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Introduction

1.1 Generals

In reinforced concrete buildings,
slabs are used to provide flat, useful surfaces. A reinforced concrete slab is
a broad, flat plate, usually horizontal, with top and bottom surfaces parallel
or nearly so.

The slabs are presented in two
groups: one-way slabs and two-way slabs. When a rectangular slab
is supported on all the sides and the length-to-breadth ratio is less than two,
it is considered to be a two-way slab. The slab spans in both the orthogonal
directions. A circular slab is a two-way slab. In general, a slab which is not
falling in the category of one-way slab is considered to be a two-way slab.

Rectangular two-way slabs can be
divided into the following types.

1) Flat plates: These slabs do
not have beams between the columns, drop panels or column capitals. Usually,
there are spandrel beams at the edges.

2) Flat slabs: These slabs do not
have beams but have drop panels or column capitals.

3) Two-way slabs with beams:
There are beams between the columns. If the beams are wide and shallow, they
are termed as band beams.

For long span construction, there
are ribs in both the spanning directions of the slab. This type of slabs is
called waffle slabs.

The
slabs can be cast-in-situ (cast-in-place). Else, the slabs can be precast at
ground level and lifted to the final height. The later type of slabs is called
lift slabs. A slab in a framed building can be a two-way slab depending upon
its length-to-breadth (L / B) ratio. Two-way slabs are also present as
mat (raft) foundation.

The following sketches show the plan of
various cases of two-way floors or roofs. The spanning directions in each case
are shown by the double headed arrows:-

Figure 1.1 Plans of two-way floor/roof
system

So the Flat Slab and Flat Plate is the reinforced concrete floor/roof
system supported directly by concrete columns without the use of beams and
girders.

Generally, the slab may be of
uniform thickness throughout the entire floor area, or a part of it,
symmetrical about the column, may be made somewhat thicker than the rest of the
slab, the thickened portion of the slab thus formed constituting what is known
as a dropped panel, or drop. Dropped panels are used to reduce
the shearing stress in the slab thickness provided by the drop also decreases
the compression stresses in the concrete and reduces the amount of steel which
required over the column heads.

Flat Slabs and Flat Plates may be
supported on two opposite side columns only, in which case the structural
action of the slab is essentially one-way, the loads being carried by the floor
in the direction perpendicular to the supports. On the other hand, there may be
supports on all four sides, so that two-way action is obtained. If the ratio of
length to width of one floor panel is larger than about 2, most of the load is
carried in the short direction. As per ACI 318-02 (Building Code
Requirements for Structural Concrete, American Concrete Institute, this
building code is almost equivalent to BNBC), the limits of span-to-depth ratios
are as follows:-

For floors 42

For roofs 48.

The
values can be increased to 48 and 52, respectively, if the deflection, camber
and vibration are not objectionable.

The following
photographs show flat plate and flat slab:-

(a)
Flat
plate (b) Flat slab

Figure
1.2
Two-way Flat Floors (Courtesy: VSL India Pvt. Ltd.)

However, due to their economy and
speed of construction, flat floors are very common structural elements for
apartments, office and institutional buildings etc. It is well established
that, the capacity of flat floors is often governed by shear capacity in the
vicinity of the columns.

In general for the
analysis purpose, the building structures are analyzed using a model structure
of that entire building with the philosophy of analysis prescribed in different
existing methods of structural engineering. For easy understanding and suitable
execution of structural behavior of any structure, the 2-D modeling &
analysis is generally done in nature. 2-D models are prepared based on the
different planes of structures. In case of 2-D model, one may consider any
existing plan or elevation of an entire structure to calculate the intended
values. Here the process to calculate desired values for any individual section
of the entire structure is also possible. As in 2-D model only the skeletal diagram
and imposed loads of the entire structure is considered, thus it is suitable to
analyze and to consider for any further action to be implemented. But it is more recommended to analyze a
structure by considering its 3-D model with its all compatibility from the view
point of precision or accuracy of intended values to determine structural
behavior, though the analysis procedures considering 3-D model are always be
considered as complex task. However, with invent of digital computer based
programs using complex structural philosophy made it a process of ease and
comfort for the structural engineers.

A digital computer based program named STAAD Pro
is referable. Where,
STAAD.Pro is the most popular structural engineering software product for 3D
model generation, analysis and multi-material design. It has an intuitive,
user-friendly GUI, visualization tools, powerful analysis and design facilities
and seamless integration to several other modeling and design software
products. For static or dynamic analysis of bridges, containment structures,
embedded structures (tunnels and culverts), pipe racks, steel, concrete,
aluminum or timber buildings, transmission towers, stadiums or any other simple
or complex structure, STAAD.Pro has been the choice of design professionals
around the world for their specific analysis needs. Another program named
ABAQUS is also referable for computing deflection of beams. ABAQUS is a
powerful finite element software package. It is used in many different
engineering fields throughout the world. ABAQUS performs static and/or dynamic
analysis and simulation on structures. It can deal with bodies with various
loads, temperatures, contacts, impacts, and other environmental conditions.

1.2 Objectives
and Scopes of the Study

Now-a-days, in case of high-rise
building construction the flat floor is a common practice. Thus, due to
importance of flat plate floor analysis to have from various points of view,
our thesis and project work is operated for achieving the following purposes
and scopes:-

To analyze a flat slab using
software STAAD Pro considering its 2-D model.

To analyze a flat slab using
software STAAD Pro considering its 3-D model.

Comparing results of
analysis obtained from 2-D & 3-D model, and also to compare the axial
force got using Equivalent Frame Method by hand calculation to with the
axial force got in the analysis done by software STAAD
Pro.

Checking the change in the
behavior when a structure is modeled 2-D and 3-D both using software STAAD
Pro.

General idea and Small
briefing about the common methods to analyze & design a flat floor.

Software compatibility and
proper basis of 2-D & 3-D modeling of a high-rise building.

Representing results
properly in tables and plotting them into graphs.

Preparing hand calculation
for design and analysis purpose in case of flat floors.

This report also includes the
following purposes as additional attachments:-

General modeling and
analysis of a beam using software ABAQUS.

Comparison of deflection of
that beam by the construction of graph based on the analysis output of ABAQUS

Review
of Literature

2.1 Background

The flat plate system, in which
columns directly support floor slabs without beams, is adopted for many
building structures recently constructed. However, the following considering
topics will clarify the idea about flat slab in general case:

It is
the simplest and most logical of all structural forms in that it consists
of uniforms slabs, connected rigidly to supporting columns.

The system, which is essentially of reinforced concrete,
is very economical in having a flat soffit requiring the most
uncomplicated formwork and, because of the soffit can be used as the
ceiling, in creating a minimum possible floor depth.

Lateral resistance depends on the flexural stiffness of
the components and their connections, with the slab corresponding to the
girder of the rigid frame.

Particularly
appropriate for hotel and apartment construction where ceiling space is
not required and where the slab may serve directly as the ceiling.

Since flat plate system was
primarily developed to resist the gravity loads, many researches on the
resistance capacity for lateral loads have been undertaken. In the analysis of
a flat plate structure subjected to gravity loads, direct design method or
equivalent frame method is generally used for the rectangular type slabs.

However, we have already informed
that flat floors/roofs are generally of two type are-

·
Flat
Slabs with dropped panel (Flat Slab)

·
Flat
Slabs without dropped panel (Flat Plate)

Characterization of Flat Slabs
due to their existing components, Flat Slabs may also be characterized in other
two more categories are-

·
Flat
slab with column head panels

·
Flat
slab with drop panel and column head

Figure
2.1 General
Types of Flat Structures

2.2 Technical
Terms of Flat Structures

2.2.1 Dropped Panel / Drop

A
part of the flat slab that is symmetrical about the column may be made somewhat
thicker than the rest of the slab is termed as dropped panel or drop.

