CC BY
53
УДК 624.012
V.S. Dorofeev, V.M. Karpyuk, E.N. Krantovskaya, N.N. Petrov, A.N. Petrov
OGASA
STRENGTH CALCULATION OF SUPPORT AREAS IN REINFORCED CONCRETE BEAM STRUCTURES
The co-authors present the main results of experiments dealing with the study of strength properties of the support areas of common, whole, pre-stressed, eccentrically tensioned and compressed reinforced concrete beams. New destruction patterns of support areas of said structures are identified and their dependence on the appropriate relationship of the studied factors was established. A new general engineering method to calculate the strength of support areas of such elements which is based upon a selection and sequential analysis of possible destruction patterns was developed.
Key words: reinforced concrete beams, support areas, strain-stress behaviour, strength.
Introduction. Resistance of reinforced concrete elements to a joint action of axial and transversal forces and bending and torsion forces remains one of the most important and underexplored problem both in the reinforced concrete theory and in practical design. Therefore, systematic experimental and theoretical research aimed at improvement of the existing and development of modern computational models of support areas in reinforced concrete elements is of essential importance.
Analysis of prior research. The priority research areas and recent publications on said topic concern development of the normative framework in the sphere of structural design and implementation of the strain method for computation of their load-bearing capacity. At that, while numerous works of domestic and foreign researchers deal with a study of the load-bearing capacity of normal shears, the load-bearing capacity of inclined shears of said elements remains understudied. Alongside with that, destruction of reinforced concrete structures due to inclined shears is very unsafe and, therefore, extremely undesirable.
Dismissal of the so-called analogue methods when calculating strength, including the frame strength, of inclined shears, which main deficiency is a distinction of the adopted computation models from actual conditions at site, and which are present in the effective European standard EC-21, has brought domestic standards in this sphere to a leading edge of science in the second half of the 20th century. However, along with that, as it was relevantly emphasized by V.V. Tur and A.A. Kondratchyk [1], an insufficiently substantiated reduction of strength margin in support areas and negligence of a number of design and external factors resulted in a considerable reduction of reliability of the computation in accordance with SNiP 2.03.01—84*2. The authors consider [1] that the maximum accuracy and reliability
1 EN 1992-1:2001(Final Draft, April, 2002) Eurocode-2: Design of Concrete Structures — Part 1: General Rules and Rules for Building. Brussels, 2002, October, 230 p.
2 SNiP 2.03.01—84*. Betonnye i zhelezobetonnye konstruktsii [Building Rules and Regulations. Concrete and Reinforced Concrete Structures]. Мoscow, CITP of Gosstroy of the USSR Publ., 1989, 80 p.
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can be achieved by the use of computational formula found in Norwegian standards NS 3473E, which are based on the postulates of the modified "contracted fields", and the Canadian standards CSA 23, which are based on the general theory of shear computation. Reliability evaluations of the EC-2 computational formulas has shown that they occupy a certain intermediate position between American standards of ACI Code 318 and Norwegian standards NS 3473E.
Taking into consideration the above, the authors (O.S. Zalesov, O.I. Zvezdov, T.A. Mykhamediyev, E.A. Chistyakov et al.) revised the standards of SNiP 2.03.01— 84* that were introduced in Russia as of 20033 and 20044 and assert that the existing methods to calculate strength of inclined shears of reinforced concrete elements under the action of transversal and axial forces, bending and torsion torques have not yet achieved such level that they can be accepted as normative methods because of the absence of a systemic approach and due account of the influence of a whole series of a number of factors, including the complex stress-strain condition of the elements. Therefore, the new Russian standards3,4 adopted a simplified scheme for calculating the support area of the reinforced concrete spans so as to make an additional safety margin.
In this context the works ofA.M. Bambura, O.B. Golyshev, O.I. Davydenko et al. [2—6] have the advantage as they allow a satisfactory determination of the strength of inclined shears of common and pre-stressed bar elements by means of the deformation method using the strength values of normal shears.
