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.
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
of Literature
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.
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.
that flat floors/roofs are generally of two type are-
Flat
Slabs with dropped panel (Flat Slab)
Flat
Slabs without dropped panel (Flat Plate)
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
2.1 General
Types of Flat Structures
Terms of Flat Structures
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.
shear strength of slab
negative moment capacity of slab
the slab and hence reduce deflection
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.
increase
shear strength of slab
reduce
the moment in the slab by reducing the clear or effective span
2.2.2 Column
Head
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
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
design strip bounded by two column strips.
2.2.3 (b)
drop
Advantages of Flat Slab/Flat Plate Floor
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
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
2.3.2 Saving
Building Height
Shorter
Construction Time
flat
plate design will facilitate the use of big table formwork to increase
productivity
2.3.3 Big Table
Formwork
Single
Soffit Level
Simplified
the table formwork needed
2.3.4 Single
Soffit Level
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
Pre-Fabricated
Welded Mesh
Prefabricated
in standard sizes
Minimized
installation time
Better
quality control
2.3.6 Pre-Fabricated
Welded Mesh
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
Structural Behavior of Flat Structures
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^{th }power of the ratio of the spans of
the considering slab. This assumption is approximate because the actual
behavior of slab is more complex.
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.
surface load w is applied, that load
is shared between imaginary slab strips l_{a }in the short direction
and l_{b }in the long direction, as described in the previous lines in
this section.
direction
carried by the long strips l_{b }is delivered to the beams B_{1 }spanning
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_{a }deliver
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.
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.
Design Consideration
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.
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 m^{3 }per square meters.
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.
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-
within acceptable tolerances as specified in the codes and
of the building
Floor
Openings
No
opening should encroach upon a column head or drop.
Sufficient
reinforcement must be provided to take care of stress concentration.
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.
2.5.6 Shear
Condition
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.
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
deflection.
Design Methodology
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.
Common
Methods of Design
The
finite element method.
The
simplified method or, direct design method.
The
equivalent frame method or cantilever method.
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-
Envelopes
structural deformation
Simplified
or Direct Design Method
in two-way slabs can be found using the semi empirical direct design method,
subject to the following restrictions:
There must be a minimum of three continuous spans in each direction.
The panels must be rectangular, with the ratio of the longer to the shorter
spans within a panel not greater than two.
The successive span lengths in each direction must not differ by more than one-third of the longer span.
of the span in the direction of the offset from either axis between centerlines
of successive columns.
live load must not exceed two times the dead load.
relative stiffness of the beams in the two perpendicular directions, given by
the ratio α_{1 }l_{2 }^{2 }/ α_{2 }l_{1 }^{2 }must be between 0.2 and 5.0
Factored Loads
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 l_{1} 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
Critical Sections
interior spans, the total static moment is apportioned between the critical
positive and negative bending sections according to the following ratios:
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.
2.6.3.3(A)
Distribution of total static moment M_{0}
and negative bending.
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.
The
Equivalent Frame Method
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.
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.
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:-
Line 2
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.
model of an equivalent frame
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,
/∑K_{c} + 1 /∑K_{t}
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
supporting member illustrating the
Frame Method
steps of analysis of a two-way slab are as follows:-
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.
2.6.4.2(b) Typical moment diagram due to gravity
loads
the CS and the MS. These components are represented as M_{u,}^{– }_{CS }and
M_{u,}^{–}_{MS},
respectively. Distribute M_{u}^{+ }to the CS and the MS. These
components are represented as M_{u,}^{+}_{CS }and
M_{u,}^{+}_{MS, }respectively.
Distribution of
moments to column strip and middle strips
If
there is a beam in the column line in the spanning direction, distribute each
of M_{u,CS }and M_{u,}^{+}_{CS }between the beam and rest
of the CS.
2.6.4.2(d) Distribution of moments to beam,
column strip and middle strips
Add
the moments M_{u,}^{–}_{MS }and M_{u,}^{+}_{MS }for
the two portions of the MS (from adjacent equivalent frames).
Calculate
the design moments per unit width of the CS and MS.
Provision of Thickness According to ACI
Code for the design and analysis of flat structures
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.
Previous Works on Related Topic
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.
Gist
of Previous Work
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.
Analysis
General of Modeling
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.
carry only uniform load over the entire surface. Important of those will be
introduced in the following paragraphs:
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.
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.
Assumptions of Modeling
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.
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.