Uses of drop panels:

•increase
shear strength of slab

•increase
negative moment capacity of slab

•stiffen
the slab and hence reduce deflection

Figure 2.2.1 Drop Panel

2.2.2 Column Head / Column Capital

The
column in practically all cases flare out toward the top, forming a capital of
a shape somewhat similar to an inverted truncated cone, is termed as Column
Head or Column Capital.

Uses of Column Capital:

·
increase
shear strength of slab

·
reduce
the moment in the slab by reducing the clear or effective span

Figure
2.2.2 Column
Head

2.2.3 Analysis Strip

Generally
the slab panel is divided into strips according to their existing line as per
the requirement of specification of standard codes, these strips are known as analysis
Strip.In general, the prospective analysis strip is subdivided into the
following identical strip region are-

Column Strip

A column strip is
defined as a strip of slab having a width of each side of the column centre
line as per specification of any standard codes for practice.

Middle Strip

A middle strip is a
design strip bounded by two column strips.

Figure 2.2.3 (a) Strip with Figure
2.2.3 (b)

no drop. Strip with
drop

2.3
Advantages of Flat Slab/Flat Plate Floor

2.3.1
Flexibility
in Room Layout

·
allows
Architect to introduce partition walls anywhere required

·
allows
owner to change the size of room layout

·
allows
choice of omitting false ceiling and finish soffit of slab with skim coating

2.3.2
Saving
Building Height

·
Lower
storey height will reduce building weight due to lower partitions and cladding
to façade

·
approx.
saves 10% in vertical members

·
reduce
foundation load

Figure
2.3.2 Saving
Building Height

2.3.3
Shorter
Construction Time

·
flat
plate design will facilitate the use of big table formwork to increase
productivity

Figure
2.3.3 Big Table
Formwork

2.3.4
Single
Soffit Level

·
Simplified
the table formwork needed

Figure
2.3.4 Single
Soffit Level

2.3.5
Ease
of Installation of M & E services

·
all
M & E services can be mounted directly on the underside of the slab instead
of bending them to avoid the beams

·
avoids
hacking through beams

2.3.6
Pre-Fabricated
Welded Mesh

·
Prefabricated
in standard sizes

·
Minimized
installation time

·
Better
quality control

Figure
2.3.6 Pre-Fabricated
Welded Mesh

2.3.7
Buildable
Score

·
allows
standardized structural members and prefabricated sections to be integrated
into the design for ease of construction

·
this
process will make the structure more buildable, reduce the number of site
workers and increase the productivity at site

·
more
tendency to achieve a higher Buildable score

2.4
Structural Behavior of Flat Structures

The Flat Slabs/Plates discussed
deform under load into an approximately cylindrical surface. The main
structural action is on way in such cases, in the direction normal to supports
on two- way opposite edges of a rectangular panel. In many cases, however,
rectangular slabs are of such
proportions and are supported in such a way that two- way action results .When
loaded , such slabs bend into a dished surface rather than a cylindrical one.
This mean that at any point of the slab is curved in both principle directions,
and since bending moments are proportional to curvatures, moments also exist in
both directions. To resist these moments, the slab must be reinforced in both
directions, by at list two layers of bars perpendicular, respectively, to two
pairs of edges. The slab must be designed to take a proportionate share of load
in each direction .In general, One sees that the large share of load is carried
in the short direction, the ratio of the two portions of the total load being
inversely proportional to the 4^thpower of the ratio of the spans of
the considering slab. This assumption is approximate because the actual
behavior of slab is more complex.

Consistent with the assumptions
of the analysis of two-way edge supported slabs; the main flexure reinforcement
is placed in an orthogonal pattern, which reinforcing bars parallel and
perpendicular to the supported edge. As the positive steel is placed in two layers,
the effective depth for the upper layer is smaller than that for the lower
layer by one bar diameter. Because the moments in the long direction are the
smaller one, it is economical to place the steel in that direction on top of
the bars in the short direction. The stacking
problem doesn’t exist for negative reinforcement perpendicular to the
supports except at the corner. Either straight bars, cut-off where they are no
longer required or bent bars may be used for two way slabs, but economy of bar fabrication
and placement will generally favor on straight bars. The precise locations of
inflection point aren’t easily determined, because they depend upon the side
ratio, the ratio of live to dead load, and continuity conditions at the edges.

In case of flat slabs, if a
surface load w is applied, that load
is shared between imaginary slab strips l_ain the short direction
and l_bin the long direction, as described in the previous lines in
this section.

l_a= Length in short direction

l_b= Length in Long
direction

The portion of the load that is
carried by the long strips l_bis delivered to the beams B₁spanning
in the short direction of the panel. The portion carried directly by the in the
short direction by the slab strips l_a, sums up to 100 percent of the
load applied to the panel. Similarly, the short-direction slab strips l_adeliver
a part of the load to long direction. That load, plus the load carried directly
in the long by the slab, includes 100 percent of the applied load. It is
clearly a requirement of statics that, for column-supported construction, 100 percent of the applied load must be carried
in each direction, jointly by the
slab and its supporting columns.

However, it is interesting to
compare the behavior of flat plate with that of two-way slabs in flat plate
analysis; the full load is assumed to be carried by the slab in each of the two
perpendicular directions. This is in apparent contrast to the analysis of
two-way slabs, in which the load is divided, one part carried by the slabs in
the short direction, and the remainder carried by the slabs in the long
direction. However, in two-way slabs, while only a part of the loads is carried
by the slabs in the short direction, the remainder is transmitted in the
perpendicular direction to marginal beams, which then also span in the short
direction. Similarly, which part of the load carried by the slab in long
direction, the remainder is transmitted by the slab in the short direction to
marginal beams which span is long direction. It is evident that in two-way
slabs, as in flat slabs, conditions of equilibrium required that the entire
load be carried in each of the two-way principal directions.

2.5
Design Consideration

2.5.1
Wall
and Column Position

·
Locate
position of wall to maximize the structural stiffness for lateral loads.

·
Facilitates
the rigidity to be located to the centre of building.

2.5.2
Optimization
of Structural Layout Plan

·
The
sizes of vertical and structural structural members can be optimized to keep
the volume of concrete for the entire superstructure inclusive of walls and
lift cores to be in the region of 0.4 to 0.5 m³per square meters.

2.5.3
Deflection
Check

·
Necessary
to include checking of the slab deflection for all load cases both for short
and long term basis.

·
In
general, under full service load, δ< L/250 or 40 mm whichever is smaller.

·
Limit
set to prevent unsightly occurrence of cracks on non-structural walls and floor
finishes.

2.5.4
Crack
Control

·
Advisable
to perform crack width calculations based on spacing of reinforcement as
detailed and the moment envelope obtained from structural analysis.

·
Good
detailing of reinforcement will-

–restrict the crack width to
within acceptable tolerances as specified in the codes and

–reduce future maintenance cost
of the building

2.5.5
Floor
Openings

·
No
opening should encroach upon a column head or drop.

·
Sufficient
reinforcement must be provided to take care of stress concentration.

2.5.6
Punching
Shear

·
Always
a critical consideration in flat plate design around the columns.

·
Instead
of using thicker section, shear reinforcement in the form of shear heads, shear
studs or stirrup cages may be embedded in the slab to enhance shear capacity at
the edges of walls and columns.

Figure
2.5.6 Shear
Condition

2.5.7
Construction
Loads

·
Critical
for fast track project where removal of forms at early strength is required.

·
Possible
to achieve 70% of specified concrete cube strength within a day or two by using
high strength concrete.

·
Alternatively
use 2 sets of forms.

2.5.8
Lateral
Stability

·
Buildings
with flat plate design are generally less rigid.

·
Lateral
stiffness depends largely on the configuration of lift core position, layout of
walls and columns.

