What are limit states and how to deal with them in relation to structural calculations? Everyone knows that there are two groups of limit states: the first and the second. What does this division mean?
The name itself " limit state" means that for any structure, under certain conditions, a state occurs in which a certain limit is exhausted. Conventionally, for the convenience of calculations, two such limits were derived: the first limit state is when the limit of strength, stability and endurance of the structure is exhausted; the second limit state is when the deformations of the structure exceed the maximum permissible (the second limit state for reinforced concrete also includes restrictions on the occurrence and opening of cracks).
Before proceeding to the analysis of calculations for the first and second limit states, it is necessary to understand which part of the structural calculation is generally divided into these two parts. Any calculation begins with collecting the load. Then follows the choice of a design scheme and the calculation itself, as a result of which we determine the forces in the structure: moments, longitudinal and transverse forces. And only after the efforts have been determined, we proceed to calculations for the first and second limit states. Usually they are performed in exactly this sequence: first the first, then the second. Although there are exceptions, more about them below.
It cannot be said what is more important for any structure: strength or deformability, stability or crack resistance. It is necessary to carry out calculations based on two limit states and find out which of the limitations is the most unfavorable. But each type of structure has its own special points that are useful to know to make it easier to navigate the environment of limit states. In this article we will use examples to analyze limit states for various types reinforced concrete structures.
So, you need to calculate a bending element, and you are wondering where to start the calculation, and how to understand if everything has been calculated? Everyone recommends making calculations not only for the first, but also for the second limit state. But what is it? Where are the specifics?
To calculate bending elements, you will need the “Manual for the design of concrete and reinforced concrete structures made of heavy concrete without prestressing reinforcement (to SNiP 2.03.01-84)” and SNiP 2.03.01-84 itself “Concrete and reinforced concrete structures”, necessarily with modification 1 (very important for calculations for the second group of limit states).
Open section 3 of the manual “Calculation of reinforced concrete elements according to limit states of the first group”, namely “Calculation of reinforced concrete elements according to strength” (starting from paragraph 3.10). Now you need to find out what stages it consists of:
- this is the part of the calculation in which we check whether our structure will withstand the influence of a bending moment. The combination of two is checked important factors: element sectional size and area of longitudinal reinforcement. If the check shows that the moment acting on the structure is less than the maximum permissible, then everything is fine and you can move on to the next stage.
2) Calculation of sections inclined to the longitudinal axis of the element- This is a calculation of a structure under the action of lateral force. To check, it is important for us to establish the cross-sectional dimensions of the element and the area of the transverse reinforcement. Just as at the previous stage of calculation, if the acting lateral force is less than the maximum permissible, the strength of the element is considered ensured.
Both stages, along with examples, are discussed in detail in the manual. These two calculations are comprehensive strength calculations for classical flexural elements. If there are any special conditions(repeatedly repeated loads, dynamics), they must be taken into account when calculating strength and endurance (often, accounting is done by introducing coefficients).
1) Calculation of reinforced concrete elements for the formation of cracks- this is the very first stage in which we find out whether cracks form in our element when exposed to forces acting on it. Cracks do not form if our maximum moment Mr is less than the crack-inducing moment Mcrc.
2) Calculation of reinforced concrete elements based on crack opening– this is the next stage at which we check the size of the crack opening in the structure and compare it with the permissible dimensions. Pay attention to paragraph 4.5 of the manual, which stipulates in which cases this calculation does not need to be performed - we don’t need any extra work. If the calculation is necessary, then you need to perform two parts:
a) calculation for the opening of cracks normal to the longitudinal axis of the element– we carry it out according to clauses 4.7-4.9 of the manual ( with mandatory consideration of amendment 1 to SNiP, because the calculation there is already radically different);
b) calculation for the opening of cracks inclined to the longitudinal axis of the element– it must be carried out according to clause 4.11 of the manual, also taking into account change 1.
Naturally, if according to the first stage of the calculation, cracks do not form, then we skip stage 2.
3) Determination of deflection– this is the last stage of calculation for the second limit state for bendable reinforced concrete elements, it is performed in accordance with clauses 4.22-4.24 of the manual. In this calculation, we need to find the deflection of our element and compare it with the deflection normalized by DSTU B.V.1.2-3:2006 “Deflections and displacements”.
If all these parts of the calculations are completed, consider that the calculation of the element for both the first and second limit states is completed. Of course, if there are any design features (trimming on the support, holes, concentrated loads, etc.), then the calculation needs to be supplemented taking into account all these nuances.
The stages of this calculation are not particularly different from the stages of calculation of bending elements, and the literature is the same.
The calculation for the limit state of the first group includes:
1) Calculation of sections normal to the longitudinal axis of the element– this calculation, just like for bending elements, determines required size section of the element and its longitudinal reinforcement. But unlike the calculation of bending elements, where the strength of the section is checked against the action of the bending moment M, in this calculation the maximum vertical force N and the eccentricity of the application of this force “e” are highlighted (when multiplied, however, they still give the same bending moment). The manual describes in detail the calculation methodology for all standard and non-standard sections (starting from paragraph 3.50).
Feature of this calculation is that it is necessary to take into account the influence of element deflection, and the influence of indirect reinforcement is also taken into account. The deflection of the element is determined when calculating according to the second group of limit states, but when calculating according to the first limit state, it is allowed to simplify the calculation by introducing a coefficient in accordance with clause 3.54 of the manual.
2) Calculation of sections inclined to the longitudinal axis of the element– this calculation for the action of lateral force according to clause 3.53 of the manual is similar to the calculation of bending elements. As a result of the calculation, we obtain the area of transverse reinforcement in the structure.
The calculation for the limit state of the second group consists of the following stages:
1) Calculation of reinforced concrete elements for the formation of cracks.
2) Calculation of reinforced concrete elements based on crack opening.
These two stages are absolutely similar to the calculation of bending elements - there are maximum forces, it is necessary to determine whether cracks are formed; and if they are formed, then, if necessary, make a calculation for the opening of cracks, normal and inclined to the longitudinal axis of the element.
3) Determination of deflection. In exactly the same way as for bending elements, it is necessary to determine the deflection for eccentrically compressed elements. Limit deflections, as always, can be found in DSTU B V.1.2-3:2006 “Deflections and displacements”.
The calculation of foundations is fundamentally different from the above calculations. As always, when calculating foundations, it is necessary to start with the collection of loads or with the calculation of the building frame, as a result of which the main loads on the foundation N, M, Q are determined.
After the loads have been collected and the type of foundation has been selected, it is necessary to proceed to the calculation of the soil foundation under the foundation. This calculation, like any other calculations, is divided into calculations for the first and second limit states:
1) ensuring the bearing capacity of the foundation base - the strength and stability of the foundations is checked (first limit state) - calculation example strip foundation ;
2) calculation of the foundation based on deformations - determination of the design resistance of the foundation soil, determination of settlement, determination of foundation roll (second limit state).
The “Manual on the design of foundations of buildings and structures (to SNiP 2.02.01-83)” will help you understand this calculation.
As you already understood from the wording, when determining the size of the base of the foundation (whether it is a strip or a columnar foundation), we first of all perform the calculation of the soil base, and not the foundation. And in this calculation (except for rocky soils), it is much more important to calculate the foundation based on deformations - everything that is listed in paragraph 2 above. Calculation based on the first limit state is often not required at all, because Preventing deformations is much more important; they occur much earlier than the loss of bearing capacity of the soil. In what cases the calculation should be performed using the first group of limit states can be found in paragraph 2.259 of the manual.
Now let's look at the calculation of the base based on deformations. Most often, designers estimate the design resistance of the soil, compare it with the load on the soil from the building, selecting the required area of the foundation, and stop there. This is the wrong approach, because... only part of the work has been completed. The foundation calculation is considered complete when all the steps listed in paragraph 2 have been completed.
Determining the settlement of foundations is very important. This is especially important under different loads or uneven soils, when there is a risk of uneven settlement of the foundations (this is described in detail in this article “What you need to know about strip monolithic foundations”). To be sure of the continued integrity of the building structures, you should always check the difference in foundation settlements according to Table 72 of the manual. If the difference in settlement is higher than the maximum permissible, there is a risk of cracks in structures.
The foundation roll must be determined in the presence of bending moments acting on the foundation. The roll also needs to be checked when there is an uneven load on the ground - it also affects the deformation of the soil base.
But after the foundation has been calculated according to the second and possibly the first limit state and the dimensions of the foundation base have been determined, you need to move on to the next stage: the calculation of the foundation itself.
When calculating the foundation, we determined the pressure under the base of the foundation. This pressure is applied to the sole as a load (directed from bottom to top), and the support is a column or wall resting on the foundation (a kind of upside down). It turns out that in each direction from the support we have a console (usually these consoles are the same), and they need to be calculated taking into account a uniformly distributed load equal to the pressure under the base of the foundation. It is good to understand the principle of calculation using an example columnar foundation you can use the “Manual for designing foundations on a natural foundation for columns of buildings and structures (to SNiP 2.03.01-84 and SNiP 2.02.01-83)” - all stages of the calculation, both the first and the second, are outlined there in examples limit state. Based on the results of the console calculation, we first determine the height of its section and reinforcement (this is a calculation based on the first limit state), then we check the crack resistance (this is a calculation based on the second limit state).
