Titel_SS06

Reinforcement Steel

A probabilistic model for the yield stress X 1 of reinforcing steel may be given as (JCSS

(2001))

fsXX X 123 (7.35)

X 1 Normal distributed random variable representing the variation in the mean of

different mills.

X 2 Normal distributed zero mean random variable, which takes into account the

variation between batches

X 3 Normal distributed zero mean random variable, which takes into account the

variation within a batch.

where it is noted that the mean value of X 1 has been found to exhibit a significant dependence

on the diameter of the bar d, see e.g. JCSS (2001).

In Table 7.5 the probabilistic models for X 1 , X 2 and X 3 are given.

Variable Type EX  xMPa Vx

X 1 Normal

 (^) 19 -
X 2 Normal 0^ 22 -
X 3 Normal 0^ 8 -
A - Anom - 0.02
Table 7.5: Probabilistic model for the yield stress of the reinforcement steel.
In Table 7.5 A is the bar cross-sectional area, Anom is the nominal cross-sectional area and 
can be taken as the nominal steel grade plus two standard deviations of X 1. For a steel grade
B500 there is:
  500 2 19^2 500 2 19 538
Accounting for the diameter variation of the yield stress the mean value can be written as:
( )dd (0.87 0.13 exp( 0.08 ))^1
The yield force for bundles of bars is the sum of the yield forces of the each bar. As it can be
assumed that the bars are produced at the same mill, their yield stress is highly correlated. In
JCSS [(2001) a correlation coefficient of 1 0.9 is given. Therefore, the probabilistic model
for the yield stress of a single reinforcement bar also applies for a bundle of reinforcement
bars.
Taking into account the coefficient of variation of the bar cross-section area, leads to a
coefficient of variation of the yield stress resistance equal to Vfy0.057.