·
Frame
action is normally insufficient to resist lateral loads in high rise buildings,
it needs to act in tendam with walls and lift cores to achieve the required
stiffness.

·
MULTIPLE
FUNCTION PERIMETER BEAMS

-lateral rigidity

-reduce slab
deflection.

2.6
Design Methodology

The study presented
here is concerned with the investigation of methods for determining moments in
reinforced concrete slabs by the analysis of equivalent two-dimensional elastic
frames and by the philosophy of approximate method in association with analysis
software. Thus, the study is based on the quantitative comparison of moments in
slabs as determined from analysis.

2.6.1
Common
Methods of Design

·
The
finite element method.

·
The
simplified method or, direct design method.

·
The
equivalent frame method or cantilever method.

2.6.2
Finite
Element Method

·
Based
upon the division of complicated structures into smaller and simpler pieces
(elements) whose behavior can be formulated.

·
E.g.,
of software includes STAAD PRO, ETABS, SAFE, ADAPT, etc.

·
Results
includes-

–moment and Shear
Envelopes

–contour of
structural deformation

2.6.3
Simplified
or Direct Design Method

2.6.3.1 Basis of Analysis

Moments
in two-way slabs can be found using the semi empirical direct design method,
subject to the following restrictions:

1.
There must be a minimum of three continuous spans in each direction.

2.
The panels must be rectangular, with the ratio of the longer to the shorter
spans within a panel not greater than two.

3.
The successive span lengths in each direction must not differ by more than one-third of the longer span.

4. Columns may be offset a maximum of 10 percent
of the span in the direction of the offset from either axis between centerlines
of successive columns.

5. Loads must be due to gravity only and the
live load must not exceed two times the dead load.

6. If beams are used on the column lines, the
relative stiffness of the beams in the two perpendicular directions, given by
the ratio α₁l₂²/ α₂l₁²must be between 0.2 and 5.0

2.6.3.2 Total Static Moment at
Factored Loads

For
purposes of calculating the total static moment M_o in a panel, the
clear span l_n in the direction of moments is used. The clear span is
defined to extend from face to face of the columns, capitals, brackets, or
walls but is not to be less than 0.65 l₁ The total factored moment
in a span, for a strip bounded laterally by the centerline of the panel on each
side of the centerline of supports, is

M_u= w_ul₂l_n² / 8

2.6.3.3 Assignment of Moments to
Critical Sections

For
interior spans, the total static moment is apportioned between the critical
positive and negative bending sections according to the following ratios:

Negative factored moment: Neg M_u = 0.65 M_o

Positive factored moment: Pos M_u = 035 M_o

The
critical section for negative bending is taken at the face of rectangular
supports, or at the face of an equivalent square support having the same
cross-sectional area as a round support.

Figure
2.6.3.3(A)
Distribution of total static moment M₀

to critical sections for positive
and negative bending.

Figure 2.6.3.3(B) Conditions of edge restraint
considered in distributing total static moment M_o to critical
sections in an end span: (a) exterior edge unrestrained, e.g., supported by a
masonry wall; (b) slab with beams between all supports; (c) slab without beams,
i.e., flat plate; (d) slab without beams between interior supports but with
edge beam; (e) exterior edge fully restrained, e.g., by monolithic concrete
wall.

2.6.4
The
Equivalent Frame Method

2.6.4.1 Basis of Analysis

The equivalent frame
method is recommended by ACI 318-02 (ACI code is almost equivalent to BNBC).
It is given in Subsection 31.5, IS:456 – 2000. This method is briefly
covered in this section for flat plates and flat slabs.

The
slab system is represented by a series of two dimensional equivalent frames for
each spanning direction. An equivalent frame along a column line is a slice of
the building bound by the centre-lines of the bays adjacent to the column line.

The width of the
equivalent frame is divided into a column strip and two middle strips. The
column strip (CS) is the central half of the equivalent frame. Each middle
strip (MS) consists of the remaining portions of two adjacent equivalent
frames. The following figure shows the division in to strips along one
direction. The direction under investigation is shown by the double headed
arrow in the figure given below:-

Figure 2.6.4.1(a) Equivalent frame along Column
Line 2

The
analysis is done for each typical equivalent frame. An equivalent frame is
modeled by slab-beam members and equivalent columns. The equivalent frame is
analyzed for gravity load and lateral load (if required), by computer or
simplified hand calculations. Next, the negative and positive moments at the
critical sections of the slab-beam members are distributed along the transverse
direction. This provides the design moments per unit width of a slab. If the
analysis is restricted to gravity loads, each floor of the equivalent frame can
be analyzed separately with the columns assumed to be fixed at their remote
ends, as shown in the following figure. The pattern loading is applied to
calculate the moments for the critical load cases.

Figure 2.6.4.1(b) Simplified
model of an equivalent frame

2.6.4.2 The Equivalent Column

In the equivalent frame method of analysis,
the columns are considered to be attached to the continuous slab beam by
torsional members that are transverse to the direction of the span for which
moments are being found; the torsional member extends to the panel centerlines
bounding each side of the slab beam under study. Torsional deformation of these
transverse supporting members reduces the effective flexural stiffness provided
by the actual column at the support. This effect is accounted for in the
analysis by use of what is termed an equivalent column having stiffness less
than that of the actual column. To allow for this effect, the actual column and
beam are replaced by an equivalent column, so defined that the total
flexibility (inverse of stiffness) of the equivalent column is the sum of the
flexibilities of the actual column and beam. Thus,

1 /K_ec= 1
/∑K_c + 1 /∑K_t

Where, K_ec = flexural stiffness of equivalent column

K_c = flexural stiffness of actual column

K_t = torsional stiffness of edge beam

The
effective cross section of the transverse torsional member, which may or may
not include a beam web projecting below the slab, as shown in Fig. 13.18, is
the

Figure 2.6.4.2(a) Torsion at a transverse
supporting member illustrating the

basis of the equivalent column.

2.6.4.3 Steps–by-Step Analysis Procedures of Equivalent
Frame Method

The
steps of analysis of a two-way slab are as follows:-

1)
Determine
the factored negative (M_u^–) and positive moment (M_u⁺)
demands at the critical sections in a slab-beam member from the analysis of an
equivalent frame. The values of M_u^–are calculated at the
faces of the columns. The values of M_u⁺are calculated at the
spans. The following sketch shows a typical moment diagram in a level of an
equivalent frame due to gravity loads.

Figure
2.6.4.2(b) Typical moment diagram due to gravity
loads

2) Distribute M_u^–to
the CS and the MS. These components are represented as M_u,^–_CSand
M_u,^–_MS,
respectively. Distribute M_u⁺to the CS and the MS. These
components are represented as M_u,⁺_CSand
M_u,⁺_MS,respectively.

Figure 2.6.4.2(c)
Distribution of
moments to column strip and middle strips

3)
If
there is a beam in the column line in the spanning direction, distribute each
of M_u,CSand M_u,⁺_CSbetween the beam and rest
of the CS.

Figure
2.6.4.2(d) Distribution of moments to beam,
column strip and middle strips

4)
Add
the moments M_u,^–_MSand M_u,⁺_MSfor
the two portions of the MS (from adjacent equivalent frames).

5)
Calculate
the design moments per unit width of the CS and MS.

2.6.5
Provision of Thickness According to ACI
Code for the design and analysis of flat structures

In order to prevent undue
deflection, certain limitations are placed on the minimum slab thickness that
can be used in a given floor panel. In as much as the actual deflection of a
flat slab cannot be computed with any appreciable degree of accuracy, these
limitations were developed from a study of the observed deflections in actual
structures. The ACI code specifies that the slab thickness, exclusive of the
drop, shall not be less than 1/40 of the longer dimension for slabs with drops,
and not less than 1/36 of the same dimension for slabs without drops. Of
course, the slab must also be thick enough so that allowable unit compressive
and shear stresses will not exceed. In this connection, the ACI Code requires
that a reduced effective width be used in calculating flexural compression
stress, in order to allow for the non-uniform variation of bending moment
across the width of the critical sections. This reduced effective width is to
be taken as ¾ ^th the width of the strip, except that on a section
through a drop panel ¾ ^th the width of the drop panel is to be used.

