concrete3

u Gaussian (Standard) normal distribution function y2 1 x F y exp 2 dx y 2 u Px u 1 Px u 1 when : u 2 u 2 2 2.275% P x u Px u 1 2 2 97.725%
i 1
1 n
2).standard deviation :

X Байду номын сангаас 2
i 1
n
3).coefficient of variation:
= /
•The littler , is ,the littler variance is,the more random variable concentrates.
●The above requirements are generally referred to as “reliability of structure”.
3.1.2.Limit state of structure
The limit states of a structure are the specified states, that a structure or part of a structure exceeds and the structure cannot satisfy the requirements for reliability. In the Chinese Code“Unified Standard for Reliability Design of Building Structures”GB50008—2001, the limit states of a structure are classified by the following:
• 2).calculating law of random variables:
x1 , x2 , xn ~ N , a). f x x1 x2 xn then: f x x x b). f x x1 x2 x3 xn then: f x x x x
26
27 28
40.9
42.8 41.7
33
34 35
43.7
34.0 41.5
=41.59Mpa
=3.40Mpa
0.082
2.Normal distribution of probability 1).normal curve:N(, )
Distribution function:
• • • • • • 1).variability of load itself. 2).variation between assumption of calculating internal fore and practical situation of stressing. 2.the uncertainty of structural resistance R 1).the irregularities in the material strength 2).the variation of section size 3).the calculating model of resistance
2.According variation of time • 1).permanent action: Within the design datum period ,its value does not vary with time. dead mass Design datum period (T):to relatively fix a datum time during analysis of the structure reliability. 50 years,100 • 2).variable action: wind load, man load • 3).accidental action: seismic load, explode • 3.According variation of space position 1).fixed action:dead mass 2).movable action: man load,wind load 4.According variation of structure response 1).static action: 2).dynamic action: seismic load,
2
3 4
39.6
37.1 45.5
9
10 11
43.8
44.5 36.9
16
17 18
38.7
41.4 49.0
23
24 25
43.5
36.3 41.0
30
31 32
38.9
40.9 42.1
5
6 7
43.9
41.5 39.6
12
13 14
47.3
42.7 44.1
19
20 21
36.1
45.9 38.7
3.2.2.Probability analysis
• 1.Random variables Xi and statistical characteristics • The variables to indicate random appearing various result is called random variables. n 1).arithmetic mean : X i / n
1 2 3 1 2
n
f
2x
i 1
n
i
f
n
2x
i 1
n
i
3.Guaranteed probability:
•
The probability that the value of random variable is not smaller than(or is not greater than) a certain value u is called as guaranteed probability about the certain value.
3 BASIC PRINCIPLES FOR THE DESIGN OF REINFORCED CONCRETE STRUCTURES
§3-1. Introduction to the Limit State Design 3.1.1 The Purpose and Requirements of Structural Design
• 2.Structural resistance R: • R is capacity that the structure sustains action
effect.
§3-2.Reliability Analysis
S, R
SR
• 3.2.1.The uncertainty of structure design • 1.the uncertainty of action effect S
Table3-1 Cubic strength of tested specimens
Speci Cubic Speci Cubic Speci Cubic Speci Cubic Speci Cubic men Stren men Stren men Stren men Stren men Stren No. gth No. gth No. gth No. gth No. gth (Mpa (Mpa (Mpa (Mpa (Mpa ) ) ) ) ) 1 40.1 8 39.5 15 45.6 22 47.1 29 39.9
f(x)
+’=1,
u-characteristics
is the guaranteed probability that the value of u x random variable is not ’ smaller than u. u= =(1) , -coefficient of guaranteed probability. The probability that x is not greater a certain value u: Px u P x u u
f(x)--density function
’ ’ F(x)
1 F x 2

1 2
x exp 2 2 dx


e
x 2
2 2
dx
x
The litter is, the more the distribution of random variable concentrates.
• Generally, an adequately designed structure should meet the following requirements: • 1.Safety:take up all normal possible actions during construction and service period under normal condition. 2.Serviceability: behave satisfactorily during service period under normal condition. 3.Durability:meet the safety and serviceability requirements in design working life under normal maintenance. • 4. Integral stability : In extreme events such as under violent earthquake, total collapse of the structure may be prevented and lives can be saved