624.042.1
Ⱥ
.
Ƚ
.
Ɍɚɦɪɚɡɹɧ
ɎȽȻɈɍ
ȼɉɈ
«
ɆȽɋɍ
»
ɊȺɋɑȿɌ
ɗɅȿɆȿɇɌɈȼ
ɄɈɇɋɌɊɍɄɐɂɃ
ɉɊɂ
ɁȺȾȺɇɇɈɃ
ɇȺȾȿɀɇɈɋɌɂ
ɂ
ɇɈɊɆȺɅɖɇɈɆ
ɊȺɋɉɊȿȾȿɅȿɇɂɂ
ɇȺȽɊɍɁɄɂ
ɂ
ɇȿɋɍɓȿɃ
ɋɉɈɋɈȻɇɈɋɌɂ
Ɍɨɱɧɨɟɢɚɞɟɤɜɚɬɧɨɟɨɩɢɫɚɧɢɟɜɧɟɲɧɢɯɜɨɡɞɟɣɫɬɜɢɣɢɧɟɫɭɳɟɣɫɩɨɫɨɛɧɨɫɬɢɦɚɬɟɪɢɚɥɚ ɤɨɧɫɬɪɭɤɰɢɢɬɪɟɛɭɟɬɩɪɢɜɥɟɱɟɧɢɹɦɟɬɨɞɨɜɬɟɨɪɢɢɜɟɪɨɹɬɧɨɫɬɟɣɢɬɚɤɨɣɯɚɪɚɤɬɟɪɢɫɬɢɤɢɤɨɧ
-ɫɬɪɭɤɰɢɢ, ɤɚɤɧɚɞɟɠɧɨɫɬɶ, ɦɟɪɨɣɤɨɬɨɪɨɣɹɜɥɹɟɬɫɹɜɟɪɨɹɬɧɨɫɬɶɛɟɡɨɬɤɚɡɧɨɣɪɚɛɨɬɵ.
Ⱥɧɚɥɢɡɪɚɫɱɟɬɚɤɨɧɫɬɪɭɤɰɢɣɩɨɡɚɞɚɧɧɨɣɧɚɞɟɠɧɨɫɬɢɩɨɤɚɡɵɜɚɟɬ, ɱɬɨɢɡɦɟɧɱɢɜɨɫɬɶɧɟ
-ɫɭɳɟɣɫɩɨɫɨɛɧɨɫɬɢ ɜɥɢɹɟɬɧɚ ɨɬɧɨɫɢɬɟɥɶɧɵɟɪɚɡɦɟɪɵɩɨɩɟɪɟɱɧɨɝɨɫɟɱɟɧɢɹɫɢɥɶɧɟɟ, ɱɟɦ
ɢɡɦɟɧɱɢɜɨɫɬɶɧɚɝɪɭɡɨɤ.
Ʉɥɸɱɟɜɵɟɫɥɨɜɚ: ɡɚɞɚɧɧɚɹɧɚɞɟɠɧɨɫɬɶ, ɧɨɪɦɚɥɶɧɨɟɪɚɫɩɪɟɞɟɥɟɧɢɟ, ɧɚɝɪɭɡɤɚ, ɧɟɫɭ
-ɳɚɹɫɩɨɫɨɛɧɨɫɬɶ, ɤɨɷɮɮɢɰɢɟɧɬɵɜɚɪɢɚɰɢɢ, ɠɟɥɟɡɨɛɟɬɨɧɧɚɹɩɥɢɬɚ,ɫɪɨɤɫɥɭɠɛɵ, ɩɨɩɟɪɟɱ
-ɧɵɟɪɚɡɦɟɪɵ.
,
-.
,
S
:
,
S
=
Kq
(1)
K
.
q
,
-
2f
q
.
,
f
2
R
[1].
.
,
-,
,
[2], . .
H
P R
S
, (2
)
Н
—
;
P
—
;
R
—
;
S
—
.
,
,
[3],
,
f
1
S
:
1 3
1
.
S
f
S
f
K
R
(3)
2 1
H
f
R
f
S dS dR
(4)
1 2
H
f
S
f
R dR dS
1
f
S
,
f
2
R
(4)
(5),
-зад
H
=
H
,
К
:
, ,
...
,
,
К
= φ
(
а а
1 2a
nH
зад)
1
, ,
2 3а а а
—
-.
Ʉ
,
.
,
,
ȿ
,
,
.
ȿ
f
5
E
.
