Design methods of seismodynamics of complex systems of underground pipelines Текст научной статьи по специальности «Строительство и архитектура»

a number of oscillations increased from 300 min-1 to 350 min-1 the seed losses developed actively and at a result it amounted in 0.8 % and 2.0 %. When a number of oscillations increased up to 400 min-1 the seed losses increased sharply that amounted in 4.0 %.

At the event when a number of oscillations was 500 min-1 the seed losses will sharply increase, and the reason for it the seeds Table 2. - Influence of sieve oscillations

actively move together with the foreign admixtures, a certain part will move throughout the sieve surface by jumping and comes out of sieve; it results in sharp increasing of the seed losses.

When oscillations amplitude was 5 mm., 10 mm., 15 mm., 20 mm. and 25 mm. the seed purity has amounted accordingly 98.2 %, 98.9 %, 99.1 %, 99.4 %, 99.4 % (table 2). amplitude on the seed purity and losses

No Performance quality indicators Sieve oscillations amplitude, mm.

5 10 15 20 25

1. Separation of foreign admixtures, in % 98.2 98.2 99.1 99.4 99.6

2. Seed losses, in % 0.3 1.3 2.4 3.7 5.8

After conducted experiments it was identified in case as the oscillations amplitude higher as the seed mixture movement ahead would be bigger; and as a result it was determined due to fast movement of seeds mixture the impure admixtures will pass through the sieve gap less.

In this case we think that due to that when the sieve's small oscillations amplitude (5 ... 10 mm.) the seed's movement ahead was smaller it will not consider the sufficient sieve gap in order for it to pass through the sieve and it slides down further on come

Table 3. - Influence of sieve slopping

out to waste; meanwhile due to higher amplitude of seed oscillations the seeds movement ahead would be so high and it outcomes in the seed losses.

The sieve sloppiness in its turn affects on the seed purity and losses (table 3). In the specified table there is shown that when slopping angle is ranging from 3 degr. to 15 degr. the grain losses and purity increase. When it was 3 degrees the seed purity amounted in 92.4 %, the losses were not noticed. And when the slopping angle was 15 degrees the seed purity and losses accordingly amounted in 99.3 % and 3.1 %. angle on the seed purity and losses

No Performance quality indicators Sieve slopping angle, in degrees

3 6 9 12 15

1. Separation of foreign admixtures, in % 92.4 96.6 98.6 99.1 99.3

2. Seed losses, in % - 0.2 0.6 1.3 3.1

As the slopping angle of seed cleaning machine was enlarging the grain purity and losses was increasing. At the event when the slopping angle was rising from 3 degr. to 9 degrees the seed purity enlarging increased. And it did outcome to when the slopping angle was rising from 12 degr. to 15 degrees the seed losses increased actively.

The seed purity and losses are characterized in a change depending on the sieve slopping angle and while the seed admixture moves slowly in small volumes slopping angle throughout the sieve surface; and its results in enlarging the volume of the small and large admixtures pass through the sieve together with the seeds; when the seed admixture moves slowly in big volumes the slopping

angle throughout the sieve surface and it results in that its most part comes out to waste.

Conclusion

In accordance with the achieved results after conducting experiments in the event when the number ofsieve oscillations ranged from between 350-400 min-1 the seed purity amounted in 98.0-99.0 % losses amounted in 2.0-4.0 %; when the oscillations amplitude ranged between 10... 15 mm. the seed purity amounted in 98.9-99.1 %, losses — 1.3-2.4 %; moreover when the slopping angle of sieve ranged between 9-12 degrees the seed purity amounted in 98.6-99.1 %, the loss — 0.6-1.3 % and more good indicators has been achieved.

References:

1. State standard - GOST 12096-76. Safflower for refinery. Technical conditions. - M., 1976. - P. 11-14.

2. Karimov M. R. Design and technologic process diagram of oily cultures preliminary cleaning machine//Creating resources-saving agricultural machines and enhancement of using them efficiently: Mat. from the Repub. sc.-pract. conf. - Gulbahor: IMEA, 2014. - P. 299-302.

Bekmirzaev Diyorbek Abdugapporovich, s. r. c., Institute seismic stability of structures Academy of sciences of Uzbekistan E-mail: diyorbek_84@mail.ru Xusainov Raxmatjon Baxrambaevich, National University of Uzbekistan, senior staff scientist

Kamilova Ra'no A., Tashkent Automobile and Road Institute

Design methods of seismodynamics of complex systems of underground pipelines

Abstract: Several problems of oscillation of complex systems of underground pipelines under seismic loading are considered in this paper. Derived system of equations is solved by the Method of finite differences of the second order of accuracy.

