Calculation of structures on the first group of limit states. Preparing for checks on limit states The first limit state of strength

by geometric sign:

an array is a design in which all sizes of one order;

bar is an element in which two sizes are many times less than the third;

the stove is an element in which one size is many times less than two others;

the rod systems are geometrically immutable system of rods interconnected by articulated or rigidly. These include building farms (beam or console)

from the point of view of static:

statically defined - structures, efforts or voltages in which can be determined only from equations of equilibrium;

statically indefinable - structures for which some static equations are not enough;

according to the materials used: steel, wooden, reinforced concrete, concrete, stone (brick);

from the point of view of a stress-strain state (i.e. arising in the structures of internal efforts, stresses and deformations under the action of external load): the simplest, simple, complex.

1. Requirements for carrying structures:

Reliability - the ability of the structure to maintain its operational qualities during the entire service life of the structure, as well as during its transportation from plants to the construction site and at the time of installation.

Durability - The deadline for the service life of buildings and structures during which they retain the required operational qualities.

Industriality –

Unification - limit the number of sizes of the parameters of buildings and typical products, taking into account their interchangeability.

1. The physical meaning of the limit states of the structures. Examples of limit states of the first and second groups. The essence of the calculation of the limit states.

Limit These states for the building, structures, as well as bases or individual structures, under which they cease to meet the specified operational requirements, as well as the requirements specified in their construction are called. The limit states of structures (buildings) are divided into two groups:

To limit states first group include: the overall loss of stability of the form; loss of sustainability of the situation; fragile, viscous or other nature of destruction; Destruction under the joint impact of power factors and adverse effects of the external environment, etc.

To limit states second group States related to the normal operation of structures (buildings) or reduce their durability due to the appearance of unacceptable movements (deflection, precipitate, rotation angles), oscillations and cracks;

The essence of the calculation:the method of calculating building structures on the limit states is to prevent any of the limit states that may arise in the design (building).

1. The structure and content of the main estimated formulas in the calculation of the limit states of the first and second groups.

When calculating the limit states of the first and second groups as the main strength indicator of the material, as already noted, its resistance is established, which (along with other characteristics) can take regulatory and calculated values:

R. n. - regulatory resistance of material , represents the main parameter of the resistance of materials External influences and is established by the relevant heads of construction norms (taking into account the conditions for the control and statistical variability of resistance). The physical meaning of the regulatory resistance R n is control or brave characteristic of material resistancewith the security of at least 0.95%;

R. - estimated material resistance determined by the formula:

γ m. - reliability coefficient by material , it takes into account possible deviations of the material resistance in the unfavorable side of the regulatory values, γ M\u003e 1.

γ c. - coefficient of working conditions , takes into account the features of the work of materials, elements and compounds of structures, as well as buildings and structures as a whole, if these features are systematic, but are not reflected in the calculations directly (taking into account temperature, humidity, aggressiveness of the medium, the approximity of the calculated schemes, etc.);

N. ; N. ; γ f. – , takes into account possible deviations of the loads into an unfavorable (greater or smaller) side from their regulatory values; γ n. - reliability coefficient responsibility , takes into account the economic, social and environmental consequences that may arise as a result of accidents.

N. s. ech. and service resistanceR. ser. are considered calculated for settlements by the limit states of the second group.

When calculating the first group of limit statesrelated to the provision of supporting ability of structures (buildings), accept Estimated values: estimated loads N I. estimated material resistance R.

The work of materials for carrying structures under load and their calculated characteristics.

Steel.

three parts of the work: 1 - a plot of elastic work; 2 - plot of plastic work; 3 - a plot of elastoplastic work.

regulatory and calculated resistances necessary for calculating structures are accepted by the yield strength

R pack - the standard resistance of steel, accepted by the yield strength; R y is the calculated steel resistance, taken over the yield strength;

R IP is the standard resistance of steel, adopted by temporary resistance; R and - the calculated steel resistance, taken by temporary resistance;

Wood

Wooden designs are performed from coniferous and hardwood timber, which are divided into round-logs, sawn - sawn timber and construction fane.

The work of wood depends on the type of loading (stretching, compression, bending, crumpled, rocking), the direction of action in relation to the direction of the fibers of the wood, the duration of the application of the load, the wood breed and other factors. The presence of vices of wood (space, bitch, cracks, etc.) has a significant impact on its strength. Wood is divided into three varieties, the highest quality wood is assigned to the first class.

Wood work diagram along the fibers: 1 - on stretching; 2 - on compression; I ^ p - temporary resistance of pure wood; C - normal stresses; E - relative deformations

Reinforced concrete. Reinforced concrete is a complex building material in which concrete and steel fittings work together. To understand the work of reinforced concrete and determining the characteristics necessary for the calculation, consider each of the materials that are part of it.