2.7
Previous Works on Related Topic

Recent time it is a common
practice that of flat slab analysis, design and construction, and its
importance is increasing with time in our country. As the gradual increasing of
use and construction of flat slab, the researches related to flat slab is also
gradually increased. Thus why, here we have represent gist of some previous
thesis as an additional compliment for the viewers, and as a completion of our
project work.

2.7.1
Gist
of Previous Work

Researchers of
Ahsanullah University of Science & Technology (AUST) did various thesis on
different relevant subject of structures. The senior students have chosen
different fields of study with the requirement of their time. The gist of their
study reports are represented below:

Value engineering of mat
foundation of the campus of Ahsanullah University of Science &
Technology by Md. Mahmudul Hasan, Swim Iqbal Munna, A.K.M Sydat and
Mosaharof Hoshain Sumon (on Seeptember 2004) under the supervision of
Professor Dr. Anwarul Mustafa (P.Engg). In this thesis all the design
criteria of AUST Campus is checked including mat foundation analytically
and value engineering of the project. They recommended mat foundation in
the case of heavy load and for weak soil strata with much variation in
water level. They also mentioned various processes for mat foundation and
they are finite difference method.

Design of prestress concrete
girder bridge by Syed Asadul Haque and Md. Rezaul Islum (on November 2002)
under the supervision of Professor Dr. Anwarul Mustafa (P.Engg). In this
thesis they want to establish a comparative study of different methods
loading analysis of bridge girder and the analytic value of bending moment,
shear force, torsion are greater than the amount found by grid analysis.
So the economic and more reliable method of prestress concrete girder
bridge is the main aspects of this thesis.

Design of steel truss bridge
by Ziaul Haque Ali and A.K.M Hasan-Al-Farouque (on November 20002) under
the supervision of Professor Dr. Anwarul Mustafa (P.Engg). In this thesis
long span highway steel truss bridge is analyzed. Their recommendation of
this bridge is economical for a range of 100m-200m; facility is easy to
establish due to lightness of this structure nad fabrication of joints at
site. But maintenance cost is quite expensive. So the value engineering is
necessary in this case, they recommended.

Computer aided analysis and
design of fifteen storied apartment building in addition to approximate
method by S.M Arif Reza Hossain, Farjana Haque, Md. Ashraf Uzzaman and
Syed Mosiur Rahman (session 2000) under the supervision of Dr. Md.
Mahmudur Rahman, Associate Professor, AUST. In this thesis they designed &
analyzed the static and dynamic load of fifteen storied apartment building
based on various analysis software, for example, STAAD Ш, GT STRUDL etc.
They also compare the difference of result between ACI Co-efficient Method
and Software. A full soil integrated analysis of their project was the
future recommendation.

Design of a 20 Storied Flat
Plate Building by A.T.M Nurujjaman Khan (session 2000-2001) under the
supervision of Professor Dr. Al-Hajj Kazi Harun-Ur-Rashid, AUST and the
Director of Shaheedullah and new Associates Ltd. In this thesis paper they
design a flat plate, and also analyze, using various method of design and
analysis. The use of Portal Frame Method for analyzing frames. The
important thing of their thesis outcome is that, flat plate creates in
high-rise building construction by reducing frame work’s cost. Reduction
of Story Height resulting from thin floor, the smooth ceiling and
possibility of slightly shifting column location to fit the room
arrangements, and all their approaches are for achieving economy and thus
creating flexibility of architectural arrangement.

Investigation on Effective
bracing System for Buildings with Soft Ground Story Under Seismic loading
by Md. Nazmul Islum, Md. Ziaul Badr and Md. Abdullah Al Mamun (on October
2008) under the supervision of Dr. Md. Mahmudur Rahman, Associate
Professor, AUST. In this thesis, they aims at proposing an effective
bracing system in the open ground story to mitigate large deflection and
lessen force demand. For this why, five different cases of bracing system
for a typical six storied building are analyzed. The three dimensional (3-D)
reinforced concrete frames are modeled by finite element software, ETABS,
under design load following Bangladesh National Building Code (BNBC).
Frames are then analyzed under lateral earthquake load provide by ETABS
following UBC 94, which shows equivalent result with BNBC. Then, story
displacement and force demand (Moment and Shear) for the system is
compared with those from open story system (Braced Frame).

Structural Analysis of the
Flat Plate of a 20 Storied Building Using Structural Software STAAD
Pro-2004 by Mukarram Mahmud Sohul and Md. Shariful Hasan Khan under the
supervision of Dr. Md. Mahmudur Rahman, Associate Professor, Ahsanullah
University of Science & Technology. In that thesis, the structural
analysis of flat plate for a 20 storied building was done with the help of
structural analysis software named STAAD Pro-2004. They analyzed
deflection, bending moments and the shear forces of the structural frame
for various sections such as, interior column strip, interior middle
strip, end span column strip, end span middle strip etc. They have also
compared the software results of the bending moment and shear forces of
flat plate of the mode at various critical sections, with the results they
got from analytical approximate calculation.

03. Modeling and
Analysis

3.1
General of Modeling

Modeling of most common type
components such as slabs, beams, columns, etc. do not require any special
techniques. However there are certain issues that need to be take care. In
order to analyze the center row of panels, it is assumed that the structure is
divided into five rows of panels in the direction of analysis. The boundaries
of the center strip are assumed to be the centerlines of the interior rows of
columns. This strip is dimensionally identical to a strip containing an
interior row of columns and bounded by the panel centerline so for simplicity,
the illustrations show the entire column at the center of the panel rather than
half of it at each side.

Flat slab floors are ordinarily designed to
carry only uniform load over the entire surface. Important of those will be
introduced in the following paragraphs:

3.1.1 Slabs:

The important considerations in
modeling slabs are what type of elements to be used, what should be the
connectivity condition between slab and beam; and how to transfer the load from
slab to other members. Precast panels with topping are modeled as one way
panels. In this case, there is no need to divide the panel into smaller
elements. The floor loads can be applied directly on the panels which are
transferred to the supporting beams/columns automatically. These panels are
membrane type elements. Two way type load transfer behavior need to be
captured, the slab can be modeled as membrane or plate type elements. If
modeled as membrane, the load is transferred to the supporting members
automatically and there is no need to divide the slab into smaller elements. In
this case there will be no interaction between the slab and supporting
elements. However the slab can also be modeled as Plate/Shell elements.

3.1.2 Columns:

Columns are relative easier to
model but relative difficult to design if they are too slender. As long as the
columns are short columns, automated design features are generally reliable.
However when the column becomes long column and subjected to more than one
action, a comprehensive design procedure need to be used. In this case, the
software estimated factors to compute the effective length factors, moment
magnification parameters, sway/non-sway checks, minimum eccentricity calculations,
etc. which have direct impact on direct (capacity, reinforcement) need to be
carefully examined and verified before accepting the program recommended
reinforcement. It is quite common that program overestimates the moment
magnification factor (5-10) for commonly used column sections in houses (20-30
x 20-30 cm and 3 m height) and computes the longitudinal bars based on
excessively magnified moments. Therefore it is extremely important to
understand the influence of different parameters in the design of long columns
(especially the connectivity condition) and also to verify whether the
automatically calculated values are reasonable or not.