Practical designers also make use ofthe method developed by L.O. Doroshkevych, B.G. Demchiny, S.B. Maksimovich, B.Yu. Maksimovich [7, 8] which links the strength calculation of inclined and normal shears. At that, the authors consider [7, 8] that the calculation of the transverse rods is similar for the beams, short cantilevers and plates, and is performed based on so-called "pushing".
However, the nature of the stress-strain behaviour, the performance and destruction of the spanned reinforced concrete elements that experience not only transversal but also axial compressing or tension forces, which are applied eccentrically, and bending and torsion torques differ considerably from those described in the works [1—8].
Objective and tasks of the studies. This paper is aimed at presenting a general characteristic of the proposed engineering method for calculating strength of support areas of plate stress elements of span elements. The tasks of the studies are to disclose the features of deformation, origination of cracks and destruction of reinforced concrete elements characterized by complex stress-strain behaviour of plate stress support areas, determination of mechanisms and description of new destruction patterns of these areas depending on correlation of the studied factors.
Study methodology. In order to achieve the set objective, a special methodology of performing systemic field and numerical tests was developed and accomplished in six series with common, pre-stressed, whole, eccentrically tensioned and com-
3 SP 52-101—2003. Betonnye i zhelezobetonnye konstruktsii bez predvaritel'nogo napryaz-heniya armatury [Regulations. Concrete and Reinforced Concrete Structures without Pre-stressed Reinforcement]. Moscow, GUP "NIIZHB" of Gosstroy of Russia Publ., 2004, 55 p.
4 SP 52-102—2004. Predvaritel'no napryazhennye zhelezobetonnye konstruktsii [Regulations. Pre-stressed Reinforced Concrete Structures]. Moscow, GUP "NIIZHB" of Gosstroy of Russia Publ., 2004, 49 p.
pressed reinforced concrete spans with due account of continuous loading and use of a special laboratory equipment. All indicated tests were made at three levels according to almost D-optimum plans of Hartley Ha5 type.
The studied elements presented hinge-propped one- and two-span beams of square and T-shaped shears having 200 mm height and the span lengths equalling 9h0. They were reinforced with two plane frames. The lower and the upper axial rods were adopted to be of A500C class while the transversal rods were taken to belong to Bp-I class.
To prepare the test specimens — beams — a heavy-weight concrete of classes C12/15, C20/25 and C30/35 was used and contained granite macadam and quartz sand with the use of a common 400 grade Portland cement without additives.
In calculation deformation models the averaged approximate diagrams illustrating deformation of concrete prisms DP NDIBK with descending branches were used, as well as known idealized two-line diagrams or diagrams of more complex shapes illustrating deformation of reinforcement steel and diverse phenomenological criteria of concrete and reinforced concrete strength.
For creating various kinds of deformation and testing the specimens — beams — special multipurpose power benches were designed and manufactured.
Deformations of concrete and reinforcement of specimens in the course of the tests were measured with the aid of strain gauges and the results of measurement were checked by clock-type indicators.
Results of the study. Peculiar features of deformation were disclosed in the course of the tests, cracking and destruction of the reinforced concrete spans under complex stress-strain behaviour of support areas; a systemic influence of the design features and external factors upon their load-bearing capacity was determined; the mechanism and new destruction patterns of these areas were revealed; adequate mathematical models of strength, crack resistance, deformability and other parameters of the load-bearing capacity of the studied elements were found out.
Depending on the correlation of the design features and external factors, a destruction of the support areas of plane-stressed spanned reinforced concrete elements can occur according to one of the patterns presented in Fig.1:
according to pattern A-1/Nb or A-2/Nh destruction occurs according to normal shears due to yield of, accordingly, the upper or the lower axial reinforcement in case its quantity is insufficient or if the axial tension force is excessive;
according to pattern B/M destruction occurs according to inclined shear under the dominant action of the bending torque and minimum (up to 1 %) and insufficient (up to 0,3 %) quantity of the transverse reinforcement;
according to pattern C/V destruction occurs according to inclined shear under the dominant action of the transverse force from the shear (slide) or due to breaking of concrete within the compressed zone with average (> 1,5 %) and great quantity of axial reinforcement;
according to pattern D//cm, i.e., destruction occurs according to the inclined compressed strip between the concentrated force and the support in the eccentrically compressed and pre-stressed elements with the shear span a < 2h0;
according to pattern F/V destruction occurs due to pushing above the middle support in kind of an upturned trapezoid with a possible formation of "plastic hing-
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es" above the middle support and in the spans, as well as due to re-distribution of external forces.