The main indicator of the quality of concrete is a compression strength class, which is established on the basis of the tests of concrete cubes at the age of 28 days.

The diagram of stresses and deformations of concrete: 1 - zone of elastic deformations; 2- zone of plastic deformations; σ bu - temporary resistance to concrete compression; σ btu is the temporary resistance of concrete stretching; EB - module of elasticity of concrete;

Armature. Armature in reinforced concrete structures is made depending on the type of construction, pre-voltage, as well as the conditions of operation of buildings and structures

According to the nature of the work of the reinforcement reflected in the diagram, there are three types of reinforcement steels: 1. Steel with a pronounced flow rate (soft reinforcement steel). The yield strength of such steels -σ in 2 - reinforcement steel with the conditional yield strength - σ 0.2. The yield strength of such steels is taken equal to the voltage, in which the residual deformations of the sample are 0.2%. 3 - reinforcement steel with a linear dependence σ 0.2 - almost to break. For these steels, the yield strength is set as for steels of the second type.

Stretching charts of reinforcement steels:

.

Masonry. Stone masonry strength depends mainly from the strength of the stone (brick) and the solution.

Chart of strain deformations in compression: 1 - zone of elastic deformations; 2- zone of plastic deformations; R and - temporary resistance (average tensile strength compression of masonry); TG φ 0 \u003d E 0 - modulus of elasticity (initial deformation module)

20.12.2018

The calculation of structures on the limit states is a clearly established two groups of limiting states of the structures that must be prevented using the system of calculation coefficients; Their administration ensures that the limit states will not occur with adverse combinations of loads and with the smallest values \u200b\u200bof the strength characteristics of the materials. Upon the occurrence of limit states, the design cease to meet the requirements of exploitation - they are destroyed or losing stability under the action of external loads and impacts, or inadmissible movements or cracks are developing. In order to more adequate and economical calculation, the limit states are divided into two fundamentally different groups - more responsible for the first (structures are destroyed when the states of this group) and less responsible second (designs cease to meet the requirements of normal operation, but they cannot be repaired). Such an approach made it possible to differentiate loads and strength indicators of materials: in order to protect the limit states in the calculations on the first group of loads, several overestimated, and the strength characteristics of materials were accepted compared with the calculations on the second group. This avoids the onset of limit states I group.

In a more responsible, the first group includes limit states on the bearing ability, in the second - on suitability for normal operation. The limit states of the first group include a fragile, viscous or other destruction; loss of stability of the form of construction or its position; fatigue destruction; Destruction from the joint impact of power factors and adverse effects of the external environment (the aggressiveness of the medium, alternate freezing and thawing, etc.). Perform calculation by strength, taking into account in the necessary cases of the design of the design before the destruction; Calculation of tipping and sliding of retaining walls, high-centerly loaded high foundations; Calculation of alarmlight or underground reservoirs; calculation on the endurance of structures under the influence of repeated moving mobile or pulsating load; Calculation of stability of thin-walled structures, etc. Recently, a new calculation was added to the calculations on the first group to the progressive collapse of high buildings under the influences not provided for by the conditions of normal operation.

The limit states of the second group include the width and long-term disclosure of cracks (if, under the operating conditions, they are permissible), unacceptable movements of structures (deflection, rotation angles, skew angles and amplitude of oscillations). Calculations on the limit states of structures and their elements are performed for the stages of manufacturing, transportation, installation and operation. Thus, for the usual bending element, the limit states of the first groups will exhaust the strength (destruction) in normal and inclined sections; The limit states of the Group II are the formation and disclosure of cracks, the deflection (Fig. 3.12). In this case, the permissible width of the splitting of cracks with a long-acting load is 0.3 mm, since with this width, the cracks in the growing crystalline coherent in the cement stone occurs. Since each tenth fraction of a millimeter permissible crack disclosure significantly affects the consumption of reinforcement in structures with conventional reinforcement, then an increase in the permissible width of the cracking of cracks even by 0.1 mm plays a very large role in the reservoir economy.

The factors belonging to the calculation of the limit states (calculated factors) are loads on the designs, their size, and mechanical characteristics of concrete and reinforcement. They are inconstant, and for them is characterized by the spread of values \u200b\u200b(statistical variability). In the calculations, the variability of loads and mechanical characteristics of materials, as well as non-station factors, and various working conditions of concrete and reinforcement, manufacturing and operation of elements of buildings and structures are taken into account. All settlement factors and calculated coefficients are normalized in the respective joint ventures.

The limit states require further deep research: so, in the calculations, normal and inclined cross sections are separated in one element (a single approach is desirable), the unrealistic destruction mechanism in the inclined section is considered, the secondary effects in the inclined crack are not taken into account (the ongoing effect of working reinforcement and the power of the engagement in the inclined Crack (see Fig. 3.12, etc.)).

