Nonlinear Analysis And Optimal Design Of Reinforced Concrete Plates And Shells

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25 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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Ministry of Higher Education
and

Scientific Research

University of Babylon

College of Engineering

Department of Civil Engineering




Nonlinear Analysis And
Optimal Design Of Reinforced
Concrete Plates And Shells


A Thesis

Submitted To The College Of Engineering Of
Babylon University In Partial Fulfilment Of The
Requirements For The Degree Of Master Of
Science In Civil Engineering


(Stractural
Engineering
)



By:

Ali Abdul Hussein M. Al
s
ultany

(B.Sc. 2005)



Supervised By:


Asst
.

Professor
Mr. Abdul Ridha S
aleh

Professor
.
Dr. Nameer A. Alwash




April 2008



ABSTRACT

This research deals with the optimal design of reinforced concrete plate and
shell structures based on nonlinear finite element method. The eight
-
node
degenerated curved shell element is used in which five degrees of freedom are
specified at each nodal poi
nt, which are three displacements and two rotations of the

normal at the node.

A layered model is considered in the modelling of the reinforced
concrete behaviour and a perfect bond between the concrete and reinforcement has
been assumed.

The compressive b
ehaviour of the concrete has been modelled by
employing two approaches both elastic
-
strain hardening and elasti
c
-

perfectly plastic
plasticity

approach. The yield condition is formulated in terms of the first stress and
second deviatoric stress invariants.

The motion of the subsequent loading surface is
controlled by the hardening rule that is extrapolated from the uniaxial stress
-
strain
relationship given by a parabolic function.

The behaviour of cracked concrete has been modelled using a smeared fixed
cra
ck approach, coupled with a tensile criterion to predict crack initiation. Gradual
bond deterioration with progressive cracking is simulated by means of a tension
stiffening model. A reduced shear modulus is employed in the crack
ed

zone. The
behaviour of s
teel reinforcement is idealized by elastic
-
perfectly plastic relation with
linear strain hardening for tensile and compressive stresses.

The nonlinear equations
of equilibrium have been solved using an incremental
-
iterative technique operating
under load c
ontrol. Modified Newton
-
Raphson method has been employed. In this
method, the stiffness matrix is updated in the second iteration of each load increment.
A load convergence criterion is adopted in the present work. Various integration rules
(full, selectiv
e, reduced) have been used in the analysis of the application presented in
this study.

A nonlinear geometrical model based on the total Lagrangian approach
and taking into account

the

v
on Karman

assumptions.

For the structural optimization problem, which i
s dealt with as a constraint
nonlinear optimization, the so
-
called Modified Hooke and Jeeves method,

(
Bunday

1984
)

is employed by considering the total cost of the structure as the objective
function and the dimensions as the design variables with geometri
cal constraints.

For the analysis of reinforced concrete plates and shells, several examples are worked
out using the present finite element analysis and the results show good agreement
with experimental results and the difference at the range of (3%
-
16.8
%) for the
ultimate load. The results of optimization for reinforced concrete plates show that the

optimal cost occurs when using of minimum thickness of slab.

The

optimal cost for
reinforced concrete cylindrical shell occurs when the thickness and curvature of the
shell increases and shell angle decreases.