Engineering methods of calculating strength of support areas of plane-stressed rod-type reinforced concrete elements [9] can be combined to a single general engineering method which means that with the aid of improved non-linear rough or improved general deformation models or the finite element method [10] it is possible to simulate the stress-strain behaviour of a spanned structure, determine the load-bearing capacities of individual normal (sometimes according to MCE and inclined) shears and, through them, the strength of support areas and inclined shears inclusively. This procedure can be simplified. Knowing the correlation between the design factors and the external influence factors, it is required to analyse step-by-step the most probable destruction patterns (Fig.) of the support areas of the structure, determine the destructive forces and adopt their minimum load-bearing capacity as the basis.
Main destruction patterns of single eccentrically tensioned and compressed common and pre-stressed reinforced beams
Thus, in the eccentrically tensioned specimens with relatively small eccentricity the nature of normal crack formation (along the entire shear) and their opening prove that the so-called 2nd pattern takes place. This being the case, the strength conditions for the destruction patterns A-1/Ne, A-1/NH look like:
(0~С12 )34; (1)
^./^34^,34 (0-С12 )) 12' (2)
and allow selecting the required quantity of axial reinforcement in the support or determining the acceptable value of N.
When an element is destructed according to pattern B/M, the strength condition of the support area in relation to the centre of gravity of the upper (erection) reinforcement will be:
M < M + M = M + M + M (3)
±v± _ ±v± S -T 1V± S-ÍV-Í S,N T -ÍV-Í S F ~ lv± SW,F v '
which can also be represented as:
M < Va + Nen - fyd,34 As 34zs - qswc^/2. (4)
Considering that N$ = N$ n + Ns f , the additional axial force NS N and the normal stress <s 34 n y of the working reinforcement caused by the axial tension force can be determined according to the deformation model through ssN and the force NS F caused by the transverse force F by means of the expression:
NS,F = NS -NSN = fyd,34As,34s,34,NAs,34 =(fyd,34 -<s,34,N)As,34. (5)
In practical calculations it is recommended that the relative length of the horizontal projection of an unsafe inclined crack c0 is determined with the aid of empirical dependencies obtained through the appropriate mathematical models cjh0 for the conducted test series, which have been published earlier by the authors:
co = f [a / ho, e,pw ,p fH ,p, fB, Np I (fckbho), p¡ (fckbho)]. (6)
In order to predict the strength of the inclined shear of a reinforced concrete span, which can be destructed according to pattern C/V, the following prerequisites have been adopted: a) the strength of inclined shears is determined through the strength of normal shears that can be found by means of the deformation or conventional methods; b) the actual normal shear of the element is replaced with the calculated one with the average deformations of the compressed concrete and tensioned reinforcement; c) the stress (deformation) in the reinforcement are determined with the aid of the deformation method in its non-linear variation; the actual curvilinear stress diagram in the concrete of the compressed zone can be replaced, when calculating the strength, with the rectangular diagram above the apex of the unsafe inclined crack, and with the triangular diagram — under it; d) possible forces in the apex of the unsafe inclined crack are not taken into account as the width of inclined cracks in non-overreinforced elements considerably exceeded possible shearing deformations; e) the calculation begins with a determination of the bearing capacity of the normal shear of the element under the concentrated force (in the shear span end) with due account of a possible increase (decrease) of the concrete strength in the compressed zone in its complex stressed condition and upon achievement by the maximum tangent stress of 50 % value of the prism (characteristic fk when determining the destructive Vu or the calculated fcd when determining the calculated V) strength of concrete.