The first calculation factor is the loads that are divided into regulatory and calculated, and the duration of action - for permanent and temporary; The latter can be short-lived and long. Separately consider more rarely manifested special loads. Continuous loads include its own weight of the structures, weight and pressure of the soil, strength of pre-voltage of reinforcement. Long loads are the weight of stationary equipment on floors, gas pressure, liquids, bulk bodies in tanks, weight of content in warehouses, libraries, and pr.; mounted part of the temporary load in residential buildings, in service and household premises; long temperature technological impacts from equipment; Snow loads for III ... VI climatic regions with coefficients of 0.3 ... 0.6. These values \u200b\u200bof loads are part of their complete value, they are entered into account taking into account the effect of the duration of the operation of the loads on the movement, deformation, the formation of cracks. The short-term loads include part of the load on the overlap of residential and public buildings; Weight of people, details, materials in equipment service and repair areas; loads arising from the manufacture, transportation and installation of structural elements; Snow and wind loads; Temperature climatic effects.

Special loads include seismic and explosive effects; loads caused by the malfunction of the equipment and a violation of the process; uneven deformations of the base. Regulatory loads are set by the standards for a predetermined probability of exceeding average values \u200b\u200bor by nominal values. Regulatory permanent loads are taken by the design values \u200b\u200bof the geometric and structural parameters of the elements and according to the average values \u200b\u200bof the density of the material. Regulatory temporary technological and installation loads are specified by the highest values \u200b\u200bprovided for normal operation; Snow and wind - on average of annual adverse values \u200b\u200bor by adverse values \u200b\u200bcorresponding to a specific average period of their repetitions. The values \u200b\u200bof the calculated loads in the calculation of structures according to the I group of limit states determine the multiplication of the regulatory load on the reliability coefficient by the UF load as a rule, Uf\u003e 1 (this is one of the factors for preventing the limit state). Coefficient uf \u003d 1.1 for its own weight of reinforced concrete structures; uf \u003d 1,2 for its own weight of concrete structures on light aggregates; uf \u003d 1.3 for various temporary loads; But Uf \u003d 0.9 for the weight of the structures in cases where the reduction in the mass deteriorates the conditions of the structure - in calculating the stability against the ascent, tipping and slipping. When calculating the less dangerous II group of limit states Uf \u003d 1.

Since the simultaneous action of all loads with maximum values \u200b\u200bis almost incredible, for greater reliability and economy of design, they are calculated for different combinations of loads: they can be the main (they include constant, long-term and short-term loads), and special (including constant, long-term, possible short-term short-term And one of the special loads). In the main combinations, when taking into account at least two temporary loads, their calculated values \u200b\u200b(or their corresponding efforts) are multiplied by the coefficients of the combination: for long loads W1 \u003d 0.95; For short-term W2 \u003d 0.9; At one time load W1 \u003d W2 \u003d 1. At three and more short-term loads, their calculated values \u200b\u200bare multiplied by combinations coefficients: W2 \u003d 1 for the first time of the importance of short-term load; w2 \u003d 0.8 for the second; w2 \u003d 0.6 for the third and all others. In special combinations of loads, W2 \u003d 0.95 for long-term loads, W2 \u003d 0.8 for short-term, except for designs of structures in seismic areas is taken. For the purpose of economical design, given the degree of probability of the simultaneous operation of loads, when calculating columns, walls, the foundations of multi-storey buildings Temporary loads on overlappings is allowed to reduce multiplication by coefficients: for residential buildings, hostels, office space, etc. With a cargo area A\u003e 9 m2

For halls read, meetings, trading, etc. Plots of service and repair of equipment in industrial premises under cargo space A\u003e 36 m2

where N is the total number of overlaps, the temporary loads from which are taken into account when calculating the section under consideration.

The calculations take into account the degree of responsibility of buildings and structures; It depends on the degree of material and social damage in achieving the designs of limit states. Therefore, when designing, the coefficient of reliability is taken into account on the appointment of un, which depends on the class of responsibility of buildings or structures. The reliability factor for the purpose is divided by the limit values \u200b\u200bof the carrier ability, the calculated resistance values, the limit values \u200b\u200bof deformations, cracking, and multiply the calculated values \u200b\u200bof loads, efforts and other effects on it. According to the degree of responsibility of the building and structures are divided into three classes: I class. yn \u003d 1 - buildings and structures having high national economic or social significance; main buildings of the TPP, NPP; television towers; indoor sports facilities with tribunes; buildings of theaters, cinemas, etc.; Class II yn \u003d 0.95 - less significant buildings and structures that are not included in classes I and III; III class yn \u003d 0.9 - warehouses, single-storey residential buildings, temporary buildings and structures.

