Titel_SS06

with:

(, )(, )

(, )

equ A

A

WxyixydA

Q

ixydA







(7.4)

and ixy(, ) denotes the influence function over the considered area. A

The mean and the variance of Qequ are given by:

EQequ m (7.5)

11 2 2

12

2

11 2 2 (,),(,) 1 2

22

2

(, )(, )

(, )

(, )( , )

(, )

A

equ

A

Ux y Ux y

AA

VU

A

Var W x y i x y dA

Var Q

ixydA

i x y i x y dA dA

ixydA

1





89



 

89





89











(7.6)

where are introduced to indicate the two different integrations over the considered area.

For live loads the correlation radius

AA 12 ,

10 i.e. the distance over which the random load field can

be considered to be strongly correlated can be assumed to be in the order of 1 meter, which for
practical purposes allows for assuming that the field is A-correlated (a so-called white noise
random field, case 1 in Figure 7.2. In particular, this assumption holds if:
2
A&&1 0 A 0 (7.7)

where is the influence area (i.e. the loaded area from which the considered load effect is
influenced) and is the so-called correlation area.

A

A 0

Therefore, the variance of Qequ can be simplified to:

2

22 22

2

(, )

(, )







89







equ

VUA VUre

A

Var Q

ixy dA

ixydA

  (^) d (7.8)
where:
red A^0
A

   (7.9)

The corresponding values for these parameters can be taken from Figure 7.2 and Table 7.2.