3.2
Assumptions of Modeling

The assumption being that no
breaks in the continuity will be maintained in case of modeling of the entire
flat slab surface. Broad strips of the slab centered on the column lines in
each direction serve the same function as the beams; for this case, also, the
full load must be carried in each direction. Here the considerable “Analysis Strips”
have chosen according to BNBC code
for approximate direct design method by hand calculation.

For 2-D modeling in analysis
software we have also used all but similar philosophy. There we have provided a
rectangular width as a supplement of real beams through the column lines as
same as of considering strip width calculated according to the philosophy of
direct design method for achieving the condition of flat slab. According to
BNBC the analysis strip width is 8^/(eight feet) in here. Existing
columns are modeled as beam elements having same as property (height, material,
cross section etc.) for actual column on the considering structural system.
However, in STAAD Pro has some form of automatic constraint system being
applied to represent the rigid region for the column-slab connection in the 2-D
model.

In case of 3-D model all the
components are modeled conventionally similar to the actual structural
philosophy. Here we have provided automated plate which is similar to actual
property of the considering flat plate. We have also meshed the plate elements
in a proportion of four by four (4 × 4 = 16) for the intended plates and two by
two (2 × 2 = 4) for the other plates to get more précised results. Columns are
modeled as beam elements having same as

property (height, material, cross
section etc.) for actual column on the considering structural system. Here all
the ends of the columns are supported as fixed support.

However, as a whole the above
assumption philosophy will be integrated with the followings:-

1. The panel is one of an infinite
array of identical panels.

2. All panels are uniformly
loaded.

3. The shear is uniformly
distributed around the perimeter of

the
column capital.

4. The
bars are weightless and undeformable.

5. The mass of the plate and the
external loads are

concentrated at the fixed
supports.

6· The resultants of the direct
stresses are bending moments

acting at the fixed supports and
at the ends of each bar.

7. The resultant of vertical
shearing stresses are shearing

forces acting at the fixed
supports and at the ends of each bar.

3.3
Model Data

Floor Area :
76^/×48 ^/ (3648 Sq. ft)

Panel
Size/Plate Size :
16^/×19 ^/

Column
to Column C/C distance in long direction :
19 ^/

Column
to Column C/C distance in short direction :
16 ^/

Rectangular
width of considering strip/ Size of the beams :
8 ^/along the direction of

analysis
for interior panels and 4 ^/for exterior panels according to BNBC
for 2-D model

Thickness of the rectangular width /
slab/plate : .625 ^/(7.5 ^//)

Height of the columns :
12 ^/for ground floor &

10
^/for upper floors for both 2-D & 3-D model

Size
of the columns :
18^// × 18^// for both 2-D

and
3-D model

Restraints
/ Supports Condition :
Conventional Fixed

Support for both 2-D & 3-D model

Material constants :
Automated material

constants
being in the analysis software (STAAD Pro) for both model

3.4
Model

The below plan is the
identical layout plan for the entire structure in case of modeling and
analysis:-

3.4.1
2-D Model:

Figure
3.4.1.1 2-D
Skeletal Model View with Panel ID

Figure
3.4.1.2 2-D
Rendered Model View

Figure
3.4.1.3 2-D
Skeletal Model View with Member Load

3.4.2
3-D
Model:

Figure
3.4.2.1 3-D
Skeletal Model View with Panel ID

Figure
3.4.2.2 3-D
Model with Full Sections & Columns with Panel ID

Figure
3.4.2.3 3-D
Rendered Model View

Figure
3.4.2.4 3-D
Model Top View with Plate ID (Roof)

Figure
3.4.2.5 3-D
Model Full View with Plate ID

Figure
3.4.2.6 3-D
Model Top View with Node ID (Roof)

Figure
3.4.2.7 3-D Full
Model View with Node ID

3.5
Generals of Analysis

Flat slab floors are
ordinarily designed to carry only uniform load over the entire surface.
However, for analysis purpose, concentrated loads are to be sustained in addition
to the uniform load; this will be introduced as nodal loads in the entire
direction. Generally the self weight is categorized as dead load and uniform
service live loads are introduced as plate loads for 3-D model and as member
loads for 2-D model in case of analysis by using the analysis software STAAD
Pro. One necessary consideration is that, where major openings in the slab
occur, they should be framed by the slab itself or by additional beams to have
the effect of restoring continuity of slab. This slab or beams should be
analyzed properly so that the portion will be given sufficient strength to
carry the entire floor load or concentrated load to be placed there. However,
we didn’t need that because we have neglected this condition here. Finally, all
the applied loads are combined to get proper idealization and best comparison
of outputs.

3.5.1
Analysis Data:

3.5.1.1
Load Data:

Self Weight of the Structure : To be calculated automatically by
the software.

Service Live Load : 100 psf (100 lb per sq.
ft.)as plate load

in
3-D model and 800 lb/ft (100psf × 8 ft = 800 lb/ft) as member load in 2-D
model.

Load
input unit : lb-ft
(Pound-Feet)

Load
combination :
Combination-1=SW+WL

3.5.1.2
Material Constants:

Automated
material constants are used, those are being in the analysis software (STAAD
Pro) as default value in this case.

3.5.2
Analysis Condition
Representation:

Figure
3.5.2(a) 3-D Pre-Processing for analysis

Figure
3.5.2(b) 3-D
During analysis

Figure
3.5.2(c) 2-D Pre-Processing for analysis

Figure
3.5.2(d) 2-D During analysis

04. Results and
Comparison

4.1 General

Here we have made
comparison tables and provide some necessary figures, which are representing
the deviations and similarities between results got from “3-D and 2-D Model” analysis is
done using the analysis software named “STAAD
PRO v8.0i”, and between results got from Equivalent Frame Method (i.e., we
also consider the axial force got by analysis software in comparison to with
axial force got by analytical hand calculation done based on Equivalent Frame
Method). This table is made because also to see the change in moment when a
structural plan turned into 3-D Model from 2-D Model with its all
compatibility. This table is a great scope to view and to consider the
structure’s conduct variation from the view point of “Mechanism of Analysis” of
any structure. We also represent the values of beam deflection got from ABAQUS
and thus concurrently it is represented in a comparable graph.

4.2 Assumption

For developing an
idealization to get most clarified imagination about the whole structure’s
behavior variation; specially in case of a high rise building, here we only
consider the “Plate-Node Moments” which have been got using analysis software “STAAD PRO v8.0i”.Where the plates are
positioned through the whole slabs and then meshed in case of 3-D modeling, and
also there we have taken the beam width as same of “Analysis Strip” width of
8(eight) feet chosen according to BNBC code
as per our honorable Project Supervisor’s guidance incase of 2-D modeling.
Finally, we have tried to compare results through the column line of panel C-C
for different floors as a whole.

