For calculations for the 1st group of limit states, what strength characteristics of materials are used. Limit State Calculation Method

Topic 3. Calculation of metal structures according to the method of limiting

states

The concept of limit states of structures; settlement situations. Calculation of structures for the first group of limit states. Calculation of structures for the second group of states. Normative and design resistances

All building structures, including metal ones, are currently calculated using the limit state method. The method is based on the concept of limit states of structures. The limit states are those states in which the structures cease to meet the requirements imposed on them during operation or during construction, specified in accordance with the purpose and responsibility of the structures.

In metal structures, two groups of limit states are distinguished:

Limit states of the first group are characterized by loss of bearing capacity and complete unsuitability of structures for operation. The limit states of the first group include:

Destruction of any nature (viscous, brittle, fatigue);

General loss of form stability;

Loss of position stability;

The transition of the structure to a changeable system;

Qualitative configuration change;

Development of plastic deformations, excessive shears in joints

Going beyond the boundaries of the first group of limit states means a complete loss of the structure's operability.

Limit states of the second group are characterized by unsuitability for normal operation, due to the appearance of unacceptable movements (deflections, angles of rotation, vibrations, etc.), as well as unacceptable crack opening (for reinforced concrete structures).

In accordance with the current standards, when calculating building structures, two design situations are realized: emergency and steady state.

The calculation for the first group of limit states is aimed at preventing an emergency design situation, which can occur no more than once during the entire life of the structure.

The calculation for the second group of limit states characterizes the established design situation corresponding to the standard operating conditions.

The calculation of the structure aimed at preventing the limit states of the first group (emergency design situation) is expressed by the inequality:

N ≤ Ф (3.1)

where N- force in the considered element (longitudinal force, bending moment, transverse force)

F is the bearing capacity of the element

In an emergency design situation, the force N depends on the ultimate design load F m , determined by the formula:

F m = F 0 ∙ g fm

where F0

gfm- reliability factor for the limit value of the load, taking into account the possible deviation of the load in an unfavorable direction. Characteristic load value F0 and coefficient gfm determined by the values of DBN.

When calculating loads, as a rule, the reliability factor for the purpose of the structure is taken into account gn, depending on the degree of responsibility of the structure

F m = F 0 ∙ g fm ∙ g n

Coefficient value gn are given in table. 3.1

Table 3.1 Reliability factors for the purpose of the structure gn

Object class	Degree of responsibility	Object examples	gn

I	Particularly important national economic and (or) social significance	Main buildings of thermal power plants, central units of blast furnaces, chimneys over 200 m high, TV towers, indoor sports facilities, theaters, cinemas, kindergartens, hospitals, museums.
II	Important national economic and (or) social importance	Objects not included in classes I and III	0,95
III	Limited national economic and social importance	Warehouses without sorting and packaging processes for storing agricultural products, fertilizers, chemicals, peat, etc., greenhouses, one-story residential buildings, communication and lighting poles, fences, temporary buildings and structures, etc.	0,9

The right side of inequality (3.1) can be represented as

Ф = SR y g c(3.2)

where Ry- the design resistance of steel, established by the yield strength, S- geometric characteristic of the section (in tension or compression - sectional area BUT, in bending - the moment of resistance W etc.),

gc- coefficient of the working conditions of the structure, the values of which

SNiP are established and are given in table. A 1 appendix A.

Substituting the value (3.2) into formula (3.1), we obtain

N ≤ SR y g c

For stretched elements with S=A

N ≤ AR y g c

Dividing the left and right sides of the inequality by BUT, we obtain the strength condition of the tensioned element

For bending elements with S=W

M ≤ WR y g c

Strength condition of the bending element

Formula for checking the stability of a compressed element

When calculating structures operating under repeated loading (for example, when calculating crane beams), a cyclic design load is used to determine the forces, the value of which is determined by the formula

F c = F 0 g fc g n

where F0- characteristic value of the crane load;

gfc- reliability coefficient for the cyclic design value of the crane load

The design of steel structures aimed at preventing the limit states of the second group is expressed by the inequality

d≤ [d], (3.3)

where d- deformations or movements of structures arising from the operational design value of loads; to determine, you can use the methods of structural mechanics (for example, the Mohr method, initial parameters);

[d] - limiting deformations or displacements established by the norms.

The operational design value of the load characterizes the conditions of normal operation and is determined by the formula

F l = F 0 g f e g n

where F0- characteristic value of the load,

g f e- reliability factor for the operational design load.

For bending elements (beams, trusses), the relative deflection is normalized f/l, where f- absolute deflection, l- beam span.

The formula for checking the stiffness of a beam on two supports is

(3.4)

where is the limiting relative deflection;

for main beams = 1/400,

for floor beams = 1/250,

q e- operational design value of the load, determined by the formula

q e = q 0 g fe g n

Characteristic load value q e and reliability factor for the operational design load gfe accepted according to the rules.

The second group of limit states also includes the calculation of crack resistance in reinforced concrete structures.

For some materials, for example, plastics, creep is characteristic - the instability of deformations over time. In this case, the verification of structural rigidity should be carried out taking into account creep. In such calculations, a quasi-constant design load is used, the value of which is determined by the formula:

F p = F 0 g fp g n

where F0- characteristic value of the quasi-constant load;

gfp- safety factor for quasi-permanent design load.

In metal structures, two types of design resistance are distinguished R:

- Ry- design resistance, established by the yield strength and used in calculations involving the elastic work of the material;

- R u- design resistance, established by the tensile strength and used in the calculations of structures where significant plastic deformations are permissible.

Design resistance Ry And R u are determined by the formulas:

R y = R yn /g m And R u = R un /g m

in which Ryn And Run- normative resistances, respectively equal to

R yn = s m

R un = s in

Where s m- yield strength,

s in- tensile strength (temporary resistance) of the material;

g m- reliability coefficient for the material, taking into account the variability of the properties of the material and the selective nature of testing samples by definition s m And s in, as well as the scale factor - mechanical characteristics are determined on small samples with short-term uniaxial tension, while the metal works for a long time in large-sized structures.