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
section etc.) for actual column on the considering structural system. Here all
the ends of the columns are supported as fixed support.
assumption philosophy will be integrated with the followings:-
array of identical panels.
loaded.
distributed around the perimeter of
column capital.
bars are weightless and undeformable.
external loads are
supports.
stresses are bending moments
at the ends of each bar.
shearing stresses are shearing
supports and at the ends of each bar.
Model Data
76^{ /}×48 ^{/} (3648 Sq. ft)
Size/Plate Size :
16^{ / }×19 ^{/}
to Column C/C distance in long direction :
19 ^{/}
to Column C/C distance in short direction :
16 ^{/}
width of considering strip/ Size of the beams :
8 ^{/ }along the direction of
for interior panels and 4 ^{/ }for exterior panels according to BNBC
for 2-D model
slab/plate : .625 ^{/ }(7.5 ^{// })
12 ^{/ }for ground floor &
^{/ }for upper floors for both 2-D & 3-D model
of the columns :
18^{//} × 18^{//} for both 2-D
3-D model
/ Supports Condition :
Conventional Fixed
Automated material
being in the analysis software (STAAD Pro) for both model
Model
identical layout plan for the entire structure in case of modeling and
analysis:-
2-D Model:
3.4.1.1 2-D
Skeletal Model View with Panel ID
3.4.1.2 2-D
Rendered Model View
3.4.1.3 2-D
Skeletal Model View with Member Load
3-D
Model:
3.4.2.1 3-D
Skeletal Model View with Panel ID
3.4.2.2 3-D
Model with Full Sections & Columns with Panel ID
3.4.2.3 3-D
Rendered Model View
3.4.2.4 3-D
Model Top View with Plate ID (Roof)
3.4.2.5 3-D
Model Full View with Plate ID
3.4.2.6 3-D
Model Top View with Node ID (Roof)
3.4.2.7 3-D Full
Model View with Node ID
Generals of Analysis
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.
Analysis Data:
Load Data:
the software.
ft.)as plate load
3-D model and 800 lb/ft (100psf × 8 ft = 800 lb/ft) as member load in 2-D
model.
input unit : lb-ft
(Pound-Feet)
combination :
Combination-1=SW+WL
Material Constants:
material constants are used, those are being in the analysis software (STAAD
Pro) as default value in this case.
Analysis Condition
Representation:
3.5.2(a) 3-D Pre-Processing for analysis
3.5.2(b) 3-D
During analysis
3.5.2(c) 2-D Pre-Processing for analysis
3.5.2(d) 2-D During analysis
Comparison
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.
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.
Representation of Results
pictures are needed to understand, and for the proper illustration of various
comparisons those will be done next:-
4.3 (a) Showing
2-D full model with considering columns
4.3 (b) Considering
columns of 2-D model with Beam ID
4.3 (c) Considering
columns of 2-D model with Nodal ID
4.3 (d) Considering
full 2-D model with Nodal ID
4.3 (e) Shear F_{Z }of 2-D model Figure 4.3 (f) A.F F_{X }of 2-D
model
lb per ft) (Scale
1:10000 lb per ft)
2-D model
1: 0.2 in per ft)
4.3 (h) Moment M_{Z }of 2-D model
4.3 (i) Moment M_{Y }of
4.3 (j) 3-D skeletal model with
considering column positioned in panel C-C
1:1)
model Figure 4.3 (l) Considering columns of
model with Beam ID
4.3 (m) Shear F_{Z }of 3-D model Figure 4.3 (n) A.F F_{X }of 3-D
model
1: 10000 Kip-in per ft)
4.3 (o) 1st^{ }Floor of 3-D
model with plate ID
4.3 (p) 1^{st }Floor of 3-D model
with nodal ID
4.3 (q) 5^{th }Floor of 3-D model
with plate ID
4.3 (r) 5th^{ }Floor of 3-D
model with nodal ID
4.3 (t) Moment M_{Z }of 3-D model for columns
1: 30 Kip-in per ft)
4.3 (u) Moment M_{Y }of 3-D model for columns
per ft)
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
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
4.1 Plate Node Moment (-ve & +ve): 3-D vs 3-D of different story
Plate Node Moment Type |
3-D Model
1 ^{st }Floor, Panel C-C Load : SW+LL Moment in kip-ft/ft |
3-D Model
5 ^{th }Floor, Panel C-C Load : 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. |
||||||||||||||
N_{3}
GL_{4-4} |
N _{12} GL_{3-3} |
N _{13} GL_{2-2} |
N_{14}
GL_{1-1} |
N_{315}
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
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) |
||||||||||||||||||||||||
B_{7 }(Gr. to 1^{st}Floor) | B_{14 }(1^{st} to 2^{nd}Floor) | B_{21 }(2^{nd} to 3^{rd}Floor) | B_{28 }(3^{rd} to 4^{th}Floor) | B_{35 }(4^{th} to 5^{th}Floor) | B_{42 }(5^{th} to 6^{th}Floor) | B_{12 }(Gr. to 1^{st }Floor) | B_{140 }(1^{st} to 2^{nd }Floor) | B_{257 }(2^{nd} to 3^{rd }Floor) | B_{277 }(3^{rd} to 4^{th}Floor) |
B_{297 }(4^{th} to 5^{th }Floor) |
B_{317 }(5^{th} to 6^{th}Floor) | ||||||||||||||
+/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | ||||||||||||||
Fx | 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 | |
Fz | 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 |
4.3Column Axial Force (-ve): 2-D vs Equivalent Frame Method
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 |
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.
