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11biaxial bending at normal temperature presented in [5], [6] and [7]. Parameters dl / h, h , fyd , fcd ,
mEd,y, mEd z and nEd shal1 be rePlaced with dLfi/hfi, hfi, fsy , fcd , mEi y , mEd zzJl and nEd . Normalized interaction curves used in fire impact are similar to curves presented in [3] and [4];
- when az = a and az > a is using normalized curves for square columns, composed in this
paper according to the proposed procedure;
d) proposed interaction curves can be applied to the determination of bearing capacity and the calculation of the reinforcement;
e) interaction curves can be used to design sections of columns, subjected to all-sides by standard fire exposure, according ISO834, or any other time heat regimes, which cause similar temperature fields in the fire exposed column;
f) reinforced concrete sections design, by the simplified calculation method "Isotherm 500°C", does not take into account the thermal expansion of material (concrete and reinforcing steel).
REFERENCES
1. БДС EN 1992-1-2:2005 и БДС EN 1992-1-2:2005/ NA - Еврокод 2: Проектиране на бетонни и стоманобетонни конструкции. Част 1-2: Общи правила. Проектиране на конструкции срещу въздействие от пожар.
2. Захариева-Георгиева Б. Проверка за огнеустойчивост на стоманобетонни колони чрез опростения изчислителен метод „Изотерма 500°С" на БДС EN 1992-1-2:2005, „сп. Строителство", бр. 6, 2012 г.
3. Нешев Хр. Огнеустойчивост на правоъгълни стоманобетонни колони със симетрична армировка, подложени на огъващ момент и осова натискова сила при едностранно пожарно въздействие в равнината на огъващия момент, Първа научно- приложна конференция с международно участие. Стоманобетонни конструкции теория и практика- София, 2015г.;
4. Нешев Хр., Огнеустойчивост на правоъгълни стоманобетонни колони със симетрична армировка, подложени на огъващ момент и осова натискова сила при четиристранно пожарно въздействие, Първа научно- приложна конференция с международно участие. Стоманобетонни конструкции теория и практика- София, 2015г.;
5. Николов П. Стоманобетонни пътни мостове. Ръководство за проектиране, София, 2013г.
6. Русев К. Стоманобетон НПБСК-ЕС2, София, 2008г.
7. Русев К., В.Янчев ЕС2. Оразмеряване на стоманобетонни конструкции по нормални сечения, София, 2011г.
8. Charif A. Biaxial bending in columns
9. http://faculty.ksu.edu.sa/charif/Documents/Columns-Biaxial.pdf
THE INFLUENCE OF THE STIFFNESS COEFFICIENT OF THE HYDRAULIC LIQUID ON THE DYNAMICAL BEHAVIOUR OF THE SYSTEM "HYDRAULIC CYLINDER -
LOAD"
PhD. Petkov Boris
Bulgaria, Sofia, University of Transport "Todor Kableshkov"
Abstract. In this paper we suggest a way how to determine the stiffness coefficient of the hydraulic liquid in a hydraulic cylinder under load and we also show its influence on the dynamical properties and behavior of the system "hydraulic cylinder- load".
Keywords: stiffness coefficient, hydraulic powered system, frequency response.
INTRODUCTION. During the calculation of the parameters of the hydraulic powered systems the elastic properties of the liquid are usually ignored. In practice, a stiff system is most often required
because of the assumption that the hydraulic fluid is incompressible. The compressibility of a liquid may be ignored in systems that do not require tight control of response and where operating pressure and liquid volume are moderate.
However, all liquids have some degree of compressibility. When applying high pressure to a large volume of liquid, a significant amount of energy can be expended to compress the liquid. The liquids, used in the hydraulics, are elastic bodies in terms of the Hook's law when operating pressure is up to 60 MPa.
The bulk modulus of elasticity [1] as the reciprocal of volume compressibility is an important property of the hydraulic liquids. Bulk modulus is a measure of a liquid's resistance to compressibility. The compressibility of a liquid has an influence on the speed of response and also on the whole dynamics of a given hydraulic system.
The stiffness coefficient of a liquid is a measure of the resistance of an elastic material to compression. For an elastic element (liquid in cylinder) with a single degree of freedom, the stiffness is correlated with bulk modulus. We will use this relation to determine the stiffness coefficient of the hydraulic liquid.
