Non-linear analysis of plane frames - Concrete Structures: Stresses and Deformations - page 456

these are not to be considered here. The initial de fl ection before the

application of the live load is D in. 1.1 mm (0.043 in.).

Because of symmetry, one span is considered. Twenty-two equally-
spaced sections are used, of which two sections (16 and 17) at zero
distance apart are assumed at C . The reference axis is chosen at 0.368 m
(14.5 in.) below the top

=

fi bre. First cracking occurs at q r = 13.4 kN/m

(0.921 kip/ft); the corresponding de 12.8 mm

(0.5 in.). After cracking, the intensity of the live load is increased up to
2 q r in steps of 0.1 q r . Figure 13.9(c) is a plot of ( D / D r ) versus ( q / q r ).

fl ection at mid-span, D r =

13.13 General
At service load, the stress in concrete is su ciently low, such that linear

stress-strain relationship can be used for uncracked concrete; thus, the non-
linearity of the analysis is required only after cracking. In spite of this simpli-
fi

cation, the amount of computations is large, making it necessary to use a
computer. The incremental or the iterative methods presented in this chapter
can be the basis of a computer program for the analysis of reinforced con-
crete frames, with or without prestressing, accounting for cracking.
For simplicity of presentation, a single loading stage is considered in this
chapter. The same analysis, with minor adjustment, can be used for multi-
stage loading. For each stage, the analysis can be applied and the results used
to update the stress, the strain and the state of cracking at all sections, before
starting the analysis for a new loading stage.

Note
1 See the reference mentioned in footnote 3 of Chapter 3.