The value of standard resistances R yn = s m And R un = s in, as well as the values of the coefficient g m set statistically. Normative resistances have a statistical security of at least 0.95, i.e. in 95 cases out of 100 s m And s in will be at least the values specified in the certificate. Safety factor by material g m established on the basis of the analysis of distribution curves of steel test results. The values of this coefficient, depending on GOST or TU for steel, are given in Table. 2 SNiP. The values of this coefficient vary from 1.025 to 1.15.

Regulatory Ryn And Run and settlement Ry And R u resistance for different steel grades, depending on the type of rolled products (sheet or style) and its thickness, are presented in Table. 51 SNiP. The calculations also use the calculated shear resistance (shear) Rs =0,58Ry, to the dismay R p = R u and etc.

Normative and design resistances for some of the most commonly used steel grades are given in Table. 3.2.

Table 3.2. Regulatory and design resistance of steel according to

GOST 27772-88.

Steel	rental table	Regulatory resistance, MPa, rolled	Design resistance, MPa, rolled
sheet	shaped	sheet	shaped
Ryn	Run	Ryn	Run	Ryn	Run	Ryn	Run
C235	2-20 2-40
C245	2-20 2-30	-	-			-	-
C255	4-10 10-20 20-40
C275	2-10 10-20
C285	4-10 10-20
C345	2-10 20-20 20-40
C345	4-10
C375	2-10 10-20 20-40

Thus, in the limit state method, all initial quantities, random in nature, are represented in the norms by some standard values, and the effect of their variability on the design is taken into account by the corresponding reliability factors. Each of the introduced coefficients takes into account the variability of only one initial value (load, working conditions, material properties, degree of responsibility of the structure). These coefficients are often called partial coefficients, and the method of calculation by limit states is called the method of partial coefficients abroad.

Literature:, p. 50-52; from. 55-58.

Tests for self-control

I. Loss of stability refers to the limit states:

1. I group;

2. II group;

3. III groups.

II. Coefficient γ m takes into account:

1. working conditions of the structure;

3. load variability.

III. Design resistance Ry determined by the formula:

1. Ry = Ryn / γ m ;

2. Ry = Run / γ n ;

3. Ry = Run / γ c.

IV. The unsuitability of structures for operation characterizes the limit

current state:

1. I group;

2. II group;

3. III groups.

V. Coefficient γn takes into account:

1. The degree of responsibility of the structure;

2. variability of material properties;

3. load variability.

VI. Design resistance Ry install:

1. elastic limit;

2. by yield strength;

3. by tensile strength.

VII. Coefficient fm used to determine the design load:

1. limit;

2. operational

3. cyclic.

VIII. Calculation for stability is performed taking into account the design load:

1. limit;

2. operational

3.cyclic.

IX. Brittle fracture refers to the limit states:

1. I group;

2. II group;

3. III groups.

X. For one-story residential buildings, the coefficient γn accept

1. γn = 1;

2. γn=0.95;

3. γn = 0.9;

XI. For especially critical buildings, the coefficient γn accept

1.γn = 1;

2.γn=0.95;

3.γn = 0.9;

XII. The second group of limit states includes the calculation:

1. for strength;

2. for hardness;

3. for sustainability.

3.2 Classification of loads. Load from the weight of the structure and soil. Loads on floors and roofs of buildings. Snow load. wind load. Load combinations .

According to the nature of the impact, the loads are divided into: mechanical and non-mechanical nature.

Mechanical loads (forces applied to the structure, or forced deformations) are taken into account directly in the calculations.

Impact non-mechanical nature , for example, the influence of an aggressive environment, as a rule, is taken into account indirectly in the calculation.

Depending on the causes of the load and impact, they are divided into

on main And episodic.

Depending on the variability in time of the load and the impact of subdivision

lyayutsya on permanent And variables (temporary). Variables (temporary)

loads are divided into: long; short-term; episodic.

The basis for assigning loads are their characteristic values.

The design values of the loads are determined by multiplying the characteristic

values on the load safety factor, depending on the type of load

niya. Depending on the nature of the loads and the purposes of the calculation, four types of design values are used - limiting; operational; cyclic; quasi-permanent.

Their values are determined respectively by the formulas:

F m = F 0 γ f m γ n ,(3.5)

F e = F 0 γ f e γ n ,(3.6)

F c = F 0 γ f c γ n ,(3.7)

F p = F 0 γ f p γ n ,(3.8)

where F0 is the characteristic value of the load;

γ f m , γ f e , γ f c , γ f p- load safety factors;

γ n - reliability factor for the purpose of the structure, taking into account

the degree of his responsibility (see Table 3.1).

The weight of the load-bearing and enclosing structures of the building;

Weight and pressure of soils (embankments, backfills);

Force from prestressing in structures.

Weight of temporary partitions, gravies, footings for equipment;

Weight of stationary equipment and its filling with liquids, free-flowing

Pressure of gases, liquids and loose bodies in tanks and pipelines;

Floor loads from stored materials in warehouses, archives, etc.;

Temperature technological impact from equipment;

The weight of the water layer in water-filled coatings;

The weight of industrial dust deposits;

Impacts caused by deformations of the base without changing the structure

soil holes;

Impacts caused by changes in humidity, aggressiveness of the environment,

shrinkage and creep of materials.

Snow loads;

wind loads;

Ice loads;

Loads from mobile handling equipment, including mos-

towed and overhead cranes;

Temperature climatic effects;

Loads from people, animals, equipment on floors of residential, public

ny and agricultural buildings;

The weight of people, repair materials in the equipment service area;

Loads from equipment arising in the start-stop, transitional and

test modes.

Seismic impacts;

Explosive impact;

Emergency loads caused by violations of the technological process,

fragile equipment;

Loads due to deformations of the base with a fundamental change

soil structure (when soaking subsiding soils) or its subsidence

in mining areas and in karst areas.