For more economical and reasonable design of reinforced concrete structures, three categories of crack resistance (to resistance to the formation of cracks in stage I or resistance to the disclosure of cracks in stage II of a stress-strain state). Requirements for the formation and disclosure of normal and inclined to the longitudinal axis of the element of cracks depend on the type of fittings used and operating conditions. At the first category, cracks are not allowed; With the second category, a short-width of a short-term cracking of cracks is allowed under the condition of their subsequent reliable closure; For the third category, a short-width and long-term disclosure of cracks are allowed. The disclosure of cracks includes the disclosure of cracks under the action of permanent, long and short-term loads; To long-term - disclosure of cracks under the action of only constant and long loads.

The limiting width of the disclosure of the ACRC cracks, in which the normal operation of buildings is ensured, the corrosion resistance of the reinforcement and the durability of the structure, depending on the category of crack resistance requirements should not exceed 0.1 ... 0.4 mm (see Table 3.1).

Pre-stressed elements under pressure from liquid or gases (tanks, pressure pipes, etc.) with a fully stretched section with a rod or wire reinforcement, as well as with a partially compressed section with wire reinforcement with a diameter of 3 mm and less, must meet the requirements of the first categories. Other pre-intense elements depending on the working conditions of the structure and the type of reinforcement must meet the requirements of the second or third category. Designs without prior voltage with the Class A400 rod fittings, the A500 must meet the requirements of the third category (see Table 3.1).

The procedure for accounting the loads when calculating structures on crack resistance depends on the category of requirements (Table 3.2). In order to prevent pulling the strainable reinforcement from concrete under load and sudden destruction of structures, at the ends of the elements within the length of the stress transmission zone from the reinforcement on concrete, the formation of cracks is not allowed under the joint action of all loads (except for special) into account with the coefficient Uf \u003d 1 . Cracks arising in the manufacture, transportation and installation in the zone, which subsequently under load will be compressed, lead to a decrease in the force of formation of cracks in the zone stretched during operation, an increase in the width of the disclosure and growth of the deflection. The influence of these cracks is taken into account in the calculations. The most important strength calculations for the design or building are based on the III stage of the stress-strain state.

Constructions have the necessary strength, if the efforts on the calculated loads (bending torque, longitudinal or transverse force, etc.) do not exceed the efforts perceived by section with the calculated resistance of materials, taking into account the coefficients of working conditions. The magnitude of the effort from the calculated loads is influenced by regulatory loads, reliability coefficients, calculation schemes, and others. The value of the force perceived by the cross section of the calculated element depends on its shape, the size of the section, the strength of the RBN concrete, RSN fittings, the reliability coefficients based on YS and UB and WB and coefficients of working conditions of concrete and WII and USI fittings. Strength conditions are always expressed in inequalities, and the left part (external impact) cannot significantly exceed the right-hand side (internal efforts); It is recommended to allow no more than 5% excess, otherwise the project's uneconomical increases.

The limit states of the second group. The calculation of the formation of cracks, normal and inclined to the longitudinal axis of the element is performed to test the crack resistance of the elements to which the requirements of the first category are presented (if the formation of cracks is unacceptable). This calculation is also produced for elements to the crack resistance of which the requirements of the second and third category are presented to establish whether cracks appear, and if they appear to go to the calculation of their disclosure.

Normal to the longitudinal axis of the crack do not appear if the bending moment from external loads does not exceed the moment of domestic forces

Inclined to the longitudinal axis of the element of the crack (in the pre-air zone) do not appear if the main tensile stresses in the concrete do not exceed the calculated values. When calculating the disclosure of cracks, normal and inclined to the longitudinal axis, determine the width of the disclosure of cracks at the level of stretched fittings so that it is no more limit width of the disclosure set by the rules

When calculating displacements (defditions), define the deflection of the elements from the loads, taking into account the duration of their operation of the FQC, so that it does not exceed the allowable deflection of FCRC, ULT. Limit deflection limit the aesthetic and psychological requirements (so that it is visually noticeable), technological requirements (to ensure the normal operation of various technological installations, etc.), constructive requirements (taking into account the influence of neighboring elements that limit deformations), physiological requirements, etc. (Table 3.3). The limit deficits of pre-stressed elements established by the aesthetic and psychological requirements, it is advisable to increase the height of the witch due to the pregnancy (construction lift), if it is not limited to technological or constructive requirements. When calculating the deflection in case of their restriction by technological or constructive requirements, the calculation is based on permanent, long and short-term loads; With their restriction, the aesthetic requirements of the design are calculated on the action of constant and long loads. The limit deflection of consoles, related to the departure of the console, increase by 2 times. The norms set limit defignments for physiological requirements. There should also be calculated by the calculation for stair marches, platforms, etc., so that additional deflection from a briefly active focused load of 1000 H with the most disadvantaged scheme of its application did not exceed 0.7 mm.

