1. CHAPTER-1
INTRODUCTION
1.1 General:
Mankind has always had a fascination for height and throughout our history, we
have constantly sought to metaphorically reach for the stars. From the ancient pyramids to
today’s modern skyscraper, a civilization’s power and wealth has been repeatedly
expressed through spectacular and monumental structures. Today's the symbol of economic
power and leadership is the skyscraper. There has been a demonstrated competitiveness
that exists in mankind to proclaim to have the building in the world.
This undying quest for height has laid out incredible opportunities for the building
profession. From the early moment frames to today's ultra-efficiency mega-braced
structures, the structural engineering profession has come a long way. The recent
development of structural analysis and design software coupled with advances in the finite
element method has allowed the creation of many structural and architecturally innovative
forms. However, increased reliance on computer analysis is not the solution to the
challenges that lie ahead in the profession. The basic understanding of structural behavior
while leveraging on computing tools are the elements that will change the way structures
are designed and built.
The design of skyscrapers is usually governed by the lateral loads imposed on the
structure. As buildings have gotten taller and narrower, the structural engineering has been
increasingly challenged to meet the imposed drift requirements while minimizing the
architectural impact of the structure. In response to this challenge, the profession has
proposed a multitude of lateral schemes that are now expressed in tall buildings across the
globe.
This study seeks to understand the evolution of the different lateral system that has
emerged and its associated structural behavior, for each lateral scheme examined, its
advantages and disadvantages will be looked at. The lateral schemes explored are the
moment frames, the braced frames, braced-rigid frame and the B – frames with outriggers.
1
2. 1.2 Structural Concept:
The key idea in conceptualizing the structural system for a narrow tall building is to
think of it as a beam cantilevering from the earth (fig1.1). The lateral directed force
generated, either due to wind blowing against or due to the inertia forces induced by
ground shaking, tends both to snap it (shear), and push it over (bending).
Fig. 1.1
Structural concept of tall building
Therefore, the building must have a system to resist shear as well as bending. In
resisting shear forces, the building must not break by shearing off (fig1.2a) and must not
strain beyond the limit of elastic recovery (fig 1.2b).
2
3. Fig 1.2 Building shear resistance; (a) Building must not break (b) Building
must not deflect excessively in shear
Similarly, the system resisting the bending must satisfy three needs (fig 1.3).The
building must not overturn from the combined forces of gravity and lateral loads due to
wind or seismic effects; it must not break by premature failure of columns either by
crushing or by excessive tensile forces: its bending deflection should not exceed the limit
of elastic recovery.
In addition, a building in seismically active region must be able to resist realistic
earthquake forces without losing its vertical load carrying capacity.
Fig 1.3 Bending resistance of building (a) Building must not overturn; (b) Columns
must not fail in tension or compression; (c) Bending deflection must not be excessive.
In the structure's resistance to bending and shear, a tug-of-war ensues that sets the
3
4. building in motion, thus creating a third engineering problem; motion perception or
vibration. If the building sways too much, human comfort is sacrificed, or more
importantly, non-structural elements may break resulting in expensive damage to the
building contents and causing danger to the pedestrians.
A perfect structural form to resist the effects of bending, shear and excessive
vibration is a system possessing vertical continuity ideally located at the farthest extremity
form the geometric center of the building. A Concrete chimney is perhaps an ideal, if not
an inspiring engineering model for a rational super-tall structural form. the quest for the
best solution lies in translating the ideal form of the chimney into a more practical skeletal
structure.
With the provision that a tall building is beam cantilevering from earth, it is evident
that all the columns should be at the edges of the plan, thus the plan shown in fig 1.4 (b)
would be preferred over the plan in fig 1.4 (a). Since the arrangement is not always
possible, it is of interest to study how the resistance to bending is affected by the
arrangement. of columns in plan. We will use two parameters, Bending Rigidity Index BRI
and Shear Rigidity Index SRI, first published in Progressive Architecture, to explain the
efficiency of structural systems.
4
5. Fig 1.4 Building plan forms; (a) Uniform distribution of columns
(b) Columns concentrated at the edges.
The Ultimate possible bending efficiency would be manifest in a square building
which concentrates all the building columns into four corner columns as shown in fig 1.5
(a) since this plan has maximum efficiency it is assigned the ideal Bending Rigidity Index
(BRI) of 100.The BRI is the total moment of inertia of all building columns about the
centroidal axes participating as an integrated system.
