0.1. 0.12) 10 5
Wood across the grain	(0.005. 0.01) 10 5
Rubber	0.00008 10 5
Textolite	(0.06. 0.1) 10 5
Getinax	(0.1. 0.17) 10 5
Bakelite	(2.3) 10 3
Celluloid	(14.3. 27.5) 10 2

Standard data for calculations of reinforced concrete structures

Table 2. Elastic moduli of concrete (according to SP 52-101-2003)

Table 2.1 Elastic moduli of concrete according to SNiP 2.03.01-84*(1996)

Notes:
1. Above the line the values are indicated in MPa, below the line - in kgf/cm².
2. For lightweight, cellular and porous concrete at intermediate values of concrete density, the initial elastic moduli are taken by linear interpolation.
3. For non-autoclaved cellular concrete, the values of E b are taken as for autoclaved concrete, multiplied by a factor of 0.8.
4. For prestressing concrete, the values of E b are taken as for heavy concrete, multiplied by the coefficient
a= 0.56 + 0.006V.

Table 3. Standard values of concrete resistance (according to SP 52-101-2003)

Table 4. Calculated values of concrete compression resistance (according to SP 52-101-2003)

Table 4.1 Calculated values of concrete compression resistance according to SNiP 2.03.01-84*(1996)

Table 5. Calculated values of concrete tensile strength (according to SP 52-101-2003)

Table 6. Standard resistances for fittings (according to SP 52-101-2003)

Table 6.1 Standard resistances for class A fittings according to SNiP 2.03.01-84* (1996)

Table 6.2 Standard resistances for fittings of classes B and K according to SNiP 2.03.01-84* (1996)

Table 7. Design resistances for reinforcement (according to SP 52-101-2003)

Table 7.1 Design resistances for class A fittings according to SNiP 2.03.01-84* (1996)

Table 7.2 Design resistances for fittings of classes B and K according to SNiP 2.03.01-84* (1996)

Standard data for calculations of metal structures

Table 8. Standard and calculated resistances in tension, compression and bending (according to SNiP II-23-81 (1990)) of sheet, wide-band universal and shaped rolled products in accordance with GOST 27772-88 for steel structures of buildings and structures

Notes:
1. The thickness of the shaped steel should be taken as the thickness of the flange (its minimum thickness is 4 mm).
2. The standard values of the yield strength and tensile strength in accordance with GOST 27772-88 are taken as the standard resistance.
3. The values of the calculated resistances are obtained by dividing the standard resistances by the reliability factors for the material, rounded to 5 MPa (50 kgf/cm²).

Table 9. Steel grades replaced by steels according to GOST 27772-88 (according to SNiP II-23-81 (1990))

Notes:
1. Steels S345 and S375 of categories 1, 2, 3, 4 according to GOST 27772-88 replace steels of categories 6, 7 and 9, 12, 13 and 15 according to GOST 19281-73* and GOST 19282-73*, respectively.
2. Steels S345K, S390, S390K, S440, S590, S590K according to GOST 27772-88 replace the corresponding steel grades of categories 1-15 according to GOST 19281-73* and GOST 19282-73*, indicated in this table.
3. Replacement of steels in accordance with GOST 27772-88 with steels supplied according to other state all-Union standards and technical specifications, not provided.

Conversion of units of elastic modulus, Young's modulus (E), tensile strength, shear modulus (G), yield strength

Conversion table for Pa units; MPa; bar; kg/cm 2; psf; psi

To convert a value in units:	In units:
	Pa (N/m2)	MPa	bar	kgf/cm 2	psf	psi
	Should be multiplied by:
Pa (N/m2) - SI unit of pressure	1	1*10 -6	10 -5	1.02*10 -5	0.021	1.450326*10 -4
MPa	1*10 6	1	10	10.2	2.1*10 4	1.450326*10 2
bar	10 5	10 -1	1	1.0197	2090	14.50
kgf/cm 2	9.8*10 4	9.8*10 -2	0.98	1	2049	14.21
psi pound square feet (psf)	47.8	4.78*10 -5	4.78*10 -4	4.88*10 -4	1	0.0069
psi inch / pound square inches (psi)	6894.76	6.89476*10 -3	0.069	0.07	144	1

Detailed list of pressure units (yes, these units coincide with pressure units in dimension, but do not coincide in meaning :)