ȿ
ȿ
*,
1
:
f
( )
( )
1 3 5
1
.
E
f
f
f
E dE
К
К
∞ ∗
∗ ∗
∗ ∗
−∞
ω
ω =
∫
H
=
H
зад,
*
К
.
f
4
h
.
,
(4),
h
расчрасч ном
,
h
=
h
− ∆
(6)
ном
h
—
;
—
,
f
4
h
H
h.
ном расч
.
h
=
h
+ ∆
(7)
4
f
h
,
(
)
ном расч
1
h,
h
=
h
− γ
A
(8)
—
H
h;
А
h—
-.
Н
задН
задН
h.
,
[4].
2
3 2
1
exp
;
2
2
q
q q
q
m
f
q
(9)
22 2
1
exp
.
2
2
R
R R
R m
f
R
(10)
[5]
22 2 2
1
exp
2
2
S
S S
S
m
f
S
K
K
(11)
,
.
S q q
m
Km
K
,
R S R q
m
m
K
2 2 2 2
.
R S R
K
q
(
)
( )
20
0
R S,
R S
m
Н
P
R
S
f Z dZ
Ф
∞
−
−
=
−
∞ =
=
σ
∫
p
p
(12)
( )
1
22Ф
2
t dt
е
γ −
−∞
γ =
π
∫
—
.
H
-.
2 2 2 2
.
R q
R S
R S R q
m
K
m
K
(13)
K
,
2
4
,
2
K
(14)
2 2 2
,
2 2 2,
2
.
q q R R R q
m
m
m m
K
,
.
(14)
2 2
2 2 2 2 2
1
,
1
R R
q R q R q
m
A
K
m
A
A
A A
(15)
, .
qR
R q
R q
A
A
m
m
,
R
A
A
q.
,
A
R
1
-,
-.
,
-F -F
R
A
A
q,
. 1 2.
F
—
,
-,
.
,
A
RF F
,
.
q
A
A
R.
—
.
,
±2
0, 9
,
У
R R
A
=
A
A
УR=
0, 54
A
R.
-R
A
A
q,
,
2
,
.
c. 1.
:1 — AR = Aq= 0,1;
2 2
.
1
R
q R q
m
K
m
A
A
(16)
. 2.
R
A a , A бq( ) Aq AR
-( ) :в
γ 1 — F F f A( q)
A
R = 0,1; 2 — F F f A( R)
0,1
q
A
-.
,
S
-,
q
. .
(1).
,
,
.
0
P
,
T
(
):
0
0 0
exp
( , ( ))
.
T
Н
P
Sf R S t dSdt
∞
=
=
−
∫ ∫
&
&
&
(17)
(17)
(1),
K
.
K
,
.
( )
S t
—
,
V R T
—
R
T
—
:
2
2 2
2 2
exp
2
.
2
R S
S
S R
S R
m
m
T
V R T
(18)
:
2
2 2
2 2
exp
exp
,
2
2
R S
S
S R
S R
m
m
T
H
(19)
2
S
—
;
2R—
;
m
S—
-;
m
R—
-;
T
—
.
[6]
2cos
sin
.
a
q q
a
K
e
(20)
α
,
K
q
2
2 2 2 2 2 2 2 2
2
0
0
.
S S S S q
d
K
K
a
K
a
d
(
21
)
2
2 2
2 2 2
2 2 2
exp
exp
,
2
2
R q
q R
q R
m
K
T a
H
K
K
(22)
.
K
0
R
( . .
,
,
-)
(22)
K
:
,
2
R
q q
m
K
m
A
(23)
2 2
2
ln
ln
H
.
A
T a
(24)
-5, 5 6, 0 м,
×
,
q
a
1
.
q q
K
e
a
h
,
H
0, 99.
:
3
1 10 КПа;
q
m
= ⋅
σ = ⋅
q1 10 КПа;
2m
R= ⋅
5 10 КПа;
5
R0;
6
50 лет
1578 10 с;
T
=
=
⋅
a
0, 707
c
1;
μ
=
0, 3,
a
,
K
q
.
,
S
K
qa
,
6
2
ln
2
ln 0, 99
ln
ln
23, 59.
1578 10
0, 707
H
A
Ta
5
3 2
5 10
296, 4.
2
10
10
2 23, 59
R
q q
m
K
m
A
2
2
,
c a
K
h
c
0, 3665
—
,
.
2 2
2
0, 3665 6, 0
21, 0 10 м,
296, 4
c a
h
К
−
⋅
⋅
=
=
=
⋅
. .
h
=
21 см
.
Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣɫɩɢɫɨɤ
1. Ʌɵɱɟɜ Ⱥ.ɋ.
// . .- . . , 1997. . 33—37.
3. ȺɪɚɫɥɚɧɨɜȺ.ɋ. -. -., 1986-. 268 -.
4. Ɍɚɦɪɚɡɹɧ Ⱥ.Ƚ.
— // .
2009. № 1. . 160—171.
5. JSO/TK 98 ST 2394 General Principles on Reliability for Structural, 1994, S. 50.
6. Ɋɚɣɡɟɪȼ.Ⱦ. : . . :
-, 1998. 304 .
ɉɨɫɬɭɩɢɥɚɜɪɟɞɚɤɰɢɸɜɚɜɝɭɫɬɟ 2012 ɝ.
: ɌɚɦɪɚɡɹɧȺɲɨɬȽɟɨɪɝɢɟɜɢɱ — ,
, ɎȽȻɈɍ ȼɉɈ «Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ
ɫɬɪɨɢɬɟɥɶɧɵɣɭɧɢɜɟɪɫɢɬɟɬ» (ɎȽȻɈɍȼɉɈ «ɆȽɋɍ»), . , 129337, ,
. 26, tamrazian@mail.ru.
:ɌɚɦɪɚɡɹɧȺ.Ƚ.
// . 2012. № 10.
. 109—115.
A.G. Tamrazyan
DESIGN OF STRUCTURAL ELEMENTS IN THE EVENT
OF THE PRE-SET RELIABILITY, REGULAR LOAD AND BEARING CAPACITY DISTRIBUTION
Accurate and adequate description of external infl uences and of the bearing capacity of the structural material requires the employment of the probability theory methods. In this regard, the characteristic that describes the probability of failure-free operation is required. The characteristic of reliability means that the maximum stress caused by the action of the load will not exceed the bearing capacity.
In this paper, the author presents a solution to the problem of calculation of structures, namely, the identifi cation of reliability of pre-set design parameters, in particular, cross-sectional dimensions. If the load distribution pattern is available, employment of the regularities of distrib-uted functions make it possible to fi nd the pattern of distribution of maximum stresses over the structure.
Similarly, we can proceed to the design of structures of pre-set rigidity, reliability and stability in the case of regular load distribution. We consider the element of design (a monolithic concrete slab), maximum stress S which depends linearly on load q. Within a pre-set period of time, the probability will not exceed the values according to the Poisson law.
The analysis demonstrates that the variability of the bearing capacity produces a stronger effect on relative sizes of cross sections of a slab than the variability of loads. It is therefore par-ticularly important to reduce the coeffi cient of variation of the load capacity. One of the methods contemplates the truncation of the bearing capacity distribution by pre-culling the construction material.
Key words: pre-set reliability, normal distribution, load, bearing capacity, coeffi cient of varia-tion, concrete slab, life cycle, cross section.
References
1. Lychev A.S. Sposoby vychisleniya veroyatnosti otkaza v kompozitsii raspredeleniy prochnosti i nagruzki [Methods of Calculation of the Probability of Failure within the Framework of the Distribution of Strength and Load]. Trudy mezhdunarodnoy nauchno-tekhnicheskoy konferentsii [Collected works of the international scientifi c and technical conference]. Samara, 1997, pp. 33—37.
2. Tichy M. In the Reliability Measure. Struct. Safety. 1988, vol. 5, pp. 227—232.
3. Araslanov A.S. Raschet elementov konstruktsiy zadannoy nadezhnosti pri sluchaynykh vzaimodeystviyakh [Calculation of Structural Elements with the Pre-set Reliability If Exposed to Random Interactions]. Moscow, 1986, 268 p.
Vestnik TsNIISK [Bulletin of Central Research and Development Institute of Building Structures]. 2009, no. 1, pp. 160—171.
5. JSO/TK 98 ST 2394. General Principles on Reliability for Structures. 1994, pp. 50.
6. Rayzer V.D. Teoriya nadezhnosti v stroitel’nom proektirovanii [Theory of Reliability in Structural Design]. Moscow, ASV Publ., 1998, 304 p.
A b o u t t h e a u t h o r: Tamrazyan Ashot Georgievich — Doctor of Technical Sciences, Professor, Department of Reinforced Concrete and Masonry Structures, Moscow State University of Civil Engi-neering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; tamrazian@mail.ru.