Civil Engineering Reference
In-Depth Information
of any 'black box' unless he understands the basis on which it has been established, or
has an alternative method of calculation to check the results.
The concept of equivalent loads is extremely valuable for understanding the effects
of prestressing on a structure, and for carrying out preliminary designs or simple fi nal
designs. It is also very useful for the mechanised calculation of prestressed structures,
but must be used with considerable caution by the designer.
Reference [5] is useful for design based on equivalent loads.
5.19 Internal and external loads
It is important that the designer of prestressed structures understands clearly the
difference between external and internal loads. The self weight, other dead loads
and traffi c loads applied to a beam are external loads. They generate reactions that
are equal and opposite to the loads. If the support for a beam is not strong enough,
when a load is applied to the beam, the support may fail; wind load on a girder may
overturn it.
The loads applied by prestressing cables to a beam are internal. They normally give
rise to bending moments and shears in the beams, but they do not add to the external
reactions. The equivalent loads shown in Figures 5.16 to 5.20 are in equilibrium; all
forces must resolve to zero, as must all moments taken about any point.
In continuous beams, discussed in more detail in Chapter 6, the prestress is likely to
shift reactions between supports, but these reactions still resolve to zero.
5.20 Prestress effect on shear force
The angle of the prestress cables with respect to the neutral axis provides a very
signifi cant shear force that may be designed to counteract the shear force due to
dead and live loads. If the cable centroid of the 32 m long beam described in
5.1 et
seq.
and in Figure 5.11 (a) had followed a parabolic shape, with an eccentricity of
y
b
- 0.2 = 1.272 m at mid-span, and zero at the beam ends, its slope at the beam end
would have been 2×1.272 / 16 = tan
-1
0.15 = 9°. The shear force due to the prestress
force of 9.38 MN acting at 9° to the horizontal would be 1.49 MN.
The ultimate shear force of 3.08 MN (
5.6
) is reduced to 3.08 - 1.49 = 1.59 MN.
In some codes of practice, the prestress shear force to be used for this calculation is
factored down, typically by a factor of 1.15. Hence the net shear force to be carried by
the beam becomes 3.08 - 1.49 × 0.87 = 1.78 MN. This shear force is compatible with
the web thickness of 0.22 m adopted for the beam. Consequently, it is not necessary to
thicken the web to carry shear force. The web would in fact be thickened for a short
distance from the beam end to accommodate the prestress anchors and to resist the
concentration of force they create.
The shear force applied by the prestress is under the control of the designer. For
instance, the average angle of the prestress cables at the end of the beam in the scheme
shown in Figure 5.11 (b) is clearly steeper than the parabola mentioned above. The
designer may adjust the slope of the cables at critical points along the beam to optimise
the shear relief provided.