In the third stage of the stress-deformed state in sections, normal to the longitudinal axis of bend and echocently compressed with relatively large eccentricity elements, with a two-digit voltage support, the same flexible stress-strain state is observed (Fig. 3.13). The efforts perceived by the cross section, normal to the longitudinal axis of the element, are determined by the calculated resistance of the materials, taking into account the coefficients of working conditions. At the same time, it is believed that the concrete stretched zone does not work (OBT \u003d O); The voltage in the concise zone concrete is equal to RB with a rectangular voltage range; voltages in longitudinal stretched fittings are RS; Longitudinal fittings in a compressed section zone experiences RSC voltage.

In terms of strength, the moment of external forces should not be more than the moment perceived by internal efforts in compressed concrete and in the stretched fittings. The condition of strength relative to the axis passing through the center of gravity of the stretched fittings

where M is the moment of external forces on the calculated loads (in the extracently compressed elements - the moment of the outer longitudinal force relative to the same axis), M \u003d Ne (E is the distance from the force n to the center of gravity of the cross section of the stretched fittings); SB is the static moment of the section of the concrete section of a compressed zone relative to the same axis; ZS is the distance between the centers of gravity stretched and compressed fittings.

The voltage in the strained fittings, located in a compressed area of \u200b\u200bthe load zone, OSC is determined by work. In the elements without pre-voltage OSC \u003d RSC. The height of the compressed zone x for sections operating on occasion 1, when extrest resistances were achieved in stretched fittings and compressed concrete, determined from the equilibrium equation of limiting efforts

where AB is the cross-sectional area of \u200b\u200bthe concise zone; For n take a minus sign with an off-centrular compression, a sign + with tension, n \u003d 0 when bending.

The height of the compressed zone x for sections, working on occasion 2, when the destruction occurs according to the compressed concrete of the fragile, and the voltages in the stretched fittings do not reach the limit value, are also determined from equation (3.12). HO In this case, the RS calculated resistance is replaced with an OS voltage.< Rs. Опытами установлено, что напряжение os зависит от относительной высоты сжатой зоны e = x/ho. Его можно определить по эмпирической формуле

where CO \u003d XO / HO is the relative height of the compressed zone at a voltage in the OS \u003d OSP fittings (oS \u003d O in elements without prior voltage).

When OS \u003d OSP (or when OS \u003d 0), the actual relative height of the compressed zone E \u003d 1, and CO can be considered as the completeness coefficient of the actual stage of stress in concrete when it is replaced by its conditional rectangular plug; In this case, the force of concrete concise zone Nb \u003d W * Ho * Rb (see Fig. 3.13). The value of the CO is called the characteristic of the deformation properties of concrete compressed zone. The boundary relative height of the compressed zone plays a big role in the calculations of the strength, since it limits the optimal case of destruction, when the stretched and compressed zone simultaneously exhaust the strength. The boundary relative height of the compressed ER \u003d XR / H0 zone, in which the tensile voltages in the reinforcement begin to reach the limit values \u200b\u200bof the RS, are found from the ER \u003d 0.8 / (1 + RS / 700), or in Table. 3.2. In general, the calculation of the strength of the cross section, normal to the longitudinal axis, is performed depending on the value of the relative height of the compressed zone. If E.< eR, высоту сжатой зоны определяют из уравнения (3.12), если же e > ER, strength is calculated. The voltage of high-strength OS fittings in the limiting state may exceed the conditional yield strength. According to the experiments, this may occur if e< eR. Превышение оказывается тем большим, чем меньше значение e, Опытная зависимость имеет вид

In calculating the strength of the cross sections, the estimated resistance of the RS reinforcement is multiplied by the coefficient of the operating conditions

where n is the coefficient taken equal: for the assembly of class A600 - 1.2; A800, BP1200, BP1500, K1400, K1500 - 1.15; A1000 - 1.1. 4 is defined at ys6 \u003d 1.

The norms set the limit percentage of reinforcement: the cross-sectional area of \u200b\u200bthe longitudinal stretched fittings, as well as compressed, if it is required by calculation, as a percentage of the concrete section area, US \u003d AS / BH0 takes no less: 0.1% - for bends, extracently stretched elements and Essentrenly compressed elements at flexibility L0 / I< 17 (для прямоугольных сечений l0/h < 5); 0,25 % - для внецентренно сжатых элементов при гибкости l0/i > 87 (for rectangular sectionsL0 / H\u003e 25); For intermediate values \u200b\u200bof the flexibility of elements, the US value is determined but interpolations. The maximum percentage of reinforced elements with single reinforcement (in a stretched zone) is determined from the equilibrium equation of limiting efforts with a height of a compressed zone equal to the boundary. For rectangular cross section

The limit percentage of reinforcement, taking into account the ER value, for precompanied elements