Design methods of seismodynamics of complex systems of underground pipelines

Software is based on the algorithm of computer realization in oriented language Borland Delphi 7. Results of the solution are presented in the form of graphs.

Keywords: complex systems of underground pipelines, seismo-dynamics, seismic effect, interaction in "pipe-soil" system, the Method of finite differences.

Seismo-dynamic theory of underground structures is based on actual data of the aftermath of strong ground motion on underground structures, namely Ashkhabad and Tashkent earthquakes [1]. Fifty years ago when a dynamic theory of seismic stability of the pipelines just began to form, the data on the damage and destruction of underground structures during the earthquakes were practically none. There existed few works on the aftermath of the USA and Japan earthquakes. This is explained by the fact that the pipe range in seismic active zones was comparatively short, so to reveal the damage was very difficult and not likely [2; 3].

Dynamic problem of the complex system of underground structures is sufficiently simplified and reduced to a problem of independent longitudinal motion of the main pipeline with reduced conditions of conjugation of a complex assembly and simple joints. With sufficient accuracy we can take that relative transverse displacements of the pipelines on a certain distance from the assembly are small compared with the amplitudes of soil oscillations, so for transverse motion of the pipeline is it enough to take the boundary conditions on other ends as the relative displacements at infinity being equal to zero. Also with sufficient accuracy we may neglect the force of inertia of relative transverse motions of the pipelines due to their small value compared with the rest of the terms of motion equation. These two conditions are validated and they considerably simplify the problem, since the determination of transverse displacement of pipes and the use of all kinematic conditions are also simplified [1; 4].

Statement of the problem

The problem of longitudinal oscillations of underground pipelines with complex assemblies is considered. It is known [5], that the system of differential equations of longitudinal oscillations of underground pipelines with complex assemblies, has the following form (in this case Iy = Iz = 0 — are axial moments of inertia):

-pF— + EF — -2nRk (1-u0) = 0; dt dx xV '

-p,F — + EF—-EF—-2nR H k" ( - u0 ) = 0; (1)

1 dt2 dx dx u uz x\ 0

dU" d2W -pF— + EF—-2nRk (1 - u0 ) = 0.

dt2 dx2 xV '

In the first and third equations of the system (1), differential equations of the motion of the left and right pipelines are given in relation to complex assembly. In the second equation a differential equation of the motion of absolutely rigid assembly is given (in point representation). Consider the system of equations (1) by the Method of finite differences of the second order of accuracy.

Transferring to dimensionless displacements and coordinates:

U = UR, u° = u R, u" = UR, x = xl, t = tt0, u0 = u0R, we get the

following system of equations in dimensionless parameters:

d2u' d2u' 2nRl2k /_, _ x „ +-:--(U - U0) = 0,

dt2 pF d2u

dx2

2—0

pFl dt2

d2w

aT pF dU du" dx dx

2nRuHuRkUl pFaT

(u0 -Uo) = 0, (2)

d2u" 2nRl n

---+-- (U - u0 ) = 0,

d~t dx1 aT pF

where aT = — .

Algorithm of solution of complex systems of underground pipelines under the effect of seismic loads

The system of differential equations (1) with account of boundary conditions is solved by the Method offinite differences. Here an approximation of the second order of accuracy with central difference scheme is mainly used [6].

d2u' UJ+1 - 2UJ + UJ1 d2u" U.1+1 - 2U1 + U11 (3)

2 , (3)

dt2 r2 d~t T

d2U U+, - 22U' + U+i - 2U' + Ui

" ' ' ' ' * h2 >

dx2

h2

dx2

d2u ° u°1+1 - 2u°1 + u11 dt2 " ' T ' '

(4)

(5)

When approximating the systems of differential equations (1) we use the approximating formulae (3)-(5) and as a result we obtain the system of algebraic equations. An obtained system of algebraic equations is solved in explicit scheme. Here t — is a step in time,

h

satisfying Currant's condition t < —. Computer realization

On the basis of developed methods a computer realization of discussed problems is formed. The algorithm of computer realization of the solution of the problem on longitudinal oscillations of a pipeline with two fixed ends is given below.