Characteristic and design values of episodic loads are determined

special regulations.

The characteristic weight of prefabricated structures should be determined from catalogues, standards, shop drawings or

passport data of manufacturers. For other structures (monolithic

reinforced concrete, brickwork, soil) the weight value is determined according to the design

ny sizes and density of materials. For reinforced concrete density accepted

ρ \u003d 2500 kg / m 3,for steel ρ \u003d 7850 kg / m 3, for brickworkρ \u003d 1800 kg / m 3.

The dead load can have three design values:

Limit, determined by the formula:

F m = F 0 γ f m γ n ,

Operational, determined by the formula:

F e = F 0 γ f e γ n ,

Quasi-permanent, determined by the formula:

F p = F 0 γ f p γ n ,

In the above formulas γn - reliability coefficient for the intended purpose

structures (see Table (3.1). The values of the reliability coefficient for the limit

load value γ f m taken according to Table 3.3. The value of the safety factor for the operational value of the load γ f e taken equal to 1,

those γ f e = 1 ; equal 1 the value of the coefficient is also taken γ fp = 1, use

used to determine the quasi-constant design value of the load, applied

used in creep calculations.

Table 3.3 Coefficient value γ f m

Values in parentheses should be used when checking the stability of the structure against overturning and in other cases when reducing the weight of structures and soils can worsen the working conditions of the structure.

Table 3.4 shows the characteristic values of uniformly distributed

ny loadings on overlappings of residential and public buildings.

Continuation of table 3.4.

The limiting operational value of loads on floors is determined

according to the formulas:

q m = q 0 γ fm γ n ,

q e = q 0 · γ fe · γ n .

Safety factors for ultimate load fm = 1,3 at q0 < 2кН/м 2 ; at q0≥ 2kN/m2 fm = 1,2 . Safety factor for operating load γfe = 1.

is a variable for which three design values are set: marginal, operational and quasi-permanent. For calculation without taking into account the rheological properties of the material, the limiting and operational design values of the snow load are used.

The limiting design value of the snow load on the horizontal projection

coverage is determined by the formula:

S m = S 0 C γ fm ,(3.9)

where S0- the characteristic value of the snow load, equal to the weight of the snow cover per 1 m 2 of the earth's surface. Values S0 are determined depending on the snow region according to the zoning map or according to Appendix E. There are six snow regions on the territory of Ukraine; The maximum value of the characteristic load for each of the snow regions is given in Table 3.5. Zaporizhia is located in the third snow region.

Table 3.5.- Maximum values of the characteristic snow load

snow area	I	II	III	IV	V	VI
S 0 , Pa

More accurate values of the characteristic snow load for some

cities of Ukraine are given in Table A.3 of Appendix A.

Coefficient from in formula (3.9) is determined by the formula:

C \u003d μ Ce Salt,

where: Se- coefficient taking into account the operating mode of the roof;

Salt

μ - coefficient of transition from the weight of the snow cover on the surface of the earth

to the snow load on the coating, depending on the shape of the roof.

For buildings with single-slope and dual-slope coatings (Fig. 3.1), the values

coefficient μ are taken equal to:

μ = 1 for α ≤ 25 0

μ = 0 for α > 60 0 ,

where α - the angle of the roof. Options 2 and 3 should be considered for buildings with

gable profiles (profile b), while option 2 - 20 0 ≤ α ≤ 30 0 ,

and option 3 - 10 0 ≤ α ≤ 30 0 only if there are navigation bridges or aeration

ny devices on the ridge of the coating.

The value of the coefficient μ for buildings

with coatings of other outlines can be

but find in appendix G.

Coefficient Se in formula (3.9), take into account

which influences the operating mode

on the accumulation of snow on the roof

(cleaning, melting, etc.), is installed

design assignment. For the insane

flax coatings of workshops with increased

heat release at roof slopes over 3% and ensuring proper

removal of melt water should be taken

Se=0.8. In the absence of data on the mode

me exploitation of the roof is allowed

accept Se =1 . Coefficient Salt - takes into account the geographical height H (km) of the location of the construction object above sea level. At H< 0,5км, Salt = 1 , at H ≥ 0.5 km the value Salt can be determined by the formula:

Salt = 1.4H + 0.3

Coefficient fm according to the limiting design value of the snow load in

formula ( 3.9) is determined depending on the specified average period of repetition

openness T according to table 3.6

Table 3.6. Coefficient fm according to the limit design value

snow load

Intermediate values fm

For mass construction facilities, an emergency recurrence period is allowed T T e f (Table A.3, Appendix A).

The operational design value of the snow load is determined by the formula:

S e \u003d S o C γ fe, (3.10)

where So And C – the same as in formula (3.9);

γfe - reliability coefficient for the operational value of the snow

load, determined according to table 3.7 depending on the fraction of time

η during which the conditions of the second limit may be violated.

leg condition; intermediate value γfe line should be determined

noah interpolation.

Table 3.7. Coefficient γfe according to the operational value of the snow load

η	0,002	0,005	0,01	0,02	0,03	0,04	0,05	0,1
γfe	0,88	0,74	0,62	0,49	0,4	0,34	0,28	0,1

Meaning η adopted according to the norms for designing structures or installing

is determined by the design task depending on their purpose, responsible

ness and consequences of going beyond the limiting state. For objects of mass construction

evidence is allowed to be taken η = 0.02 (2% of the time of the service life of the structure

is a variable for which two calculations are established -

values: limiting and operational.

The limiting design value of the wind load is determined by the formula:

W m = W 0 C γ fm , (3.11)

where FROM - coefficient determined by the formula (3.12);

fm - reliability coefficient for the limiting value of the wind load;

W0 - the characteristic value of the wind load, equal to the average (static

cal) component of wind pressure at a height of 10 m above the surface

earth. The value of W 0 is determined depending on the wind region according to

zoning map or according to Appendix E.