The traditional tall building of the past, such as Empire State building, used all
columns as part of the lateral resisting system. For columns arranged with regular bays, the
BRI is 33 (fig 1.5b).
5
6. Fig 1.5 Column Layout and bending rigidity index (BRI); (a) Square building with
Corner columns BRI=100; (b) Traditional building of 1930's BRI = 33.
A modern tall building of the 1980'd and 90’s have closely spaces exterior columns
and long clear span to the elevator core in an arrangement called a "tube". If only perimeter
columns are used to resist the lateral loads, the BRI is 33. An example of this plan type is
the World Trade Center in New York City fig 1.5 (c). The seat Tower in Chicago uses all
its columns as part of the lateral system in a configuration called a "bundled tube". It also
has a BRI of 33 (fig 1.5d).
Fig 1.5 Column Layout and bending rigidity index (BRI); (c) Modern tube building
6
7. BRI=100; (d) Sear Tower BRI = 33.
The Citicorp tower fig 1.5 (e), uses all of its columns as part of its lateral system,
but because columns could not be placed in the corner, its BRI is reduced to 31. If the
columns were moved to the corners, the BRI would be increased to 56 (fig 1.5f). Because
there are eight columns in the core supporting the loads, the BRI falls short of 100.
Fig 1.5 Column Layout and bending rigidity index (BRI); (e) City Corp Tower
BRI=31; (f) Building with corner and core columns BRI = 56, (g) Southwest tower
BRI=63.
The plan of Bank of southwest tower, a proposed tall building in Houston, Texas,
approaches the realistic ideal for bending with a BRI of 63 (fig 1.5f). The corner columns
are split and displaced from the corners to allow generous views from office interiors.
In order for the columns to work as elements of an integrated system, its necessary
to interconnect hem with an effective shear-resisting system. Let us look at some of the
possible solutions and their relative Shear Rigidity Index (SRI).
The ideal shear system is a plate or wall without openings with an ultimate Shear
Rigidity Index (SRI) of 100 (fig 1.6a). The second-best shear system is a diagonal web
system at 45 degree angles which has an SRI of 62.5 (fig 1.6b). A more typical bracing
system which combines diagonals and horizontals but use more material is shown in (fig
1.6c). Its SRI depends on the slope of the diagonals and has a value of 31.3 for the most
usual brace angle of 45 degrees.
7
8. The most common shear systems are rigidity joined frames as shown in (fig 1.6d-g).
The efficiency of the frame as measured by its
SRI depends on the proportions of member’s
lengths and depths. A frame with closely spaced
columns, like used in all four faces of a square
building has high shear rigidity and doubles up
as an efficient
bending configuration, The
resulting configuration is called as
"tube” and is the basis of innumerable tall
building includes the world's two most famous
buildings, the Sears tower and the World trade center.
Fig
1.6
8
9. Tall Building Shear System; (a) Shear wall system; (b) Diagonal web system;
(c) Web system with diagonal and horizontals; (d)-(f) Rigid Frames.
In designing the lateral bracing system for building it is important to distinguish
between a "wind design" and "seismic design". The building must be designed for
horizontal forces generated by wind or seismic loads, whichever is greater, as prescribed by
the building code or site-specific study accepted by the building Official However, Since
the actual Seismic forces, when they are occur, are likely to be significantly larger then
code-prescribed forces, seismic design requires material limitations and detailing
requirements in addition to strength requirements. Therefore, for buildings in high-seismic
zones, even when wind forces govern the design, the detailing and proportioning
requirements of seismic resistance must also be satisfied. The requirements get
progressively higher.
CHAPTER-2
LITERATURE REVIEW
2.0 General:
As the height of the building increases the effect of lateral loads (seismic and wind
loads) become very predominant. This chapter will discuss the previous work done on this
subject. Many of the scholars have studies on performance of RC frame with different type
of bracings, shear walls etc. Some of the papers are discussed below.
2.1 Literature Review:
A brief literature review is presented on this topic as follows.
9
10. Wang et. al (2012), explored the effect of different types of bracing like steel bracing and
bracing with concrete filled steel tube struts are introduced in RC frame structures to
evaluate the seismic performance of building. These models are analyzed with base-shear
method, superposition of modal responses method and time history method respectively.
The results show that the steel-stiffness and the top displacement of the fame structure
decreases significantly. The models are analyzed in Etabs software.
Jiang et. al (2012), Conducted seismic performance evaluation of a steel-concrete hybrid
frame tube in high rise building. In this study a non linear time history analysis is done on a
tall building with the hybrid frame-tube structure. The analytic model of the structure is
established with the aid of PERFORM_3D program. The 61 storey office building with the
seismic intensity of eight is taken foe analysis. The hybrid superstructure consists of an
outer steel reinforced concrete frame and a steel reinforced concrete core tube. The elastic
dynamic characteristics, the global displacement responses, the performance levels and the
deformation demand-to-capacity ratios of structural components under different levels of
earthquake are presented. Numerical analysis results indicate that the hybrid structure has
good seismic performance.
Richards (2011), has studied seismic behavior of irregular high-rise RC structure using
eccentrically braces. In this study, an anti-seismic analysis of two structures is performed to
evaluate their torsion vibration response in earthquake. The self-vibration character and
relative displacement between different floors are compared. A 25 storey multi-functioned
building is considered under seismic intensity 7 and soil type III, the earthquake resistance
rank is II level. The eccentricity braces are made of Q235 rolled wide flange H-beam, and
welded with embedded parts in reinforced concrete members. It is found that eccentrically
braces properly can reduce the response of torsional vibration and other seismic response of
the structures efficient. It is verified that this method is a simple and economic one.
Ali and Moon (2007), Presented a study of structural development in tall buildings, in this
paper reviews of evolution of tall building developments for the primary structural systems,
a new classification-interior structures and exterior structures are presented. While most
representative structural systems for tall buildings are discussed, the emphasis in this
review paper is on current trends such as outrigger systems and diagrid structures.
10
11. Auxiliary damping aerodynamic and twisted forms, which directly or indirectly affect the
structural performance of tall buildings, are reviewed. Finally, the future of structural
developments in tall buildings is envisioned briefly.
Kim and Choi (2004), Has compared the Special Concentric Braced Frames (SCBFs) and
Ordinary Concentric Braced Frames (OCBFs) for evaluating the over strength, ductility
and the response modification factor by performing pushover analysis of model structures
with various storey’s and span lengths. The results were compared with those from
nonlinear incremental dynamic analysis. According to the analysis results, the response
modification factors of model structures computed from pushover analysis were generally
smaller than the values given in the design codes except in low-rise SCBFs. The generally
incremental dynamic analysis generally matched well with those obtained from pushover
analysis.
Maheri and Akbari (2003), has explained the seismic behavior factor, R, for steel X-
braced and knee braced RC buildings. The R factor components including ductility
reduction factor and over strength factor are extracted from inelastic pushover analysis of
brace-frame system of different heights and configurations. The effects of some parameters
influencing the value of R factor, including the higher of the frame, shear of bracing system
from the applied load and the type of building system are investigated. It is found that the
two latter parameters have a more localized effect on the R values and their influence does
not warrant generalization at this stage. However, the height of this type of lateral load-
resisting system has a profound effect on the R factor, as it directly affects the ductility
moment-resisting RC frame dual system for different ductility demands.
11
12. CHAPTER-3
METHODOLOGY
3.1 Loading and Design Criteria:
In this study an office building of 10 storey’s and 30 storey’s having same plan
dimension and column arrangement is selected. The building is 33m X 33m in plan with
columns spaced at 5.5m from center to center. A floor to floor height 3.3m is assumed. The
location of the building assumed to be at imphal. An elevation and plan view of a typical
structure is shown in fig 2.1 (a) and 2.1 (b). The facade system of the structure is also
assumed to transfer the wind loading applied to the main lateral load carrying system (e.g.
moment frame, bracing) as point loads. This allowed the application of the wind loading to
node points in the Etabs model and eliminated local deformation that might occur at the
windward face columns.
12
13. Fig 3.1 (a) Building plan dimension (Common to all floors, all models; units 'm')
13
14. Fig 3.1 (b) Storey Height (Common to all models; unit 'm')
3.2 Live load:
Live load is assumed as per IS 875 (part 2-imposed loads) table 1.Since the building
is assumed to be a office building the live load was taken as KN/m2
(office building with
no separate storage) for all floors except the top floor where the live load is taken as
2KN/m2
. Apart from live load a uniform cladding load of 7KN/m is assumed for all floors
for peripheral beams only. Also a slab dead load is applied assuming a 125mm thick
concrete slab on all floors (to avoid complicated load calculations involving composite
floor system). Those slabs panels are assumed as rigid diaphragm. Also a SDL of 2KN/m2
is assumed on all floors to take care of furnishing and other things.
3.3 Wind load:
Wind load in this study is established in accordance with IS 875 (part 3-wind
loads). The location selected is Imphal. The basic wind speed as per the code is Vb=47m/s.
The coefficient K1 and K2 are taken as 1.0. The terrain category is taken as category 4 with
structure class B for 10 storey models and class C for thirty storey models. Taking internal
pressure coefficient as +0.2 the net pressure coefficient Cp (windward) works out as +0.9
and Cp (leeward) as -0.05 based on h/w and l/w ratio of table 4 of IS 875 (part 3). Using
the above data the ETABS automatically interpolates the coefficient K3 and eventually
calculates lateral wing load at each storey. Same load is applied along positive and negative
X & Y axis one direction at a time to determine the worst loading condition.
3.4 Quake load:
Quake load in this study is established in accordance with IS 1893 (part 1)-2002.
The seismic zone of the previously selected location in zone 5 (Z=0.36). The importance
factor (I) of the building is taken as 1.0. The site is assumed to be hard/rocky site (type I).
The response reduction factor R is taken as 5.0 for all frames.
The fundamental time period (Ta) of all frames was calculated as per clause 7.6.1 of
the before mentioned code.
14
15. Ta =0.085 * h0.75
.........................................Eq. 3.1
Based on the above data the Etabs calculates the design horizontal seismic
coefficient (Ah) using the Sa/g value from the appropriate response spectrum. The Ah value
calculated is utilized in calculating the design seismic base shear (VB) as,
VB= Ah * W .........................................Eq. 3.2
Where, W=Seismic weight of building.
The design seismic bear shear so calculated is distributed along the height of the
building as per the expression,
Qi = VB * (Wi * hi
2
) * (Wj * hj
2
)-1
.........................................Eq. 3.3
Where, Qi = Design lateral force at floor i.
Wi = Seismic weight of the floor i.
hi = height of the floor I measured from base
j= 1 to n, n being no. of floors in building at which masses are located.
3.5 Building Design and Optimizing Criteria:
The structural component of the building viz. beams, columns and braces are
designed as per IS 800-1984. The following load combinations are used to determine the
maximum stress in the steel sections.
i. DL+LL
ii. DL+LL+WL(x or y)
iii. DL+LL+EL(x or y)
iv. DL+WL(x or y)
v. DL+EL(x or y)
A stress ration limit of 0.9 is used in design of all the members to ensure safe design.
15
16. The following limitations are used for optimization of structure:
• The lateral displacement on any floor in case of wind loads does not exceed H/500.
• The lateral displacement on any floor in case of quake loads does not exceed H/250.
• The stress ratio shall be lie between 0.7-0.9 in case of members designed for
strength.
3.6 Optimization procedure:
After modeling the structure and appropriate loads in Etabs, the members are
assigned with initial sections for analysis. After running the analysis for first time accurate
forces in each member is known. The structure is then designed as per IS 800-1984. The
members initially assigned may or may not satisfy the above guidelines, therefore, the
member sections are either increased or decreased suitably to meet lateral displacement and
stress ratio criterion. The second iteration of analysis is then performed with new set of
sections to find new forces in members. The iteration involved in analysis and subsequent
design are repeated number of times till the lateral displacement and stress ratio is satisfied.
In some type of structures like moment frames, the strength design of members is not
sufficient to limit the lateral displacement. It requires a stiffness design wherein the
members are ensured sufficient stiffness to ensure lateral displacements are within the
limits. In such case the stress ratio limit of 0.7-0.9 cannot be satisfied, therefore, this
guideline is omitted
16
17. CHAPTER-4
LATERAL SYSTEMS
4.1 Rigid frames:
A frame is considered rigid when its beam-to column connection has sufficient
rigidity to hold virtual unchanged the original angles between intersecting members. A
rigid frame high-rise structure typically comprises of parallel or orthogonally arranged
bents consisting of columns and girders with moment resistant joints. Resistance to
horizontal loading is provided by the bending resistance of columns, girders and joints. The
continuity of the frame also assist in assisting gravity loading more efficiently by reducing
the positive moment in the center span of girders.