4.3 Pictures Showing Diagrammatic
Representation of Results

Following represented
pictures are needed to understand, and for the proper illustration of various
comparisons those will be done next:-

Figure
4.3 (a) Showing
2-D full model with considering columns

(Scale 1:1)

Figure
4.3 (b) Considering
columns of 2-D model with Beam ID

Figure
4.3 (c) Considering
columns of 2-D model with Nodal ID

Figure
4.3 (d) Considering
full 2-D model with Nodal ID

(Scale 1:1)

Figure
4.3 (e) Shear F_Zof 2-D model Figure 4.3 (f) A.F F_Xof 2-D
model

(Scale 1:550
lb per ft) (Scale
1:10000 lb per ft)

Figure 4.3 (g) Deflected view of
2-D model

(Scale
1: 0.2 in per ft)

Figure
4.3 (h) Moment M_Zof 2-D model

(Scale 1: 150 Kip-in per ft) Figure
4.3 (i) Moment M_Yof

2-D model

(Scale 1: 50 Kip- in per ft)

Figure
4.3 (j) 3-D skeletal model with
considering column positioned in panel C-C

(Scale
1:1)

Figure 4.3 (k) Considering columns of 3-D
model Figure 4.3 (l) Considering columns of

with Nodal ID 3-D
model with Beam ID

Figure
4.3 (m) Shear F_Zof 3-D model Figure 4.3 (n) A.F F_Xof 3-D
model

(Scale 1: 400 Kip-in per ft) (Scale
1: 10000 Kip-in per ft)

Figure
4.3 (o) 1stFloor of 3-D
model with plate ID

Figure
4.3 (p) 1^stFloor of 3-D model
with nodal ID

Figure
4.3 (q) 5^thFloor of 3-D model
with plate ID

Figure
4.3 (r) 5thFloor of 3-D
model with nodal ID

Figure 4.3 (s) Deflected view of 3-D model

(Scale 1: 0.2 in per ft)

Figure
4.3 (t) Moment M_Zof 3-D model for columns

(Scale
1: 30 Kip-in per ft)

Figure
4.3 (u) Moment M_Yof 3-D model for columns

(Scale 1: 60 Kip-in
per ft)

4.4 Comparison Tables & Graphs

The below tables & graphs are
prepared for understanding of deviation of results and thus, variations in
structure’s behavior under different condition at different considerable
positions. The graphs are made with the help of Microsoft Excel, where
automated graph can be got according to selected input data

For comparison of nodal moments
of 3-D model between story one and five, it is important to note that, here the moment for plate corner stress is
considered and thus moments for the plates around a node are sum-up in case of
their negative and positive values of moments of the surrounding plates

Table
4.1 Plate Node Moment (-ve & +ve): 3-D vs 3-D of different story

Plate
Node Moment Type

3-D Model

1 ^stFloor, Panel C-C

Load
Case: Combination-1

: SW+LL

Moment in kip-ft/ft

3-D Model

5 ^thFloor, Panel C-C

Load
Case: Combination-1

: SW+LL

Moment in kip-ft/ft

REMARKS

M_X

Same Localized Nodes

(Through Panel C-C)

Same Localized Nodes

(Through Panel C-C)

The moment values have similarity &
dissimilarity both.

N₃

GL_4-4

N
₁₂

GL_3-3

N
₁₃

GL_2-2

N₁₄

GL_1-1

N₃₁₅

GL_4-4

N
₃₁₆

GL_3-3

N
₃₁₇

GL_2-2

N
₃₁₈

GL_1-1

+ve

-ve

+ve

-ve

+ve

-ve

+ve

-ve

+ve

-ve

+ve

-ve

+ve

-ve

+ve

-ve

-15.138

–31.857

-47.249

-25.097

-14.06

-36.26

6.7

-28.209

2.93

-13.782

M_Y

-37.675

43.035

-5.849

-43.803

-6.734

6.827

-16.506

-45.829

11.336

7.215

-6.803

Note: GL =
Grid Line

Table
4.2 Column Shear (-ve & +ve): 2-D vs 3-D Model

Column Shear Type

2-D Model

Exterior Column in C-C Panel

Load Case: Combination-1

: SW+LL

Shear in Kip

3-D Model

Exterior Column in C-C Panel

Load Case: Combination-1

: SW+LL

Shear in Kip

Same Localized Beams

(Through Panel C-C)

Same Localized Beams

(Through Panel C-C)

B₇(Gr. to 1^stFloor)

B₁₄(1^st to 2^ndFloor)

B₂₁(2^nd to 3^rdFloor)

B₂₈(3^rd to 4^thFloor)

B₃₅(4^th to 5^thFloor)

B₄₂(5^th to 6^thFloor)

B₁₂(Gr. to 1^stFloor)

B₁₄₀(1^st to 2^ndFloor)

B₂₅₇(2^nd to 3^rdFloor)

B₂₇₇(3^rd to 4^thFloor)

B₂₉₇(4^th
to 5^thFloor)

B₃₁₇(5^th to 6^thFloor)

+/-

60.135

-64.185

56.174

-52.79

48.367

-44.991

39.052

-35.677

27.790

-24.415

14.405

-11.030

0.618E+02

-0.6552E+02

0.566E+02

-0.538E+02

0.489E+02

-0.454E+02

39.502

-36.523

27.992

-24.857

14.735

-11.560

10.764

-10.765

4.095

-4.095

3.325

-3.325

1.350

-1.350

0.044

-0.044

4.571

-4.571

9.955

-9.955

4.532

-4.532

3.976

-3.976

1.530

-1.530

0.075

-0.075

5.025

-5.025

Table
4.3Column Axial Force (-ve): 2-D vs Equivalent Frame Method

(Cantilever
Method)

Story ID	Story Height in ft	A.F from Software Analysis (2-D Model, Fz) in Kip	A.F from Equivalent Frame Method in Kip
GF	12	-10.765	-10.129
1 ^st	10	-8.017	-7.009
2 ^nd	10	-5.054	-4.421
3 ^rd	10	-3.325	-2.489
4 ^th	10	-1.350	-1.145
5 ^th	10	-0.852	-0.305

05. Discussion

In our analysis we have got
results for different conditions, we desired. Necessary results are shown in
the “chapter-5: Results & Comparisons”. In this chapter we have made
various comparison tables, comparing graphs to execute our main purposes. The
comparisons will give the scope to discuss about whole structure’s behavior
under different conditions considered.

Comparing the moments across the
entire structure shows that the moments obtained by considering 2-D model may
be compared favorably with measured moments in the center bay of panels (panel
C-C) in case of 3-D model. The difference at the negative moment section can be
ascribed to as a difference in the stiffness of the columns is not assumed in
the analysis or to as change in the property for 3-D model. AF (Axial Forces)
computed by the proposed frame analysis (by Equivalent Frame Method) are
generally in agreement with the measured AF by the software in case of 2-D
model in the considering same direction (Fz). Although differences exist at
individual sections, the over-all agreement is the best of any of the computed
AF. The analysis of a flat slab by two-dimensional (2-D) Equivalent Frame
Method is at best only a good approximation. It can be seen that the axial
force obtained by the proposed frame analysis are in good agreement with those
obtained by plate theory automated in the analysis software. Although a
two-dimensional frame analysis should not be expected to give the exact moments
in slabs, it does give the values which are sufficiently accurate for design
purposes. The comparisons show that even though the moments obtained by the
proposed frame analysis differ from measured moments at some sections, the
agreement is generally good. However, with this slight dissimilar outcome it is
also apparent that variations of the slab stiffness, loading arrangement, and
support conditions in the third dimensional (3-D) analysis will influence the
moments in the direction considered. The influence of these variations can be
studied by the use of the theory of flexure for plates for 3-D model using
digital computer based programs developed based on some reliable method such as
‘Finite Element Method’ or on other available methods, but where there are no
rigorous method is available for determining their effects by a two-dimensional
analysis.

This study involves the
quantitative comparison of moments in reinforced concrete slabs as determined
by the analysis of equivalent two dimensional elastic frames, by analysis based
on the theory of flexure for plates, and by tests on both elastic and
reinforced concrete models. In the first portion of the investigation moments
determined from the analysis of equivalent frames are compared with the moments
based on plate theory (based on FEM).

However, though we
have obtained some slight differences in the resulted values. This is because
of difference between methods for calculation used software and approximate
analytical hand calculation. For instance, here the A.Fs from EQV.FM are
calculated by hand with lower precision, and on the other hand, this analysis
software is prepared based on FEM with higher precision & to have with all
the compatibility of structures, thus the comparative A.F values are deviated.

Finally, it can be
said that, the variations of resulted values may be negligible to consider this
analysis outputs for further proceeding design or decision to be made for
further analysis.