Five wind regions have been identified on the territory of Ukraine; maximum characteristics

load values for each of the wind regions are given in Table

face 3.8. Zaporozhye is located in the III wind region.

Table 3.8. Maximum characteristic values of wind load

wind region	I	II	III	IV	V
W0,

More accurate values of the characteristic wind load for some cities of Ukraine are given in Table A.2 app. BUT.

Coefficient FROM in formula (3.11) is determined by the formula:

C = Caer Ch Calt Crel Cdir Cd (3.12)

where Saer – aerodynamic coefficient; CH - coefficient taking into account the height of the structure; Calt – coefficient of geographical height; Crel - relief coefficient; cdir – direction coefficient; CD – coefficient of dynamism.

Modern standards provide for several aerodynamic coefficients:

External influence Se;

Friction C f;

Internal impact C i;

Drag C x ;

Shear force C y .

The values of the aerodynamic coefficients are determined according to Appendix I

depending on the shape of the structure or structural element. When calculating the frame frames of buildings, the aerodynamic coefficient of external influence is usually used Se . Figure 3.2 shows structures of the simplest form, schemes of wind pressure on the surface and aerodynamic coefficients of external influence to them.

a - free-standing flat solid structures; b - buildings with gable roofs.

Fig.3.2. Wind load diagrams

For buildings with gable roofs (Fig. 3.2, b), the aerodynamic coefficient

active pressure Ce = + 0.8; coefficient values Ce1 and Ce2 depending on the

building dimensions are given in tab. 3.9, coefficient Se3- in table 3.10.

Table 3.9. Coefficient values Ce1 And Ce2

Coefficient	α, deg.	Values Se 1 ,Ce2 at h/l equal to
	0,5		≥ 2
Ce1			- 0,6	- 0,7	- 0,8
	+ 0,2	- 0,4	- 0,7	- 0,8
	+ 0,4	+0,3	- 0,2	- 0,4
	+ 0,8	+0,8	+0,8	+0,8
Ce2	≤ 60	- 0,4	- 0,4	- 0,5	- 0,8

Table 3.10. Coefficient values Se3

b/l	Values Se3 at h/l equal to
≤ 0,5		≥ 2
≤ 1	- 0,4	- 0,5	- 0,6
≥ 2	- 0,5	- 0,6	- 0,6

The plus sign of the coefficients corresponds to the direction of wind pressure on the surface, the minus sign - from the surface. Intermediate values of the coefficients should be determined by linear interpolation. Maximum coefficient value for slope Se3= 0,6.

Structure height factor CH takes into account the increase in wind load along the height of the building and depends on the type of surrounding area and is determined according to table 3.11.

Table 3.11. Coefficient values CH

Z(m)	CH for terrain type
	I	II	III	IV
≤ 5	0,9	0,7	0,40	0,20
	1,20	0,90	0,60	0,40
	1,35	1,15	0,85	0,65
	1,60	1,45	1,15	1,00
	1,75	1,65	1,35	1,10
	1,90	1,75	1,50	1,20
	1,95	1,85	1,60	1,25
	2,15	2,10	1,85	1,35
	2,3	2,20	2,05	1,45

The types of terrain surrounding the structure are determined for each calculation

wind direction separately:

I - open surfaces of seas, lakes, as well as plains without obstacles, subject to

resistant to the action of wind in a section with a length of at least 3 km;

II - rural area with fences (fences), small structures, houses

mi and trees;

III - suburban and industrial zones, extensive forest areas;

IV - urban areas in which at least 15% of the surface is occupied

buildings with an average height of more than 15 m.

The structure is considered to be located on the terrain of this type for determining

calculated calculated wind direction, if in the considered direction such

the area is at a distance 30Z at full height of the building Z< 60м or

2 km at Z> 60m (Z is the height of the building).

Geographic height factor Calt takes into account the height H (km) accommodation

construction object above sea level and is determined by the formula:

Calt = 2H, at H > 0.5 km,

Calt = 1 , at H ≤ 0.5 km.

Terrain coefficient Crel takes into account the microrelief of the area near the area

ki, on which the construction object is located, and is taken equal to one

except in cases where the construction site is located on a hill or on

Direction coefficient cdir takes into account the uneven wind load

in the direction of the wind and, as a rule, is taken equal to one. CDir ≠ 1 at-

taken with special justification only for open flat terrain

Dynamic coefficient CD takes into account the influence of the pulsating component

wind load and spatial correlation of wind pressure on

building. For structures that do not require the calculation of wind dynamics CD = 1.

Reliability coefficient for the limiting design value of wind loading

ruzki fm is determined depending on the specified average period of repetition

bridges T according to table 3.12.

Table 3.12. Reliability factor for the limit design value of the wind load fm

Intermediate values fm should be determined by linear interpolation.

For objects of mass construction, an average recurrence period is allowed T taken equal to the established service life of the structure Tef

(according to Table A.3. Appendix A).

The operational design value of the wind load is determined by the formula:

We = Wo C γfe , (3.13)

where Wo And C – the same as in formula (3.12);

γfe - reliability factor according to the operational design value

The limiting state is such a state in which the structure (construction) ceases to meet operational requirements, i.e. loses the ability to resist external influences and loads, receives unacceptable displacements or crack opening widths, etc.

According to the degree of danger, the norms establish two groups of limit states: the first group - by bearing capacity;

the second group - on to normal operation.

The limit states of the first group include brittle, ductile, fatigue or other failure, as well as loss of shape stability, loss of position stability, destruction from the combined action of force factors and adverse environmental conditions.

Limit states of the second group are characterized by the formation and excessive opening of cracks, excessive deflections, angles of rotation, vibration amplitudes.

The calculation for the first group of limit states is the main and mandatory in all cases.

The calculation for the second group of limit states is carried out for those structures that lose their performance due to the onset of the above reasons.

The task of limit state analysis is to provide the required guarantee that none of the limit states will occur during the operation of a structure or structure.

