Civil Engineering Reference
In-Depth Information
Figure 6.21
Prestress scheme 2
6.18 Non-zero stress limits
For continuous beams, it is usually the case that the designer is working to non-zero limits
of stress on the extreme fi bres. This is because either the code of practice allows tensile
stresses under some load combinations, or it is necessary to maintain a compressive
residual to cope with the stresses due to some of the effects described in
6.13
.
As was explained in
5.10
, this may be easily carried out by changing the notional
boundaries of the central kern. For instance, if at section 2.5 it is necessary to maintain
a residual of 1.5 MPa on the bottom fi bre, under maximum sagging moments the
centre of pressure may only move up from the prestress centroid to the limit of the
reduced top of the kern,
a
t
1
, Figure 6.22 (a).
a
t
1
may be calculated by assuming that
the stress on the bottom fi bre reduces linearly from P/A, when the centre of pressure is
at the neutral axis, to zero when it is at the top of the kern
a
t
.
Assume that
P
/
A
= 4 MPa, then
a
t
1
=
a
t
×(4 - 1.5)/4 = 0.625
a
t
.
As
a
t
= 0.534 m,
a
t
1
= 0.334 m. Consequently, the new prestress lever arm for use in
equations 4 and 5 (
6.16.1
),
l
a
= 1.361 - 0.2 + 0.334 = 1.495 m
reduced from its original value of 1.695 m.
