Non-linear analysis of plane frames - Concrete Structures: Stresses and Deformations - page 448

Figure 13.7 Reinforced concrete beam analysed in Example 13.3: (a) beam
dimensions; (b) coordinate system for member AC with end C fixed.

the global coordinates. The cross-sectional area properties before crack-
ing are:

A 1 = 221.3 × 10 −3 m 2 ; B 1 = 0; I 1 = 9.595 × 10 −3 m 4

Eleven sections equally spaced at 0.1 l are considered in the analysis. The
positive or negative moment that is just su cient to produce cracking

is:

M r = ± f ct W 1 = ±68.5 kN-m

The units used in all calculations given below are Newton and metre.

Iteration cycle 1
In this cycle, the structure is assumed uncracked. A linear analysis gives:

M A cycle 1 = 0; M B cycle 1 = − 135 × 10 3 ;

M C cycle1 = 112.5 × 10 3 (a)

The corresponding displacements at the three coordinates at end A
(Fig. 13.7(b) ) are: