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.
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
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
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.
values can be increased to 48 and 52, respectively, if the deflection, camber
and vibration are not objectionable.
photographs show flat plate and flat slab:-
plate (b) Flat slab
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.
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
- 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
- Checking the change in the
behavior when a structure is modeled 2-D and 3-D both using software STAAD
- 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
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.
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-
Slabs with dropped panel (Flat Slab)
Slabs without dropped panel (Flat Plate)
due to their existing components, Flat Slabs may also be characterized in other
two more categories are-
slab with column head panels
slab with drop panel and column head
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.
shear strength of slab
the moment in the slab by reducing the clear or effective span
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.
Advantages of Flat Slab/Flat Plate Floor
in Room Layout
Architect to introduce partition walls anywhere required
owner to change the size of room layout
choice of omitting false ceiling and finish soffit of slab with skim coating
storey height will reduce building weight due to lower partitions and cladding
saves 10% in vertical members
plate design will facilitate the use of big table formwork to increase
2.3.3 Big Table
the table formwork needed
of Installation of M & E services
M & E services can be mounted directly on the underside of the slab instead
of bending them to avoid the beams
hacking through beams
in standard sizes
standardized structural members and prefabricated sections to be integrated
into the design for ease of construction
process will make the structure more buildable, reduce the number of site
workers and increase the productivity at site
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 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.
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 la in the short direction
and lb in the long direction, as described in the previous lines in
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.
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.
and Column Position
position of wall to maximize the structural stiffness for lateral loads.
the rigidity to be located to the centre of building.
of Structural Layout Plan
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.
to include checking of the slab deflection for all load cases both for short
and long term basis.
general, under full service load, δ< L/250 or 40 mm whichever is smaller.
set to prevent unsightly occurrence of cracks on non-structural walls and floor
to perform crack width calculations based on spacing of reinforcement as
detailed and the moment envelope obtained from structural analysis.
detailing of reinforcement will-
within acceptable tolerances as specified in the codes and
of the building
opening should encroach upon a column head or drop.
reinforcement must be provided to take care of stress concentration.
a critical consideration in flat plate design around the columns.
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.
for fast track project where removal of forms at early strength is required.
to achieve 70% of specified concrete cube strength within a day or two by using
high strength concrete.
use 2 sets of forms.
with flat plate design are generally less rigid.
stiffness depends largely on the configuration of lift core position, layout of
walls and columns.
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
FUNCTION PERIMETER BEAMS
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.
Methods of Design
finite element method.
simplified method or, direct design method.
equivalent frame method or cantilever method.
upon the division of complicated structures into smaller and simpler pieces
(elements) whose behavior can be formulated.
of software includes STAAD PRO, ETABS, SAFE, ADAPT, etc.
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 α1 l2 2 / α2 l1 2
must be between 0.2 and 5.0
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
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.
Distribution of total static moment M0
and negative bending.
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
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:-
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,
/∑Kc + 1 /∑Kt
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
supporting member illustrating the
steps of analysis of a two-way slab are as follows:-
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.
18.104.22.168(b) Typical moment diagram due to gravity
the CS and the MS. These components are represented as Mu,– CS and
respectively. Distribute Mu+ to the CS and the MS. These
components are represented as Mu,+CS and
moments to column strip and middle strips
there is a beam in the column line in the spanning direction, distribute each
and Mu,+CS between the beam and rest
of the CS.
22.214.171.124(d) Distribution of moments to beam,
column strip and middle strips
the moments Mu,–MS and Mu,+MS for
the two portions of the MS (from adjacent equivalent frames).
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
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
- 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.
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
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.
distributed around the perimeter of
bars are weightless and undeformable.
external loads are
stresses are bending moments
at the ends of each bar.
shearing stresses are shearing
supports and at the ends of each bar.
76 /×48 / (3648 Sq. ft)
Size/Plate Size :
16 / ×19 /
to Column C/C distance in long direction :
to Column C/C distance in short direction :
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
/ Supports Condition :
being in the analysis software (STAAD Pro) for both model
identical layout plan for the entire structure in case of modeling and
Skeletal Model View with Panel ID
Rendered Model View
Skeletal Model View with Member Load
Skeletal Model View with Panel ID
Model with Full Sections & Columns with Panel ID
Rendered Model View
Model Top View with Plate ID (Roof)
Model Full View with Plate ID
Model Top View with Node ID (Roof)
126.96.36.199 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
ft.)as plate load
3-D model and 800 lb/ft (100psf × 8 ft = 800 lb/ft) as member load in 2-D
input unit : lb-ft
material constants are used, those are being in the analysis software (STAAD
Pro) as default value in this case.
3.5.2(a) 3-D Pre-Processing for analysis
3.5.2(c) 2-D Pre-Processing for analysis
3.5.2(d) 2-D During analysis
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 FZ
of 2-D model Figure 4.3 (f) A.F FX of 2-D
lb per ft) (Scale
1:10000 lb per ft)
1: 0.2 in per ft)
4.3 (h) Moment MZ of 2-D model
4.3 (i) Moment MY of
4.3 (j) 3-D skeletal model with
considering column positioned in panel C-C
model Figure 4.3 (l) Considering columns of
model with Beam ID
4.3 (m) Shear FZ of 3-D model Figure 4.3 (n) A.F FX of 3-D
1: 10000 Kip-in per ft)
4.3 (o) 1st
Floor of 3-D
model with plate ID
4.3 (p) 1st Floor of 3-D model
with nodal ID
4.3 (q) 5th Floor of 3-D model
with plate ID
4.3 (r) 5th
Floor of 3-D
model with nodal ID
4.3 (t) Moment MZ of 3-D model for columns
1: 30 Kip-in per ft)
4.3 (u) Moment MY of 3-D model for columns
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
1 st Floor, Panel C-C
Moment in kip-ft/ft
5 th Floor, Panel C-C
Moment in kip-ft/ft
Same Localized Nodes
(Through Panel C-C)
Same Localized Nodes
(Through Panel C-C)
The moment values have similarity &
- Note: GL =
4.2 Column Shear (-ve & +ve): 2-D vs 3-D Model
Column Shear Type
Exterior Column in C-C Panel
Load Case: Combination-1
Shear in Kip
Exterior Column in C-C Panel
Load Case: Combination-1
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)
B317 (5th to 6th Floor)
4.3Column Axial Force (-ve): 2-D vs Equivalent Frame Method
(2-D Model, Fz) in Kip
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
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
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
includes four functional components:
element program, designed primarily to model the behavior of solids and
structures under externally applied loading. ABAQUS includes the following
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:
memory-related parameters to improve the performance of the job.
where and how scratch files are written.
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
four main libraries are:
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
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:-
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.
left side rebar layer setup.
then right side.
the plastic plastic value.
show in (fig-09)
figures are as likely below:-
6.2(a) 3-D Model View from ABAQUS after
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
6.2(e) General Cracking View after
Deflection based on the analysis outputs is represented below:-
6.0 Time VS 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:
Plate analysis may be done in other available methods, such as- FEM, ELM etc to
make Flat Plate analysis so much realistic and effective.
details of design procedure & design of Flat Plate based on our analysis
report may be possible in the future.
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
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
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
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
of various types of beams can be studied by approximate analytical hand
calculation and by the sophisticated software to compare.