The unknown internal forces, the height of the compressed zone of concrete and other performance parameters of the support area of the reinforced concrete element span at its destruction according to pattern C/V are determined as follows:
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±N = Nlct + n\д2 - N\,34; (7)
V = Vlct + + Vs ; (8) mi=mn = mu,m+v = mu.m = n* (h> - 0,5xt ) +
с (9)
+ Nln {ho-cl2) + VsCo + V^ у,
where Nct =oc,i2 Act ; (10)
Vc\ =( 2/3)VRdAct ; (11)
Vsw = qswC0 = eswfywdAsw Co/Ssw ; (12)
V = m J a = MUM+v/a, (13)
where Act is a part of the shear I — I of heightX; Psw = ^ swz/fywk is a coefficient characterizing a normal stress level in the transverse reinforcement. The average values equal Psw = 0,8 for the common eccentrically tensioned and pre-stressed beams, and Psw = 0,6 for the whole beams;
Mu0 = MuM+V(1 -Co/a) -NS,12 (h0 -c12) + 0,5qswC02; (14)
0,5<j'cnbXf +[(2/3)VrC -<иh0]bXt +Mu0 = 0 (15)
where B1 = 0,5a^ 12b ; B2 =
(2/3)VRdC0 ,12h0
B = M
u0 •
Vs = V - (2/3)VRdbXt - qswC0 < [Vs ] (16)
л
where [Vs ] < 0,05V = 0,05Mi/a for the common single-span, whole, eccentrically
A
tensioned and compressed beams; [Vs ] = fl a/ho, bf jb, hfho, pw, p/( fckbho ) for
the pre-stressed T-shaped reinforced concrete elements is proposed to be determined with the aid of the appropriate mathematical model.
Verification: Ns = a]At + ,12As,12 ± N (17)
with the condition that remains:
Ns < Ns,I =Ys6fyd,34As,34- (18)
In case the condition (18) is not observed, the calculation pattern C/V should be replaced with the simpler B/M, however Vs = 0; v}t = 0 should remain, and for it
M < Ms + Msw = fyd,34Л,34 (( - c12 ) + qswco/2 = MI = VI(19) Taking into account the actual stressed state and the domestically adopted dialectic singularity of approaches to calculating the load-bearing capacity of reinforced concrete elements that are destructed according to the inclined compressed strip (pattern fl//str.), it is expedient to adopt the condition of strength of the inclined compressed strip in its conventional expression:
V <ф; fcdbho , (20)
where 9* is a coefficient that, as distinct from the old domestic and new Russian and Belarus standards, has a variable value and integrally accounts for the existing factors. It can be determined for the common and eccentrically compressed reinforced concrete beams in accordance with the empirical dependence below:
qC = 0,30- 0,09(c -25) /10 + 0,01(pw - 0,0035) / 0,00145, (21)
and for the pre-stressed reinforced concrete elements in accordance with the expression:
< A
q* = 0,398 - 0,008c + 13,889pw - 0,007 sp sp . (22)
1 bh0
Strength conditions of the support areas of the whole reinforced concrete beams which destruction occurs above the middle support according to the pushing pattern F/V is as follows:
FB = 2VB ^ Fc + Fsw = acfctdUmh0 +Pwfywd Z Aw,2C0, (23)
where FB is a value of reaction above the middle support; VB — calculated values of the transverse forces on the left and right of the support; Fc — shearing force taken up by concrete; Fsw — shearing force acting on the transverse reinforcement located on the side planes of the pushing body of an aggregate area X ; a c = ac / fckk — a coefficient that characterizes the level of normal to the beam axis stresses in concrete on the sides of the pushing body, and is determined according to the empirical formula: ac = f (a / ho, c, pw, p fu, pfB), ac = 0,60...4,16; Pw =<sw/fyk — a coefficient that characterizes the stress level in the transverse reinforcement of the support areas, which crosses the side planes of the pushing body and is determined according to the similar empirical relation: Pw = 0,15...1,00; Um — the arithmetic mean of the perimeters of the upper and lower base of the pushing body within the limits of the working height of the shear h0.
