Civil Engineering Reference
In-Depth Information
Figure 6.15
Distortion of box girder
6.13.4 Stresses due to distortion of the cross section and torsional warping
Box sections under the effect of eccentric live loads will distort as shown in Figure 6.15.
This distortion causes longitudinal stresses on the extreme fi bres of the webs, as well as
transverse bending moments in the box.
The longitudinal stresses due to distortion are greater in a rectangular box than
in a trapezoidal box, and disappear in a box of triangular cross section. If the box is
very wide for its depth, the effect becomes greater. At the limit, the two webs become
virtually independent of each other, and the deck behaves more like a twin rib deck than
a box. Longitudinal stresses are also caused by torsional warping of the cross section.
At preliminary design, the longitudinal stresses due to these effects may be taken
into account most easily by maintaining a margin with respect to the limiting stresses.
Thus if the limiting stress is zero, the prestress would be sized for an appropriate
compressive residual. For decks up to about 60 m span and of normal proportions,
subjected to full British HB loading, it is usually conservative to reserve a residual
of 1.5 MPa on the bottom fi bre at mid-span, and 0.8 MPa on the top fi bre at the
supports. Where the governing loads are distributed rather than concentrated, half of
these values is typical.
Alternatively, the residual stresses may be converted into equivalent moments and
added to the table of bending moments.
It is of course essential at some stage to carry out an accurate calculation of these
effects [6, 7 and 8].
6.13.5 Rounding of support moments
If a continuous beam is supported on a bearing of fi nite width
d
, the moment on the
axis of the support will be less than the theoretical value by a parabolic decrement
Rd
/8, where
R
is the beam reaction, Figure 6.16 (a). In addition, if the height from the
bottom fi bre to the neutral axis is
y
b
, the effective width of the bearing is
d
+2
y
b
×
tan35
°
,
and the reduction in the peak moment is
R
(
d
+2
y
b
×
)/8, Figure 6.16 (b). Usually,
this reduction is arbitrarily limited to 10 per cent of the peak moment.
The reduction of moment due to the physical width of the bearing is purely
mechanical, and is effective both at working and ultimate loads. The spread through
the height of the beam is an elastic effect, and should not be used at the ULS.
This rounding is important in the design of prestressed concrete beams. If the
prestressing cable is designed to cater precisely for the peak, unrounded moment, it
tan35
°