The transition of a structure to one or another limit state depends on many factors, the most important of which are:

1. external loads and impacts;

2. mechanical characteristics of concrete and reinforcement;

3. working conditions of materials and construction.

Each factor is characterized by variability during operation, and the variability of each factor separately does not depend on the others and is a random process. So loads and impacts may differ from the given probability of exceeding the average values, and the mechanical characteristics of materials - from the given probability of reducing the average values.

Limit state calculations take into account the statistical variability of loads and strength characteristics of materials, as well as various unfavorable or favorable operating conditions.

2.2.3. Loads

Loads are divided into permanent and temporary. Temporary, depending on the duration of the action, are divided into long-term, short-term and special.

Constant loads include the weight of load-bearing and enclosing structures, the weight and pressure of the soil, and the pre-compression force.

Long-term live loads include the weight of stationary equipment on floors; pressure of gases, liquids, bulk solids in containers; loads in warehouses; long-term temperature technological effects, part of the payload of residential and public buildings, from 30 to 60% of the weight of snow, part of the loads of overhead cranes, etc.

Short-term loads or temporary loads of short duration are: the weight of people, materials in service and repair areas; part of the load on the floors of residential and public buildings; loads arising during manufacture, transportation and installation; loads from overhead and overhead cranes; snow and wind loads.

Special loads arise during seismic, explosive and emergency impacts.

There are two groups of loads - standard and design.

Regulatory loads are those loads that cannot be exceeded during normal operation.

Regulatory loads are established on the basis of experience in the design, construction and operation of buildings and structures.

They are accepted according to the norms, taking into account the given probability of exceeding the average values. The values of permanent loads are determined by the design values of the geometric parameters and the average values of the density of the materials.

Regulatory temporary loads are set according to the highest values, for example, wind and snow loads - according to the average of the annual values for the unfavorable period of their action.

Estimated loads.

The variability of loads, as a result of which there is a possibility of exceeding their values, and in some cases even reducing them, in comparison with the normative ones, is estimated by introducing a reliability factor.

Design loads are determined by multiplying the standard load by the safety factor, i.e.

(2.38)

where q

When calculating structures for the first group of limit states is taken, as a rule, greater than unity, and only in the case when a decrease in load worsens the working conditions of the structure, take < 1 .

The calculation of the structure for the second group of limit states is carried out for design loads with a coefficient =1, given the lower risk of their occurrence.

Combination of loads

Several loads act simultaneously on the structure. Simultaneous achievement of their maximum values is unlikely. Therefore, the calculation is made for various unfavorable combinations of them, with the introduction of the coefficient of combinations.

There are two types of combinations: basic combinations, consisting of permanent, long-term and short-term loads; special combinations consisting of permanent, long-term, possible short-term and one of the special loads.

If the main combination includes only one short-term load, the combination coefficient is assumed to be equal to one, when two or more short-term loads are taken into account, the latter are multiplied by 0.9.

When designing, the degree of responsibility and capitalization of buildings and structures should be taken into account.

Accounting is carried out by introducing the reliability coefficient for the intended purpose , which is accepted depending on the class of structures. For structures of the 1st class (unique and monumental objects)
, for objects of class II (multi-storey residential, public, industrial)
. For class III buildings

BLOCK BASE AND FOUNDATIONS

limit state calculation

Principles for calculating bases by limit states (I and II).

1 limit state- providing conditions for the impossibility of loss of bearing capacity, stability and shape.

2 limit state- ensuring the suitability for normal operation of buildings and structures while preventing deformations in excess of the norm (no loss of stability occurs).

For 1 PS, the calculation is always carried out, for 2 (for crack resistance) - only for flexible foundations (strip, slab).

For 1 PS, calculations are carried out if:

1) a significant horizontal load is transferred to the base.

2) the foundation is located on a slope or near it, or the foundation is composed of large-falling soil plates.

3) the base is composed of slowly compacting water-saturated silty-clayey soils with a water saturation index S r ≥ 0.8 and a consolidation factor with y ≤10 7 cm 2 /year - the strength of the soil skeleton at neutral pressure.

4) the base is composed of rocky soil.

Design condition for 1 PS:

F u - the strength of the ultimate resistance of the base,

γ c \u003d 0.8..1.0 - set of operating conditions of the soil base,

γ n = 1,1..1,2 - reliability factor, depends on the purpose of the building.

2 PS each - always conducted.

S ≤ Su- estimated catch (at P ≤ R), where P is the pressure under the base of the foundation.

R is the calculated soil resistance.

Method Essence

The method of calculation of structures by limit states is a further development of the method of calculation by destructive forces. When calculating by this method, the limit states of structures are clearly established and a system of design coefficients is introduced that guarantees the structure against the onset of these states under the most unfavorable combinations of loads and at the lowest values of the strength characteristics of materials.

The stages of destruction, but the safety of the structure under load is evaluated 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

The limit states are considered to be the states in which the structures cease to 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 the calculation for two groups of limit states: for bearing capacity - the first group of limit states; according to suitability for normal operation - the second group of limit states.

The calculation for the limit states of the first group is performed to prevent:

Brittle, ductile or other type of fracture (strength calculation, taking into account, if necessary, the deflection of the structure before destruction);

loss of stability of the structure shape (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 reservoirs, etc.);

fatigue failure (fatigue analysis of structures under the influence of a repetitive movable or pulsating load: crane beams, sleepers, frame foundations and ceilings for unbalanced machines, etc.);

destruction from the combined effect of force factors and adverse environmental influences (periodic or constant exposure to an aggressive environment, the action of alternate freezing and thawing, etc.).

The calculation for the limit states of the second group is performed to prevent:

the formation of excessive or prolonged opening of cracks (if the formation or prolonged opening of cracks is permissible under the operating conditions);

excessive movements (deflections, angles of rotation, skew angles and vibration amplitudes).

The 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; at the same time, design schemes must comply with the adopted design solutions and each of the listed stages.

