Modulus of deformation of steel and its elasticity. Design resistances and moduli of elasticity for building materials Modulus of elasticity of aluminum kg cm2
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When calculating building structures you need to know the calculated 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 |
Elastic modulus 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 |
Masonry granite | (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. Modulus 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)
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 cellular concrete non-autoclave hardening, 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 design resistances in tension, compression and bending (according to SNiP II-23-81 (1990)) of sheet, wide universal and shaped rolled products according to GOST 27772-88 for steel structures 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. Taken as normative resistance standard values yield strength and tensile strength according to GOST 27772-88.
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.
Design resistances for steel used for the production of profiled sheets are not shown here.
One of the main tasks engineering design is the choice of construction material and optimal cross section profile. 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 steel I-beam use 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 international standard system units are measured in MPa. But in practice, engineers prefer to use the dimension kgf/cm2.
The elastic modulus is determined empirically V scientific laboratories. The essence this method lies in the gap 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 immediately note 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 area cross section 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 strain to the 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 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 is necessary to mention that some types of materials have different mechanical properties depending on the direction of the load. Such materials are characterized as anisotropic. Vivid examples Wood, laminated plastics, some types of stone, fabrics, etc. are used.
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 more or less permanent module 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 of kgf/cm2) of some materials:
- 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.
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 the increase in strength characteristics, tools and production methods were improved.
Types of loads
When using metals, different static and dynamic loads are applied. In strength theory, it is customary to define loads the following types.
- Compression - an acting force compresses an object, causing a decrease in length along the direction of application of the load. This deformation is felt by 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 mid-17th century 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 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 for a certain material is derived experimentally, 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 methods of changing strength indicators 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 are characterized different meanings strength. 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 research is especially relevant for building materials. At enterprises where reinforced concrete products are produced, tests are regularly carried out to determine limit values.
Before using any material in construction work, you should familiarize yourself with it physical characteristics in order to know how to handle it, what mechanical impact will be acceptable for it, and so on. One of important characteristics, which is very 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 modulus of elasticity of a material is called set of physical quantities, which characterize the ability of any solid elastically deform when a force is 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:
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 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 start Let's look at the hard 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 as n about Young's modulus, and by shear modulus, both in some units of measurement (MPa) and in others (kg/cm2, newton*m2).
Steel and several different grades
The elasticity values of steel vary because there are several modules at once, which are calculated and calculated differently. 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 them straight away and calculate them in full, then this characteristic of steel will be equal to: E=200000 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 various alloys steel and for various 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
Calculated resistances and elastic moduli of heavy concrete, mPa
table 2
Characteristics | CONCRETE CLASS |
||||||||
B7.5 | AT 10 | B15 | IN 20 | B25 | B30 | B35 | B40 |
||
For |
|||||||||
Axial compression (prismatic | |||||||||
Axial tension R bt | |||||||||
For |
|||||||||
Compression R
b
, | |||||||||
Axial tension R
bt
, | |||||||||
Elementary | |||||||||
Elementary |
Note.
Calculated
concrete resistance for extreme
states of the 2nd group are equal to the normative ones:
R b ,
ser
=
R b ,
n ;
R bt ,
ser
=
R
bt ,
n .
Calculated resistances and elastic moduli of some reinforcing steels, mPa
Table
3
CLASS FITTINGS (designation according to DSTU 3760-98) | Calculated | Module E
s
|
|||
for calculation according to extreme | For R s , ser |
||||
stretching | R sc |
||||
R s | R sw |
||||
А240С | |||||
А300С | |||||
А400С | |||||
А400С | |||||
А600С | |||||
B
p
I
| |||||
B
p
I
| |||||
B
p
I
|
Note.
Calculated
steel resistance for extreme
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 cross-section of a column made of I-beam 20K1 according to STO ASChM 20-93 from steel S235.
Compressive force: N=600kN.
Column height: L=4.5m.
Effective length factor: μ x =1.0; μ y =1.0.
Solution.
Design resistance of steel C235: R y = 230 N/mm 2 = 23.0 kN/cm 2.
Modulus of elasticity of steel C235: E=2.06x10 5 N/mm 2.
Operating condition coefficient for columns public buildings at constant load γ c = 0.95.
We find the cross-sectional area of the element according to the assortment for the 20K1 I-beam: A = 52.69 cm 2.
The radius of inertia of the section relative to the x axis, also according to the assortment: i x = 4.99 cm.
The radius of inertia of the section relative to the y-axis, also according to the product range: i y = 8.54 cm.