06.
Details of study on Beam deflection by software ABAQUS

6.1 Introduction

ABAQUS is a powerful finite
element software package. It is used in many different engineering fields throughout the world. ABAQUS
performs static and/or dynamic analysis and simulation on structures. It can
deal with bodies with various loads, temperatures, contacts, impacts, and other
environmental conditions.

ABAQUS
includes four functional components:

Analysis
Modules

Preprocessing
Module

Postprocessing
Module

Utilities

ABAQUS is a highly sophisticated, general purpose finite
element program, designed primarily to model the behavior of solids and
structures under externally applied loading. ABAQUS includes the following
features:

·
·
·
·
·
·
The abaqus.env is an
environmental file available to users for use in configuring micro-environments
for running different jobs. When a user runs a certain job on ABAQUS, he/she
may need to control various aspects of an ABAQUS job’s execution. Variables
called environmental variables are used to control the job’s execution.
These variables are assigned default values by the ABAQUS Site but the user can
modify the environment file, abaqus.env, to run different jobs. For
example, a user may:

Change
memory-related parameters to improve the performance of the job.

Control
where and how scratch files are written.

Provide
his/her own default values for some parameters to make operations easier.

Also
many other aspects of a job’s execution can be configured via the abaqus.env.When
a job is submitted, ABAQUS will first search for the environmental file(s) in
the following order:

The ABAQUS
site subdirectory where abaqus.env defined by ABAQUS must exist.

The user’s
home directory where abaqus.env is optional and will affect all
ABAQUS jobs submitted from user’s account.

The current
working directory where abaqus.env is optional and will affect all
ABAQUS jobs submitted from the current working directory.

Input Files

The
ABAQUS input file is an ASCII file with an extension of .inp. This file
helps users communicate with the ABAQUS analysis modules and it must be created
first. As a general finite element package, ABAQUS has multiple built-in
libraries.

The
four main libraries are:

Element
Library

Material
Library

Loading
Library

Procedure
Library

Each
library implements many keywords with their required and optional parameters
and data lines. These keywords and parameters are readable both by ABAQUS and
by the user. In comparison with most computer languages, the construction of
the ABAQUS input file is simple. The key is to select the correct keywords and
parameters to configure the models and the analysis procedures. There are two
kinds of input lines used in an input file: keyword lines and data lines.

We have worked on a RCC beam by ABAQUS to show the deflection
due to load.we applied to concentrated load at two points of beam on the bean
and then analyze it.we wanted to compare the value of deflection with a
theoretical(known) value.

6.2 Literature Review on ABAQUS

Al-Taan and Ezzadeen (1995) developed a numerical
procedure based on the FE method for the geometric and material nonlinear analysis
of RC members. A beam element with a composite layer system was used to model
the structure. For the nonlinear solution, an

incremental-iterative technique
based on Newton-Raphson’s method was employed. Only

the displacement components were
considered as DOFs where a parabolic interpolation function for axial
displacement, and cubic interpolation function for other displacement was used.
The numerical solutions of a number of reinforced fibrous concrete beams were
compared with published experimental test results and showed a good agreement.

To see the monotonic behavior of
RC beams and beam-column assemblages, Kwak and Filippou (1997) introduced a FE
model. In this model, concrete and reinforced bars were represented by separate
material models. Another model was used between reinforcement bars and concrete
to describe the behavior of the composite RC material. The concrete was modeled
by eight-node elements with 3×3 Gauss integration. The reinforcement was
modeled by the two-node truss element. Between these two, a bond link element
was used. Improved cracking criteria derived from fracture mechanics principles
was used asthe basis for developing this smeared finite- element model.

Later Kwak and Kim (2002)
introduced a new FE model for beams based on the moment-curvature relations of
RC sections including the bond-slip and tension softening branch. They used the
well established Timoshenko beam theory in the analysis. Bhatt and Kader (1998)
presented a 2D parabolic isoparametric quadrilateral FE based on the tangent
stiffening method for predicting the shear strength of RC rectangular beams.
Wang and Hsu (2001) developed the FE analysis program FEAPRC from FEAP by
introducing a new set of constitutive models for analyzing RC beams. The
fixed-angle softened-truss model (FA-STM), which assumes cracks develop along
the direction of principal compressive stresses applied at initial cracking,
and that cracks are fixed at this angle thereafter, was used in the new set

of constitutive models. The
numerical results for beams, panels and framed shear walls

were compared with the
experimental results. Recently, Abbas et al (2004) presented a

3D nonlinear FE model for RC
structures under impact loading. They used an elasto visco-plastic two surface
model in the FE. The reinforcement was smeared as a two dimensional membrane of
equivalent thickness. The layer was assumed to resist only the axial stresses
in the direction of the bars. A simply supported beam with dynamic point
loading was considered for numerical verification. Then experimental and
numerical analyses were done on a circular plate with impact loading.
Considerable work has been reported in recent literature relating to the
development and application of FE procedures for RC slabs, plates, panels, and shells.
Vecchio (1989) developed a nonlinear FE procedure to predict the response of RC
structures. A smeared crack approach was included for concrete. A secant
stiffness approach was used in the procedure incorporating the constitutive
relations for concrete. Only low order FE analysis was used in the procedure.
Numerical results were verified with the experimental data for square panels,
deep beams and perforated walls. Later Polak and Vecchio (1993) modified the FE
model for analysis of RC shell structures. In this adapted model, a 42 DOFs
heterosis type degenerate isoparametric quadrilateral element was developed
using a layered-element formulation. During the same time, Vecchio et al.
(1993) investigated the thermal load effect on RC slabs by nonlinear FE
analysis. In the FE analysis they considered the concrete tension stiffening
effect. Hu and Schnobrich (1990) derived a set

of constitutive equations
suitable for incremental FE analysis, and developed a nonlinear

material model for cracked RC
structures. This model was able to describe the post cracking

behavior of RC structures.
Reinforcement was treated as an equivalent uniaxial layered material placed at
the depth of the centerline of the bar. For concrete nonlinear behavior,
Saenz’s (Saenz and Luis, 1964) stress-strain curve was used. The model
considered smeared crack representation, rotating crack approach, tension
stiffening, stress degrading effect for concrete parallel to the crack
direction, and shear retention of concrete on the crack surface. The model was
verified against a set of experimental data of RC panels. Cerioni and Mingardi
(1996) introduced a FE model for analysis of a RC foundation plate, where the
RC plate was modeled with materially nonlinear layered FEs.

Jiang and Mirza (1997) developed a rational
numerical model for the nonlinear analysis of RC slabs. Material nonlinearities
for both concrete and steel were considered. In the model, a RC slab was first
divided into a number of composite elements, and each of the composite elements
was then assembled into a single concrete plate element and a small number of
steel beam elements. Kirchhoff thin plate theory was used in the plate element.
Very recently, Phuvoravan and Sotelino (2005) presented a FE model for
nonlinear analysis of RC slabs that combined a four node Kirchhoff shell
element for concrete with two-node Euler beam elements for the steel
reinforcement bars. A rigid link was considered between these two element
types. This model takes care of the exact location of steel reinforcement bars.

Over the last decade, civil
engineers have become very interested in the use of FRP due

to its positive characteristics
over the steel reinforcement. A large number of experiments

on the topic were done in this
time period. Many researchers also focus on the development of finite-element
models for the analysis of FRP RC structures. Shahawy etal. (1996) used a
2-dimensional non-linear FE computer program for analyzing beams strengthened
with carbon fiber reinforced plastic (CFRP).