It is recommended to predict the load bearing capacity of the spanned reinforced elements experiencing a complex stress taking into account their compressed or free torsion in accordance with the non-linear deformation calculation model that was improved by the authors.
Comparative analysis of the test results and the results obtained by calculations in accordance with the proposed engineering methodologies yielding the strength values of the studied elements support areas (Table) has proved their satisfactory coincidence (variation coefficient u < 12 %).
The results of the work are used in practical design of the leading construction companies of Odessa (LLC «Stikon», PSMO «Odesbud», RCC «Ekobud», LLC «Golovbud» etc.) when reinforcing the foundation of the Odessa Academic Opera & Ballet Theatre, renewal of the Cathedral of the Transfiguration of the Saviour in Odessa, new construction and reconstruction of the symbolic for Odessa buildings and facilities as well as in the training courses in Odessa State Academy of Civil Engineering and Architecture (3 candidate theses and 19 masters' diplomas were successfully defended), and are, partially, implemented in the effective national design standards.
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Results of the comparison of the test and calculated values of the destructing transverse loading
Test No. Series I Series III-A Series III-B Series IV Series V
Test value of the destructive transverse force Q , kH Calculated value of the destructive transverse force Q , kH Destruction pattern Test value of the destructive transverse force Q , kH Calculated value of the destructive transverse force Q , kH Destruction pattern Test value of the destructive transverse force Q , kH Calculated value of the destructive transverse force Q , kH Destruction pattern Test value of the destructive transverse force Q , kH Calculated value of the destructive transverse forse Q , kH Destruction pattern Test value of the destructive transverse force Q , kH Calculated value of the destructive transverse force Q , kH Destruction pattern
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 63 52 as 63 52 ВМ 97 132 Д/str 86 73 В/М 189 160 F/V
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 119 106 Д/str 119 106 ^ ^ 150 132 Д/str 93 86 Д/str 269 271 F/V
3 118 123 Д/str 118 123 C/V 131 93 * 76 78 Д/str 206 199 F/V
4 32 27 as 32 27 C/V 60 31 * 64 64 C/V 93 78 F/V
5 146 123 Д/str 146 123 В/М 143 132 Д/str 93 86 Д/str 366 375 F/V
6 43 61 В/М 43 61 C/V 64 46 * 80 73 В/М 136 147 F/V
7 35 33 as 35 33 В/М 78 31 * 69 77 C/V 93 109 F/V
8 92 106 Д/str 92 106 C/V 139 132 Д/str 77 78 Д/str 162 167 F/V
9 158 135 Д/str 158 135 C/V 162 132 Д/str 95 86 Д/str 256 254 F/V
10 50 64 В/М — — — 74 132 Д/str 81 83 В/М 129 106 F/V
11 34 33 as — — — 53 31 * 64 54 C/V 139 129 F/V
12 93 101 Д/str — — — 122 132 Д/str 73 78 Д/str 233 221 F/V
13 117 135 Д/str — — — 156 132 Д/str 78 78 Д/str 324 314 F/V
14 33 27 as — — — 77 31 * 65 55 C/V 109 147 F/V
15 58 61 В/М — — — 65 132 Д/str 89 83 В/М 135 149 F/V
16 105 101 Д/str — — — 126 132 Д/str 90 86 Д/str 189 196 F/V
17 47 48 В/М — — — 74 39 * 80 70 В/М 128 127 F/V
18 119 132 Д/str — — — 144 132 Д/str 83 81 Д/str 251 251 F/V
19 76 70 В/М — — — 103 132 Д/str 81 82 C/V 182 182 F/V
20 56 70 В/М — — — 94 132 Д/str 81 80 C/V 134 134 F/V
21 71 72 В/М — — — 113 132 Д/str 82 80 C/V 160 158 F/V
22 67 69 В/М — — — 91 128 Д/str 80 80 C/V 156 155 F/V
23 86 91 В/М — — — 106 132 Д/str 90 96 C/V 178 178 F/V
24 58 52 В/М — — — 98 132 Д/str 70 69 C/V 139 140 F/V
25 71 70 В/М — — — 104 132 Д/str 82 92 C/V 190 189 F/V
26 70 70 В/М — — — 100 132 Д/str 80 100 C/V 127 125 F/V
27 71 70 В/М — — — 102 132 Д/str 81 96 C/V 158 157 F/V
var. coeff. v = 15,4 % v = 5,9 % v = 25,0 % v = 8,1 % v = 8,0 %
* concrete crushing in the simple bending zone.
