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To solve the static part of the problem, we reduce the cross-sectional shape of a reinforced concrete floor slab with round voids (Appendix 2, Fig. 6.) to the calculated tee.
Let us determine the bending moment in the middle of the span from the action of the standard load and the own weight of the slab:
where q / n- standard load per 1 linear meter of the slab, equal to:
The distance from the lower (heated) surface of the panel to the axis of the working reinforcement will be:
mm,
where d– diameter of reinforcing bars, mm.
The average distance will be:
mm,
where BUT- cross-sectional area of \u200b\u200bthe reinforcing bar (clause 3.1.1.), mm 2.
Let us determine the main dimensions of the calculated tee cross-section of the panel:
Width: b f = b= 1.49 m;
Height: h f = 0,5 (h-P) = 0.5 (220 - 159) = 30.5 mm;
Distance from the unheated surface of the structure to the axis of the reinforcing bar h o = h – a= 220 - 21 = 199 mm.
We determine the strength and thermal characteristics of concrete:
Normative resistance to tensile strength R bn= 18.5 MPa (Table 12 or clause 3.2.1 for class B25 concrete);
Reliability factor b = 0,83 ;
Design resistance of concrete according to tensile strength R bu = R bn / b= 18.5 / 0.83 = 22.29 MPa;
Coefficient of thermal conductivity t = 1,3 – 0,00035T Wed\u003d 1.3 - 0.00035 723 \u003d 1.05 W m -1 K -1 (clause 3.2.3. ),
where T Wed- the average temperature during a fire, equal to 723 K;
Specific heat FROM t = 481 + 0,84T Wed\u003d 481 + 0.84 723 \u003d 1088.32 J kg -1 K -1 (clause 3.2.3.);
Reduced coefficient of thermal diffusivity:
Coefficients depending on the average density of concrete TO= 39 s 0.5 and TO 1 = 0.5 (clause 3.2.8, clause 3.2.9.).
Determine the height of the compressed zone of the plate:
We determine the stress in the tensile reinforcement from the external load in accordance with adj. 4:
because X t= 8.27 mm h f= 30.5 mm, then
where As- the total cross-sectional area of the reinforcing bars in the tensioned zone of the cross-section of the structure, equal to 5 bars 12 mm 563 mm 2 (clause 3.1.1.).
Let us determine the critical value of the coefficient of change in the strength of reinforcing steel:
,
where R su- design resistance of reinforcement in terms of tensile strength, equal to:
R su = R sn / s= 390 / 0.9 = 433.33 MPa (here s- reliability coefficient for reinforcement, taken equal to 0.9);
R sn- standard resistance of reinforcement in terms of tensile strength, equal to 390 MPa (Table 19 or clause 3.1.2).
Got that stcr1. This means that the stresses from the external load in the tensile reinforcement exceed the normative resistance of the reinforcement. Therefore, it is necessary to reduce the stress from the external load in the armature. To do this, increase the number of reinforcing bars of the panel12mm to 6. Then A s= 679 10 -6 (clause 3.1.1.).
MPa
.
Let us determine the critical heating temperature of the supporting reinforcement in the tension zone.
According to the table in clause 3.1.5. using linear interpolation, we determine that for class A-III reinforcement, steel grade 35 GS and stcr = 0,93.
t stcr= 475C.
The heating time of the reinforcement to the critical temperature for a slab of a solid cross section will be the actual fire resistance limit.
c = 0.96 h,
where X– argument of the Gaussian (Krump) error function equal to 0.64 (section 3.2.7. ) depending on the value of the Gaussian (Krump) error function equal to:
(here t n- the temperature of the structure before the fire, we take equal to 20С).
The actual fire resistance limit of a floor slab with round voids will be:
P f = 0.9 = 0.960.9 = 0.86 h,
where 0.9 is a coefficient that takes into account the presence of voids in the slab.
Since concrete is a non-combustible material, it is obvious that the actual fire hazard class of the structure is K0.
As mentioned above, the fire resistance limit of bent reinforced concrete structures may occur due to heating to a critical temperature of the working reinforcement located in the stretched zone.