Nitereka and Neale (1999)
developed a nonlinear FE layered model to predict the complete load-deformation
response of RC beams strengthened in flexure by composite materials. This model
considered both material and geometric nonlinearities. The numerical results
confirmed the effectiveness of using externally bonded fiber reinforced
composite laminates as a viable technique for strengthening concrete beams in
flexure. Ferreira et al. (2001) presented an FE model for analyzing RC beams
with FRP re-bars. They used the first order shear deformation theory in the
analysis of concrete shells reinforced with internal composite unidirectional
re-bars. The concrete was modeled with smeared crack concepts. A perfect
plastic and a strain-hardening plasticity approach were used to model the
compressive behavior of the concrete. A dual criterion for yielding and
crushing in terms of stresses and strains was considered. For tension in
concrete, the influence that the cracked concrete zones had on the structural
behavior was considered. Smeared crack model was used. The response of concrete
under tensile stresses was assumed to be linear elastic until the fracture
surface was reached. A sudden and total release of the normal stress in the
affected direction, or its gradual relaxation according to the tension
stiffening diagram was adopted after cracking had occurred. Cracking in two
principal stress directions in the plane of the structure was considered. In
this model, the reinforcing bars were modeled as layers of equivalent
thickness, having strength and stiffness characteristics in the bar direction
only. In tension, it is elastic up to failure. The FE was implemented in the
degenerated shell element by considering the theory discussed above. The model
was verified against the experimental data for simply supported concrete beams
reinforced with composites re-bars. A good agreement between the experimental
and numerical results for beams was obtained.

Supaviriyakit elal (2004)
developed a FE model to analyze RC beams strengthened with externally bonded
FRP plates. The concrete and reinforcing steel were modeled together by 8-node
2D isop plane stress RC elements. The RC element considered the effect of
cracks and reinforcing steel as being smeared over the entire element. Perfect
compatibility between cracked concrete and reinforcing steel was considered.
The FRP plate was modeled as a 2D elasto-brittle element. As the epoxy is
usually much stronger than the concrete, it was assumed a full compatibility
between FRP and concrete. The model was verified against the experimental data
of load-deformation, load capacity and failure mode of the FRP strengthen beam.
Fanning (2001) used commercial software ANSYS to analyze reinforced and
post-tensioned concrete beams. Hu et al. (2004) introduced a proper
constitutive model to simulate nonlinear behavior of RC beams strengthened by
FRP. They used the FE program ABAQUS. Reliable constitutive models for steel
reinforcing bars and concrete are available in the material library. Only the nonlinearity
of the FRP was added to ABAQUS as an external subroutine by the researchers. To
model the nonlinear in-plane shear behavior, the nonlinear stress-strain
relation for a composite lamina suggested by Hahn and Tsai (1973) was adopted.
Tsai and Wu (1971) failure criteria were also used in the model. During the FE
analysis, aperfect bonding between FRP and the concrete was assumed. The model
was verified for load-deflection data of RC beams strengthened by FRP.

6.3 Step-by-Step Description of Working
Procedure in ABAQUS:

It is a abaqus software.In the software we design
column & beam.It is an advance software.In our thesis paper we design beam
by using abaqus software.By using abaqus software we only design beam &
column.Here we design beam.

>Here
is our design procedur:-

1. At first, length=3.6m

Width=0.17m,

& depth=0.26m,

We draw a beam.(fig-1)

2. Then propertyàedit material–then
name—concrete& elasticàyoung
modulusà2.25*10^10 N/m2 & poission
ratio 0.2 then ok.

3. Concrete sectionàsection 1àconcreteàsolidàhomogenousàcontinue then coming dialog box
then thickness1 then ok.

4. Assign section.(fig-2)

5. Then part1—surf1àRebar1 then continous &
choose surface select.(fig-3)

6. Then edit materialàmaterial nameàsteel—elastic elastic—young
modulus 2.1*10^11N/m2 & poission ratio 0.3,

7. Then concrete sectionàsectionàsection2àsteelàcontinueàedit sectionàdialog boxàmaterialàsteelàmembrane thickness 2.5” &
0.635 give to draw Rebar layer setup.

Rebar layer Material steel Area per bar Spacing
orientation angle

1 Steel 0.0000634147 0.07 90

2 Steel 0.00031414 0.04
0

8. Part1àsurface2àRebar2àsurface select then done.

9. Concrte sectionàsteel1àShellàmembraneàcontinue—surfaceàrebar layer—Same as.

10. Again surface-3àrebar3—Surface select.

11.Again go to create sectionàshellàmembrane thickness 0.0635 &
left side rebar layer setup.

Layer name Material Area per bar Spacing Angle

1 steel 0.0000636174 0.07
90

12.Again same as 10 &11 repeat
then right side.

13.Rebar reference orientation &
datum setup.

14.For steel & concrete we put
the plastic plastic value.

15.assemblyàdependentàok.(fig-4)

16.Loadàload manageràCreat loadàPressureàcontinue.

17.Then select the surface & put the magnitude value 10Mpa &
then click.

18.Boundary conditionàDisplacement notationàcontinue.

19.Meshàselect partàseed partàglobal seed(global size2.5)àok.(fig-05)

20.Element typeàelement type—C308k.

21.Mesh partàyes.(fig-6)

22.Job manageràedit jobàokàsubmit.(fig-07)

23.Show cracking shape in
(fig-08)

24.We find a deflection vs time
show in (fig-09)

These corresponding identical
figures are as likely below:-

6.4 Modeling and Analysis by ABAQUS

Model Data:

We modeled a RCC beam which,

Length=360cm

Width=18cm

Height=17cm

Re bar orientation:

Top sur>

Bottom sur>

Model of the Beam in ABAQUS:

Figure
6.2(a) 3-D Model View from ABAQUS after
modeling

Figure
6.2(b) 3-D Model View from ABAQUS after
introducing material property

Figure
6.2(c) 3-D Model View from ABAQUS after
Meshing the Beam

Resulted Views after Analysis:

Figure
6.2(d) Deformed View after Analysis with
Legends

Figure
6.2(e) General Cracking View after
Analysis

Comparison Curve:

The graph is drawn against Time V_SDeflection based on the analysis outputs is represented below:-

Graph
6.0 Time V_SNodal Deflection

07. Conclusion

As a whole, it can be concluded that, the main
purpose of the study to analyze a Flat Plate structure with its 2-D & 3-D
model by software and conventional hand calculation methods and to make various
comparisons between them is executed successfully. The column moments, plate
node moments and A.F (axial force) of the considering column at different
locations are successfully determined. Where, all of the outputs of the
analysis have expressed the behavior of Flat Plate Structure and its structural
philosophy. Also, all the purposes and scopes of this study including beam
deflection using software ABAQUS are completed successfully. Where, by ABAQUS,
we have successfully analyzed the model. After analyzing the model, we have
found the deflected shape of the beam, the highly stressed portion and cracking
portion of beam. We also found out the ‘Time versus Deflection’ curve. So,
these précised outcomes can be used in any recognized or desired purposes.

08. Future Recommendation

Based on the lesson
and knowledge of our thesis and project work, we may recommend the followings
as future provision:

1.
Flat
Plate analysis may be done in other available methods, such as- FEM, ELM etc to
make Flat Plate analysis so much realistic and effective.

2.
The
details of design procedure & design of Flat Plate based on our analysis
report may be possible in the future.

3.
The
Flat Plate structures may be analyzed with some sophisticated software, such
as- MIDAS GEN, ANSYS and MIDAS CIVIL etc. to make the analysis more reliable
& dependable.

4.
An automatic software using programming
language VISUAL BASIC based on our study report and other trusted publications
may be made as an entry to new era for analyzing & designing the Flat Plate
structures only.

5.
This
study report may be repeated by others for only to verify and discover the
variation of column moments and plate node moments in the same positions for
various floors.

6.
Column-to-Column
joint behavior for different floors in case of Flat Plate structure analysis
through our assumptions and theorems may be the topic for the upcoming students
or fellows.

7.
Deflection
of various types of beams can be studied by approximate analytical hand
calculation and by the sophisticated software to compare.

Disclaimer:

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