We need to act in exactly the same way in the case of calculating a strip foundation: having the protrusion of the sole in one direction from the wall and the pressure under this sole, we calculate cantilever plate(with pinching on the support), the length of the console is equal to the overhang of the sole, the width is taken for convenience of calculation to be equal to one meter, the load on the console is equal to the pressure under the base of the foundation. We find the maximum moment and shear force in the console and perform calculations for the first and second limit states - exactly as described in the calculation of bending elements.
Thus, when calculating foundations, we go through two cases of calculation based on the limit states of the first and second groups: first when calculating the foundation, then when calculating the foundation itself.
conclusions. For any calculation, it is important to follow the sequence:
1) Collection of loads.
2) Selection of design scheme.
3) Determination of forces N, M and Q.
4) Calculation of the element based on the first limit state (strength and stability).
5) Calculation of the element based on the second limit state (deformability and crack resistance).
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0 #15 Irina 10/17/2018 19:39
Quote:
And you are also wrong.I also know that in the past, proginas were praised according to normative standards
Quote:The calculated value of the load should be determined as the product of its standard value by the load reliability factor SNiP 2.01.07-85* Loads and impacts (with Amendments No. 1, 2), corresponding to the limit state under consideration and accepted: a)* when calculating strength and stability - in accordance with clauses 2.2, 3.4, 3.7, 3.11, 4.8, 6.11, 7.3 and 8.7; b) when calculating endurance - equal to one; c) in calculations for deformations - equal to one, unless other values are established in the design standards for structures and foundations; d) when calculating for other types of limit states - according to the design standards for structures and foundations.
I recommend that you, as well as Russian-speaking Valery (if you are different Valeries), read the articleFrom me I would like to discuss how it is possible, obviously, to update the standards, to use the standard (characteristic) values of the vantage, but nevertheless, it is necessary to adjust to the different values, but without coefficients for CC1...CC3. If it’s not so, then it’s still written down.
1. Essence of the method
The method for calculating structures based on limit states is further development method of calculation based on destructive forces. When calculating using this method, the limiting states of structures are clearly established and a system of design coefficients is introduced that guarantee the structure against the occurrence of these states under the most unfavorable combinations of loads and when lowest values strength characteristics of materials.
Stages of destruction, but the safety of the structure under load is assessed not by one synthesizing safety factor, but by a system of design coefficients. Structures designed and calculated using the limit state method are somewhat more economical.
2. Two groups of limit states
Limit states are considered to be those in which structures no longer meet the requirements imposed on them during operation, i.e., they lose the ability to resist external loads and influences or receive unacceptable movements or local damage.
Reinforced concrete structures must meet the requirements of calculation for two groups of limit states: for bearing capacity - the first group of limit states; in terms of suitability for normal operation - the second group of limit states.
loss of stability of the shape of the structure (calculation for the stability of thin-walled structures, etc.) or its position (calculation for overturning and sliding of retaining walls, eccentrically loaded high foundations; calculation for the ascent of buried or underground tanks, etc.);
fatigue failure (calculation of the endurance of structures under the influence of repeated moving or pulsating loads: crane beams, sleepers, frame foundations and floors for unbalanced machines, etc.);
destruction from the combined influence of force factors and unfavorable influences external environment(periodic or constant exposure to an aggressive environment, alternating freezing and thawing, etc.).
Calculations based on limit states of the second group are performed to prevent:
formation of excessive or prolonged opening of cracks (if, according to operating conditions, the formation or prolonged opening of cracks is permissible);
excessive movements (deflections, rotation angles, skew angles and vibration amplitudes).
Calculation of the limit states of the structure as a whole, as well as its individual elements or parts, is carried out for all stages: manufacturing, transportation, installation and operation; in this case, the design schemes must comply with accepted standards constructive solutions and each of the listed stages.
3. Calculation factors
Design factors - loads and mechanical characteristics of concrete and reinforcement (tensile strength, yield strength) - have statistical variability (scatter of values). Loads and impacts may differ from the specified probability of exceeding average values, and the mechanical properties of materials may differ from the specified probability of decreasing average values. Calculations for limit states take into account the statistical variability of loads and mechanical characteristics of materials, factors of a non-statistical nature and various unfavorable or favorable physical, chemical and mechanical conditions for the operation of concrete and reinforcement, the manufacture and operation of elements of buildings and structures. Loads, mechanical characteristics of materials and calculated coefficients normalize.
The values of loads, resistance of concrete and reinforcement are established according to the chapters of SNiP “Loads and Impacts” and “Concrete and Reinforced Concrete Structures”.
4. Classification of loads. Standard and design loads
Depending on the duration of action, loads are divided into permanent and temporary. Temporary loads, in turn, are divided into long-term, short-term, and special.
Loads from the weight of load-bearing and enclosing structures of buildings and structures, the mass and pressure of soils, and the effects of prestressing reinforced concrete structures are constant.
Long-term loads are caused by the weight of stationary equipment on floors - machines, apparatus, engines, containers, etc.; pressure of gases, liquids, granular bodies in containers; loads in warehouses, refrigerators, archives, libraries and similar buildings and structures; the part of the live load established by the standards in residential buildings, office and household premises; long-term temperature technological effects from stationary equipment; loads from one overhead or one overhead crane, multiplied by factors: 0.5 for medium-duty cranes and 0.7 for heavy-duty cranes; snow loads for III-IV climatic regions with coefficients of 0.3-0.6. The indicated values of cranes, some temporary and snow loads form part of their full value and are included in the calculation when taking into account the duration of the action of loads of these types on displacement, deformation, and crack formation. The full values of these loads are short-term.
Short-term loads are caused by the weight of people, parts, materials in equipment maintenance and repair areas - passages and other areas free from equipment; part of the load on the floors of residential and public buildings; loads arising during the manufacture, transportation and installation of structural elements; loads from overhead and overhead cranes used in the construction or operation of buildings and structures; snow and wind loads; temperature climatic influences.
Special loads include: seismic and explosive impacts; loads caused by malfunction or breakdown of equipment and sudden disruption technological process(for example, with a sharp increase or decrease in temperature, etc.); the effects of uneven deformations of the base, accompanied by a radical change in the structure of the soil (for example, deformation of subsidence soils during soaking or permafrost soils during thawing), etc.
Standard loads are established by standards based on a predetermined probability of exceeding average values or based on nominal values. Standard permanent loads are taken based on the design values of geometric and structural parameters and on average density values. Standard temporary technological and installation loads are established according to highest values intended for normal use; snow and wind - according to the average of annual unfavorable values or according to unfavorable values corresponding to a certain average period of their repetitions.
Design loads for calculating structures for strength and stability are determined by multiplying the standard load by the load safety factor Vf, usually greater than one, for example g=gnyf. Reliability factor from the weight of concrete and reinforced concrete structures Yf = M; on the weight of structures made of concrete with light aggregates (with an average density of 1800 kg/m3 or less) and various ties, backfills, insulation, performed in the factory, Yf = l,2, during installation yf = \,3; from various temporary loads depending on their value yf = it 2. 1.4. The overload coefficient from the weight of structures when calculating the stability of the position against floating, capsizing and sliding, as well as in other cases when a decrease in mass worsens the operating conditions of the structure, is taken to be 7f = 0.9. When calculating structures at the construction stage, the calculated short-term loads are multiplied by a factor of 0.8. Design loads for calculating structures for deformations and displacements (for the second group of limit states) are taken equal to standard values with coefficient Yf -1-
Combination of loads. Structures must be designed for various combinations loads or corresponding forces if the calculation is carried out according to an inelastic scheme. Depending on the composition of the loads taken into account, the following are distinguished: main combinations, consisting of constant, long-term and short-term loads or forces from low-voltage loads; special combinations consisting of constant, long-term, possible short-term and one of the special loads or efforts from them.
All groups of basic load combinations are considered. When calculating structures for the main combinations of the first group, constant, long-term and one short-term loads are taken into account; When calculating structures for the main combinations of the second group, constant, long-term and two (or more) short-term loads are taken into account; while the values of short-term
loads or corresponding efforts must be multiplied by a combination coefficient equal to 0.9.
When calculating structures for special combinations, the values of short-term loads or the corresponding forces must be multiplied by a combination factor equal to 0.8, except for cases specified in the design standards for buildings and structures in seismic areas.
The standards also allow reducing temporary loads when calculating beams and crossbars, depending on the area of the loaded floor.
5. Degree of responsibility of buildings and structures
The degree of responsibility of buildings and structures when structures reach limit states is determined by the amount of material and social damage. When designing structures, one should take into account the reliability coefficient for the purpose of the unitary enterprise, the value of which depends on the responsibility class of buildings or structures. The maximum values of load-bearing capacity, calculated values of resistance, maximum values of deformations, crack openings should be divided by the reliability coefficient for the intended purpose, or the calculated values of loads, forces or other influences should be multiplied by this coefficient.
