CC BY
30
Razzakov Sobirjon Juraevich, Associate professor, Ph. D. Holmirzaev Sattar Abdujabbarovich, Associate professor, Ph. D. Juraev Bahtiyor Gulomovich, Senior teacher Uzbekistan, Namangan engineering-pedagogical institute, Construction faculty E-mail: [email protected]
The study of seismic stability of a single-storey building with an internal partition with and without taking into account the frame
Abstact: The article presents data from a study on the dynamics of the carcass impact (periods and forms the fundamental vibrations) and the stress-strain state of the building with frame and without frame.
Keywords: individual buildings, the stress-strain state, the oscillation period, the form ofvibrations, dynamic characteristics, finite element method, a spatial model.
We consider the one-storey building with an inner wall, consisting of two rooms, made of burnt bricks, with the masonry modulus E = 300 MPa. Overlap weight is 52 kN. Estimated structure model — spatial box with partition. The method used to determine the stress state of the structure — the finite element method
(FEM). We will explore the carcass impact on the dynamics (periods and forms the fundamental vibrations) and the stress-strain state of the building with frame and without frame under static load. The study was conducted in parallel to the structure without the frame (fig. 1a) and a frame (fig. 1b).
a) b)
Fig.1. Model of a single-storey structure with an internal partition: without frame — a) and a frame — b)
Using the finite element method, we obtain a number of tasks for one-story box with internal baffle with and without taking into account the framework set in increments of 1 m around the perimeter of the exterior walls and internal partition. The framework was considered in two variants: wood, consisting of round logs (0 12 cm), and the concrete pillar of square section (a = 12 cm) with reinforcement.
The forms and periods of natural oscillations of a single-storey structure with an internal partition. According to the algorithm to solve the problem on their own forms and periods of oscillation. Forms for building vibrations are shown in fig. 2 (without the frame) and fig. 3 (with the frame). Comparison of the respective waveforms shows that the first form, which is the overlap shift for the model without the frame (fig. 2) is accompanied by bending the overlap in their plane. Thus deformed wall portions immediately adjacent to the joints of the walls opposite direction, and an upper layer near ceiling wall. The second form, which represents the torsion of overlap, it is also accompanied by bending and deformation of the wall in its own plane. It can be seen from fig. 2 the deformations rectilinear boundaries of finite elements.
An analysis of the forms of natural oscillations with a skeleton model shows that the vertical and horizontal lines, dividing the model into finite elements do not undergo fracture and overlapping moves like a hard drive, without bending deformations in the plane (fig. 3). I. e. with a skeleton construction works as a spatial system without deformations of each wall separately.
The periods of natural oscillations models without frame for the first two forms, shown in fig. 2, respectively, T = 0,075 seconds and T2 = 0,068 seconds and for the model with a skeleton (fig. 3) — T1d = 0,13 seconds and T2d = 0,1 seconds (for wooden frame) and T1b = 0,1 seconds and T2b = 0,086 seconds (concrete pillars). Increasing periods of natural oscillations of the building with the frame is also evidence linking the role of a skeleton. As a result, the frame installation box varies as a whole without deformation of its individual faces (walls). A single oscillation system occurs with a longer period than the fluctuation of its individual parts. The relative reduction in oscillation periods built with concrete pillars compared with wooden building explains the increase in stiffness, while the character waveforms remains unchanged irrespective of the carcass.
a) b)
Fig.2. The first (a) and second (b) forms of natural oscillation model with the internal structure of a single-storey partition
a)
Figure 3. The first (a) and second (b) forms of natural vibration
Investigation of stress-strain state of one-storey buildings with an inner partition, taking into account the weight of the overlap and the partition. Used for the brickwork, have been found experimentally, the calculation method, the modulus of elasticity E = 300 MPa. Weight overlap in both cases is 52 kN. Diagrams vertical displacements are shown in fig. 4, where the maximum displacement is achieved in the upper levels of buildings. For buildings with load-bearing brick walls (fig. 4a) the maximum displace-
a)
-3.7 e -7.4 e -1,1 e
-1,5 e
-1,8 e -2,2 e -2,6 e
-2,9 e -3,3 e max u min u=
b)
-3.7 e -7.4 e -1.1 e -1.5 e -1.9 e -2.2 e -2.6 e
-3.0 e -3.3 e max u minu=
5 (9) 5 (8) 4 (7) 4 (6) 4 (5) 4 (4) 4 (3) 4 (2); 4 (1) =0
-3.7 e
7 (9) 7 (8)
6 (7) 6 (6) 6 (5) 6 (4) 6 (3) 6 (2); 6 (1) =0
-3.7 e
[m]
c)
-1.7 e--3.5 e--5.2 e--7.0 e--8.7 e--1.0 e--1.2 e--1.4 e--1.6 e-max u =0 minu=-1.7 e-
7 (9) 7 (8) 7 (7) 7 (6) 7 (5) 6 (4) 6 (3) 6 (2); 6 (1)
b)
model with one-story structure with an internal partition frame
ment under its own weight of overlap and the walls themselves are 0,3 mm by almost two orders of magnitude higher than in the construction of a wooden frame (fig. 4b), vertical movement of which, in its turn half superior movement in the construction of a concrete frame. The nature of the distribution diagrams for structures with different frame is the same, quantitative difference reached displacements presented in the tables: with wooden frame - b; with concrete - c.
