Time-dependent internal forces in uncracked structures: analysis by the displacement method - Concrete Structures: Stresses and Deformations - page 150

Figure 5.2 Analysis of the time-dependent changes in the end forces of a member caused
by fixity introduced after loading: (a) totally fixed beam subjected at time t 0 to a
system of forces; (b), (c), (d) statically determinate beams loaded at time t 0 ,
statical system changed to totally fixed beam at time t 1 ; (e), (f), (g) coordinate
systems.

common practice to calculate the internal forces due to prestressing by con-
sidering the forces exerted by the prestress tendons on the remainder of the
structure, the concrete and non-prestressed reinforcement. This is the mean-
ing adopted here where reference is made to the internal forces caused by
prestress loss.
Now, consider that the beam in Fig. 5.2(a) is constructed in three di erent

ways. At age t 0 , we assume that the external loads are applied on one of the
statically determinate systems in Fig. 5.2(b), (c) or (d). Subsequently, at age t 1
the beam is made totally

ff

xed as shown in Fig. 5.2(a). Time-dependent
changes in the forces at the end of the member will gradually develop; the
equations derived below can be used to calculate the member-end forces at
any time t 2 later than t 1 .
A system of three coordinates, 1*

fi

− 3* is de fi ned in each of Fig. 5.2(e), (f)