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.
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).
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.
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.
Details of study on Beam deflection by software ABAQUS
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.
includes four functional components:
- Analysis
Modules
- Preprocessing
Module
- Postprocessing
Module
- Utilities
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.
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.
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.
four main libraries are:
- Element
Library
- Material
Library
- Loading
Library
- Procedure
Library
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.
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.
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
based on Newton-Raphson’s method was employed. Only
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.
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.
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
numerical results for beams, panels and framed shear walls
experimental results. Recently, Abbas et al (2004) presented a
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
suitable for incremental FE analysis, and developed a nonlinear
structures. This model was able to describe the post cracking
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.
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.
engineers have become very interested in the use of FRP due
over the steel reinforcement. A large number of experiments
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).
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.
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.
Procedure in ABAQUS:
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.
is our design procedur:-
name—concrete& elasticàyoung
modulusà2.25*10^10 N/m2 & poission
ratio 0.2 then ok.
then thickness1 then ok.
choose surface select.(fig-3)
modulus 2.1*10^11N/m2 & poission ratio 0.3,
0.635 give to draw Rebar layer setup.
orientation angle
0
left side rebar layer setup.
90
then right side.
datum setup.
the plastic plastic value.
then click.
(fig-08)
show in (fig-09)
figures are as likely below:-
6.2(a) 3-D Model View from ABAQUS after
modeling
6.2(b) 3-D Model View from ABAQUS after
introducing material property
6.2(c) 3-D Model View from ABAQUS after
Meshing the Beam
6.2(d) Deformed View after Analysis with
Legends
6.2(e) General Cracking View after
Analysis
6.0 Time V_{S }Nodal Deflection
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.
and knowledge of our thesis and project work, we may recommend the followings
as future provision:
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.
The
details of design procedure & design of Flat Plate based on our analysis
report may be possible in the future.
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.
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.
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.
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.
Deflection
of various types of beams can be studied by approximate analytical hand
calculation and by the sophisticated software to compare.
REPORT ON HIGH RISE BUILDING
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:-
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.
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.
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 ABAQUSReview 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
Advantages of Flat Slab/Flat Plate Floor
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
Lower storey height will reduce building weight due to lower partitions and cladding to façadeapprox. saves 10% in vertical membersreduce foundation load
Figure 2.3.2 Saving Building Height
Shorter Construction Time flat plate design will facilitate the use of big table formwork to increase productivity
Figure 2.3.3 Big Table Formwork
Single Soffit Level
Simplified the table formwork needed
Figure 2.3.4 Single Soffit Level
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
Pre-Fabricated Welded Mesh
Prefabricated in standard sizes
Minimized installation time
Better quality control
Figure 2.3.6 Pre-Fabricated Welded Mesh
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.
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 4th power 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 la in the short direction and lb in the long direction, as described in the previous lines in this section.
la= Length in short direction
lb= Length in Long direction
The portion of the load that is carried by the long strips lb is delivered to the beams B1 spanning in the short direction of the panel. The portion carried directly by the in the short direction by the slab strips la, sums up to 100 percent of the load applied to the panel. Similarly, the short-direction slab strips la deliver 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.
Design Consideration
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.
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 m3 per square meters.
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.
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
Floor Openings
No opening should encroach upon a column head or drop.
Sufficient reinforcement must be provided to take care of stress concentration.
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
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.
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.
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.
Common Methods of Design
The finite element method.
The simplified method or, direct design method.
The equivalent frame method or cantilever method.