1. Initial data:

2. k = 1; 3. j = 0;

T 2nRuzhRkJ 77»tf) T PFl (77'»(k 1) _ 77'»(k 1) ^

4. u01№) =-

p1F1a,

-u " +-

2hp1F1

T2pFl t „

2hp1F1

(1) - &0(k 1)1

2

5. 1 < i < N -1;

2r2nRl2k _1(,

-^^ Uoi

aT pF

6. WUk' -

7. uI(k >

8. j=1;

9. i = 1;

10. u02 (k)

2

2i2nRl %_ Ul aT pF 2

r _T22nRHRkl

plFlaT

—oi(k) , T 2nRuhRkJ 1(k) U1 +--U01 "

P1F1aT

+11PE (k 1) _ ui <k 1) yllPE ((1 <k 1) _ U'1 <k 1)

2hp1F1

2hp1F1

11. u[2,t> =|2 - ^^--

h

2i2nR\%_l(k

--— uoi

aT pF

t2 Tr2nRl 2k

aT pF

x uHk>«21<k)+;

12. u"2№> = moi№> +f 2 -2 — - 2rlnRllk' II(t^ — ■ 1 " ^ h2 a\pF

2r2nRl2k _,

1 h2 2

aT pF

2

+

OI

13. i = i +1 ;

14. u2,k> =ll u;1« +

h

+ 2t2kRÏ% I№,

2 y 0i

ar pF

y 2t2kRI %

15. 2№» = TU?»-h

h2 aj, pF

2__ 2r2nRl2kr

h2 aj pF

u ut»+ £_ u'1,»»-

' h2 •+'

2r2nRl %_ 1k

2 ^ Oi '

aT pF

16. j < N - 2 if the condition is fulfilled turn to item 13, otherwise — to item 17;

17. i = N -1;

18. UN'1 > =— UN( ? +

N 1 h N 2

, 2r2nRlX^ uk,

2_2T^_2i1nRl %

19.

aT pF

u„ =— u„ ,

N 1 fc2 N 2

_x2nRl %_ 1((

h2 aj pF

2__ 2i1nRl%

fc2 a_ pF

2 y ON 1'

a_ PF

20. J = J +1 ;

21. i = 1 ;

22. m,0 /+I№ ) = ( 2 y2nRhRKX 2 Uy (k) - u0 y m +

' I PFoT J 1 1

+ TT2nRm kj2 (t i) - (k i),

pFa

T2pFl( ^, 2hpiFI

2hpF

Ut+Uk) -\ 2 2T 2T ¡Ut (k) +T u > (k )

23. u -|2-2h-^rpr P + h2u -

1 2 y 01

aT pF

24. U""® = U0(k) +f 2-2-- 2x171 Rlk "W'(k) + —wf(k) -1 1 ^ h aT pF J 1 h2 2

y i(k) + 2t2nRl2kx-j(k);

-U, +-;-M„I ,

aT pF

25. i = i +1 ;

26. U'+1 = U.\ +1 2 - 2— -

h2 11

,r2 2t2nRl 2k

h2 aT pF J ' h

T2_

u'.' +—u"1 -- 2 '+1

_ i , 2r2nRl2fc '

aT pF

r

27. U'+I = Uj +

h

I i I

v

2_nj2

2 __t_ _ 2TnRl% h aT pF

! 2t nRl%_, aT pF

28. i < N -2 if the condition is fulfilled turn to item25, otherwise to item 29;

29. i = N -1;

30. = j +

2 _2T_ 2r2nRl%

h2 aT pF

U' > + u0 '(k > _

uj i(t) + 2TnRl2kx uj(%) _ _UN 1 +--:-K,

aT pF

31 77" — T!" '(k)

1 = h2 UNN 2 '

2x2nRl2k (

r2 _ 2T_ _ 2x2nRl2k A v h2 aT pF j

N 1 N :

a_ pF

32. j < Z — 1 if the condition is fulfilled turn to item20, otherwise to item 33;

33. i = 1,0 < j < Z -1 ;

34. j«;0'№> - U1 (t <e if the condition is fulfilled turn to item 2, otherwise to item 35;

35. 1 < j < Z -1 ;

36. i = 0 ;

,R 1

37. a''= E-—(-3U0m + 4U'№> -№)1

l 2hy '

38. a"j(k) = ER—(-3Û0'm + 4U'm -Uj(k));

0 l 2h 0 1 2 '

39. 1 < i < N -1 ;

40. a"(k) = ER—(U+f ' -U>,<">);

' l 2h 1+1 " '

41. a»i<k> = eR—(U'\(t> -U'f );

' l 2h ,+I " '

42. i = N ;

43. = Ej^C^ -+);

44. <№) = eR^((<k) -+j);

45. The end.

Problem. Consider cast-iron underground pipeline with fixed ends. This problem is solved on the basis of an algorithm of computer realization.

Mechanical and geometrical parameters of underground pipeline and soil are taken in the following form:

E = 1,15-105 MPa.; p= 7,2-103 kg/m 3; F = ~m 2;

4

DH = 0,4 m.; DB = 0,39 m; l = 10 m; kx = 1-104 kN/m 3.