Typical deformations of a moment resistant frame under lateral are indicated in (fig
4.1). The point of contra flexure is normally located near the mid height of the columns and
mid-span of the beams. The lateral deformation of a frame as will be seen shortly is partly
due to frame racking, which might be called shear sway, and partly to column shortening.
17
18. The shear-sway component constitutes approximately 80 to 90 percent of the overall lateral
deformation of the frame. The remaining component of deformation is due to column
shortening, also called cantilever or chord drift component.
Fig 4.1 (a) Response of rigid frame to lateral loads; (b) flexural deformation of beams
and columns due to non deformability of connections.
The size of member in a moment-resisting frame is often controlled by stiffness
rather than strength to control drift under lateral loads. The lateral drift is a function of both
the column stiffness and beam stiffness. In a typical application, the beam spans are 6m to
9m while the storey heights are usually between 3.65m to 4.27m. Since the beam spans are
greater that the floor heights, the beam moment of inertia needs to be greater than the
column inertia by the ratio of beam span to story heights for an effective moment-resisting
frame.
Moment-resisting frames are normally efficient for building upto 20 stories in
height. The lack of efficiency for taller buildings is due to the moment resistance derived
primarily through flexure of its members.
The connections in steel moment resisting frames are important design elements.
Joint rotation can account for a significant portion of the lateral away. The strength and
ductility of the connection are also important considerations especially for frames designed
to resist seismic loads.
4.1.2 Deflection Characteristics:
18
19. The lateral deflection components of rigid frame can be thought of as being caused
by two components similar to the deflection components of prismatic cantilever beam. One
component can be likened to the bending deflection and other to the shear deflection.
Normally for prismatic members when the span-to-depth ratio is greater than 10 or so, the
bending deflection is by far the more predominant component. Shear deflections contribute
a small portion to over all deflection and are therefore generally neglected in calculating
deflections. The deflection characteristics of a rigid frame, one the other hand, are just
opposite; the component analogue to the beam shear deflection dominates the deflection
picture and many amounts to as much as 80% of the total deflection, while the remaining
20% come from the bending component. The bending and shear components of deflection
are usually referred to as the cantilever bending and frame racking each with its own
distinct deflection mode.
A) Cantilever bending component:
This phenomenon is also known as chord-drift. The wind load acting on the vertical
face of the building causes an overall bending moment on any horizontal cross-section of
the building. This moment, which reaches its maximum value at the base of the building,
causes the building to rotate about the leeward columns and is called the overturning
moment. In resisting the overturning moment, the frame behaves as a vertical cantilever
responding to bending through the axial deformation of columns resulting in compression
in the leeward columns and tension or uplift in the windward columns. The columns
lengthen on the windward face of the building and shorten on the leeward face. This
Column length change causes the building to rotate and results in the chord drift
component of the lateral deflection, as shown in (fig 4.2a).
Because of the cumulative rotation up the height, the storey drift due to overall
bending increasing with height, while that due to racking tends to decrease. Consequently
the contribution to storey drift from overall bending may, in the uppermost stories, exceed
that from racking. The contribution of overall bending to the total drift, however, will
19
20. usually not exceed 10 to 20 percent of that of racking, except in very tall, slender, rigid
frames. Therefore the overall deflected shape of medium-rise frame usually has a shear
configuration.
For normally proportioned rigid frame, as a first approximation, the total lateral
deflection can be thought of as a combination of three factors.
1. Deflection due to axial deformation of columns (15 to 20 %).
2. Frame racking due to beam rotation (50 to 60 %).
3. Frame racking due to column rotation (15 to 20 %).
In addition to the above, there is a fourth that contributes to the deflection of the
frames which is due to deformation of the joint. In a rigid frame, since the size of joint are
relatively small compared to column and beam length, it is a common practice to ignore the
effect of joint deformation. However, its contribution buildings drift in very tall buildings
consisting of closely spaced columns and deep spandrels could be substantial, warranting a
close study. This effect
is called panel zone
deformation.