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
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 α1 l2 2 / α2 l1 2 must 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 Mo in a panel, the clear span ln 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
Mu = wul2ln2 / 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 Mu = 0.65 Mo
Positive factored moment: Pos Mu = 035 Mo
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 Mo 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.
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 /Kec = 1 /∑Kc + 1 /∑Kt
Where, Kec = flexural stiffness of equivalent column
Kc = flexural stiffness of actual column
Kt = 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:-
Determine the factored negative (Mu–) and positive moment (Mu+) demands at the critical sections in a slab-beam member from the analysis of an equivalent frame. The values of Mu– are calculated at the faces of the columns. The values of Mu+ 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
Distribute Mu– to the CS and the MS. These components are represented as Mu,– CS and Mu,–MS, respectively. Distribute Mu+ to the CS and the MS. These components are represented as Mu,+CS and Mu,+MS, respectively.
Figure 2.6.4.2(c) Distribution of moments to column strip and middle strips
If there is a beam in the column line in the spanning direction, distribute each of Mu,CS and Mu,+CS between the beam and rest of the CS.
Figure 2.6.4.2(d) Distribution of moments to beam, column strip and middle strips
Add the moments Mu,–MS and Mu,+MS for the two portions of the MS (from adjacent equivalent frames).
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.
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.
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
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.
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:-
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.
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
Model
The below plan is the identical layout plan for the entire structure in case of modeling and analysis:-
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-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
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.
Analysis Data:
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
Material Constants:
Automated material constants are used, those are being in the analysis software (STAAD Pro) as default value in this case.
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 FZ of 2-D model Figure 4.3 (f) A.F FX of 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 MZ of 2-D model
(Scale 1: 150 Kip-in per ft) Figure 4.3 (i) Moment MY of
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 FZ of 3-D model Figure 4.3 (n) A.F FX of 3-D model
(Scale 1: 400 Kip-in per ft) (Scale 1: 10000 Kip-in per ft)
Figure 4.3 (o) 1st Floor of 3-D model with plate ID
Figure 4.3 (p) 1st Floor of 3-D model with nodal ID
Figure 4.3 (q) 5th Floor of 3-D model with plate ID
Figure 4.3 (r) 5th Floor 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 MZ of 3-D model for columns
(Scale 1: 30 Kip-in per ft)
Figure 4.3 (u) Moment MY of 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 st Floor, Panel C-C |
3-D Model
5 th Floor, Panel C-C |
REMARKS | ||||||||||||||
MX |
Same Localized Nodes (Through Panel C-C) |
Same Localized Nodes (Through Panel C-C) |
The moment values have similarity & dissimilarity both. | ||||||||||||||
N3 GL4-4 |
N 12 GL3-3 |
N 13 GL2-2 |
N14 GL1-1 |
N315 GL4-4 |
N 316 GL3-3 |
N 317 GL2-2 |
N 318 GL1-1 |
||||||||||
+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 | ||
MY |
× | -37.675 | 43.035 | -5.849 | -43.803 | -6.734 | 6.827 | × | × | -16.506 | × | -45.829 | × | 11.336 | 7.215 | -6.803 |
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 1st Floor) | B14 (1st to 2nd Floor) | B21 (2nd to 3rd Floor) | B28 (3rd to 4th Floor) | B35 (4th to 5th Floor) | B42 (5th to 6th Floor) | B12 (Gr. to 1st Floor) | B140 (1st to 2nd Floor) | B257 (2nd to 3rd Floor) | B277 (3rd to 4th Floor) | B297 (4th to 5th Floor) | B317 (5th to 6th Floor) | ||||||||||||||
+/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | +/- | ||||||||||||||
Fx | 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 | |
Fz | 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 |
(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 |
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:
Capabilities for both static and dynamic problems
The ability to model very large shape changes in solids, in both two and three dimensions
A very extensive element library, including a full set of continuum elements, beam elements, shell and plate elements, among others.
A sophisticated capability to model contact between solids
An advanced material library, including the usual elastic and elastic – plastic solids; models for foams, concrete, soils, piezoelectric materials, and many others.
Capabilities to model a number of phenomena of interest, including vibrations, coupled fluid/structure interactions, acoustics, buckling problems, and so on.
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 surface=3nos
Bottom surface=2nos
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 VS Deflection based on the analysis outputs is represented below:-
Graph 6.0 Time VS Nodal Deflection07. 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:
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.
The details of design procedure & design of Flat Plate based on our analysis report may be possible in the future.
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.
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.
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.
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.
Deflection of various types of beams can be studied by approximate analytical hand calculation and by the sophisticated software to compare.