For elements without prior voltage

The maximum percentage of reinforcement decreases with an increase in the class of fittings. The cross sections of the bending elements are considered converted if their percentage of reinforcement is higher than the limit. The minimum percentage of reinforcement is necessary to perceive not taken into account by calculating shrinking, temperature and other efforts. Usually umin \u003d 0.05% for longitudinal stretched fittings of bending elements of rectangular sections. Stone and arm-via structures are calculated similarly to reinforced concrete structures in two groups of limit states. The calculation according to the I group should prevent the design from the destruction (calculation of the bearing capacity), on the loss of stability of the form or position, fatigue destruction, destruction during the joint action of the power factors and the influence of the external environment (freezing, aggression, etc.). The calculation of the II group is aimed at preventing the structure from unacceptable deformations, excessive disclosure of cracks, detachment of masonry cladding. This calculation is performed when cracks are not allowed or limited to the disclosure (tank cladding, echocently compressed walls and pillars for large eccentricity, etc.), or limited the development of deformation from the collaboration conditions (filling the walls, frame, and t .d.).

Building structures should, first of all, have a sufficient reliability - i.e. the ability to perform certain functions in appropriate conditions for a certain SRO-KA. The termination of the construction construction of at least one of the functions provided for it is called refusal.

Thus, under the refusal to understand the possibility of an onset of such a random event, the result of which is social or economic losses. It is believed that the design at the time preceding the failure is translated into the limit state.

These states are called the limit, upon the occurrence of which the design ceases to meet the requirements imposed on it, that is, it loses the ability to resist external loads or gets unacceptable movement or local damage.

The causes of the offensive in the construction structures of the limit states may be overload, low quality mothers of the Mother Als, of which they are made, and the other.

The main difference of the method under consideration from the previous methods of calculation (calculated voltage calculation) is that it is clearly established by the limit state of structures and instead of a single stock reserve factor k.a system of calculated coefficients is introduced into the calculation, guaranteed design with a certain security from the onset of these states under the most adverse (but really possible) conditions. Currently, this calculation method is adopted as the main official.

Reinforced concrete structures can lose the necessary operational qualities for one of two reasons:

1. As a result of the exhaustion of the bearing capacity (the destruction of the material in the most loaded sections, the loss of stability of individual elements or the entire structure as a whole);

2. In the investigation of excessive deformations (deflection, fluctuations, precipitates), as well as due to the formation of cracks or excessive disclosure.

In accordance with the following two reasons, which can cause the loss of the operational qualities of the structures, the norms of the norms of their limit states are set:

On the bearing ability (first group);

For suitability to normal operation (second group).

The task of calculation is to prevent the occurrence of the construction of any limit state during the production, transportation, installation and operation period.

Calculations on the limit states of the first group must ensure during the period of operation of the structure and for other hundred work its strength, form stability, sustainability, endurance, etc.

Calculations on the limit states of the second group are performed to prevent the design of its work during the period of operation and on the other stages of its work, leading to premature corrosion of reinforcement, or their education, as well as excessive movements.

Settlement factors

These are loads and mechanical characteristics of materials (concrete and reinforcement). They possess statistical variability or time-throwing values. Calculations on the limit states take into account (in an implicit form) variability of the loads and mechanical characteristics of materials, as well as various unfavorable or beneficial conditions of concrete and fittings, the conditions for the manufacture and operation of elements of buildings and structures.

Loads, mechanical characteristics of materials and calculating coefficients are normalized. When designing ferro-ton structures, the values \u200b\u200bof loads, resistance of concrete and ar -thomature are installed on chapters SNiP 2.01.07-85 * and SP 52-101-2003.

Classification of loads. Regulatory and calculating loads

Loads and exposure to buildings and structures Depending on the duration of their action, they are divided into permanent and temporary. The latter, in turn, are divided into long-term, short-matting and special.

The weight of the carriers and enclosing structures of buildings and structures, the weight and pressure of the soils, the effect of the pre-tension of the reinforced concrete structures.

include: the weight of stationary equipment at the floors - machines, devices, engine, containers, etc.; Pressure of gases, liquids, bulk bodies in the containers; loads on overlapping from stored materials and shelving equipment in warehouses, refrigerators, granaries, books, books, archives and similar cohesives; Temperature technological impacts from stationary equipment; Weight layer of water on water-filled plane coatings, etc.

Include: Weight of people, repair materials in the maintenance and repair areas, snow loads with full regulatory value, wind-load, loads arising from the manufacture, transportation and installation of structural elements and some other dr.

include: seismic and explosive operations; Loads caused by sharp violations of the technological process, temporary malfunction or breakdown of equipment and so on.

Loads in accordance with SNiP 2.01.07-85 * are also divided into regulatory and calculated.

Regulatory is called loads or influences close in magnitude to the greatest possible in normal operation of buildings and structures. Their values \u200b\u200bare given in the rules.