Experimental studies carried out in prefabricated factories reinforced concrete products, showed that for heavy concrete and concrete on porous aggregates the coefficient of variation V
0.135, which is accepted in the standards.
In mathematical statistics, using pa or ni, the probability of repetition of values of temporary resistance less than B is estimated. If we take x = 1.64, then repetition of values is likely<В не более чем у 5 % (и значения В не менее чем у 95 %) испытанных образцов. При этом достигается нормированная обеспеченность не менее 0,95.
When monitoring the class of concrete for axial tensile strength, the standard resistance of concrete to axial tensile Rbtn is taken equal to its guaranteed strength (class). axial tension.
The design resistances of concrete for calculations for the first group of limit states are determined by dividing the standard resistances by the corresponding reliability coefficients for concrete in compression yc = 1.3 prn, tension ^ = 1.5, and when monitoring tensile strength yy = \.3. Design resistance of concrete to axial compression
The calculated compressive strength of heavy concrete of classes B50, B55, B60 is multiplied by coefficients that take into account the peculiarity mechanical properties high-strength concrete (reduction of creep deformations), respectively equal to 0.95; 0.925 and 0.9.
The calculated concrete resistance values with rounding are given in the appendix. I.
When calculating structural elements, the design resistances of concrete Rb and Rbt are reduced, and in some cases increased by multiplying by the corresponding coefficients of the operating conditions of the concrete uc, taking into account the characteristics of the properties of concrete: the duration of the load and its repeated repetition; conditions, nature and stage of operation of the structure; the method of its manufacture, section dimensions, etc.
The calculated compressive resistance of the reinforcement Rsc, used in the calculation of structures for the first group of limit states, when the reinforcement is bonded to concrete, is taken equal to the corresponding calculated tensile resistance of the reinforcement Rs, but not more than 400 MPa (based on the ultimate compressibility of concrete tub). When calculating structures for which the design resistance of concrete is assumed under long-term load action, taking into account the operating conditions coefficient y&2 When calculating structural elements, the design resistances of the reinforcement are reduced or, in some cases, increased by multiplying by the corresponding operating conditions coefficients ySi, taking into account the possibility of incomplete use of its strength characteristics due to the uneven distribution of stresses in the section, low strength of concrete, anchoring conditions, and the presence of bends , the nature of the tensile diagram of steel, changes in its properties depending on the operating conditions of the structure, etc. When calculating elements under the action of transverse force, the design resistance of transverse reinforcement is reduced by introducing the operating conditions coefficient -um^OD, which takes into account the uneven distribution of stresses in the reinforcement along the length of the inclined section. In addition, for welded transverse reinforcement from wire of classes BP-I and rod reinforcement of class A-III, the coefficient Vs2 = 0.9 has been introduced, taking into account the possibility of brittle fracture of the welded joint of the clamps. The values of the calculated resistances of transverse reinforcement when calculating for transverse force Rsw, taking into account the coefficients yst, are given in table. 1 and 2 adj. V. In addition, the calculated resistances Rs, Rsc and Rsw should be multiplied by the operating conditions coefficients: Ys3, 7*4 - with repeated application of load (see Chapter VIII); ysb^lx/lp or uz 1x/1ap - in the zone of stress transmission and in the zone of anchoring non-prestressed reinforcement without anchors; 7^6 - when working with high-strength reinforcement at stresses above the nominal yield strength (7o.2. The calculated resistances of the reinforcement for calculations for the second group of limit states are set at a reliability factor for the reinforcement of 7s = 1, i.e. are taken equal to the standard values of Rs,ser=Rsn and are included in the calculation with the coefficient of operating conditions of the reinforcement The crack resistance of a reinforced concrete structure is its resistance to crack formation in stage I of the stress-strain state or its resistance to crack opening in stage II of the stress-strain state. When calculating, different requirements are imposed on the crack resistance of a reinforced concrete structure or its parts, depending on the type of reinforcement used. These requirements apply to normal cracks and cracks inclined to the longitudinal axis of the element and are divided into three categories: The opening of cracks under constant, long-term and short-term loads is considered short-lived; Long-lasting is considered to be the opening of cracks under the action of only constant and long-term loads. The maximum crack opening width (isgs\ - short-term and asgs2 long-term), which ensures normal operation of buildings, corrosion resistance of reinforcement and durability of the structure, depending on the category of crack resistance requirements, should not exceed 0.05-0.4 mm (Table II .2). Prestressed elements under liquid or gas pressure (tanks, pressure pipes, etc.), with a fully stretched section with rod or wire reinforcement, as well as with a partially compressed section with wire reinforcement with a diameter of 3 mm or less, must meet the requirements of the First categories. Other prestressed elements, depending on the structural conditions and type of reinforcement, must meet the requirements of the second or third category. The procedure for taking into account loads when calculating crack resistance depends on the category of requirements for crack resistance: for the requirements of the first category, the calculation is carried out according to design loads with a safety factor for load yf>l (as in strength calculations); for the requirements of the second and third categories, the calculation is carried out under the action of loads with the coefficient V/=b. Calculation for the formation of cracks to determine the need for checking for short-term crack opening; for the requirements of the second category, the calculation is carried out for the action of design loads with the coefficient yf>U; calculation for the formation of cracks to determine the need Tests for crack opening under the requirements of the third category are carried out under the action of loads with a coefficient of Y/-1. When calculating crack resistance, the combined action of all loads, except special ones, is taken into account. Special loads are taken into account in the calculation of crack formation in cases where cracks lead to a catastrophic situation. Calculation for closing cracks under the requirements of the second category is carried out under the action of constant and long-term loads with a coefficient y/-1. The procedure for taking into account loads is given in table. P.Z. At the end sections of prestressed elements within the length of the zone of stress transfer from reinforcement to concrete 1P, the formation of cracks is not allowed under the combined action of all loads (except special ones) introduced into the calculation with the coefficient Y/=L. THIS requirement is caused by the fact that premature formation of cracks in concrete at the end sections of elements - can lead to the reinforcement being pulled out of the concrete under load and sudden destruction. increasing deflections. The influence of these cracks is taken into account in structural calculations. For elements operating under conditions of repeated repeated loads and designed for endurance, the formation of such cracks is not allowed. Limit states of the first group. Strength calculations are based on stage III of the stress-strain state. The section of the structure has the required strength if the forces from the design loads do not exceed the forces perceived by the section at the design resistance of the materials, taking into account the operating conditions coefficient. The force from design loads T (for example, bending moment or longitudinal force) is a function of standard loads, reliability factors and other factors C (design scheme, dynamic coefficient, etc.). Limit states of the second group. Calculation of the formation of cracks, normal and inclined to the longitudinal axis of the element, is carried out to check the crack resistance of elements that are subject to the requirements of the first category, as well as to determine whether cracks appear in elements whose crack resistance is subject to the requirements of the second and third categories. It is believed that cracks normal to the longitudinal axis do not appear if the force T (bending moment or longitudinal force) from the action of loads does not exceed the force TSgs, which can be absorbed by the section of the element It is believed that cracks inclined to the longitudinal axis of the element do not appear if the main tensile stresses in the concrete do not exceed the calculated values, Calculation of crack opening, normal and inclined to the longitudinal axis, consists of determining the crack opening width at the level of tensile reinforcement and comparing it with the maximum opening width. Data on the maximum crack opening width are given in table. II.3. Calculation based on displacements consists of determining the deflection of an element due to loads, taking into account the duration of their action and comparing it with the maximum deflection. Limit deflections are set by various requirements: technological, due to the normal operation of cranes, technological installations, cars, etc.; structural, due to the influence of neighboring elements that limit deformations, the need to withstand given slopes, etc.; aesthetic. The maximum deflections of prestressed elements can be increased by the height of the deflection, if this is not limited by technological or design requirements. The procedure for taking into account loads when calculating deflections is established as follows: when limited by technological or design requirements - for the action of constant, long-term and short-term loads; when limited by aesthetic requirements - to the effect of constant and long-term loads. In this case, the load reliability factor is taken to be Yf The maximum deflections established by the standards for various reinforced concrete elements are given in Table II.4. The maximum deflections of the consoles, related to the overhang of the console, are assumed to be twice as large. In addition, additional fragility calculations must be performed for non-neighboring elements. reinforced concrete slabs floors, flights of stairs, platforms, etc.: the additional deflection from a short-term concentrated load of 1000 N with the most unfavorable scheme for its application should not exceed 0.7 mm. Limit state calculation method When calculating using this method, the structure is considered in its design limit state. The design limit state is taken to be the state of the structure in which it ceases to meet the operational requirements imposed on it, i.e., it either loses its ability to resist external influences, or receives unacceptable deformation or local damage. For steel structures, two design limit