In this regard, the calculation of fire resistance hollow core slab overlaps will be determined by the time of heating up to the critical temperature of the tensile working reinforcement.
The section of the slab is shown in Figure 3.8.
b p b p b p b p b p
h h 0
A s
Fig.3.8. Estimated section of a hollow-core floor slab
To calculate the slab, its cross section is reduced to a tee (Fig. 3.9).
b´ f
x topic ≤h´ f
h´ f
h h 0
x topic >h´ f
A s
a∑b R
Fig.3.9. Tee section of a multi-hollow slab for calculating its fire resistance
Subsequence
calculation of the fire resistance limit of flat flexible multi-hollow reinforced concrete elements
3. If, then s , topic is determined by the formula
Where instead b
used ;
If , then it must be recalculated according to the formula:
According to 3.1.5 is determined t s , cr(critical temperature).
The Gaussian error function is calculated by the formula:
According to 3.2.7, the argument of the Gaussian function is found.
The fire resistance limit P f is calculated by the formula:
Example number 5.
Given. Hollow-core floor slab freely supported on both sides. Section dimensions: b=1200 mm, working span length l= 6 m, section height h= 220 mm, protective layer thickness but l = 20 mm, class A-III tension reinforcement, 4 rods Ø14 mm; heavy concrete class B20 on crushed limestone, weight moisture content of concrete w= 2%, average dry concrete density ρ 0s\u003d 2300 kg / m 3, void diameter d n = 5.5 kN/m.
Define the actual fire resistance limit of the slab.
Solution:
For concrete class B20 R bn= 15 MPa (clause 3.2.1.)
R bu\u003d R bn / 0.83 \u003d 15 / 0.83 \u003d 18.07 MPa
For reinforcement class A-III R sn = 390 MPa (clause 3.1.2.)
R su= R sn /0.9 = 390/0.9 = 433.3 MPa
A s= 615 mm 2 = 61510 -6 m 2
Thermophysical characteristics of concrete:
λ tem \u003d 1.14 - 0.00055450 \u003d 0.89 W / (m ˚С)
with tem = 710 + 0.84450 = 1090 J/(kg ˚C)
k= 37.2 p.3.2.8.
k 1 = 0.5 p.3.2.9. .
The actual fire resistance limit is determined:
Taking into account the hollowness of the slab, its actual fire resistance must be multiplied by a factor of 0.9 (clause 2.27.).
Shelegov V.G., Kuznetsov N.A. "Buildings, structures and their stability in case of fire". Textbook for the study of discipline. - Irkutsk.: VSI MIA of Russia, 2002. - 191 p.
Shelegov V.G., Kuznetsov N.A. Building construction. Reference manual for the discipline "Buildings, structures and their stability in case of fire". - Irkutsk.: VSI Ministry of Internal Affairs of Russia, 2001. - 73 p.
Mosalkov I.L. and others. Fire resistance of building structures: M .: CJSC "Spetstechnika", 2001. - 496 p., illustration
Yakovlev A.I. Fire resistance calculation building structures. - M .: Stroyizdat, 1988.- 143s., Ill.
Shelegov V.G., Chernov Yu.L. "Buildings, structures and their stability in case of fire". A guide to completing a course project. - Irkutsk.: VSI Ministry of Internal Affairs of Russia, 2002. - 36 p.
Manual for determining the fire resistance limits of structures, the limits of fire propagation along structures and the flammability groups of materials (to SNiP II-2-80), TsNIISK im. Kucherenko. – M.: Stroyizdat, 1985. – 56 p.
GOST 27772-88: Rolled products for building steel structures. General specifications/ Gosstroy of the USSR. - M., 1989
SNiP 2.01.07-85*. Loads and impacts / Gosstroy of the USSR. - M.: CITP Gosstroy USSR, 1987. - 36 p.
GOST 30247.0 - 94. Building structures. Test methods for fire resistance. General requirements.
SNiP 2.03.01-84*. Concrete and reinforced concrete structures / Ministry of Construction of Russia. - M.: GP TsPP, 1995. - 80 p.
1ELLING - a structure on the shore with a specially arranged sloping foundation ( slipway), where the ship's hull is laid down and built.