The estimated length of the column is determined by the formula:
l ef,x = μ x l x = 1.0*4.5 = 4.5 m;
l ef,y = μ y l y = 1.0*4.5 = 4.5 m.
Section flexibility relative to the x axis: λ x = l x /i x = 450/4.99 = 90.18.
Section flexibility relative to the y-axis: λ y = l y /i y = 450/8.54 = 52.69.
Maximum permissible flexibility for compressed elements(belts, support braces and racks transmitting support reactions: spatial designs from single corners, spatial structures made of pipes and paired corners of St. 50m) λ u = 120.
Checking conditions
: λx< λ u ; λ y < λ u:
90,18 < 120; 52,69 < 120
- the conditions are met.
The stability of the section is checked according to the greatest flexibility. IN in this exampleλ max = 90.18.
The conditions for element flexibility 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 = 9.87(1-α+β*λ’)+λ’2 = 9.87(1-0.04+0.09*3.01)+3.012 = 21.2.
The stability coefficient is determined by the formula:
φ = 0.5(δ-√(δ 2 -39.48λ' 2)/λ' 2 = 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’.
Checking the condition:
N/φAR y γ c ≤ 1,
600,0/(0,643*52,69*23,0*0,95) = 0,81 ≤ 1.
Since the calculation was carried out based on maximum flexibility relative to the x-axis, there is no need to perform a check regarding the y-axis.
Examples:
spravkidoc.ru
Elastic modulus of steel in kgf\cm2, examples
One of the main tasks of 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 an integral part of Hooke's law (the 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 tear dumbbell-shaped samples of material using special equipment. 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 immediately note 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 strain to the relative transverse strain. 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 of kgf/cm2) 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 steels 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.
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Material |
Elastic moduli, MPa |
Coefficient Poisson |
|
Young's modulus E |
Shear modulus G |
||
Cast iron white, gray Malleable cast iron |
(1.15…1.60) 10 5 1.55 10 5 |
4.5 10 4 |
0,23…0,27 |
Carbon steel Alloy steel |
(2.0…2.1) 10 5 (2.1…2.2) 10 5 |
(8.0…8.1) 10 4 (8.0…8.1) 10 4 |
0,24…0,28 0,25…0,30 |
Rolled copper Cold drawn copper Cast copper |
1.1 10 5 0.84 10 5 |
4.0 10 4 |
0,31…0,34 |
Rolled phosphor bronze Rolled manganese bronze Cast aluminum bronze |
1.15 10 5 1.05 10 5 |
4.2 10 4 4.2 10 4 |
0,32…0,35 |
Cold drawn brass Rolled ship brass |
(0.91…0.99) 10 5 1.0 10 5 |
(3.5…3.7) 10 4 |
0,32…0,42 |
Rolled aluminum Aluminum wire drawn Rolled duralumin |
0.69 10 5 0.71 10 5 |
(2.6…2.7) 10 4 2.7 10 4 |
0,32…0,36 |
Rolled zinc |
0.84 10 5 |
3.2 10 4 |
0,27 |
Lead |
0.17 10 5 |
0.7 10 4 |
0,42 |
Ice |
0.1 10 5 |
(0.28…0.3) 10 4 |
– |
Glass |
0.56 10 5 |
0.22 10 4 |
0,25 |
Granite |
0.49 10 5 |
– |
– |
Limestone |
0.42 10 5 |
– |
– |
Marble |
0.56 10 5 |
– |
– |
Sandstone |
0.18 10 5 |
– |
– |
Granite masonry Limestone masonry Brick masonry |
(0.09…0.1) 10 5 (0.027…0.030) 10 5 |
– |
– |
Concrete at ultimate strength, MPa: (0.146…0.196) 10 5 (0.164…0.214) 10 5 (0.182…0.232) 10 5 |
0,16…0,18 0,16…0,18 |
||
Wood along the grain Wood across the grain |
(0.1…0.12) 10 5 (0.005…0.01) 10 5 |
0.055 10 4 |
– |
Rubber |
0.00008 10 5 |
– |
0,47 |
Textolite |
(0.06…0.1) 10 5 |
– |
– |
Getinax |
(0.1…0.17) 10 5 |
– |
– |
Bakelite |
(2…3) 10 3 |
– |
0,36 |
Vishomlit (IM-44) |
(4.0…4.2) 10 3 |
– |
0,37 |
Celluloid |
(1.43…2.75) 10 3 |
– |
0,33…0,38 |
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An indicator of the load limit on steel - Young's modulus of elasticity
Before using any building material, 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 given to the modulus of elasticity - it is also called Young’s modulus.