states are established: The first calculated limit state is expressed by the inequality where N is the design force in the structure from the sum of the effects of the design loads P in the most unfavorable combination; F - load bearing capacity structures that are a function geometric dimensions design, design material resistance R and operating conditions coefficient m. The maximum loads established by the standards (SNiP) that are allowed during normal operation of structures are called standard loads Rn (see Appendix I, Loads and preload factors). The design loads P for which the structure is calculated (based on the limit state) are taken to be slightly higher than the normative ones. The design load is defined as the product of the standard load by the overload factor n (greater than unity), taking into account the danger of exceeding the load compared to its standard value due to possible load variability: The values of coefficients p are given in the table Standard and design loads, overload factors. Thus, structures are considered under the influence of design loads rather than operational (standard) loads. From the influence of design loads in the structure, design forces are determined (axial force N or moment M), which are found by general rules strength of materials and structural mechanics. Right side of the main equation (1.I)- load-bearing capacity of the structure F - depends on the maximum resistance of the material to force influences, characterized by the mechanical properties of the material and called the standard resistance R n, as well as on the geometric characteristics of the section (sectional area F, moment of resistance W, etc.). For building steel, the standard resistance is assumed to be equal to the yield strength, (for the most common building steel grade St. 3 σ t = 2,400 kg/cm 2). The design resistance of steel R is taken to be a voltage equal to the standard resistance multiplied by the uniformity coefficient k (less than unity), taking into account the risk of a decrease in the resistance of the material compared to its standard value due to variability in the mechanical properties of the material For ordinary low-carbon steels k = 0.9, and for high-quality steels (low-alloy) k = 0.85. Thus, the calculated resistance R- this is a stress equal to the lowest possible value of the yield strength of the material, which is accepted for the structure as the limiting value. In addition, for the safety of the structure, all possible deviations from normal conditions caused by the operating features of the structure must be taken into account (for example, conditions conducive to increased corrosion, etc.). To do this, the operating conditions coefficient m is introduced, which for most structures and connections is taken equal to unity (see Operating Conditions Coefficients m appendix). Thus, the main design equation (1.I) will have the following form: where N and M are the calculated axial forces or moments from the calculated loads (taking into account overload factors); F nt - net cross-sectional area (minus holes); W nt - moment of resistance of the net section (minus holes); where F br and W br - area and moment of resistance of the gross section (without deduction of holes); φ and φ b are coefficients that reduce the design resistance to values that ensure stable equilibrium. Usually, when calculating the intended structure, the cross-section of the element is first selected and then the stress from the design forces is checked, which should not exceed the design resistance multiplied by the operating conditions coefficient. Therefore, along with formulas of the form (4.I) and (5.I), we will write these formulas in working form in terms of calculated stresses, for example: where σ is the design stress in the structure (based on the design loads). It is more correct to write the coefficients φ and φ b in formulas (8.I) and (9.I) on the right side of the inequality as coefficients that reduce the calculated resistance to critical stresses. And only for the sake of convenience of calculations and comparison of results, they are written in the denominator of the left side of these formulas. *
The values of standard resistances and uniformity coefficients are given in the “Building Norms and Rules” (SNiP), as well as in the “Norms and Technical Conditions for the Design of Steel Structures” (NiTU 121-55). "Design of steel structures" There are several categories of voltages: main, local, additional and internal. Fundamental stresses are stresses that develop inside the body as a result of balancing the effects of external loads; they are taken into account in the calculation. When the power flow is unevenly distributed over the cross-section, caused, for example, by a sharp change in the cross-section or the presence of a hole, a local stress concentration occurs. However, in plastic materials, which include construction steel,… When calculating the permissible stresses, the structure is considered in its operating condition under the influence of loads allowed during normal operation of the structure, i.e., standard loads. The condition for the strength of the structure is that the stresses in the structure from standard loads do not exceed the permissible stresses established by the standards, which represent a certain part of the maximum stress of the material accepted for building steel... Limit state calculation method - Methodology for calculation of steel structures - Design fundamentals - Design of steel structures Limit states are considered to be those in which structures no longer meet the requirements imposed on them during operation, i.e., they lose the ability to resist external loads and influences or receive unacceptable movements or local damage. Reinforced concrete structures must meet the requirements of calculation for two groups of limit states: for bearing capacity - the first group of limit states; in terms of suitability for normal operation - the second group of limit states. Calculation based on the limit states of the first group is performed to prevent: Brittle, viscous or other type of failure (strength calculation taking into account necessary cases deflection of the structure before failure); Loss of stability of the shape of the structure (calculation for the stability of thin-walled structures, etc.) or its position (calculation for overturning and sliding of retaining walls, eccentrically loaded high foundations; calculation for the ascent of buried or underground tanks, etc.); Fatigue failure (calculation of the endurance of structures under the influence of repeated moving or pulsating loads: crane beams, sleepers, frame foundations and floors for unbalanced machines, etc.); Destruction from the combined influence of force factors and unfavorable influences of the external environment (periodic or constant exposure to an aggressive environment, alternating freezing and thawing, etc.). Calculations based on limit states of the second group are performed to prevent: Formation of excessive or prolonged opening of cracks (if, according to operating conditions, the formation or prolonged opening of cracks is permissible); Excessive movements (deflections, rotation angles, skew angles and vibration amplitudes). Calculation of the limit states of the structure as a whole, as well as its individual elements or parts, is carried out for all stages: manufacturing, transportation, installation and operation; in this case, the design schemes must correspond to the adopted design decisions and each of the listed stages. Design factors - loads and mechanical characteristics of concrete and reinforcement (tensile strength, yield strength) - have statistical variability (scatter of values). Loads and impacts may differ from the specified probability of exceeding average values, and the mechanical properties of materials may differ from the specified probability of decreasing average values. Calculations for limit states take into account the statistical variability of loads and mechanical characteristics of materials, factors of a non-statistical nature and various unfavorable or favorable physical, chemical and mechanical conditions for the operation of concrete and reinforcement, the manufacture and operation of elements of buildings and structures. Loads, mechanical characteristics of materials and design coefficients are normalized. The values of loads, resistance of concrete and reinforcement are established according to the chapters of SNiP “Loads and Impacts” and “Concrete and Reinforced Concrete Structures”. Classification of loads. Standard and design loads Depending on the duration of action, loads are divided into permanent and temporary. Temporary loads, in turn, are divided into long-term, short-term, and special. Loads from the weight of load-bearing and enclosing structures of buildings and structures, the mass and pressure of soils, and the effects of prestressing reinforced concrete structures are constant. Long-term loads are caused by the weight of stationary equipment on floors - machines, apparatus, engines, containers, etc.; pressure of gases, liquids, granular bodies in containers; loads in warehouses, refrigerators, archives, libraries and similar buildings and structures; part of the temporary load established by the standards in residential buildings, office and domestic premises; long-term temperature technological effects from stationary equipment; loads from one overhead or one overhead crane, multiplied by factors: 0.5 for medium-duty cranes and 0.7 for heavy-duty cranes; snow loads for III-IV climatic regions with coefficients of 0.3-0.6. The indicated values of crane, some temporary and snow loads form part of their full value and are entered into the calculation when taking into account the duration of the action of loads of these types on displacement, deformation, and crack formation. The full values of these loads are short-term. Short-term loads are caused by the weight of people, parts, materials in equipment maintenance and repair areas - passages and other areas free from equipment; part of the load on the floors of residential and public buildings; loads arising during the manufacture, transportation and installation of structural elements; loads from overhead and overhead cranes used in the construction or operation of buildings and structures; snow and wind loads; temperature climatic influences. Special loads include: seismic and explosive impacts; loads caused by a malfunction or breakdown of equipment and a sudden disruption of the technological process (for example, a sharp increase or decrease in temperature, etc.); the effects of uneven deformations of the base, accompanied by a radical change in the structure of the soil (for example, deformation of subsidence soils during soaking or permafrost soils during thawing), etc. Standard loads are established by standards based on a predetermined probability of exceeding average values or based on nominal values. Standard constant loads are accepted based on the design values of the geometric and design parameters and Average density values. Regulatory temporary; technological and installation loads are set according to the highest values provided for normal operation; snow and wind - according to the average of annual unfavorable values or according to unfavorable values corresponding to a certain average period of their repetitions. Design loads for calculating structures for strength and stability are determined by multiplying the standard load by the load safety factor Yf, usually greater than one, for example G=
Gnyt.
