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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
Numerical simulation of the mechanical performance of deep beam
tive Analysis-ACNL [10]. The program was developed according to
incremental iterative procedure and the finite element method (MEF),
on an Orthotropic non-Linear Formulation [9]. It includes in its algo-
rithmic framework the element formulations described on the item 2.
4. Computational program validation
From the computational program adopted for calculation support a
beam 1.80 m height and length and 0.20 m thick was analyzed, Figure
4.a. It was casted using C 20 concrete, reinforced by two CA-50 steel
bars with diameter equal to 6.3 mm. The beam has undergone a couple
of loads applied on its top, in equidistant points to 0.30 m from to the
(12)
2 1
2 1
2
.
2
25.0 ).
1(
EE
E E G
In the present analysis it was adopted finite elements in their iso-
parametric versions and quadratic approximation.
The region of the mass of concrete will be simulated from the eight
nodal point quadrilateral plane elements, Q8, Figure 3.b.
The steel behavior is considered elastic perfectly plastic. Because of the
great transverse flexibility of the reinforcement steel bars it is just considered
its axial stiffness which is simulated by three nodal point linear elements, L3,
Figure 3.a. Thus, the referred stiffnessmatrix shall be expressed by:
(13)
2 1- 1-
1- 1
0
1- 0
1
2
L
AE K
where “E” represents the steel Young modulus, and it is considered,
in this work, equal to 210000 MPa. “A” is the cross section area of
the reinforcement steel bars, for each one-dimensional element. “L”
represents the length of one-dimensional finite element.
3. Computational Support
In order to obtain the results focused on the fulfillment of the objec-
tives of this work, it was employed the “software” nonlinear Constitu-
Figure 3 – Finite elements: a- Linear L3; b-Plane Q8
Figura 4 – Validation: a-Beam Geometry; b-Stress Diagrams