DETERMINATION OF THE STIFFNESS COEFFICIENT. The bulk modulus [2] K is the change of the pressure Ap which produces a relative change AV in the liquid's volume V :
K = —
Ap
AVIV'
, MPa
(1)
If we denote with F the magnitude of the acting force and with S the piston area in a hydraulic cylinder (fig. 1) and apply Ap=F/S and that AV=S. Ax, where Ax is the value of the compression, we can define:
S AV
F V
Ax S2
(2)
From Hook's law the stiffness coefficient k is: k=F/Ax and according to (2):
k=N/m
V
DYNAMICAL PROPERTIES. To study the its dynamical properties, we can represent the system "hydraulic cylinder - load" (fig.2) in the following way. We substitute the liquid's amount under the piston with a linear spring with stiffness coefficient k; and we apply a dynamical forced disturbance Psin(rnt) and load with mass m to the piston rod. Thus we can write [3] the differential equation for the small vibrations using D'Alamber principle:
(3)
my + ky = Psin(öt) + mg
(4)
Psinul
]
AV
Fig.1 Hydraulic cylinder (computational scheme)
Fig.2 Hydraulic cylinder-load
If the frequency w of the forced disturbance becomes equal to the natural frequency wn
(o)n = J— ) , a dynamical multiplication (resonance) will appear. This may damage the construction.
The solution of the differential equation (4) is obtained for the following parameters: m = 10 t, P = 1000 N, w = Wn = 42,2 s1 , k= 17 MN/m .
The stiffness coefficient k is determined for a hydraulic cylinder with a piston's diameter D = 0,1 m and stroke st = 0,5 m.
The bulk modulus for the mineral oil with temperature t = 60 oC is K = 1,4.103 MPa. The solution (fig.3) shows the multiplication of the amplitude due to the resonance effect.
Motion of the lead
0 0.5 1 1.5 2 25 3 3.5 4 45 5 t. s
Fig.3 The law of motion of the load in case of resonance
The frequency response is the change of the amplitude A of the load in relation to the frequency a of the disturbance force: A = f (a).
This function can be derived with Laplace Transformation of the equation (4). The transfer function of the system is:
WO) = (ms2 + k)
(5)
where s is the Laplace operator.
After substitution of s with iw ( i = ^(—1) ) we can define the amplitude A which is the modulus of the complex transfer function W(ia):
A(a) = (\k-m ¿y2|)_1
(6)
Equation (6) is the frequency response of the undamped system "hydraulic cylinder - load". Figure 4 shows the graphical form of the frequency response for two loads with masses 10 t and 5 t, respectively
i
m=lC m=S
i • J
J... ¡A
>
30 35 40 It SO SS 60 65 70 75 omega 6-1
Fig. 4 Frequency response of the undamped system "hvdraidic cylinder - load" The values of the asymptotes are the natural frequencies for the each mass.
CONCLUSIONS. The stiffness coefficient of the liquid in a hydraulic cylinder can be defined using its elasticity in terms of Hook's low.
The stiffness coefficient of the liquid determines important dynamical characteristics of hydraulic powered systems.
We recommend taking into consideration dynamical verifications, using the stiffness coefficient of the liquid, when calculating the parameters of hydraulic systems operating huge masses with hydraulic cylinders with large amounts of liquid.
REFERENCES
1. Herman F.G., Allan B., What is the bulk modulus and when it is important", Hydraulics and Pneumatics, The Lubrisor corp., Ohio, www.lubrisor.com
2. Комитовски М., Елементи на хидро- и пневмозадвижването, Техника, София, 1985
3. ПисаревА., Курс по теоретична механика II ч., Техника, София, 1975
SOLUTION OF THE PROBLEM IN THE DRYING OF FLAT INFRARED HEATING MATERIAL LAYER AT STATIONARY
MOISTURE TRANSFER
PhD. Safarov J. E, Sultanova Sh. A, Mamatkulov M. M., Abduraxmanova Z. A., Saloxiddinov S. R.
100095, Republic of Uzbekistan, Tashkent Tashkent state technical university named after A.R.Beruni
Abstract. Nonlinear process when the moisture has a stationary position from the point of the analytical research is needed for theoretical and applied problems. In this paper we investigate the distribution of the heat provided stationary moisture where heat distribution has a pattern differs from the linear interaction between moisture and heat. Permanence moisture sampling is the result of a relatively steady drying mode. In the drying chamber we have a closed volume, it is particularly noticeable for the vacuum chambers, and therefore there is almost stationary process between stable heating and evaporation. Obtained linear problem of parabolic type to accomplish this task with the appropriate boundary conditions, we can apply for the interval (0, l), separation of variables. The solution for linear and non-linear interaction of moisture and temperature in the case of stationary moisture have a predetermined temperature field as a result of solution of the nonlinear system that is needed to assess the effect of non-linearity which clearly identifies with a solution.
Keywords: drying, infrared radiation, mathematical model, moisture transfer.
One of the modern and increasingly used in industry promising processes is the heating of materials containing water, intense radiation [1].
The equation of drying A.V.Lykov [2], when the heat drying of the material takes place under the influence of the microwave field it has been investigated in the thesis Kazartsev D.A. [3]. In its task of heating is volumetric throughout the material as the physical nature of microwaves has the property.
The scientists of the Tashkent state technical university carried out a study of agricultural drying [4-6].
We write the well-known system of equations for our problem:
[c,Tt-eWt = ATx -c[dWx + dTTÁ]TÁ + Q
1(1-^= (flwx + X . ()