Reliability factor from the weight of concrete and reinforced concrete structures Yf = M; on the weight of structures made of concrete with light aggregates (with an average density of 1800 kg/m3 or less) and various screeds, backfills, and insulation materials made in the factory, Yf = l.2, during installation Yf = l>3; from various temporary loads depending on their value Yf = l. 2. 1.4. The overload coefficient from the weight of structures when calculating the stability of the position against floating, capsizing and sliding, as well as in other cases when a decrease in mass worsens the operating conditions of the structure, is assumed to be yf = 0.9. When calculating structures at the construction stage, the calculated short-term loads are multiplied by a factor of 0.8. Design loads for calculating structures for deformations and displacements (for the second group of limit states) are taken equal to standard values with the coefficient Yf = l- Combination of loads. Structures must be designed for various combinations of loads or corresponding forces if the calculation is carried out using an inelastic scheme. Depending on the composition of the loads taken into account, the following are distinguished: main combinations, consisting of constant, long-term and short-term loads or forces from low-voltage loads; special combinations consisting of constant, long-term, possible short-term and one of the special loads or efforts from them. Two groups of main load combinations are considered. When calculating structures for the main combinations of the first group, constant, long-term and one short-term loads are taken into account; When calculating structures for the main combinations of the second group, constant, long-term and two (or more) short-term loads are taken into account; in this case, the values of short-term loads or the forces corresponding to them must be multiplied by a combination coefficient equal to 0.9. When calculating structures for special combinations, the values of short-term loads or the corresponding forces must be multiplied by a combination factor equal to 0.8, except for cases specified in the design standards for buildings and structures in seismic areas. Reduced loads. When calculating columns, walls, foundations multi-storey buildings temporary loads on floors can be reduced, taking into account the degree of probability of their simultaneous action, by multiplying by a factor Where a - is taken equal to 0.3 for residential buildings, office buildings, dormitories, etc. and equal to 0.5 for various rooms: reading rooms, meetings, shopping rooms, etc.; t is the number of loaded floors above the section under consideration. The standards also allow reducing temporary loads when calculating beams and crossbars, depending on the area of the loaded floor. Precast concrete and reinforced concrete: features and production methods Industrial technologies have been actively developing in the USSR since the middle of the last century, and the development of the construction industry required large quantity various materials. The invention of prefabricated reinforced concrete became a kind of technical revolution in the life of the country, ... DIY pile driver A pile driver or a pile driver can be organized using a car with the rear fender removed (rear-wheel drive on mechanics), raised on a jack and using only the rim instead of a wheel. A cable will be wound around the rim - this is... RECONSTRUCTION OF INDUSTRIAL BUILDINGS 1. Tasks and methods of reconstruction of buildings Reconstruction of buildings can be associated with the expansion of production, technological modernization. process, installation of new equipment, etc. At the same time, it is necessary to solve complex engineering problems associated ... rollers (flattening machine) diameter from 400 mm., electric food dryer (flow), conveyors, conveyors, augers. Two groups of limit states In accordance with the current standards in Russia, wooden structures must be calculated using the limit state method. Limit states of structures are those at which they cease to meet operating requirements. The external cause that leads to the limit state is force action (external loads, reactive forces). Limit states may occur under the influence of operating conditions wooden structures, as well as the quality, dimensions and properties of materials. There are two groups of limit states: 1 – in terms of load-bearing capacity (strength, stability). 2 – by deformations (deflections, displacements). First group limit states are characterized by loss of bearing capacity and complete unsuitability for further operation. Is the most responsible. In wooden structures, the following limit states of the first group can occur: destruction, loss of stability, overturning, unacceptable creep. These limit states do not occur if the following conditions are met: those. when normal stresses ( σ
) and shear stress ( τ
) do not exceed a certain limit value R,
called design resistance. Second group limit states are characterized by such features in which the operation of structures or structures, although difficult, is not completely excluded, i.e. the design becomes unsuitable only for normal operation. The suitability of a structure for normal operation is usually determined by deflections This means that bending elements or structures are suitable for normal operation when the largest value of the deflection-to-span ratio is less than the maximum permissible relative deflection [
f/
l]
(according to SNiP II-25-80). The purpose of structural calculations is to prevent the occurrence of any of the possible limit states, both during transportation and installation, and during operation of structures. The calculation for the first limit state is carried out according to the calculated load values, and for the second - according to the standard values. Standard values of external loads are given in SNiP “Loads and Impacts”. The calculated values are obtained taking into account the load safety factor γ
n. Structures are designed to withstand an unfavorable combination of loads (own weight, snow, wind), the probability of which is taken into account by combination coefficients (according to SNiP “Loads and Impacts”). The main characteristic of materials by which their ability to resist force is assessed is normative resistance R
n
.
The standard resistance of wood is calculated based on the results of numerous tests of small samples of clean (without defects) wood of the same species, with a moisture content of 12%: R n =
,
Where – arithmetic mean value of tensile strength, V– variation coefficient, t– indicator of reliability. Regulatory resistance R
n
is the minimum probabilistic strength limit of pure wood, obtained by statically processing the results of tests of standard small-sized samples for short-term loads. Design resistance R
- this is the maximum stress that a material in a structure can withstand without collapsing, taking into account all the unfavorable factors under operating conditions that reduce its strength. When moving from normative resistance R n to the calculated R it is necessary to take into account the influence on the strength of wood of long-term loads, defects (knots, cross-layers, etc.), the transition from small standard samples to elements building dimensions. The combined influence of all these factors is taken into account by the safety factor for the material ( To). The calculated resistance is obtained by dividing R n on the safety factor for the material: To dl=0.67 – duration coefficient under the combined action of permanent and temporary loads; To one =
0.27÷0.67 – uniformity coefficient, depending on the type of stress state, taking into account the influence of defects on the strength of wood. Minimum value To one taken during stretching, when the influence of defects is especially great. Calculated resistances To are given in table. 3 SNiP II-25-80 (for wood coniferous species). R wood of other species is obtained using transition coefficients, also given in SNiP. The safety and strength of wood and wooden structures depend on temperature and humidity conditions. Humidification promotes wood rotting, and elevated temperatures (beyond a certain limit) reduce its strength. Taking these factors into account requires the introduction of working condition coefficients: m V ≤1, m T ≤1. In addition, SNiP requires taking into account the ply coefficient for glued elements: m sl =
0.95÷1.1; beam coefficient for high beams with a height of more than 50 cm: m b ≤1; bending coefficient for bent-glued elements: m gn≤1, etc. The modulus of elasticity of wood, regardless of the species, is assumed to be equal to: The design characteristics of construction plywood are also given in SNiP, and when checking stresses in plywood elements, as for wood, operating condition coefficients are introduced m. In addition, for the design resistance of wood and plywood, a coefficient is introduced m dl=0.8 if the total design force from permanent and temporary loads exceeds 80% of the total design force. This factor is introduced in addition to the reduction that is included in the safety factor for the material. Lecture No. 2 Fundamentals of calculation by limit states Limit states- these are conditions in which the structure can no longer be used as a result of external loads and internal stresses. In structures made of wood and plastics, two groups of limit states can arise - the first and second. Calculation of limit states of structures as a whole and its elements must be carried out for all stages: transportation, installation and operation - and must take into account all possible combinations of loads. The purpose of the calculation is to prevent either the first or the second limit states during the processes of transportation, assembly and operation of the structure. This is done based on taking into account the standard and design loads and resistances of materials. The limit state method is the first step in ensuring reliability building structures. Reliability is the ability of an object to maintain the quality inherent in the design during operation. The specificity of the theory of reliability of building structures is the need to take into account random values of loads on systems with random strength indicators. Characteristic feature The method of limit states is that all initial values operated in the calculation, random in nature, are represented in the standards by deterministic, scientifically based, normative values, and the influence of their variability on the reliability of structures is taken into account by the corresponding coefficients. Each of the reliability coefficients takes into account the variability of only one initial value, i.e. is of a private nature. Therefore, the limit state method is sometimes called the partial coefficient method. Factors whose variability affects the level of reliability of structures can be classified into five main categories: loads and impacts; geometric dimensions of structural elements; degree of responsibility of structures; mechanical properties of materials; operating conditions of the structure. Let's consider the listed factors. A possible deviation of standard loads up or down is taken into account by the load safety factor 2, which, depending on the type of load, has a different value greater or less than one. These coefficients, along with standard values, are presented in chapter SNiP 2.01.07-85 Design Standards. “Loads and impacts.” The probability of the combined action of several loads is taken into account by multiplying the loads by the combination factor, which is presented in the same chapter of the standards. Possible unfavorable deviation of the geometric dimensions of structural elements is taken into account by the accuracy coefficient. However, this coefficient is pure form not acceptable. This factor is used when calculating geometric characteristics, taking the calculated parameters of sections with a minus tolerance. In order to reasonably balance the costs of buildings and structures for various purposes, a reliability coefficient for the intended purpose is introduced< 1. Степень капитальности и ответственности зданий и сооружений разбивается на три класса ответственности. Этот коэффициент (равный 0,9; 0,95; 1) вводится в качестве делителя к значению расчетного сопротивления