For the shaft (cylinder): E = 2,5 -104 MPa.; p = 2 -103 kg/m 3; DHz= 1,2 m.; DBz= 1,1 m.;

F =

_n(D2Huz - DBuz )

4

H m3; H = 1 m; k= 1-104 kN/m3;

uz uz x

2n

u0 = a0sm©£; a0 = 0,002 m; w ~~; T = 0,3 s.

Fig. 1a shows the change in node displacement in time under sinusoid impulse loading of the pipeline of the length l = 10 m., fig. 1b — the change in pipeline displacements along the length of the pipeline at given time.

Fig. 2a shows the change in stresses in pipelines in time, fig. 2b — the change in stresses along the length of the pipeline at given time. If reason from fig. 2a and 2b with decreased length of the pipelines the stresses appearing in pipelines are increasing. In discussed problems the values of maximum displacements of the pipelines are achieved near the assembly and equal to assembly displacement.

We have substantiated that the Building Code KMK 2.01.03-96, functioning on the territory of the Republic of Uzbekistan, has a number of shortcomings and demands revision with consideration of research results of recent years in seismic engineering.

The Building Code is too bulky and overloaded with ratios and schemes; this makes the work of designers very complicated. So, it is necessary to work out the recommendations and proposals on mentioned studies, their development being the further directions of our research. These studies are aimed to be included into a new version ofRepublican Building Code KMK in seismic-resistant construction.

t _

2 i+1

h

+

U1'k. > + U.0I№ > +

N 1

u:im +

N 1

T

Calculation of cylindrical shells of tower type, reinforced along the generatrix by circular panels

a)

b)

Fig. 1. а) — The change in assembly displacement in time under sinusoid impulse loading (l = 10 m.); b) — The change in the displacements of a pipeline at given time in х coordinate axis

a) b)

Fig. 2. а) — The change in stresses in pipelines near the assembly in time under sinusoid impulse loading; b) — The change in stresses on pipelines at given time along the axis of a pipeline (l = 10 m.)

So, discussed earlier bases of dynamic theory of seismic stability of underground structures did not lose their urgency and importance, but gained with time further development and at present are on a new more progressive stage of their improvement.

Conclusions

• An algorithm and applied program package developed on current stage allow us to determine the stress-strain state of a complex system of underground pipelines under seismic effects (for linear problems) depending on all parameters: Mach number (ratio of velocities of longitudinal waves in soil and

pipeline), attachment parameters, characteristics of a complex assembly (geometry of an assembly and soil density in an assembly), depth of bedding, intensity of seismic effect, etc. Developed software allow us to carry out strength analysis of underground pipelines under seismic effects and to realize system approach to the determination of the aftermath of earthquakes on stress-strain state of the pipeline and to plan engineering measures to provide safe and reliable operation of underground pipelines in dangerous (from the point of view of seismicity) zones.

References:

1. Rashidov T. R. Dynamic Theory of Seismic Stability of Complex Systems of Underground Structures. - Tashkent: FAN, 1973. - 180 p.

2. Rashidov T. R., Bekmirzaev D. A. Seismodynamics of Pipelines Interacting With the Soil//Soil Mechanics and Foundation Engineering. - New York, July 2015. - Vol. 52, № 3. - P. 149-153.

3. Rashidov T. R., Bekmirzaev D. A. Seismodynamic Problems of Underground Pipelines of Complex Configuration//Journal "Seismic Engineering. Safety of Structures". - Moscow, 2015. - № 3. - P. 33-37.

4. Ilyushin A. A., Rashidov T. R. Simplified Equations of Seismodynamics of Complex Systems of Underground Structures//Proc. Academy of Sciences RUz, Technical sciences. - 1970. - № 2. - P. 20-31.

5. Rashidov T. R., Bekmirzaev D. A. Numeric Method in Research of Seismodynamics of Complex Systems of Underground Pipe-lines//Proc. MGTU «MAMI». Natural sciences. - Moscow, 215. - № 4(26), V. 4. - P. 100-105.

6. Samarsky A. A., Gulin A. V. Numeric Methods. - Moscow: Nauka, 1989.

Akramov Khusnitdin Akhrarovich, Doctor of Technical Sciences, Professor

Davlyatov Shokhrukh Muradovich, Senior Scientific Worker - Researcher, Tashkent Architecture and Construction Institute E-mail: davlatshoh@inbox.ru

Calculation of cylindrical shells of tower type, reinforced along the generatrix by circular panels

Abstract: a simplified method of calculation of tower-type structures in the form of a cylinder shell, reinforced along the generatrix by circular panels based on limiting states of the first and second groups is proposed in the paper.