1 Pa (N/m 2) = 0.0000102 Atmosphere (metric)
1 Pa (N/m 2) = 0.0000099 Standard atmosphere Atmosphere (standard) = Standard atmosphere
1 Pa (N/m2) = 0.00001 Bar / Bar
1 Pa (N/m 2) = 10 Barad / Barad
1 Pa (N/m2) = 0.0007501 Centimeters Hg. Art. (0°C)
1 Pa (N/m2) = 0.0101974 Centimeters in. Art. (4°C)
1 Pa (N/m2) = 10 Dyne/square centimeter
1 Pa (N/m2) = 0.0003346 Foot of water (4 °C)
1 Pa (N/m2) = 10 -9 Gigapascals
1 Pa (N/m2) = 0.01 Hectopascals
1 Pa (N/m2) = 0.0002953 Dumov Hg. / Inch of mercury (0 °C)
1 Pa (N/m2) = 0.0002961 InchHg. Art. / Inch of mercury (15.56 °C)
1 Pa (N/m2) = 0.0040186 Dumov v.st. / Inch of water (15.56 °C)
1 Pa (N/m 2) = 0.0040147 Dumov v.st. / Inch of water (4 °C)
1 Pa (N/m 2) = 0.0000102 kgf/cm 2 / Kilogram force/centimetre 2
1 Pa (N/m 2) = 0.0010197 kgf/dm 2 / Kilogram force/decimetre 2
1 Pa (N/m2) = 0.101972 kgf/m2 / Kilogram force/meter 2
1 Pa (N/m 2) = 10 -7 kgf/mm 2 / Kilogram force/millimeter 2
1 Pa (N/m 2) = 10 -3 kPa
1 Pa (N/m2) = 10 -7 Kilopound force/square inch
1 Pa (N/m 2) = 10 -6 MPa
1 Pa (N/m2) = 0.000102 Meters w.st. / Meter of water (4 °C)
1 Pa (N/m2) = 10 Microbar / Microbar (barye, barrie)
1 Pa (N/m2) = 7.50062 Microns Hg. / Micron of mercury (millitorr)
1 Pa (N/m2) = 0.01 Millibar / Millibar
1 Pa (N/m2) = 0.0075006 Millimeter of mercury (0 °C)
1 Pa (N/m2) = 0.10207 Millimeters w.st. / Millimeter of water (15.56 °C)
1 Pa (N/m2) = 0.10197 Millimeters w.st. / Millimeter of water (4 °C)
1 Pa (N/m 2) = 7.5006 Millitorr / Millitorr
1 Pa (N/m2) = 1N/m2 / Newton/square meter
1 Pa (N/m2) = 32.1507 Daily ounces/sq. inch / Ounce force (avdp)/square inch
1 Pa (N/m2) = 0.0208854 Pounds force per square meter. ft / Pound force/square foot
1 Pa (N/m2) = 0.000145 Pounds force per square meter. inch / Pound force/square inch
1 Pa (N/m2) = 0.671969 Poundals per sq. ft / Poundal/square foot
1 Pa (N/m2) = 0.0046665 Poundals per sq. inch / Poundal/square inch
1 Pa (N/m2) = 0.0000093 Long tons per square meter. ft / Ton (long)/foot 2
1 Pa (N/m2) = 10 -7 Long tons per square meter. inch / Ton (long)/inch 2
1 Pa (N/m2) = 0.0000104 Short tons per square meter. ft / Ton (short)/foot 2
1 Pa (N/m2) = 10 -7 Tons per sq. inch / Ton/inch 2
1 Pa (N/m2) = 0.0075006 Torr / Torr

The development of metallurgy and other related areas for the production of metal objects is due to the creation of weapons. At first they learned to smelt non-ferrous metals, but the strength of the products was relatively low. Only with the advent of iron and its alloys did the study of their properties begin.

The first swords were made quite heavy to give them hardness and strength. Warriors had to take them in both hands to control them. Over time, new alloys appeared and production technologies were developed. Light sabers and swords came to replace heavy weapons. At the same time, tools were created. With increasing strength characteristics, tools and production methods were improved.

Types of loads

When using metals, different static and dynamic loads are applied. In the theory of strength, it is customary to define the following types of loads.

Compression - an acting force compresses an object, causing a decrease in length along the direction of application of the load. Such deformation is felt by the frames, supporting surfaces, racks and a number of other structures that can withstand a certain weight. Bridges and crossings, car and tractor frames, foundations and fittings - all these structural elements are under constant compression.

Tension - the load tends to lengthen the body in a certain direction. Lifting and transport machines and mechanisms experience similar loads when lifting and carrying loads.

Shear and shear - such loading is observed in the case of forces directed along the same axis towards each other. Connecting elements (bolts, screws, rivets and other hardware) experience this type of load. The design of housings, metal frames, gearboxes and other components of mechanisms and machines necessarily contains connecting parts. The performance of devices depends on their strength.

Torsion - if a pair of forces acting on an object are located at a certain distance from each other, then a torque occurs. These forces tend to produce torsional deformation. Similar loads are observed in gearboxes; the shafts experience just such a load. It is most often inconsistent in meaning. Over time the value active forces is changing.

Bending – a load that changes the curvature of objects is considered bending. Bridges, crossbars, consoles, lifting and transport mechanisms and other parts experience similar loading.

The concept of elastic modulus

In the middle of the 17th century, materials research began simultaneously in several countries. A variety of methods have been proposed for determining strength characteristics. The English researcher Robert Hooke (1660) formulated the main provisions of the law on the elongation of elastic bodies as a result of the application of a load (Hooke's law). The following concepts were also introduced:

Stress σ, which in mechanics is measured in the form of a load applied to a certain area (kgf/cm², N/m², Pa).
Elastic modulus E, which determines the ability of a solid body to deform under loading (applying force in a given direction). Units of measurement are also defined in kgf/cm² (N/m², Pa).

