Time-dependent internal forces in uncracked structures: analysis by the displacement method - Concrete Structures: Stresses and Deformations - page 155

Figure 5.5 Example of a continuous composite structure: (a) statically indeterminate frame;
(b), (c) alternative composite cross-sections for part AD of the frame in (a).

for a speci ed period may be determined by application of the displacement

method to the continuous frame in two stages as discussed in the preceding
section. The

fi

rst stage is concerned with the joint displacements and the
member-end forces produced at time t 0 immediately after application of
loads. The joints are arti

fi

fi cially locked in this position, causing time-

dependent fi xed-end forces to develop gradually during a speci fi ed period t 0

to t . In the second stage of analysis, the arti cial restraining forces are

removed, producing changes in joint displacements and member-end forces,
calculated by a second application of the displacement method. The follow-
ing are additional remarks to be considered in the second stage of analysis
when calculating the cross-section properties and the changes in

fi

fi xed-end

forces in composite members.
For any of the composite sections in Fig. 5.5, the cross-section to be used
in the second stage of analysis should be the age-adjusted transformed sec-
tion (see Section 1.11.1). The

xed-end forces to be used in the same stage are
to be determined at the centroid of the age-adjusted transformed section.
The age-adjusted modulus of elasticity of concrete depends upon t 0 and t ,
the ages of concrete at the beginning and the end of the period considered.
Thus, the centroid of the transformed section will be changing when analys-
ing for di

fi

ff erent time periods or when considering the instantaneous e ff ects of