Civil Engineering Reference
In-Depth Information
Figure 5.18
Equivalent loads for general case
w
= 8
Pd
/
L
2
kN/m,
where
P
kN is the force in the cable and
d
and
L
are the amplitude of the cable and the
span of the beam in metres.
This is often a useful concept in preliminary calculations, for calculating the
defl ection of a beam due to prestress, for instance. (If the cable is attached at the ends
of the beam at the level of the neutral axis, amplitude
d
= eccentricity
e
c
.)
Any shape of prestressing cable may be broken down into a series of angular
deviations, straight lengths and parabolas, and thus, when combined with end moments
and forces, one may convert the effect of the cable into a set of equivalent loads,
Figure 5.18. This is particularly useful when analysing a structure as a grillage or space
frame, as the prestress can then be treated as any other load.
However, care has to be taken about two aspects of this idealisation. First, the shape
of a prestressing cable must be referred to the neutral axis of the beam. Thus even if
the cable is straight and the neutral axis is defl ected, the effect is the same as for a
straight neutral axis and a defl ected cable. For instance, consider the roof beam shown
in Figure 5.19. The neutral axis is defl ected in a 'V' shape, while the cable is straight.
The equivalent load due to the prestress is identical with that of the straight neutral
axis and the defl ected tendon. Similarly, if the cross section of a beam changes along
its length, with the result that the neutral axis is deviated, equivalent point loads are
created by a straight cable, Figure 5.20.
Second, the force in a prestressing cable is not constant along its length, due to
friction between the cable and its sheath. Thus for an accurate translation of a cable
into equivalent loads, it is necessary to include the forces tangential to the cable that
correspond to the friction forces imparted by the cable on the structure. Although this
effect may be ignored in simple preliminary calculations, it must be considered for
detailed design.
Consequently, equivalent forces are not easy to calculate by hand for a structure of
any complexity. There exist computer programs that will transform any cable geometry
and structural shape into equivalent loads, but, as always, the designer should be wary
