Analysis of time-dependent internal forces with conventional computer programs - Concrete Structures: Stresses and Deformations - page 177

6.1 Introduction
Computers are routinely used in practice to analyse structures, particularly
when linear stress-strain relationship of the material is acceptable and when
displacements are small. These assumptions are commonly accepted in the
analysis of structures in service. Thus, many of the available computer pro-
grams perform linear analysis, in which the strain is proportional to the stress
and superposition of displacements, strains, stresses and internal forces is
allowed. The present chapter demonstrates how conventional linear
computer programs can be employed for approximate analysis of the
time-dependent e ects of creep and shrinkage of concrete and relaxation of

prestressed steel. Only framed structures are considered here. These can be
idealized as assemblages of beams (bars). Thus, the computer programs of
concern are those for plane or space frames, plane or space trusses or plane
grids. 1
The procedure discussed in this chapter can be used to solve time-
dependent problems of common occurrence in practice. As an example, con-
sider the e

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ff ects of shortening, due to creep and shrinkage, of a prestressed

fl oor supported on columns constructed in an earlier stage. Analysis of the

e erential shortening of columns in a high-rise building provides

another example; the compressive stress and the change in length due to creep
are commonly greater in interior than exterior columns. Bridge structures are
frequently composed of members (segments), precast or cast-in-situ, made of
concrete of di

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erent ages or of concrete and steel (e.g. cable stays). The
precast members are erected with or without the use of temporary supports
and made continuous with cast-in-situ joints or with post-tensioned tendons.
In all these cases, the time-dependent analysis can be done by the application
and the superposition of the results of conventional linear computer
programs.

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6.2 Assumptions and limitations
Immediate strain and creep of concrete are proportional to the stress (com-
pressive or tensile) and the e

ect of cracking is ignored. Structures are ideal-
ized as prismatic bars (members) connected at nodes. The cross-sectional area
properties of any bar are those of a homogeneous section. Thus, the presence
of the reinforcing bars or the tendons in a cross-section is ignored in calcula-
tion of the cross-sectional area properties. Alternatively, a tendon or a
reinforcing bar can be treated as a separate member connected to the nodes by
rigid arms (Fig. 6.1(a) ). The axes of members coincide with their centroidal
axes. Because the cross-section of an individual member is considered homo-
geneous, no transformed cross-sectional area properties are required and the
variation of the location of the centroids of transformed sections due to
creep of concrete does not need to be considered. A composite member

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