The high strength of steel allows it to be used in construction high-rise buildings and openwork structures of stadiums and bridges. Additives to steel of some 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 normal steel. Strength in construction is usually 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 elastic modulus as a physical quantity is (E), this indicator characterizes the elastic resistance of the product material to deforming loads applied to it:
- longitudinal – tensile and compressive;
- transverse - bending or performed in the form of a shear;
- voluminous - twisting.
The higher the value (E), the higher , the stronger the product made 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, iron - 190, and for steel up to 220 GPa.
Definition
Elastic modulus is a summary term that includes other physical indicators elastic properties hard materials– under the influence of a force to change and regain its previous shape after its cessation, that is, to deform elastically. This is the ratio of stress in a product - force pressure per unit area - to elastic deformation (a dimensionless quantity determined by the ratio of the size of the product to its original size). Hence its dimension, like voltage, is the ratio of force to unit area. Since stress in metric SI is usually measured in Pascals, so is the strength indicator.
There is another, not very correct definition: modulus of elasticity is pressure, capable of doubling the length of the product. But the yield strength of many materials is significantly lower than the applied pressure.
Elastic moduli, their types
There are many ways to change the conditions for the application of force and the deformations caused by this, and this presupposes a large number of types of elastic moduli, but in practice in accordance with deforming loads There are three main ones:
![](https://i1.wp.com/martand.ru/wp-content/uploads/modul-uprugosti-stali-s235_7.jpg)
The characteristics of elasticity are not exhausted by these indicators; there are others that carry other information and have different dimension and meaning. These are also the Lamé elasticity indices and Poisson's ratio, widely known among experts.
How to determine the modulus of elasticity of steel
To define parameters various brands steel there are special tables containing regulatory documents in the field of construction - in building codes and rules (SNiP) and state standards(GOST). So, elastic modulus (E) or Young's modulus, for white and gray cast iron from 115 to 160 GPa, for malleable – 155. As for steel, the modulus of elasticity of C245 carbon steel has values from 200 to 210 GPa. Alloy steel has slightly higher values - 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 twists of high-strength wire 200 GPa;
- steel cables with a metal rod 150 GPa;
- steel ropes with organic core 130 GPa.
As you can see, the difference is significant.
The values of shear modulus or stiffness (G) can be seen in the same tables, they have smaller values, for rolled steel – 84 GPa, carbon and alloy – from 80 to 81 GPa, and for steels St.3 and St.45–80 GPa. The reason for the difference in elasticity parameter values is the simultaneous action of three main modules, calculated according to different methods. However, the difference between them is small, which indicates sufficient accuracy in the study of elasticity. Therefore, you should not get hung up on calculations and formulas, but should take a specific elasticity value and use it as a constant. If you do not perform calculations on individual modules, but do the calculation in a comprehensive manner, the value (E) will be 200 GPa.
It is necessary to understand that these values differ for steels with different additives and steel products that include parts made 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 steel processing - hot rolling or cold stamping, does not have a significant effect.
When choosing steel products, they also use one more indicator, which is regulated in the same way as the elastic modulus in the tables of GOST and SNiP publications- this is the calculated resistance to tensile, compressive and bending loads. The dimension of this indicator is the same as that of the elastic modulus, 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. Thus, the design resistance of steel C255 with a rolled thickness from 10 to 20 mm is 240 MPa, with a standard value of 245 MPa. The calculated resistance of rolled products from 20 to 30 mm is slightly lower and amounts to 230 MPa.
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| Welding world
Elastic modulus
Modulus of elasticity (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 exposed to a force 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/mm 2 = 10 -6 kgf/m 2 = 9.8 10 6 N/m 2 = 9.8 10 7 dynes/cm 2 = 9.81 10 6 Pa = 9.81 MPa
Material | E | ||
---|---|---|---|
kgf/mm 2 | 10 7 N/m 2 | 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.
- Guide to 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.
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 materials in construction and repair work - steel. These indicators for other materials will also be considered, for the sake of 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 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:
Table of material elasticity indicators
Before moving 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 measured in MPa.
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 start Let's look at the hard numbers and derive different indicators of this characteristic for different types of 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 given all the general information about this characteristic of steel. Values will be given as n about Young's modulus, and by shear modulus, both in some units of measurement (MPa) and in others (kg/cm2, newton*m2).
Steel and several different grades
The elasticity values of steel vary because there are several modules at once, which are calculated and calculated differently. You can notice the fact that, in principle, the indicators do not differ greatly, which indicates in favor of different studies of the elasticity of 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 them straight away and calculate them in full, then this characteristic of steel will be equal to: E=200000 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.