The formula according to Hooke's law is written as ε = σz/E, where:

ε – relative elongation;
σz – normal stress.

Demonstration of Hooke's law for elastic bodies:

From the above dependence the value of E is derived for certain material empirically, E = σz/ε.

The modulus of elasticity is a constant value that characterizes the resistance of a body and its construction material under normal tensile or compressive load.

In the theory of strength, the concept of Young's modulus of elasticity is adopted. This English researcher gave a more specific description of the ways in which strength parameters change under normal loads.

The elastic modulus values for some materials are given in Table 1.

Table 1: Modulus of elasticity for metals and alloys

Elastic modulus for different steel grades

Metallurgists have developed several hundred grades of steel. They have different strength values. Table 2 shows the characteristics for the most common steels.

Table 2: Elasticity of steels

*Name of steel*	*Elastic modulus value, 10¹² Pa*
Low carbon steel	165…180
Steel 3	179…189
Steel 30	194…205
Steel 45	211…223
Steel 40Х	240…260
65G	235…275
X12MF	310…320
9ХС, ХВГ	275…302
4Х5МФС	305…315
3Х3М3Ф	285…310
R6M5	305…320
P9	320…330
P18	325…340
R12MF5	297…310
U7, U8	302…315
U9, U10	320…330
U11	325…340
U12, U13	310…315

Video: Hooke's law, modulus of elasticity.

Strength modules

In addition to normal loading, there are other force effects on materials.

The shear modulus G determines the stiffness. This characteristic shows the maximum load value for changing the shape of an object.

The bulk modulus of elasticity K determines the elastic properties of a material to change volume. With any deformation, the shape of the object changes.

Poisson's ratio μ determines the change in the ratio of relative compression to tension. This value depends only on the properties of the material.

For different steels, the values of the indicated modules are given in Table 3.

Table 3: Strength moduli for steels

*Name of steel*	*Young's modulus of elasticity, 10¹² Pa*	*Shear modulus* *G, 10¹²Pa*	*Modulus of bulk elasticity, 10¹² Pa*	*Poisson's ratio, 10¹²·Pa*
Low carbon steel	165…180	87…91	45…49	154…168
Steel 3	179…189	93…102	49…52	164…172
Steel 30	194…205	105…108	72…77	182…184
Steel 45	211…223	115…130	76…81	192…197
Steel 40Х	240…260	118…125	84…87	210…218
65G	235…275	112…124	81…85	208…214
X12MF	310…320	143…150	94…98	285…290
9ХС, ХВГ	275…302	135…145	87…92	264…270
4Х5МФС	305…315	147…160	96…100	291…295
3Х3М3Ф	285…310	135…150	92…97	268…273
R6M5	305…320	147…151	98…102	294…300
P9	320…330	155…162	104…110	301…312
P18	325…340	140…149	105…108	308…318
R12MF5	297…310	147…152	98…102	276…280
U7, U8	302…315	154…160	100…106	286…294
U9, U10	320…330	160…165	104…112	305…311
U11	325…340	162…170	98…104	306…314
U12, U13	310…315	155…160	99…106	298…304

For other materials, strength characteristics are indicated in specialized literature. However, in some cases individual studies are carried out. Such studies are especially relevant for building materials. At enterprises where reinforced concrete products are produced, tests are regularly carried out to determine limit values.

When calculating building structures, you need to know the design resistance and modulus of elasticity for a particular material. Here is data on the main building materials.

Table 1. Elastic moduli for basic building materials

Material	Modulus of elasticity E, MPa
Cast iron white, gray	(1.15...1.60) 10 5
Malleable cast iron	1.55 10 5
Carbon steel	(2.0...2.1) 10 5
Alloy steel	(2.1...2.2) 10 5
Rolled copper	1.1 10 5
Cold drawn copper	1.3 10 3
Cast copper	0.84 10 5
Rolled phosphor bronze	1.15 10 5
Rolled manganese bronze	1.1 10 5
Cast aluminum bronze	1.05 10 5
Cold drawn brass	(0.91...0.99) 10 5
Rolled ship brass	1.0 10 5
Rolled aluminum	0.69 10 5
Aluminum wire drawn	0.7 10 5
Rolled duralumin	0.71 10 5
Rolled zinc	0.84 10 5
Lead	0.17 10 5
Ice	0.1 10 5
Glass	0.56 10 5
Granite	0.49 10 5
Lime	0.42 10 5
Marble	0.56 10 5
Sandstone	0.18 10 5
Granite masonry	(0.09...0.1) 10 5
Brick masonry	(0.027...0.030) 10 5
Concrete (see table 2)
Wood along the grain	(0.1...0.12) 10 5
Wood across the grain	(0.005...0.01) 10 5
Rubber	0.00008 10 5
Textolite	(0.06...0.1) 10 5
Getinax	(0.1...0.17) 10 5
Bakelite	(2...3) 10 3
Celluloid	(14.3...27.5) 10 2

Standard data for calculations of reinforced concrete structures

Table 2. Modules of elasticity of concrete (according to SP 52-101-2003)

Table 2.1 Modules of elasticity of concrete according to SNiP 2.03.01-84*(1996)