Non-linear analysis of plane frames - Concrete Structures: Stresses and Deformations - page 432

Figure 13.3 Input data defining the geometry and initial stresses: (a) a number of sections
defined on a typical member; (b) cross-section geometry and initial stress
distribution at a typical section; also, positive sign convention for σ O , γ , N and M .

displacements. A typical element S ij of the tangent sti ness matrix is equal to

the force increment at coordinate i due to a small unit displacement at
coordinate j . The cross-sectional area properties A, B and I are assumed
variable; where A, B and I are the area, its

ff

rst moment and its second
moment about an axis through the reference point O (Fig. 13.3(a) ). The
variation of the cross-sectional area properties can be caused by variation of
geometry or by cracking.
The tangent sti

fi

ff ness matrix [ S *] can be partitioned into 3 × 3 submatrices:

[ S 11 ]
[ S 21 ]

[ S 12 ]
[ S 22 ]

[ S *] = (13.2)