Prestressing for continuous beams - The Design of Prestressed Concrete Bridges - page 146

Most codes of practice cover the matter by proposing reductions in the width of
slab that should be assumed to be associated with each web for the calculation of
bending stresses. The effect on the calculation of the stresses due to prestress is that
the compressive component P / A is assumed to spread over the full area of the cross
section, while the stresses due to the bending component Pe are calculated with the
section properties corresponding to the modifi ed cross section. Thus in the expression
P / A ± Pe / z , P / A is calculated using the complete cross section, while Pe / z uses the
section properties of the shear lagged cross section. Similarly, the stresses due to
bending moments caused by applied loads are calculated with the shear lagged section
properties.
It should be clearly understood that the codifi ed calculations are approximate, and
that the real bending stresses in the section are not identical to those calculated. It is
also clear that the effects of shear lag will be reduced by the presence of slab haunches,
as they will reduce the shear stress in the slabs, and hence their shear deformations.
In the interests of simplicity and clarity, the effects of shear lag have been ignored
in the current example.
6.11 Comment on the accuracy of calculations
Designers should be aware of the approximate nature of the calculations required for
the detailed design of concrete bridge decks.
All codes of practice known to the author assume that the bending stresses will be
calculated by the 'engineer's bending theory', which only considers uni-axial stresses
and which assumes that plane sections remain plain, and that consequently stresses
vary linearly. The structure is deemed to be acceptable at working load if the limiting
stresses, calculated by this theory, remain below certain values.
The designer must be careful not to apply the 'deemed to satisfy' provisions of
codes of practice to sophisticated analyses that they were not intended to cover. If a
structure that was satisfactory under this simplifi cation was to be analysed in three
dimensions by fi nite elements it is likely that local areas of stress will be found that
exceed the permitted limits. For instance, above the bridge bearings, which have
contact stresses of the order of 20 MPa, the lateral Poisson's ratio effects will combine
with the overall bending stresses to produce local areas of compressive stress that may
exceed the limiting values defi ned by the code of practice. In general these excess
stresses may be safely ignored; the strength of concrete is increased when it is subjected
to bi-axial or tri-axial states of compressive stress. However, the designer must use his
judgement and experience to decide if high stresses defi ned by elastic analysis are in
fact acceptable.
The approximations used to cater for the effect of shear lag, as defi ned in 6.10.2
above, for the effect of creep on bending moments, described in 6.21 and for the effect
of creep on the section properties described in 6.22 , should make clear that there is no
point in carrying out a very sophisticated analysis for code compliance, when the basic
assumptions themselves are approximate.
However, code compliance is only one component of a designer's task. He must
work to understand how the structure behaves in complex areas, and sophisticated
elastic analysis can be extremely useful in some circumstances.