B) Shear racking component:
This phenomenon is analogous to the shear defection in a beam and is caused in
rigid frame by the bending of beam and columns. The accumulated horizontal shear above
any storey of rigid frame is resisted by shear in the columns of that storey (fig 4.3b). The
shear causes the storey-height columns to bend in double curvature with points of contra
flexure at approximately mid-storey--height level the moment applied to join from the
column above and below are resisted by the attached girders, which also bend in double
curvature, with points of contra flexure at approximately mid-span. Those deformations of
20
21. columns and girders allow racking of the frame and horizontal deflection in each storey.
The overall reflected shape of a rigid frame structure due to racking has a shear
configuration with the concavity upwind, a maximum inclination near the base and a
minimum inclination at the top, as shown in the (fig 4.2b).
Fig 4.2 Rigid frame deflection: (a) forces and deformation caused by external
overturning moment; (b) Forces and deformation caused by external shear.
This mode of deformation accounts for about 80% of the total sway of structure. In
a normally proportioned rigid-frame building with columns spacing at about 10.6m to
12.2m and a
storey height
of 3.65m
to 4m beam
flexural
contributes about 50 to 65% of the total sway. The column rotation, one the other hand,
contributes about 10 to 20 % of the total deflection. This is because in most unbraced
21
22. frames the ratio of columns stiffness to girder stiffness is very high, resulting in larger joint
rotations of girders. So generally when it is desired to reduce the deflection of unbraced
frames, the place to start adding stiffness is in the girders. However, in non-typical frames,
such as those that occur in framed tubes with column spacing approaching floor-to-floor
height, it is necessary to study the relative girder and column stiffness before making
adjustments in the member properties.
4.1.3 Calculation of drift:
Calculation of drift due to the lateral loads is a major task in the analysis of tall
building frames. Although it is convenient to consider the lateral displacements to be
composed of two distinct components, whether or not the cantilever or the rocking
component dominates the deflection is dependent on factors such as height-to-width ratio
of the building and the relative rigidity of column to girder. Unless the building is very tall
or very slender, it’s usually the racking component that dominates the deflection picture. A
simple method for determining the deflection of a tall building is to assume that the entire
structure acts as a vertical cantilever in which the axial stress in each column is
proportional to its distance from the centroidal axis of the frame. This approach assumes
that the frame is infinitely stiff with respect to the longitudinal shear and hence
underestimates the deflection.
However, the above tedious calculation can be minimized using a simple stick
model. In this method a single cantilever is modeled equal to the height of the given
structure, having same number of storey. The moment of inertia of each storey in the stick
model is set equal to the sum of second moment of all column cross sections presenting the
actual model.
For example, if a1,a2,......an represents the cross sectional area of all the columns in the
given storey similarly if d1,d2,......dn, represents the distance of these columns from the neutral
axis of the structure, then M.I. of a storey in stick model is given by;
I = a1*d1
2
+a2*d2
2+
a3*d3
2+...........................+
an*dn
2
The calculated 'I' values for each storey using the above formula are used for stick
22
23. model in Etabs. The lateral loads either wind or seismic, whichever is critical are also
modeled at respective storey. An analysis performed with this data will yield in chord drift
component of the moment frame. The shear racking component due to combined column
and girder flexure can also be estimated using the same technique. However, instead of
using the 'I' value, shear areas Av are used calculated following formula.
Av=30*[H*(1/Σ{I/H) col.+1/Σ{I/L}gir.)]-1
4.2 Braced Frames:
Rigid frame systems are not efficient for buildings taller than about 30 stories
because the shear racking components of deflection due to the bending of columns are
girders causes the drift to be too large. A braced frame attempts to improve upon the
efficiency of rigid frame by virtually eliminating the bending of columns and girders. This
is achieved by adding web members such as diagonals or chevron braces. The horizontal
shear is now primarily absorbed by the web & not by the columns. The webs carry the
lateral shear predominantly by the horizontal component of axial action allowing for nearly
a pure cantilever behavior.
4.2.1 Physical Behavior:
In simple term, braced frames may be considered as cantilevered vertical trusses
resisting lateral loads primarily through the axial stiffness of columns and braces. The
columns act as a chord in resisting the overturning moment, with tension in the windward
column and compression in the leeward column. The diagonals and the girders work as the
web members in resisting the horizontal shear, with diagonals in axial compression are
tension depending upon their direction inclination. The girders act axially, when the system
is a fully triangulated truss. They undergo bending also when the braces are eccentrically
connected to them. Because the lateral load on the building is reversible, braces are
subjected in turn, to both compression and tension; consequently, they are most often
designed for more stringent case of compression.