Conclusions
1. Peculiar features of the strain-stress behaviour of the studied specimen beams are disclosed. The dependence of the nature and kind of destruction of these areas on the appropriate relationship of the design and external factors was for the first time established. The known and identified destruction patterns pertaining to the plane-stressed (A-1/Ne, A-2/NH, B/M, C/V, fl//str, F/V,) and complex-stressed (E/Tcompr, E/T^) support areas of spanned reinforced concrete elements have been classified. Peculiar features of the internal force re-distribution in the studied elements were identified which takes place due to non-linear nature of deformation of these materials and formation of the conventional "plastic hinges" in the whole beams. 2. The analysis of calculation methods applicable to strength of the spanned reinforced concrete structure support areas, that are prescribed by the national design standards of the developed countries, and of the methods developed by the authors has proved that the absolute majority of such methods is based upon the partially improved methods, which were applied in old standards at a certain time, and not upon a new general method. In particular, the EC-2 calculation methods and the methods of other foreign countries are based on various conventional schemes and similarities which necessitate an empirical approach and use of the ever increasing number of formulae of the indicated origin.
Comparative analysis of the calculated and test values of load bearing capacity of various types of support areas in spanned structures that were calculated following the recommendations of various national design standards has proved that, for one part, their coincidence is unsatisfactory on the whole, and, for the other part, that the reliability of the proposed formulae is insufficient as the calculated strength for a rather great number of test specimens, particularly of complex stressed, with great shear spans, exceeded considerably their actual bearing capacity. 3. Diverse forms of the complex strain-stress behaviour and of the destruction patterns make it impossible to develop a single simple and, at the same time, universal calculation model applicable to rapid evaluation of support area bearing capacity in various types of spanned structures, which can adequately reflect the influence both of design factors and external factors. The proposed new general engineering method of calculating strength of support areas in plane-stressed spanned reinforced concrete structures that is based upon a selection of the most probable destruction patterns depending on the relationship of the studied factors and their sequential analysis with a view of determining the minimum bearing capacity allows of narrowing the existing scatter "corridor" of the test and calculated bearing capacity values of said areas from u = 20...60 % to u = 6...12 %.
References
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Поступила в редакцию в ноябре 2013 г.
About the authors: Dorofeev Vitaliy Stepanovich — Doctor of Technical Sciences, Professor, Rector, Head, Department of Reinforced Concrete and Masonry Structures, Odessa State Academy of Civil Engineering and Architecture (OGASA), 4 Didrikhsona st., Odessa, 65029, Ukraine; rector@ogasa.org.ua;
Karpyuk Vasiliy Mikhaylovich — Doctor of Technical Sciences, Professor, Vice-rector for Research and Education, International Relations and Eurointegration, Department of Reinforced Concrete end Masonry Structures, Odessa State Academy of Civil Engineering and Architecture (OGASA), 4 Didrikhsona st., Odessa, 65029, Ukraine; v.karpiuk.@ukr.net;
Krantovskaya Elena Nikolaevna — Candidate of Technical Sciences, Associate Professor, Professor, Department of Strength of Materials, Odessa State Academy of Civil Engineering and Architecture (OGASA), 4 Didrikhsona st., Odessa, 65029, Ukraine; elena12122007@mail.ru;
Petrov Nikolay Nikolaevich — Candidate of Technical Sciences, Associate Professor, Department of Strength of Materials, Odessa State Academy of Civil Engineering and Architecture (OGASA), 4 Didrikhsona st., Odessa, 65029, Ukraine, petrov.n.n@mail.ru;
Petrov Aleksey Nikolaevich — Chief of Laboratory, Department of Strength of Materials, Odessa State Academy of Civil Engineering and Architecture (OGASA), 4 Didrikhsona st., Odessa, 65029, Ukraine, petrov.a.n84@mail.ru.