или в качестве множителя к значению расчетных нагрузок и воздействий. The main parameter of a material’s resistance to force influences is the standard resistance set regulatory documents based on the results of statistical studies of the variability of mechanical properties of materials by testing material samples using standard methods. A possible deviation from standard values is taken into account by the reliability coefficient for the material ym > 1. It reflects the statistical variability of the properties of materials and their difference from the properties of tested standard samples. The characteristic obtained by dividing the standard resistance by the coefficient m is called the design resistance R. This main characteristic of wood strength is standardized by SNiP P-25-80 “Design Standards. Wooden structures." The unfavorable influence of the environmental and operating environment, such as: wind and installation loads, section height, temperature and humidity conditions, are taken into account by introducing operating conditions coefficients t. Coefficient t may be less than one if this factor or a combination of factors reduces the load-bearing capacity of the structure, and more units – in the opposite case. For wood, these coefficients are presented in SNiP 11-25-80 “Design standards. Standard limit values of deflections meet the following requirements: a) technological (ensuring conditions for normal operation of machinery and handling equipment, instrumentation, etc.); b) structural (ensuring the integrity of adjacent structural elements, their joints, the presence of a gap between load-bearing structures and partition structures, half-timbering, etc., ensuring specified slopes); c) aesthetic and psychological (providing favorable impressions from the appearance of structures, preventing the feeling of danger). The magnitude of the maximum deflections depends on the span and the type of applied loads. For wooden structures covering buildings under constant and temporary long-term loads, the maximum deflection ranges from (1/150) - i to (1/300) (2). The strength of wood is also reduced under the influence of certain chemicals from biological damage, embedded under pressure in autoclaves to a considerable depth. In this case, the operating condition coefficient Tia = 0.9. The influence of stress concentration in the design sections of tensile elements weakened by holes, as well as in bending elements made of round timber with trimming in the design section, is reflected by the operating condition coefficient t0 = 0.8. When calculating wooden structures for the second group of limit states, the deformability of wood is taken into account by the basic modulus of elasticity E, which, when the force is directed along the wood fibers, is assumed to be 10,000 MPa, and 400 MPa across the fibers. When calculating stability, the elastic modulus was assumed to be 4500 MPa. Basic module the shear of wood (6) in both directions is 500 MPa. The Poisson's ratio of wood across the fibers with stresses directed along the fibers is assumed to be equal to pdo o = 0.5, and along the fibers with stresses directed across the fibers, n900 = 0.02. Since the duration and level of loading affects not only the strength, but also the deformation properties of wood, the value of the modulus of elasticity and shear modulus is multiplied by the coefficient mt = 0.8 when calculating structures in which stresses in elements arising from permanent and temporary long-term loads exceed 80% of the total voltage from all loads. When calculating metal-wood structures, the elastic characteristics and design resistances of steel and connections of steel elements, as well as reinforcement, are taken according to the chapters of SNiP for the design of steel and reinforced concrete structures. Of all the leafy ones construction materials When using wood raw materials, only plywood is recommended to be used as elements of load-bearing structures, the basic design resistances of which are given in Table 10 of SNiP P-25-80. Under appropriate operating conditions for glue-plywood structures, calculations based on the first group of limit states provide for multiplying the basic design resistances of plywood by the operating conditions coefficients TV, TY, TN and TL. When calculating according to the second group of limit states, the elastic characteristics of plywood in the plane of the sheet are taken according to table. 11 SNiP P-25-80. Modulus of elasticity and shear modulus for structures located in different conditions operation, as well as those exposed to the combined influence of constant and temporary long-term loads, should be multiplied by the corresponding coefficients of operating conditions adopted for wood First group most dangerous. It is determined by unsuitability for use when a structure loses its load-bearing capacity as a result of destruction or loss of stability. This does not happen while the maximum normal O or shearing stresses in its elements do not exceed the calculated (minimum) resistance of the materials from which they are made. This condition is written by the formula The limiting states of the first group include: destruction of any kind, general loss of stability of a structure or local loss of stability of a structural element, violation of joints that turn the structure into a variable system, development of residual deformations of unacceptable magnitude. The load-bearing capacity calculation is carried out based on the probable worst case, namely: the highest load and the lowest resistance of the material, found taking into account all the factors influencing it. Unfavorable combinations are given in the norms. Second group less dangerous. It is determined by the unsuitability of the structure for normal operation when it bends to an unacceptable amount. This does not happen until the maximum relative deflection of its /// does not exceed the maximum permissible values. This condition is written by the formula The calculation of wooden structures according to the second limit state for deformations applies mainly to bendable structures and is aimed at limiting the magnitude of deformations. The calculations are based on standard loads without multiplying them by safety factors, assuming elastic operation of the wood. The calculation for deformations is carried out based on the average characteristics of the wood, and not on the reduced ones, as when checking the load-bearing capacity. This is explained by the fact that an increase in deflection in some cases, when low-quality wood is used, does not pose a danger to the integrity of the structures. This also explains the fact that deformation calculations are carried out for standard, and not for design, loads. To illustrate the limit state of the second group, we can give an example when, as a result of unacceptable deflection of the rafters, cracks appear in roofing. The leakage of moisture in this case disrupts the normal operation of the building, leading to a decrease in the durability of the wood due to its moisture, but at the same time the building continues to be used. Calculation based on the second limit state, as a rule, has a subordinate meaning, because the main thing is to ensure load-bearing capacity. However, limitations on deflections are especially important for structures with ductile connections. Therefore, deformations of wooden structures (composite posts, composite beams, board and nail structures) must be determined taking into account the influence of the compliance of the connections (SNiP P-25-80. Table 13). Loads, acting on structures are determined by Building Codes and Regulations - SNiP 2.01.07-85 “Loads and Impacts”. When calculating structures made of wood and plastics, mainly the constant load from the dead weight of structures and other building elements is taken into account g and short-term loads from the weight of snow S, wind pressure W. Loads from the weight of people and equipment are also taken into account. Each load has a standard and design value. It is convenient to denote the standard value with the index n. Standard loads are the initial values of the loads: Temporary loads are determined as a result of processing data from long-term observations and measurements. Constant loads are calculated based on the dead weight and volume of structures, other building elements and equipment. Standard loads are taken into account when calculating structures for the second group of limit states - for deflections. Design loads are determined on the basis of normative ones, taking into account their possible variability, especially upward. To do this, the values of standard loads are multiplied by the load safety factor y, the values of which are different for different loads, but all of them are greater than unity. Distributed load values are given in kilopascals (kPa), which corresponds to kilonewtons per square meter (kN/m). Most calculations use linear load values (kN/m). Design loads are used when calculating structures for the first group of limit states, for strength and stability.
Chapter 2. Experimental foundations of the theory of resistance of reinforced concrete and methods of calculation of reinforced concrete structures Calculation method based on limit states 1. Essence of the method Method Limit state calculation method
When calculating using this method, the structure is considered in its design limit state. The calculated limit state is taken to be the following state... Two groups of limit states
Reinforced concrete
Limit states are considered to be those in which structures no longer meet the requirements imposed on them during operation, i.e., they lose Fundamentals of calculations based on limit states. Calculation of structural elements of solid section.
Lecture No. 2 Fundamentals of calculations based on limit states. Calculation of structural elements of solid section. In accordance with current standards in Russia, wooden structures must be calculated according to Calculation based on limit states
The standard snow load s H is determined based on the standard weight of the snow cover so, which is given in load standards (kN/m 2) of the horizontal projection of the cover depending on the snow region of the country. This value is multiplied by the coefficient p, which takes into account the slope and other features of the shape of the coating. Then the standard load s H = s 0 p- For gable roofs with a ^ 25°, p = 1, for a > 60° p = 0, and for intermediate slope angles of 60° >*<х > 25° p == (60° - a°)/35°. This. the load is uniform and can be two- or one-sided.
With vaulted coverings along segmental trusses or arches, the uniform snow load is determined taking into account the coefficient p, which depends on the ratio of the span length / to the height of the arch /: p = //(8/).
When the ratio of the height of the arch to the span f/l= A 1/8 snow load can be triangular with a maximum value of s” at one support and 0.5 s” at the other and zero value at the ridge. Coefficients p that determine the maximum snow load at the ratios f/l= 1/8, 1/6 and 1/5, respectively equal to 1.8; 2.0 and 2.2. The snow load on lancet-shaped coverings can be determined as on gable roofs, considering the roof to be conditionally gable along planes passing through the chords of the axes of the floor at the arches. The design snow load is equal to the product of the standard load and the load safety factor 7- For most light wooden and plastic structures with the ratio of standard constant and snow loads g n /s H < 0,8 коэффициент y = 1.6. For large ratios of these loads at =1,4.
The load from the weight of a person with a load is assumed to be equal - standard R"= 0.1 kN and design R = p and y = 0.1 1.2 = 1.2 kN. Wind load. Standard wind load w consists of pressure w’+ and suction w n – wind. The initial data when determining the wind load are the values of wind pressure directed perpendicular to the surfaces of the roofing and walls of buildings Wi(MPa), depending on the wind region of the country and accepted according to the norms of loads and impacts. Standard wind loads w" are determined by multiplying the normal wind pressure by the coefficient k, taking into account the height of buildings, and the aerodynamic coefficient With, taking into account its shape. For most wood and plastic buildings whose height does not exceed 10 m, k = 1.