The effect of the chords axial deformations on the lateral deflection of the frame is
to tend to cause a "flexural" configuration of the structure, that is, with concavity download
23
24. and a maximum slope at the top (fig 4.3a). The effect of the web member deformations,
however, is to tend cause a "shear" configuration of the structure (i.e., with downwind and
a maximum slope at the top; (fig 4.3b). The resulting deflected shape serves with a
resultant configuration depending on their relative magnitudes, as determined mainly by
the type of bracing; nevertheless, it is the flexural deflection that most often dominates the
deflection characteristics.
Fig 4.3 Braced frame
deformation:
(a) Flexural
deformation;
(b) Shear
deformation; (c) Combined configuration
The role of web members in resisting shear can be demonstrated by following the
path of the horizontal shear down the braced bent. Consider the typical braced frames,
shown in (fig 4.4 a-e), subjected to an external shear force at the top. In (fig 4.4a), the
diagonal in each storey is in compression, causing the beam to be in axial tension;
therefore, the shortening of the diagonal and extension of the braces connecting to each
beam end are in equilibrium horizontally when the beam carrying insignificant axial load.
In (fig 4.4c), half of each beam is in compression while the other half is in tension.
In (fig 4.4d), the braces are alternately in compression and tension while the beams remain
basically unstressed. And finally in (fig 4.4e), the end parts of the beam are in compression
and tension with the entire beam subjected to double curvature bending, observed that with
a reversal in the direction of the horizontal load, all actions and deformations in each
24
25. member will also be reserved.
Fig 4.4 Load path for horizontal shear through web numbers: (a) single diagonal
bracing (b) X-bracing; (c) chevron bracing; (d) single-diagonal, alternate direction
bracing; (e) Knee bracing.
Fig 4.5 Gravity Load path: (a) single diagonal
single direction bracing (b) X-bracing;
In braced frame the principal function of web members is to resist the horizontal
shear forces. However, depending upon the configuration of the bracing, the web members
may pick up substantial compressive forces as the columns shorten vertically under gravity
25
26. loads. Consider for example, the typical bracing configuration shown in (fig 4.5). As the
columns in (4.5 a,b), shorten, the diagonals are subjected to compression forces because the
beams at each end of the braces are effective in resisting the horizontal component of the
compressive forces in the diagonal. At a first glance this may appear to be the case for the
frame shown in (fig 4.4 c). However, the diagonal shown in (fig 4.5 c) will not attract
significant gravity forces because there is no triangulation at the ends of beams where
diagonals are not connected (nodes A and D, in fig 4.5c). The only horizontal resistant at
the beam end is by the bending resistance of columns, which usually is of minor
significance in the overall behavior, similarly in (fig 4.5 d), the vertical restraint from the
bending stiffness of the beam is not large; therefore as in previous case, the diagonal
experience only negligible gravity forces.
4.2.2 Calculation of Drifts:
In considering the deflected shape of a braced frame, it is important to appreciate
the relative influence of the flexure and shear mode contributions, due to column axial
deformations whereas shear deformations occur due to diagonal and girder deformations.
4.2.3 Calculation of Flexural Component:
The flexural component can be calculated using the same computer model
discussed earlier in chapter 3. the only change that is to be incorporated is that previously
in moment frame the entire column structure contributed to lateral resistance, however, in
case of braced frames only the column attached to braces core provides lateral resistance.
Thus only second moment of c/s area of columns attached to brace core is considered rather
than the complete structure.
4.2.4 Calculation of shear component:
The following table 4.1 shows the formulas to be used for calculating the shear
deformations due to girder and diagonal deformations. It should be noticed that some forms
of bracing arrangement induce axial forces or moments in girders, while some leave the
girders significantly unstressed.
