Nonlinear Finite Element Analysis of Concrete Structures

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Z
Fig- 4.2-3: Cracking in an element
where
T =
cos a
. 2
sin a
0
. 2
sin a
2
cos a
0
0
0
1
t
-5
h
sin2a
sin2a
0
(4.2-15)
sin2a
-sin2a
0
cos2a
The elastic energy in an infinitesimal volume element dV is
given by \ e o dV irrespective of the applied coordinate system;
i.e.
£ T a = e ,T o' (4.2-16)
applies, where the prime indicates that reference is made to the
rotated R'Z'-coordinate system. Ignoring for convenience initial
stresses and strains we have in accordance with eq. (9)
= D' e' (4.2-17)
By use of this equation, a'
use of eq. (14) then yields
can be eliminated from eq. (16) and