Aerodynamic coefficient With depends on the shape of the building, its absolute and relative dimensions, slopes, relative heights of coverings and wind direction. On most pitched roofs, the angle of inclination of which does not exceed a = 14°, the wind load acts in the form of suction W-. At the same time, it generally does not increase, but rather reduces the forces in structures from constant and snow loads and may not be taken into account in the safety factor when calculating. Wind load must be taken into account when calculating the pillars and walls of buildings, as well as when calculating triangular and lancet-shaped structures.
The calculated wind load is equal to the standard load multiplied by the safety factor y= 1.4. Thus, w = = w”y.
Regulatory resistance wood RH(MPa) are the main characteristics of the strength of wood in areas free from defects. They are determined by the results of numerous laboratory short-term tests of small standard samples of dry wood with a moisture content of 12% for tension, compression, bending, crushing and chipping.
95% of the tested wood samples will have a compressive strength equal to or greater than its standard value.
The values of standard resistances given in the appendix. 5 are practically used in laboratory testing of wood strength during the manufacturing of wooden structures and in determining the load-bearing capacity of operating load-bearing structures during their inspections.
Calculated resistances wood R(MPa) are the main characteristics of the strength of real wood elements of real structures. This wood has natural defects and has been subject to stress for many years. Calculated resistances are obtained based on standard resistances taking into account the reliability coefficient for the material at and loading duration coefficient t al according to the formula
Coefficient at significantly more than one. It takes into account the decrease in the strength of real wood as a result of heterogeneity of structure and the presence of various defects that do not occur in laboratory samples. Basically, the strength of wood is reduced by knots. They reduce the working cross-sectional area by cutting and pushing apart its longitudinal fibers, creating eccentricity longitudinal forces and the inclination of the fibers around the knot. The inclination of the fibers causes wood to stretch across and at an angle to the fibers, the strength of which in these directions is much lower than along the fibers. Wood defects reduce the strength of wood in tension by almost half and by about one and a half times in compression. Cracks are most dangerous in areas where wood is being chipped. As the cross-sectional sizes of the elements increase, the stresses upon their destruction decrease due to the greater heterogeneity of the stress distribution across the sections, which is also taken into account when determining the design resistances.
Load duration coefficient t dl<С 1- Он учитывает, что древесина без пороков может неограниченно долго выдерживать лишь около половины той нагрузки, которую она выдерживает при кратковременном нагружении в процессе испытаний. Следовательно, ее длительное R in resistance I am almost ^^ half the short-term /tg.
The quality of wood naturally affects the values of its calculated resistances. 1st grade wood - with the least defects, has the highest calculated resistance. The calculated resistances of wood of the 2nd and 3rd grades are respectively lower. For example, the calculated compression resistance of pine and spruce wood of the 2nd grade is obtained from the expression
The calculated resistances of pine and spruce wood to compression, tension, bending, chipping and crushing are given in the appendix. 6.
Working conditions coefficients T The design resistance of wood takes into account the conditions in which wooden structures are manufactured and operated. Breed coefficient T" takes into account the different strength of wood of different species, different from the strength of pine and spruce wood. The load factor t„ takes into account the short duration of wind and installation loads. When crushed tn= 1.4, for other types of voltages t n = 1.2. The section height coefficient when bending wood of glued-wood beams with a section height of more than 50 cm /72b decreases from 1 to 0.8, and even more with a section height of 120 cm. The thickness coefficient of the layers of glued-wood elements takes into account the increase in their strength in compression and bending as the thickness of the boards being glued decreases, as a result of which the homogeneity of the structure of the glued wood increases. Its values are within 0.95. 1.1. The bending coefficient m rH takes into account the additional bending stresses that arise when the boards bend during the production of bent glued-wood elements. It depends on the ratio of the bending radius to the thickness of the r/b boards and has a value of 1.0. 0.8 when this ratio increases from 150 to 250. Temperature coefficient m t takes into account the reduction in the strength of wood in structures operating at temperatures from +35 to +50 °C. It decreases from 1.0 to 0.8. Humidity coefficient t ow takes into account the decrease in the strength of wood in structures operating in a humid environment. When indoor air humidity is from 75 to 95%, tvl = 0.9. Outdoors in dry and normal areas t ow = 0.85. With constant hydration and in water t ow = 0.75. Stress concentration factor t k = 0.8 takes into account the local reduction in wood strength in areas with cut-ins and holes during tension. The load duration coefficient t dl = 0.8 takes into account the decrease in wood strength as a result of the fact that long-term loads sometimes account for more than 80% of the total loads acting on the structure.
Modulus of elasticity of wood, determined in short-term laboratory tests, E cr= 15-10 3 MPa. When taking into account deformations under long-term loading, when calculating by deflections £=10 4 MPa (Appendix 7).
The standard and calculated resistances of building plywood were obtained using the same methods as for wood. In this case, its sheet shape and an odd number of layers with mutually perpendicular fiber directions were taken into account. Therefore, the strength of plywood in these two directions is different and along the outer fibers it is slightly higher.
The most widely used in structures is seven-layer plywood of the FSF brand. Its calculated resistances along the fibers of the outer veneers are equal to: tensile # f. p = 14 MPa, compression #f. c = 12 MPa, bending out of plane /? f.„ = 16 MPa, shearing in plane # f. sk = 0.8 MPa and shear /? f. avg - 6 MPa. Across the fibers of the outer veneers, these values are respectively equal to: tensile I f_r= 9 MPa, compression # f. s = 8.5 MPa, bending # F.i = 6.5 MPa, shearing R$. CK= 0.8 MPa, cut # f. av = = 6 MPa. The moduli of elasticity and shear along the outer fibers are equal, respectively, Ё f = 9-10 3 MPa and b f = 750 MPa and across the outer fibers £ f = 6-10 3 MPa and G$ = 750 MPa.
Calculation based on limit states
Limit states of structures according to the degree of possible consequences are divided as follows:
In accordance with the calculation method based on limit states, instead of the previously used single safety factor (according to the permissible stress method), several independent coefficients are used, taking into account the operating characteristics of the structure, each of which has a certain contribution to ensuring the reliability of the structure and guarantees against the occurrence of a limit state.
The limit state method, developed in the USSR and based on research led by Professor N. S. Streletsky, was introduced by building codes and regulations in 1955 and in the Russian Federation is the main method for calculating building structures.
This method is characterized by a complete assessment of the load-bearing capacity and reliability of structures due to taking into account:
Calculation of a structure using the limit state method must guarantee the non-occurrence of a limit state.
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limit state- The condition of a structure in which it loses the ability to maintain one of its fire protection functions. [GOST R 53310 2009] [GOST R 53310 2013] limit state The state of an object in which its further operation is unacceptable or ... Technical Translator's Guide
In structural mechanics, the state of a structure (structure) in which it ceases to meet operational requirements. The limit state method is the main one in the Russian Federation when calculating building structures... Big Encyclopedic Dictionary
Limit state- 2.5. Limiting state Limiting state The state of an object in which its further operation is unacceptable or impractical, or restoring its operational state is impossible or impractical Source: GOST 27.002 89:... ...
- (in structural mechanics), the state of a structure (structure) in which it ceases to meet operational requirements. The limit state method is the main one in Russia when calculating building structures. * * * LIMITAL… … encyclopedic Dictionary
Limit state of AL- 2.2. Limit state AL is the state of a ladder truck in which its further operation is unacceptable or impractical, or restoration of its working condition is impossible or impractical. Source … Dictionary-reference book of terms of normative and technical documentation
limit state- ribinė būsena statusas T sritis Standartizacija ir metrologija apibrėžtis Objekto būsena, kai tolesnis jo naudojimas neleistinas arba netikslingas. atitikmenys: engl. limiting state vok. Grenzzustand, m rus. limit state, n pranc. état… … Penkiakalbis aiškinamasis metrologijos terminų žodynas
limit state- ribinė būsena statusas T sritis fizika atitikmenys: engl. limiting state vok. Grenzzustand, m rus. limit state, n pranc. état limite, m … Fizikos terminų žodynas
The condition of the product, in which its further use for its intended purpose is unacceptable or impractical, or restoring its serviceable or operational condition is impossible or impractical... Big Encyclopedic Polytechnic Dictionary
Limit state- – the state of an object in which its further operation is unacceptable or impractical, or restoration of its working condition is impossible or impractical. GOST 27.002 89 ... Commercial power generation. Dictionary-reference book
limit state- the state of an object in which its further operation must be terminated due to an irreparable violation of safety requirements, or an irreparable decrease in the level of performance, or an unacceptable decrease in operating efficiency ... Polytechnic terminological explanatory dictionary
geometrically:
array - a structure in which all dimensions are of the same order;
timber - an element in which two sizes are many times smaller than the third;
slab - an element in which one size is many times smaller than the other two;
rod systems are geometrically unchangeable systems of rods connected to each other hingedly or rigidly. These include construction trusses (beam or cantilever)
from a static point of view:
statically determinable - structures in which forces or stresses can be determined only from equilibrium equations;
statically indeterminate – structures for which static equations alone are not enough;
according to materials used: steel, wood, reinforced concrete, concrete, stone (brick);
from the point of view of the stress-strain state(i.e., internal forces, stresses and deformations arising in structures under the influence of external load): simplest, simple, complex.
