Civil Engineering Reference
In-Depth Information
predict the effect on the parasitic moment of any local adjustment of the cable profi le
by simple hand calculation; it is not necessary to re-run the whole structure. This is a
great improvement over adjusting the cable profi le by trial and error. It is even possible
to make minor adjustments to the parasitic moment at one support by changing the
cable profi le in a remote span.
As parasitic moments vary linearly between points of support, infl uence lines are
required at support positions only. These infl uence lines may be used for more complex
structures such as beams built in to their supports, or portal frames, with the bending
moment due to the unit distortion calculated by simple computer programs.
6.21 Modifi cation of bending moments due to creep
6.21.1 General
Creep or the deferred deformation of concrete, is described in
3.9.1
. If the statical
defi nition of a structure is changed during construction, then creep will change the
distribution of bending moments. Most concrete structures are in fact built in phases,
whether it is a building where adjacent fl oor slabs are built successively, or a bridge
deck being built span by span, and consequently creep changes their self weight
bending moments.
The simplest demonstration of this behaviour of concrete is illustrated in Figure 6.24.
A reinforced concrete beam is built as a single span, and the falsework struck, allowing
the beam to defl ect elastically under its self weight, Figure 6.24 (a). Then the statical
defi nition is changed by placing an additional support beneath the beam at mid-span,
just in contact, Figure 6.24 (b). As the beam tries to continue its creep defl ection as
a single span, it gradually loads up this additional support, Figure 6.24 (c), and the
bending moment is progressively modifi ed. The fi nal shape of the bending moment
depends on the relative magnitudes of the elastic defl ection and the creep defl ection. If
the creep defl ection were very large compared with the elastic value, the fi nal moment
diagram would be similar to that of a two-span beam, which is the limit towards which
the bending moment is tending. If the beam had been made of well-matured precast
segments that creep little, the bending moment would remain closer to the statically
determinate value.
The bending moment diagram for the simply supported beam shown in Figure 6.24 (a)
is known as the 'as-built moment diagram', or
M
ab
. The bending moment diagram for
a continuous beam built ab-initio as two spans shown in Figure 6.24 (e), which is the
diagram to which the structure is tending as it creeps, is known as the 'monolithic
moment diagram' or
M
mono
. The fi nal bending moment in the structure, shown in
Figure 6.24 (d) is the 'design moment diagram' or
M
des
.
Then
M
des
= (
M
ab
+
φ
M
mono
)/(1+
φ
).
The above formula is the simplest defi nition of creep; other, more complicated
formulae exist. However, it should be borne in mind that the value of the creep
coeffi cient
is not known with any precision, and it is illusory to seek too much
sophistication in the calculation of creep. Consequently, it is good practice to design
concrete bridges to limit the difference between the as-built moment diagram and the
monolithic diagram, so that the amount of creep, and hence the uncertainty on the
φ