3. Estimated factors

Design factors - loads and mechanical characteristics of concrete and reinforcement (tensile strength, yield strength) - have statistical variability (scatter of values). Loads and actions may differ from the given probability of exceeding average values, and the mechanical characteristics of materials may differ from the given probability of falling average values. Limit state calculations take into account the statistical variability of loads and mechanical characteristics of materials, non-statistical factors 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 set according to the chapters of SNiP "Loads and effects" and "Concrete and reinforced concrete structures".

4. Classification of loads. Regulatory and design loads

Depending on the duration of the action, the load is divided into permanent and temporary. Temporary loads, in turn, are divided into long-term, short-term, special.

Loads from the weight of the bearing and enclosing structures of buildings and structures, the mass and pressure of soils, and the impact of prestressing reinforced concrete structures are constant.

Long-term loads are from the weight of stationary equipment on floors - machine tools, apparatus, engines, tanks, etc.; pressure of gases, liquids, bulk solids in containers; loads in warehouses, refrigerators, archives, libraries and similar buildings and structures; part of the temporary load established by the norms in residential buildings, office and amenity premises; long-term temperature technological effects from stationary equipment; loads from one overhead or one overhead crane, multiplied by the coefficients: 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 specified values of crane, some temporary and snow loads are part of their total value and are entered into the calculation taking into account the duration of the action of these types of loads on displacements, deformations, and cracking. The full values of these loads are short-term.

Short-term are the loads from the weight of people, parts, materials in the areas of maintenance and repair of equipment - walkways 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 effects.

Special loads include: seismic and explosive effects; loads caused by a malfunction or breakdown of equipment and a sharp violation of the technological process (for example, with a sharp increase or decrease in temperature, etc.); the impact of uneven deformations of the base, accompanied by a fundamental change in the structure of the soil (for example, deformations of subsiding soils during soaking or permafrost soils during thawing), etc.

The normative loads are set by the norms according to a predetermined probability of exceeding the average values or according to the nominal values. Regulatory constant loads are taken according to the design values of geometric and structural parameters and according to the average density values. Regulatory temporary technological and installation loads are set at 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 repetition.

Design loads for designing 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 coefficient from the weight of concrete and reinforced concrete structures Yf = M; from the weight of structures made of concrete on light aggregates (with an average density of 1800 kg / m3 or less) and various screeds, backfills, heaters, performed in the factory, Yf = l.2, at installation yf = \.3; from various live loads depending on their value yf = it 2...1.4. The coefficient of overload from the weight of structures when calculating the stability of the position against ascent, overturning and sliding, as well as in other cases when a decrease in mass worsens the conditions for the operation of the structure, is taken 7f = 0.9. When calculating structures at the stage of construction, the calculated short-term loads are multiplied by a factor of 0.8. The design loads for the calculation of structures for deformations and displacements (for the second group of limit states) are taken equal to the standard values with the coefficient Yf -1-

combination of loads. Structures must be designed for various combinations of loads or the corresponding forces if the calculation is carried out according to an inelastic scheme. Depending on the composition of the loads taken into account, there are: the main combinations, consisting of permanent, long-term and short-term loads or forces from nx; special combinations consisting of permanent, long-term, possible short-term and one of the special loads or efforts from them.

^ve groups of basic combinations of loads 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; in the calculation of 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 forces should be multiplied by a combination factor equal to 0.9.

When calculating structures for special combinations, the values of short-term loads or the corresponding forces should be multiplied by a combination factor equal to 0.8, except for the cases specified in the design standards for buildings and structures in seismic regions.

The norms also allow to reduce live loads when calculating beams and crossbars, depending on the area of the loaded floor.

5. The degree of responsibility of buildings and structures

The degree of responsibility of the building and structures when the structures reach the limit states is determined by the amount of material and social damage. When designing structures, one should take into account the reliability factor for the purpose of the unitary enterprise, the value of which depends on the class of responsibility of buildings or structures. The limiting values of the bearing capacity, the design values of resistances, the limiting values of deformations, crack openings, or the design values of loads, forces or other influences should be multiplied by this coefficient according to the purpose.

Experimental studies carried out at factories of prefabricated reinforced concrete products showed that for heavy concrete and concrete on porous aggregates, the coefficient of variation is Y ~ 0.135, which is accepted in the norms.

In mathematical statistics, using pa or neither, the probability of repeating values of temporary resistance less than V is estimated. If we accept 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 controlling the class of concrete in terms of axial tensile strength, the normative resistance of concrete to axial tensile Rbtn is taken equal to its guaranteed strength (class) on. axial stretch.

The design resistance of concrete for the calculation for the first group of limit states is determined by dividing the standard resistances by the corresponding safety factors for concrete in compression ybc = 1.3 prn tensile ^ = 1.5, and in the control of tensile strength yy = 1.3. 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 of the mechanical properties of high-strength concrete (reduction of creep deformations), respectively equal to 0.95; 0.925 and 0.9.

The values of the design resistance of concrete with rounding are given in App. I.

When calculating structural elements, the calculated resistances of concrete Rb and Rbt are reduced, and in some cases they are increased by multiplying by the corresponding coefficients of the concrete working conditions uj, taking into account the properties of concrete: the duration of the load and its repeated repetition; conditions, nature and stage of operation of the structure; method of its manufacture, cross-sectional dimensions, etc.

The design compressive resistance of reinforcement Rsc used in the calculation of structures for the first group of limit states, when reinforcement is bonded to concrete, is taken equal to the corresponding design tensile strength of 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 taken for a long-term load, taking into account the coefficient of working conditions y&2

When calculating structural elements, the design resistances of reinforcement are reduced or in some cases increased by multiplying by the corresponding coefficients of working conditions ySi, taking into account the possibility of incomplete use of its strength characteristics due to uneven distribution of stresses in the cross section, low strength of concrete, anchoring conditions, the presence of bends , the nature of the steel tensile diagram, the change in its properties depending on the operating conditions of the structure, etc.