For citation: Dorofeev VS., Karpyuk V.M., Krantovskaya E.N., Petrov N.N., Petrov
A.N. Strength Calculation of Support Areas in Reinforced Concrete Beam Structures. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 12, pp. 55—67.
B.С. Дорофеев, В.М. Карпюк, Е.Н. Крантовская, Н.Н. Петров, А.Н. Петров
РАСЧЕТ ЖЕЛЕЗОБЕТОННОГО СТЕРЖНЯ В ОБЩЕМ СЛУЧАЕ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ
Приведены основные результаты экспериментальных исследований прочности приопорных участков обычных, неразрезных, предварительно напряженных, внецентренно растянутых и сжатых железобетонных балок.
Произведен анализ методов расчета прочности приопорных участков пролетных железобетонных конструкций, заложенных в национальных нормах проектирования развитых стран мира, а также авторских методов. Показано, что абсолютное большинство из них базируется не на новом общем методе, а на частично усовершенствованных методах, которые использовались в свое время в старых нормах. В частности, методы расчета ЕС-2 и других зарубежных стран базируются на различных условных схемах и аналогиях, которые требуют применения эмпирического подхода и использования все большего количества формул указанного происхождения.
Раскрыты особенности деформирования, трещинообразования и разрушения пролетных железобетонных конструкций со сложным напряженно-деформированным состоянием приопорных участков, определено системное влияние конструктивных факторов и факторов внешнего воздействия на их несущую способность, выявлен механизм и новые схемы разрушения этих участков, получены адекват-
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ные математические модели прочности, трещиностойкости, деформативности и другие параметры несущей способности исследовательских элементов.
Предложен новый общий инженерный метод расчета прочности приопорных участков плосконапряженных пролетных железобетонных конструкций, который базируется на выборе наиболее вероятных схем их разрушения в зависимости от соотношения исследовательских факторов и в поочередном их рассмотрении с целью определения минимальной несущей способности, позволяющий сузить существующий «коридор» разногласий экспериментальных и расчетных значений несущей способности указанных участков с о = 20 ... 60 % до о = 6...12 %.
Ключевые слова: железобетонные балки, приопорные участки, напряженно-деформированное состояние, прочность.
Библиографический список
1. Тур В.В., Молош В.В. Новые подходы к расчету сопротивления местному срезу (продавливанию) плоских плит // Вестник БрГТУ. Строительство и архитектура. 2011. № 2. С. 18—31.
2. Голышев А.Б., Колчунов В.И., Смоляго Г.А. Экспериментальные исследования железобетонных элементов при совместном действии изгибающего момента и поперечной силы // Исследование строительных конструкций и сооружений : сб. тр. МИСИ и БТИСМ. М., 1980. С. 26—42.
3. Бамбура А.Н. К оценке прочности железобетонных конструкций на основе деформационного подхода и реальных диаграмм деформирования бетона и арматуры // Бетон на рубеже третьего тысячелетия : материалы 1-й Всеросс. конф. по проблемам бетона и железобетона : в 3 кн. М. : МИ, 2001. Кн. 2. С. 750—757.
4. К расчету прочности сечений, наклонных к продольной оси элемента с использованием полной программы деформирования бетона / А.И. Давыденко, А.Н. Бамбура, С.Ю. Беляева, Н.Н. Присяжнюк // Мехашка i фiзика руйнування буфвельних матерiалiв та конструкцш : Зб. наук. праць фiз-мех. ш-ту iм. Г.В. Карпенка НАН УкраТни. Львiв : Каменяр, 2007. № 7. С. 209—216.