Reliability– the ability of a structure to maintain its performance qualities throughout the entire service life of the structure, as well as during its transportation from factories to the construction site and at the time of installation.
Durability- the maximum service life of buildings and structures, during which they maintain the required performance qualities.
Industrialism –
Unification- limiting the number of standard sizes of building parameters and standard products, taking into account their interchangeability.
Limit These are the conditions for a building, structure, as well as the foundation or individual structures, in which they cease to satisfy the specified operational requirements, as well as the requirements specified during their construction. Limit states of structures (buildings) are divided into two groups:
Towards limit states first group include: general loss of shape stability; loss of position stability; brittle, ductile or other type of failure; destruction under the combined influence of force factors and unfavorable influences of the external environment, etc.
Towards limit states second group These include conditions that impede the normal operation of structures (buildings) or reduce their durability due to the occurrence of unacceptable movements (deflections, settlement, rotation angles), vibrations and cracks;
The essence of the calculation: The method of calculating building structures using limit states aims to prevent the occurrence of any of the limit states that may occur in a structure (building).
When calculating the limit states of the first and second groups, as already noted, the main strength indicator of the material is its resistance, which (along with other characteristics) can take standard and design values:
R n - standard material resistance , represents main parameter of material resistance external influences and is established by the relevant chapters of building codes (taking into account control conditions and statistical variability of resistances). The physical meaning of the standard resistance R n is control or rejection characteristic of material resistance with a security of at least 0.95%;
R - design material resistance , is determined by the formula:
γ m - material safety factor , takes into account possible deviations of the material resistance in an unfavorable direction from the standard values, γ m > 1.
γ c - working conditions factor , takes into account the features of the operation of materials, elements and connections of structures, as well as buildings and structures in general, if these features are of a systematic nature, but are not reflected in the calculations directly (taking into account temperature, humidity, aggressiveness of the environment, approximation of design schemes, etc.);
N ; N ; γ f – , takes into account possible deviations of loads in an unfavorable (more or less) direction from their standard values; γ n - reliability coefficient for liability , takes into account the economic, social and environmental consequences that may arise from accidents.
N s eg And service resistanceR ser are considered design values for calculations based on limit states of the second group.When calculating for the first group of limit states, which are related to ensuring the load-bearing capacity of structures (buildings), accept calculated values: design loads N and calculated material resistances R.
Performance of materials for load-bearing structures under load and their design characteristics.
Steel.
three sections of steel work: 1 - section of elastic work; 2 - area of plastic work; 3 - area of elastoplastic work.
standard and design resistances required for structural calculations are taken based on the yield strength
R up - standard resistance of steel, taken according to the yield strength; R y - design resistance of steel, taken according to the yield strength;
R ip - standard resistance of steel, taken according to temporary resistance; R and is the design resistance of steel, taken from the temporary resistance;
Wood
Wooden structures are made from coniferous and hardwood timber, which are divided into round - logs, sawn - lumber and construction plywood.
The work of wood depends on the type of load (tension, compression, bending, crushing, chipping), the direction of action of the force in relation to the direction of the wood fibers, the duration of the load, the type of wood and other factors. The presence of wood defects (cross-layers, knots, cracks, etc.) has a significant impact on its strength. Wood is divided into three grades, the highest quality wood is classified as first grade. 
Diagram of the work of wood along the grain: 1 - in tension; 2 - for compression; R^p is the temporary resistance of pure wood; c - normal stresses; e - relative deformations
Reinforced concrete. Reinforced concrete is complex building material, in which concrete and steel reinforcement work together. To understand the operation of reinforced concrete and determine the characteristics necessary for the calculation, we will consider each of its constituent materials.
The main indicator of concrete quality is the compressive strength class, which is established based on tests of concrete cubes at the age of 28 days. 
Diagram of stress and deformation of concrete: 1 - elastic deformation zone; 2- zone of plastic deformation; σ bu - temporary compressive strength of concrete; σ btu - temporary tensile strength of concrete; Eb - elastic modulus of concrete;
Fittings. Reinforcement in reinforced concrete structures is accepted depending on the type of structure, the presence of prestress, as well as the operating conditions of buildings and structures
According to the nature of the work of the reinforcement, reflected in the diagram, three types of reinforcing steels are distinguished: 1. Steel with a pronounced yield plateau (mild reinforcing steel). The yield strength of such steels is σ y 2 - Reinforcing steel with a conditional yield strength is σ 0.2. The yield strength of such steels is taken to be equal to the stress at which the residual deformation of the sample is 0.2%. 3 - Reinforcing steel with linear dependenceσ 0.2 - almost to the point of rupture. For such steels, the yield strength is set as for steels of the second type.
Tensile diagrams of reinforcing steels:
.
Masonry. The strength of masonry depends mainly on the strength of the stone (brick) and mortar.
Diagram of deformation of masonry during compression: 1 - elastic deformation zone; 2- zone of plastic deformation; R and - temporary resistance (average compressive strength of masonry); tan φ 0 = E 0 - elastic modulus (initial deformation modulus)
When calculating using this method, the structure is considered in its design limit state. The design limit state is taken to be the state of the structure in which it ceases to meet the operational requirements imposed on it, i.e., it either loses the ability to resist external influences, or receives unacceptable deformation or local damage.
For steel structures, two design limit states are established:
The first calculated limit state is expressed by the inequality
where N is the design force in the structure from the sum of the effects of the design loads P in the most unfavorable combination;
Ф is the load-bearing capacity of the structure, which is a function of the geometric dimensions of the structure, the design resistance of the material R and the operating conditions coefficient m.
The design loads P for which the structure is calculated (based on the limit state) are taken to be slightly higher than the normative ones. The design load is defined as the product of the standard load by the overload factor n (greater than unity), taking into account the danger of exceeding the load compared to its standard value due to possible load variability:
The values of coefficients p are given in the table Standard and design loads, overload factors.
Thus, structures are considered under the influence of design loads rather than operational (standard) loads. From the influence of design loads in a structure, design forces (axial force N or moment M) are determined, which are found according to the general rules of resistance of materials and structural mechanics.
Right side of the main equation (1.I)- load-bearing capacity of the structure F - depends on the maximum resistance of the material to force influences, characterized by the mechanical properties of the material and called the standard resistance R n, as well as on the geometric characteristics of the section (sectional area F, moment of resistance W, etc.).
For building steel, the standard resistance is assumed to be equal to the yield strength,
(for the most common building steel grade St. 3 σ t = 2,400 kg/cm 2).
The design resistance of steel R is taken to be a voltage equal to the standard resistance multiplied by the uniformity coefficient k (less than unity), taking into account the risk of a decrease in the resistance of the material compared to its standard value due to variability in the mechanical properties of the material
For ordinary low-carbon steels k = 0.9, and for high-quality steels (low-alloy) k = 0.85.
Thus, the calculated resistance R- this is a stress equal to the lowest possible value of the yield strength of the material, which is accepted for the structure as the limiting value.
Thus, the main design equation (1.I) will have the following form:
where N and M are the calculated axial forces or moments from the calculated loads (taking into account load factors); F nt - net cross-sectional area (excluding holes); W nt is the moment of resistance of the net section (minus the holes);
where F br and W br are the area and moment of resistance of the gross section (without deducting holes); φ and φ b are coefficients that reduce the design resistance to values that ensure stable equilibrium.
Usually, when calculating the intended structure, the cross-section of the element is first selected and then the stress from the design forces is checked, which should not exceed the design resistance multiplied by the operating conditions coefficient.
Therefore, along with formulas of the form (4.I) and (5.I), we will write these formulas in working form in terms of calculated stresses, for example:
where σ is the design stress in the structure (based on the design loads).
It is more correct to write the coefficients φ and φ b in formulas (8.I) and (9.I) on the right side of the inequality as coefficients that reduce the calculated resistance to critical stresses. And only for the sake of convenience of calculations and comparison of results, they are written in the denominator of the left side of these formulas.
* The values of standard resistances and uniformity coefficients are given in the “Building Norms and Rules” (SNiP), as well as in the “Norms and Technical Conditions for the Design of Steel Structures” (NiTU 121-55).
"Design of steel structures"
K.K. Mukhanov
There are several categories of voltages: main, local, additional and internal. Fundamental stresses are stresses that develop inside the body as a result of balancing the effects of external loads; they are taken into account in the calculation. When the power flow is unevenly distributed over the cross-section, caused, for example, by a sharp change in the cross-section or the presence of a hole, a local stress concentration occurs. However, in plastic materials, which include construction steel,…
When calculating the permissible stresses, the structure is considered in its operating condition under the influence of loads allowed during normal operation of the structure, i.e., standard loads. The condition for the strength of the structure is that the stresses in the structure from standard loads do not exceed the permissible stresses established by the standards, which represent a certain part of the maximum stress of the material accepted for building steel...