[m]
Fig. 4. Diagrams vertical displacements in one-storey building with an internal partition with load bearing brick walls (a) and to the frame (b — wooden, c — concrete) under its own weight
where the first table numeric values refers to the construction of a wooden frame, and the second - with concrete.
The resulting static loading its own weight and vertical tangents .{ctz} .{tzx}, .{fzy} stresses in the planes of the walls shown in fig. 5 (for building without a frame) and in fig. 6 (with a frame),
a)
-1 e-2 (6); -2 e-2 (5); -3 e-2 (4); -4 e-2 (3); -5 e-2 (2);
-6 e-2 (1)
max ct =-4e-3 min ct =-6.4 e-2 [MPa]
b)
+2.7 e-3 (5); + 1.4 e-3 (4); + 1.2 e-4 (3); -1.2 e-3 (2); -2.5 e-3 (1) max T^ =+4.2e-3 min T =-3.5 e-3 [MPa] c)
+ 1.25 e-3 (4); +5 e-4 (3); —2.5 e-4 (2); — 1 e-3 (1)
max T =+1.9e-3
yz
min Tyz =-1.7 e-3
[MPay]z
Fig. 5. Diagrams of normal vertical (a) and tangential (b, c) stress in the one-storey building with an internal partition with load bearing brick walls under its own weight
-5.8 e-5 (5); -2 e-4 (4); -3.4 e-4 (3); -4.8 e-4 (2); -6.2 e-4 (l) max o =-5e-5 min o =-6.8 e-4 [MPa] b)
+2.5 e-5 (6); + 1 e-5 (5); -5 e-6 (4);
-2 e-5 (3); -3.5 e-5 (2);
-5 e-5 (1)
max Td =+5e-5 min t =-5.5 e-5 [MPa] c)
3 e-5 (7);
2 e-5 (6);
1 e-5 (5); 0 (4);
-1 e-5 (3);
-2 e-5 (2);
-3 e-5 (1) max t =+3.3e-5
yz
min t =-3.3 e-5 [MPal
-1.7 e-4 (5); -2 e-4 (4); -2.3 e-4 (3); -2.6 e-4 (2); -2.9 e-4 (1) max o =-2.4e-5 min o =-3.2 e-4 [MPaz
+7 e-6 (6); -1 e-6 (5);
-9 e-6 (4); -1.7 e-5 (3); -2.5 e-5 (2); -3.3 e-5 (1) max t D=+3.8e-5 min t =-4 e-5 [MPaf
9 e-6 (7); 4,5 e-6 (6); 0 (5);
-4.5 e-6 (4); -9 e-6 (3); -1.3 e-5 (2); -1.8 e-5 (1)
max t =+2.2e-5
yz
min t =-2.2 e-5 [MPaf
Fig. 6. Diagrams normal vertical (a) and tangential (b, c) stress in the one-storey brick building with an internal partition with a skeleton under its own weight
Comparison of vertical stress values in fig. 5a and fig. 6a shows that the installation of the frame leads to a more uniform distribution of the normal vertical stresses in the plane of the wall even if the wall openings. The maximum compressive stresses in the lower part of the building without a skeleton near the doorway, reaching values of 0,06 MPa (fig. 5a). In the case of a frame, receiving the load from the ceiling, the compressive stresses induced by the action of its own weight only, two orders of magnitude less. Approximately the same quantitative ratio observed in buildings without a frame and with frame and shear stresses in the planes of the longitudinal and transverse walls. At the same time the largest in magnitude shear stresses arise in the front wall in the areas immediately adjacent to the corners of openings (fig. 5b). The presence of the frame not only reduces shear stresses, but also leads to a more even distribution of them on the walls
of the plane (fig. 6b). Concrete frame reduces the stress produced even doubled comparing with the structure having a wooden frame. In general, the vertical static load of its own weight and the weight of the slab does not cause a high tension of the walls of the building, not even a reinforced frame. Of course, this applies to the particular case, when the overlap weight, as stated above, is equal to 52 kN. [1, 158-169].