The variability of loads in the unfavorable side is evaluated by the reliability coefficient by load γ F..

The estimated load value of the design of the design for other things or stability is determined by multiplying its normative value g P.on the coefficient γ f, usually more than 1

Values \u200b\u200bare differentiated depending on the nature of the on-load and their magnitude. For example, when taking into account your own weight of concrete and reinforced concrete structures \u003d 1.1; When taking into account the sifting weight of various screeds, frustration, insulation, performed in factory conditions, \u003d 1.2, and on the construction site \u003d 1.3. The reliability coefficients for the uniform, but distributed loads should be taken:

1.3 - with a full regulatory value of less than 2 kPa (2 kN / m 2);

1,2 - with the full regulatory value of 2 kPa (2 kN / m 2) and bole. The reliability coefficient for its own weight when calculating the design on the stability of the position against the floors, tipping and slip, as well as in other cases where the mass decreases deteriorates the conditions of operation of the structure, accept equal to 0.9.

Calculations according to the limit states of the second group lead according to normal loads or according to the calculated, taken with γ f \u003d 1.

Buildings and facilities are subjected to simultaneous action of various loads. Therefore, the calculation of the building or structures in the tsera, or its individual elements, should be carried out taking into account the most adverse combinations of these loads or efforts that are signed by them. Adverse, but actually possible combinations of loads during design are chosen in accordance with RECO-Mendations SNiP 2.01.07-85 *.

Depending on the composition of the adjusted loads, combinations distinguish:

- maintenanceincluding constant, long and short-term load

T \u003d σt post + ψ 1 σt + ψ 2 σt

where t \u003d m, t, q;

ψ - the coefficient of combinations (if 1 short-term load is taken into account, then ψ 1 \u003d ψ 2 \u003d 1.0, if the combination includes 2 and more short-term loads, then ψ 1 \u003d 0.95, ψ 2 \u003d 0.9);

- special, In addition to constant, long-term and short loads, a special load (ψ 1 \u003d 0.95, ψ 2 \u003d 0.80).

The calculation of the structure aimed at preventing the limit states of the first group is expressed in inequality:

N ≤ f, (2.1)

where N. - force in the element under consideration (longitudinal force, bending moment, transverse force) from the action of marginal settlement values \u200b\u200bof loads; F. - Bentchable ability of the element.

To test the limit states of the first group, the limit calculated values \u200b\u200bof the loads F M are used, defined by the formula:

F m \u003d f 0 g FM,

where F 0. - characteristic load value, g FM, - The reliability factor for the limiting value of the load, which takes into account possible deviation of the load in the unfavorable side. Characteristic values \u200b\u200bof loads F 0. and the values \u200b\u200bof the coefficient g FM. Determine in accordance with DBN. These issues are devoted to sections 1.6 - 1.8 of this methodological development.

When the load counting, as a rule, take into account the reliability coefficient to appoint a structure g N., the values \u200b\u200bof which, depending on the class of responsibility of the structure and the type of settlement situation, are shown in Table. 2.3. Then the expression to determine the limit load values \u200b\u200bwill take the form:

F m \u003d f 0 g FM ∙ g n

The right side of inequality (1.1) can be represented as:

F \u003d S R y g c,(2.2)

where R y. - the calculated resistance of steel, installed on the yield strength; S.- geometric segment characteristics (when tensile or compression S. represents the cross section BUTWhen bending - the moment of resistance W.); g C. - The coefficient of working conditions, the values \u200b\u200bof which, depending on the design material, are set by the corresponding standards. For steel designs values g C. Led in Table. 2.4.

Substituting in formula (2.1) the value (2.2), we obtain the condition

N ≤ s r y g c

For stretched elements when S \u003d A.

N ≤ a r y g c

Sharing the left and right parts of inequality to the area BUT, We obtain the condition of the strength of the stretched or compressed element:

For bending elements when S \u003d W, then

M ≤ w r y g c

From the last expression, the formula implies to verify the strength of the bent element

The formula for testing the stability of the compressed element has the form:

where φ – the coefficient of longitudinal bending, depending on the flexibility of the rod