5. Вдосконалений деформацмний метод розрахунку мщност приопорних дтянок непереармованих пропнних залiзобетонних конструкцм / В.С. Дорофеев, В.М. Карпюк, Ф.Р Карп'юк, О.М. Крантовська, Н.М. Ярошевич // Мiжвiдомчий науково-техн. зб. наук. праць (буфвництво) Держ. наук. досл. Ы-т буд. кон-цш Мш-ва репон. розв. та буд-ва Украши. Киев : НД1БК, 2008. Вип. 70. С. 103—116.
6. Деформацмний метод розрахунку мщносл приопорних дтянок залiзобетонних конструкцм / В.С. Дорофеев, В.М. Карпюк, Ф.Р. Карп'юк, Н.М. Ярошевич // Вюник ОдеськоТ державно!' академп буфвництва та архп"ектури. Одеса : Тов. «Зовншрекламсервю», 2008. Вип. № 31. С. 141—150.
7. Пропозици до розрахунку мщносп похилих перерiзiв згинальних залiзобетонних елеменпв (до роздту 4.11.2. ДБН В.2.6.) / Л.О. Дорошкевич, Б.Г. Демчина, С.Б. Максимович, Б.Ю. Максимович // Мiжвiдомчий науково-техн. зб. наук. праць Держ. наук. досл. нт буд. кон-цй Киев : НД1БК, 2007. Вип. 67. С. 601—612.
8. Нестандартный метод расчета поперечной арматуры железобетонных изгибаемых элементов / Л.А. Дорошкевич, Б.Г. Демчина, С.Б. Максимович, Б.Ю. Максимович // Проблемы современного бетона и железобетона : сб. науч. тр. Минск : Изд-во НП ООО «Стрикон», 2007. С. 164—177.
9. Залесов А.С., Климов Ю.А. Прочность железобетонных конструкций при действии поперечных сил. Киев : Буфвельник, 1989. 105 с.
10. Клованич С.Ф. Механика железобетона в расчетах конструкций // Буфвельы конструкцп : зб. наук. праць. Кив : НД1БК, 2000. Вип. 52. С. 107—115.
Об авторах: Дорофеев Виталий Степанович — доктор технических наук, профессор, ректор, заведующий кафедрой железобетонных и каменных конструкций, Одесская государственная академия строительства и архитектуры (ОГАСА), 65029, Украина, г Одесса, ул. Дидрихсона, д. 4, rector@ogasa.org.ua;
Карпюк Василий Михайлович — доктор технических наук, проректор по научно-педагогической работе, международным связям и евроинтеграции, профессор кафедры железобетонных и каменных конструкций, Одесская государственная академия строительства и архитектуры (ОГАСА), 65029, Украина, г. Одесса, ул. Дидрихсона, д. 4, v.karpiuk.@ukr.net;
Крантовская Елена Николаевна — кандидат технических наук, доцент кафедры сопротивления материалов, Одесская государственная академия строительства и архитектуры (ОГАСА), 65029, Украина, г Одесса, ул. Дидрихсона, д. 4, elena12122007@mail.ru;
Петров Николай Николаевич — кандидат технических наук, доцент кафедры сопротивления материалов, Одесская государственная академия строительства и архитектуры (ОГАСА), 65029, Украина, г. Одесса, ул. Дидрихсона, д. 4, petrov.n.n@mail.ru;
Петров Алексей Николаевич — заведующий лабораторией кафедры сопротивления материалов, Одесская государственная академия строительства и архитектуры (ОГАСА), 65029, Украина, г. Одесса, ул. Дидрихсона, д. 4, petrov.a.n84@mail.ru.
Для цитирования: Strength calculation of support areas in reinforced concrete beam structures / V.S. Dorofeev, V.M. Karpyuk, E.N. Krantovskaya, N.N. Petrov, A.N. Petrov // Вестник МГСУ 2013. № 12. С. 55—67.