In general, based on the analysis of the stress-strain state of a single-storey building with an internal partition, you can draw the following conclusion:
Availability carcass unites longitudinal and transverse walls and floor in a single spatial system that has increased resistance applied static load, resulting in movement and level of stresses arising in the walls are greatly reduced in comparison with the same characteristics in the walls are not supported by the frame.
References:
1. Razzaqov S. J. The earthquake-resistance and stability of buildings and structures built from clay. Moderner Lehmbau - 2003. Nachhaltiger Wonungsbau-Zukunft Ökologisches Bauen. Fraunhofer IRB Verlag. Auferstehungs-kirche-Berlin, Germany. - S. 158-169.
Sagatov Bahodir Uktamovich, Tashkent Architecture and Construction Institute, Senior Fellow Researcher, E-mail: [email protected]
About transfer of effort through cracks in ferro-concrete elements
Abstract: The paper discusses new mechanisms of nonlinear behaviour of RC with regard tostress transfer across the cracks. It also gives the results of testing and realization of contact interaction model in cracks. Keywords: ferroconcrete, nonlinear behavior, cracks.
Qualitative change is intense-deformed state ferroconcrete elements after formation of cracks is connected with considerable anisotropy of properties of a material, display of nonlinear deformations, and also variety influence insufficiently known features of teamwork of concrete and armature. Uncertainty these factors bring the greatest at calculations of the ferroconcrete designs having the difficult physical mechanism of destruction as, for example, it takes place at shift or a cross-section bend. For the account of nonlinear properties of ferroconcrete, besides more exact estimation of its fundamental properties, it is necessary to pay attention to creation of models and methods of calculation of the ferroconcrete, reflecting the valid character of their behaviour under loading and a physical essence of problems arising thus.
At calculation of ferroconcrete designs with cracks numerical methods of final differences, the variation — differential and final elements are usually used. As a rule, convergence of iterative process is defined by accuracy of calculations on efforts of values hardly which essentially differ for stages before formation of cracks. In existing programs the account cracks formations is made by various models of the discrete crack which development on border of final elements is represented rupture of communications in knots. Common faults of this approach are restriction of a direction of development of a crack of orientations of knots of a final element and discount contact interaction of coast of a crack. Partially these restrictions are eliminated by «spreading» cracks on element volume in the assumption that directions of the main pressure or are parallel or perpendicular orientations of the cracks which surface is not capable to transfer stretching or shifting efforts. It automatically excludes what or redistribution of efforts after cracks formations, and the module of shift rigidity G thus is accepted equal to zero.
Other extreme measure, i. e. maximum resistance to a cut after cracks formations, is offered in norms CEB — FIP [3]. Probably, the decision at which decrease in rigidity of an element to certain size depending on width of disclosing of the cracks formed in it would be considered is compromise.
The made observations specify in extreme importance of researches of the mechanism of transfer of pressure through cracks in ferroconcrete elements. Such researches demand studying various mechanical and geometrical parameters in this connection working out of corresponding mathematical models should lean against adequate experimental data. First of all it concerns researches of the mechanism and features of transfer of shift pressure through a crack in the course of contact interaction of its coast. An important step forward in this direction was the deformation theory ferroconcrete with the cracks. In it ferroconcrete considers as physically nonlinear anisotropic material, and receiving on its basis of dependence and the calculation program on the computer are confirmed experimentally and spreading in designing practice. If at compression and a stretching mechanism transfers of pressure through cracks has found a sufficient experimentally-theoretical substantiation at a cut it is investigated obviously insufficiently. Here it is a question of the new factors shown in cracks at mutual shift of their coast: tangents of forces hitchs and treenail actions armatures cores. Cracks in concrete, developing, pass through a cement stone, grains of a filler and a contact zone, forming two cooperating rough surfaces of difficult geometry. They also provide transfer of shifting pressure through cracks by mechanical gearing and a friction. Researches have shown [2] that the assumption of full restraint of tangents of displacement in cracks at such gearing does not represent the facts. More over, displacement tangents can serve more exact exponents