Table 2.4 - Operating Coefficient G with

Elements of structures	g S.
1. Exploid beams and compressed elements of farms of overlaps under the halls of theaters, clubs, cinemas, under the premises of shops, archives, etc. With a temporary load that does not exceed the overlap weight 2. Columns of public buildings and supports of water towers. 3. Columns of one-storey industrial buildings with bridge cranes 4. Compressed basic elements (except support) of the composite tank grille from the corners of welded coatings and overlap farms when calculating the stability of these with flexibility L ≥ 60 5. Tightening, traction, delay, suspension in the calculations For strength in unreparable sections 6. Elements of steel structures with a yield strength up to 440 N / mm 2, carrying static loads, in the calculations for strength in a section, weakened by the bolt holes (except for friction compounds) 8. Compressed elements from single corners attached by one Shelf (for non-equivalent corners - less Polto) Except for the elements of the spatial structural lattice and flat farms from single corners 9 Supporting plates made of steel with a yield strength up to 390 N / mm 2, carrying static load, thickness, mm: a) up to 40 inclusive b) from 40 to 60 inclusive B) from 60 to 80 inclusive	0,90 0,95 1,05 0,80 0,90 1,10 0,75 1,20 1,15 1,10
Notes: 1. G C refers< 1 при расчете одновременно учитывать не следует. 2. При расчетах на прочность в сечении, ослабленном отверстиями для болтов, коэффициенты g frompos. 6 and 1, 6 and 2, 6 and 5 should be considered simultaneously. 3. When calculating the reference slabs, the coefficients shown in the pos. 9 and 2, 9 and 3, should be considered simultaneously. 4. When calculating the compounds of the coefficients G C for the elements given in the pos. 1 and 2, should be taken into account along with the G coefficient in. 5. In cases not specified in this table, in the calculated formulas should be taken g S. =1

When calculating the structures operating under recharge conditions (for example, when calculating the crane beams), a cyclic calculation load is used to determine the efforts, the value of which is determined by the formula.

Calculation of strength can be carried out according to one of two techniques - at the limit state, or by allowable stresses. The method of calculating for allowable stresses is adopted when calculating machine-building structures, and its uses are given aware of the resistance of the materials. When calculating building structures, the calculation method was adopted by a limit state, more perfect than the calculation method for allowed voltages.

Limit stressful state- The state when the point occurs in a tense state leading to the emergence of a new process. For example, to the development of plastic deformation, to the formation of cracks, etc. Various PNSs occur with various types of loading.

Limit- This condition in which the design loses performance or its condition becomes unwanted. Efforts caused ultimate condition are called limit

The limit states and limit stress states should be distinguished. Not always these concepts coincide. Examples:

An increase in stresses in bending beam to the yield strength leads to the achievement of the PNS at points as remote from the neutral line. A further increase in the load leads to the achievement of the flow limit level in the entire section - the limit state in the section, in the design, qualitative changes occur, the movement increases sharply, since a plastic hinge is formed in the most loaded section.

An increase in tension voltages leads to a sequential appearance of the following limit stress states: a) the beginning of uniform plastic deformation; b) shaky formation; c) destruction.

Method of calculating for limit states

In accordance with GOST 27751-88, "reliability of building structures and grounds. Basic provisions for the calculation" The limit states are divided into two groups:

the first group includes marginal states that lead to complete unsuitability for the operation of structures, grounds (buildings or structures in general) or to full (partial) loss of the carrier ability of buildings and structures as a whole;

the second group includes marginal states that make it difficult to normal operation of structures (grounds) or reduce the durability of buildings (structures) compared to the provisted service life.

The limit states of the first group are characterized by:

the destruction of any nature (for example, plastic, fragile, fatigue);

loss of stability of the form leading to complete unsuitability of operation;

loss of sustainability of the situation;

transition to a variable system;

qualitative change in configuration;

other phenomena under which there is a need to stop exploitation (for example, excessive deformations as a result of creep, plasticity, shift in compounds, cracking, as well as the formation of cracks).

The limit states of the second group are characterized by:

the achievement of limit deformations of the structure (for example, limit defunitions, turns) or limit deformations of the foundation;

achieving limit levels of oscillations of structures or bases;

formation of cracks;

the achievement of limit disclosures or crack lengths;

loss of sustainability of the form leading to difficulty operation;

other phenomena in which there is a need to temporarily restrict the operation of the building or structure due to the unacceptable reduction in their service life (for example, corrosion damage).

The first limit state for stretched and compressed elements is expressed by the ratio:

where
- calculated resistance on the yield strength;

- yield strength;

- the reliability coefficient by material (γ C\u003e 1);

- calculated resistance to the strength limit;

- tensile strength;

- coefficient of working conditions (Γ with<1);

-Cheffer reliability for structural elements calculated for strength using calculated resistances R. u. ;

- The cross-sectional area of \u200b\u200bthe stretched (compressed) element.

For bending elements:

Formally the value in the right-hand side of inequalities (2 .0), (2 .0), (2 .0), we can take for the allowable voltage, the calculation of the calculation of the limit state and allowable voltages coincide, however, when calculating the ultimate states, the general and unchanged The stock reserve coefficient is replaced by several variables. This allows when calculating the limit state to design operational equal structures.

When determining the calculated resists for welds R W, the following is taken into account: the main material of the welded structure, the auxiliary materials used in welding (brand of coated electrodes, electrode wires), the presence of or no physical methods for controlling the weld.