2 Viaduct - a bridge across land routes (or over a land route) at their intersection. Provides movement on them at different levels.
3FLASHBACK - a construction in the form of a bridge for passing one path over another at the point of their intersection, for mooring ships, and also in general for creating a road at a certain height.
4 STORAGE TANK - container for liquids and gases.
5 GAS CONTAINER– facility for acceptance, storage and release of gas to the gas network.
6blast furnace- shaft furnace for smelting pig iron from iron ore.
7Critical temperature is the temperature at which the normative resistance of the metal R un decreases to the value of the normative stress n from the external load on the structure, i.e. at which there is a loss of bearing capacity.
8 Nagel - a wooden or metal rod used to fasten parts of wooden structures.
Consider the calculation of the fire resistance limit of a beamless ceiling using an example that is quite common in construction practice. Beamless reinforced concrete floor has a thickness of 200 mm from concrete of class B25 in compression, reinforced with a mesh with cells of 200x200 mm from reinforcement of class A400 with a diameter of 16 mm with a protective layer of 33 mm (to the center of gravity of the reinforcement) at the lower surface of the floor and A400 with a diameter of 12 mm with a protective layer 28 mm (up to c.t.) at the top surface. The distance between the columns is 7m. In the building under consideration, the ceiling is a fire barrier of the first type according to and must have a fire resistance limit for the loss of heat-insulating ability (I), integrity (E) and bearing capacity (R) REI 150. Assessment of the fire resistance limit of the ceiling according to existing documents can be determined by calculation only from the thickness of the protective layer (R) for a statically determinate structure, from the thickness of the ceiling (I) and, if possible, brittle fracture in a fire (E). At the same time, the calculations of I and E give a fairly correct assessment, and the bearing capacity of the ceiling in case of fire as a statically indeterminate structure can only be determined by calculating the thermally stressed state, using the theory of elastic-plasticity of reinforced concrete during heating or the theory of the method of limit equilibrium of the structure under the action of static and thermal loads during fire . The latter theory is the simplest, since it does not require the determination of stresses from a static load and temperature, but only the forces (moments) from the action of a static load, taking into account changes in the properties of concrete and reinforcement during heating until plastic hinges appear in a statically indeterminate structure when it turns into mechanism. In this regard, the assessment of the bearing capacity of a beamless floor in case of fire was made according to the method of limit equilibrium, and in relative units to the bearing capacity of the floor in normal conditions operation. The working drawings of the building were reviewed and analyzed, calculations were made of the fire resistance limits of a reinforced concrete beamless ceiling upon the onset of signs of limit states normalized for these structures. The calculation of the fire resistance limits for the bearing capacity is made taking into account the change in the temperature of concrete and reinforcement for 2.5 hours of standard tests. All thermodynamic and physical-mechanical characteristics of construction materials given in this report are taken on the basis of data from VNIIPO, NIIZHB, TsNIISK.
Let us determine by formula (5) the temperature distribution over the thickness of the floor after 2.5 hours of fire. Let us determine by formula (6) the thickness of the floors, which is necessary to achieve a critical temperature of 220C on its unheated surface in 2.5 hours. This thickness is 97 mm. Therefore, a 200 mm thick overlap will have a fire resistance limit for the loss of heat-insulating ability of at least 2.5 hours.
The initial data for a reinforced concrete floor slab are given in Table 1.2.1.1
Type of concrete - lightweight concrete density с = 1600 kg/m3 with large expanded clay filler; slabs are multi-hollow, with round voids, the number of voids is 6 pcs, the slabs are supported on two sides.
1) The effective thickness of a hollow-core slab teff for assessing the fire resistance limit in terms of heat-insulating ability in accordance with paragraph 2.27 of the Manual to SNiP II-2-80 (Fire resistance):
2) We determine according to the table. 8 Allowances for the fire resistance of the slab on the loss of thermal insulation capacity for a slab of lightweight concrete with an effective thickness of 140 mm:
The fire resistance limit of the plate is 180 min.