When calculating the elements for the action of a transverse force, the design resistances of the transverse reinforcement are reduced by introducing the coefficient of working conditions -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 made of wire of classes Вр-I and rod reinforcement of class A-III, the coefficient Vs2=0.9 is introduced, which takes into account the possibility of brittle fracture of the welded joint of clamps. Table 1 and 2 app. v.

In addition, the design resistances Rs, Rsc and Rsw should be multiplied by the coefficients of operating conditions: Ys3, 7 * 4 - with repeated application of the load (see Chapter VIII); ysb^lx/lp or uz~1x/lap - in the zone of stress transfer and in the zone of anchoring of non-tensioned reinforcement without anchors; 7 ^ 6 - during operation of "high-strength reinforcement at stresses above the conditional yield strength (7o.2.

The design resistance of reinforcement for the calculation for the second group of limit states is set at a reliability factor for reinforcement 7s = 1, i.e. are taken equal to the standard values Rs, ser = Rsn and are taken into account with the coefficient of reinforcement operating conditions

The crack resistance of a reinforced concrete structure is its resistance to crack formation in stage I of the stress-strain state or crack opening resistance in stage II of the stress-strain state.

Different requirements are imposed on the crack resistance of a reinforced concrete structure or its parts in the calculation, 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 the action of constant, long-term and short-term loads is considered short; continuous crack opening is considered under the action of only constant and long-term loads. The maximum width of crack opening (accr - short and accr2 long), which ensures the normal operation of buildings, the corrosion resistance of reinforcement and the durability of the structure, depending on the category of requirements for crack resistance, should not exceed 0.05-0.4 mm (Table II .2).

Prestressed elements under liquid or gas pressure (tanks, pressure pipes, etc.), in a fully tensioned section with rod or wire reinforcement, as well as in 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 design conditions and the type of reinforcement, must meet the requirements of the second or third category.

The procedure for taking into account loads in the calculation for crack resistance depends on the category of requirements for crack resistance: with the requirements of the first category, the calculation is carried out according to the design loads with a safety factor for the load yf>l (as in the calculation for strength); under the requirements of the second and third categories, the calculation is carried out for the action of loads with the coefficient V / \u003d b The calculation for the formation of cracks to determine the need for checking for short-term opening of cracks for the requirements of the second category, the calculation for the formation of cracks is performed for the action of design loads with the coefficient yf>U checks for crack opening under the requirements of the third category are performed under the action of loads with a coefficient Y / -1. In the calculation of crack resistance, the joint action of all loads, except for special ones, is taken into account. Special loads are taken into account in the calculation of the formation of cracks in cases where cracks lead to a catastrophic situation. The calculation for closing cracks under the requirements of the second category is carried out for the action of constant and long-term loads with a coefficient y / -1. The procedure for accounting for 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, cracking is not allowed under the combined action of all loads (except special ones) entered into the calculation with the coefficient Y / = L THIS requirement is due to the fact that premature cracking in concrete at the end sections of the elements - can lead to pulling out of the reinforcement from the concrete under load and sudden destruction.

increase in deflection. The effect of these cracks is taken into account in structural calculations. For elements operating under S& conditions of action of repeated loads and calculated for endurance, the formation of such cracks is not allowed.

Limit states of the first group. Strength calculations proceed from stage III of the stress-strain state. The section of the structure has the necessary strength if the forces from the design loads do not exceed the forces perceived by the section at the design resistances of the materials, taking into account the coefficient of working conditions. The force from design loads T (for example, bending moment or longitudinal force) is a function of standard loads, safety factors and other factors C (design model, dynamic factor, etc.).

Limit states of the second group. The calculation for the formation of cracks, normal and inclined to the longitudinal axis of the element, is carried out to check the crack resistance of elements to which the requirements of the first category are imposed, and also to determine whether cracks appear in elements whose crack resistance is imposed by 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 TSgf, which can be perceived by the section of the element

It is considered that cracks inclined to the longitudinal axis of the element do not appear if the main tensile stresses in concrete do not exceed the design values,

The calculation for crack opening, normal and inclined to the longitudinal axis, consists in determining the crack opening width at the level of tension reinforcement and comparing it with the maximum opening width. Data on the maximum crack opening width are given in Table. II.3.

Displacement calculation consists in determining the deflection of the element from loads, taking into account the duration of their action and comparing it with the ultimate deflection.

Limit deflections are set by various requirements: technological, due to the normal operation of cranes, technological installations, machines, etc.; constructive, due to the influence of neighboring elements that limit deformations, the need to withstand specified slopes, etc.; aesthetic.

Limit deflections of prestressed elements can be increased by the height of the bend, if this is not limited by technological or design requirements.

The procedure for taking into account loads when calculating deflections is as follows: when limited by technological or design requirements - for the action of permanent, long-term and short-term loads; when limited by aesthetic requirements - to the action of constant and long-term loads. In this case, the load safety factor is taken as Yf

Limit deflections established by the norms for various reinforced concrete elements are given in Table II.4. The limiting deflections of the consoles, related to the outreach of the console, are taken twice as large.

In addition, an additional sway calculation should be performed for reinforced concrete floor slabs, flights of stairs, landings, etc. not connected with neighboring elements: additional deflection from a short-term concentrated load of 1000 N with the most unfavorable scheme of its application should not exceed 0.7 mm.

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

N ≤ Ф, (2.1)

where N- force in the element under consideration (longitudinal force, bending moment, transverse force) from the action of limiting design values of loads; F is the bearing capacity of the element.

To check the limit states of the first group, the limit design values of loads F m are used, determined by the formula:

F m = F 0 g fm ,

where F0- characteristic value of the load, gfm,- reliability factor for the limit value of the load, taking into account the possible deviation of the load in an unfavorable direction. Characteristic values of loads F0 and coefficient values gfm determined in accordance with DBN. Sections 1.6 - 1.8 of this methodological development are devoted to these issues.

When calculating loads, as a rule, the reliability factor for the purpose of the structure is taken into account gn, the values of which, depending on the class of responsibility of the structure and the type of design situation, are given in Table. 2.3. Then the expression for determining the limiting values of loads will take the form:

F m = F 0 g fm ∙g n

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

Ф \u003d S R y g c,(2.2)

where Ry- the design resistance of steel, established by the yield strength; S- geometric characteristic of the section (in tension or compression S is the cross-sectional area BUT, in bending - the moment of resistance W); gc- coefficient of the working conditions of the structure, the values of which, depending on the material of the structure, are established by the relevant standards. For steel structures, values gc are given in table. 2.4.

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

N ≤ S R y g c

For stretched elements with S=A

N ≤ A R y g c

Dividing the left and right sides of the inequality by the area BUT, we obtain the strength condition of a stretched or compressed element:

For bending elements with S=W then

M ≤ W R y g c

From the last expression follows the formula for checking the strength of the bending element

The formula for checking the stability of a compressed element is:

where φ – buckling coefficient depending on the flexibility of the bar

Table 2.4 - Coefficient of working conditions g with

Structural elements	g with

1. Solid beams and compressed elements of floor trusses under the halls of theaters, clubs, cinemas, under the premises of shops, archives, etc. with a temporary load that does not exceed the weight of the ceiling 2. Columns of public buildings and supports of water towers. 3. Columns of one-story industrial buildings with overhead cranes 4. Compressed main elements (except for supporting ones) lattices of composite tee section from the corners of welded trusses of coatings and ceilings in calculations for the stability of these with flexibility l ≥ 60 5. Puffs, rods, braces, suspensions in calculations for strength in unweakened sections 6. Structural elements made of steel with a yield strength of up to 440 N / mm 2, bearing a static load, in strength calculations in a section weakened by bolt holes (except for friction joints) 8. Compressed elements from single corners attached by one shelf (for unequal angles - a smaller shelf) with the exception of lattice elements of spatial structures and flat trusses from single angles 9 Base plates made of steel with a yield strength of up to 390 N / mm 2, bearing a static load, thickness, mm: a) up to 40 inclusive b) from 40 to 60 inclusive c) 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. Coefficients g with< 1 при расчете одновременно учитывать не следует. 2. При расчетах на прочность в сечении, ослабленном отверстиями для болтов, коэффициенты gfrom pos. 6 and 1, 6 and 2, 6 and 5 should be considered simultaneously. 3. When calculating the base plates, the coefficients given in pos. 9 and 2, 9 and 3 should be taken into account simultaneously. 4. When calculating connections, the coefficients g with for the elements given in pos. 1 and 2 should be taken into account together with the factor g in. 5. In cases not specified in this table, in the calculation formulas should be taken g with =1

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

The calculation for the limit states of the first group is performed to prevent:

Brittle, ductile or other type of fracture (strength calculation, taking into account, if necessary, the deflection of the structure before destruction);

Loss of stability of the structure shape (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 reservoirs, etc.);

Fatigue failure (fatigue calculation of structures under the influence of a repetitive movable or pulsating load: crane beams, sleepers, frame foundations and ceilings for unbalanced machines, etc.);

Destruction from the combined effect of force factors and adverse environmental influences (periodic or constant exposure to an aggressive environment, the action of alternate freezing and thawing, etc.).

The calculation for the limit states of the second group is performed to prevent:

Formation of excessive or prolonged crack opening (if the formation or prolonged crack opening is permissible under operating conditions);

Excessive movements (deflections, angles of rotation, skew angles and vibration amplitudes).

Estimated factors

The values of loads, resistance of concrete and reinforcement are set according to the chapters of SNiP "Loads and effects" and "Concrete and reinforced concrete structures".

Classification of loads. Regulatory and design loads

Depending on the duration of the action, the load is divided into permanent and temporary. Temporary loads, in turn, are divided into long-term, short-term, special.

Loads from the weight of the bearing and enclosing structures of buildings and structures, the mass and pressure of soils, and the impact of prestressing reinforced concrete structures are constant.

Long-term loads are from the weight of stationary equipment on floors - apparatuses, engines, tanks, etc.; pressure of gases, liquids, bulk solids in containers; loads in warehouses, refrigerators, archives, libraries and similar buildings and structures; part of the temporary load established by the norms in residential buildings, office and amenity premises; long-term temperature technological effects from stationary equipment; loads from one overhead or one overhead crane, multiplied by the coefficients: 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 specified values of crane, some temporary and snow loads are part of their total value and are entered into the calculation taking into account the duration of the action of these types of loads on displacements, deformations, and cracking. The full values of these loads are short-term.

Average density values. Normative 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 repetition.

The 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 coefficient from the weight of concrete and reinforced concrete structures Yf = M; on the weight of structures made of concrete on light aggregates (with an average density of 1800 kg / m3 or less) and various screeds, backfills, heaters, performed in the factory, Yf = l,2, on installation Yf = l>3; from various live loads depending on their value Yf = l. 2...1.4. The coefficient of overload from the weight of structures when calculating the stability of the position against ascent, overturning and sliding, as well as in other cases when a decrease in mass worsens the working conditions of the structure, is taken yf = 0.9. When calculating structures at the stage of construction, the calculated short-term loads are multiplied by a factor of 0.8. The design loads for the calculation of structures for deformations and displacements (for the second group of limit states) are taken equal to the standard values with the coefficient Yf = l-

Two 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; in the calculation of 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 corresponding efforts should be multiplied by a combination factor equal to 0.9.

Load reduction. When calculating columns, walls, foundations of 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 coefficient

T) = a + 0.6/Km~, (II-11)

Where a - is taken equal to 0.3 for residential buildings, office buildings, dormitories, etc. and equal to 0.5 for various halls: reading rooms, meetings, trade, etc.; m is the number of loaded floors over the considered section.

It is also allowed to reduce live loads when calculating beams and crossbars, depending on the area of the loaded floor.

home > Maths

For calculations for the 1st group of limit states, what strength characteristics of materials are used. Limit State Calculation Method

2.2.3. Loads

We also recommend