3) Determine the distance from the heated surface of the plate to the axis of the rod reinforcement:
4) According to Table 1.2.1.2 (Table 8 of the Handbook), we determine the fire resistance limit of the slab according to the loss of bearing capacity at a = 40 mm, for lightweight concrete when supported on two sides.
Table 1.2.1.2
Fire resistance limits of reinforced concrete slabs
The desired fire resistance limit is 2 hours or 120 minutes.
5) According to clause 2.27 of the Handbook, a reduction factor of 0.9 is applied to determine the fire resistance limit of hollow core slabs:
6) We determine the total load on the plates as the sum of permanent and temporary loads:
7) Determine the ratio of the long-acting part of the load to the full load:
8) Correction factor for load according to paragraph 2.20 of the Handbook:
9) According to clause 2.18 (part 1 b) of the Benefit, we accept the coefficient for reinforcement
10) We determine the fire resistance limit of the slab, taking into account the coefficients for the load and for the reinforcement:
The fire resistance limit of the plate in terms of bearing capacity is
Based on the results obtained in the course of calculations, we obtained that the fire resistance limit of a reinforced concrete slab in terms of bearing capacity is 139 minutes, and in terms of heat-insulating capacity is 180 minutes. It is necessary to take the smallest fire resistance limit.
Conclusion: fire resistance limit of reinforced concrete slab REI 139.
Type of concrete - heavy concrete with a density of c = 2350 kg/m3 with a large aggregate of carbonate rocks (limestone);
Table 1.2.2.1 (Table 2 of the Handbook) shows the values of the actual fire resistance limits (POf) reinforced concrete columns from different characteristics. In this case, POf is determined not by the thickness of the concrete protective layer, but by the distance from the surface of the structure to the axis of the working reinforcing bar (), which includes, in addition to the thickness of the protective layer, also half the diameter of the working reinforcing bar.
1) Determine the distance from the heated surface of the column to the axis of the bar reinforcement by the formula:
2) According to clause 2.15 of the Handbook for structures made of concrete with carbonate aggregate, the cross-sectional size can be reduced by 10% with the same fire resistance limit. Then the width of the column is determined by the formula:
3) According to Table 1.2.2.2 (Table 2 of the Handbook), we determine the fire resistance limit for a lightweight concrete column with the parameters: b = 444 mm, a = 37 mm when the column is heated from all sides.
Table 1.2.2.2
Fire resistance limits of reinforced concrete columns
The desired fire resistance limit is between 1.5 hours and 3 hours. To determine the fire resistance limit, we use the linear interpolation method. Data are given in table 1.2.2.3
The most common material in
construction is reinforced concrete. It combines concrete and steel reinforcement,
rationally laid in the design for the perception of tensile and compressive
efforts.
Concrete has good compressive strength and
worse - stretching. This feature of concrete is unfavorable for bending and
stretched elements. The most common flexible building elements
are slabs and beams.
To compensate for adverse
concrete processes, it is customary to reinforce structures with steel reinforcement. Reinforce
slabs with welded meshes, consisting of rods located in two mutually
perpendicular directions. Grids are laid in slabs in such a way that
the rods of their working reinforcement were located along the span and perceived
tensile forces arising in structures during bending under load, in
according to the diagram of bending loads.
IN
under fire conditions, the slabs are exposed to high temperatures from below,
a decrease in their bearing capacity occurs mainly due to a decrease in
strength of heated tensile reinforcement. Typically, these elements
are destroyed as a result of the formation of a plastic hinge in the cross section with
maximum bending moment by reducing the tensile strength
heated stretched reinforcement to the value of operating stresses in its cross section.
Providing fire
building security requires increased fire resistance and fire safety
reinforced concrete structures. For this, the following technologies are used:
These measures will ensure proper fire safety of the building.
The reinforced concrete structure will acquire the necessary fire resistance and
fire safety.
Used Books:
1. Buildings and structures, and their sustainability
in case of fire. Academy of State Fire Service EMERCOM of Russia, 2003
2. MDS 21-2.2000.
Guidelines for calculating the fire resistance of reinforced concrete structures.
- M. : State Unitary Enterprise "NIIZhB", 2000. - 92 p.