Table 4.1 Shear deformation formulas
26
27. Type of brace Shear deflection per storey
Single Diagonal
(Alternate)
V d3
E L2
* Ad
Double Diagonal V d3
2E L2
* Ad
4.3.1 Rigid-Braced Frames:
Even for building in the range of 10-15 stories unreasonably heavy columns result if
lateral bracing is confined to the building service core because the available depth for
bracing is usually limited. In addition, high uplift forces that may occur at the bottom of
core columns can present foundation problems. In such instances an economical structural
solution can be arrived at by using rigid frames in conjunction with the core bracing
system. Although deep girders and moment connections are required for frame actions,
rigid frame are often preferred because they are least objectionable from the interior space
planning consideration. Often times, architecturally, it may be permissible to use the
spandrels and closely spaced columns on the building because usually the column will not
interfere with the space planning and the depth of spandrel need not be shallow for passage
of air-conditioning duct. A schematic floor plan of a building use these concept is shown if
(fig 5.1 a).
Fig 4.6 Types of rigid brace frames; (a) braced core and perimeter frames.
For slender building with the height-width ratios in excess of 5, an interacting
system of moment frame and the braces becomes uneconomical if braces are placed within
the building core. In such situation, a good structural solution is to be separate the bracing
27
28. of the full width of the building facades if such a system does not compromise the
architecture of the building. If it does, then a possible solution is to be moved the full depth
bracing to the interior of the building. Such a bracing concept is shown in (fig 4.6 d), in
which moment frames located at the building facade interact with interior-braces bends.
Those bend stretch out for the full width of the building form giant K braces, resisting,
overturning the shear force by developing predominantly axial forces.
Fig 4.6 (d) Full-depth interior bracing and exterior frames,
All of the bracing systems and any number of their vibrations can be used either
singly or in combination and can be made interact with the moment-connected frames. The
magnitude of their interaction can be controlled by the varying the relative stiffness of the
various structural elements to achieve an economical structural system.
4.3.2 Physical Behavior:
If the lateral deflection patterns of braced and un-braced frames are similar, the
lateral loads can be distributed between the two systems according to their relative
stiffness. However, in normally proportioned buildings the un-braced and braced frames
deform with their own characteristic shapes, necessitating that we study their behavior as a
unit.
Insofar as the lateral-load-resistance in concerned, the rigid and braced frames can
28
29. be considered as two distinct units. The basis of the classification is the mode of
deformation of unit when subjected to lateral loading. The deflection characteristics of
braced framed are similar to those of a cantilever beam. Near the bottom the vertical truss
is very stiff; therefore the floor-floor deflection will be less than half the values near the
top. Near the top the floor-floor deflection increase rapidly maintained due to the
cumulative effect of chord drift. The column strains at the bottom of the building produce a
deflection at the top; and since this same effect occurs at every floor, the resulting drift at
the top is cumulative. This type of deflection often referred to chord drift is difficult to
control requiring material quantities well in excess required for gravity needs.
Rigid frame deforms predominantly in a shear mode. The relative storey deflection
depends primarily on the magnitude of the shear applied at each storey level. Although near
the bottom deflections are large, and near the top smaller as compared to the braced frame,
the floor-floor deflection can be consider more nearly uniform. When the two systems, the
braced and rigid frames are connected by rigid floor diaphragms, a non-uniform shear force
develops between the two. The resulting interaction helps in extending the range od
application of the two system to buildings up to about 40 stories in height.
(Fig 4.5a) shows the individual deformation pattern of a braced and un-braced
frame subjected to lateral loads. Also shown are the horizontal shear forces between the
two frames connected by rigid floor slabs. Observe that the braced frame acts as a vertical
cantilever beam, with the slope of the deflection greatest at the top of the building,
indicating that in this region the braced frame contributes the least to the lateral stiffness.
The rigid frame has a shear mode deformation, with the slope of deformation
greater at the base of the structure where the maximum shear is acting. Because of the
different lateral deflection characteristics of two elements, the frame tends to pull back the
brace in the upper portion of the building while pushing it forward in the lower portion. As
a result, the frame participates more effectively in the upper portion of the building where
lateral shears are relatively less. The braced frame carries most of the shear in the lower
portion of the building. Thus, because of the distinct difference in the deflection
characteristics, the two systems help each other a great deal. The frame tends to reduce the
lateral deflection of the trusted core at the top, while the trussed core supports the frame
29
30. near the base. A typical variation of horizontal shear carried by each frame is shown in (fig
4.2 b) in which the length of arrow conceptually indicated the magnitude of interacting
shear forces.
Fig 4.7 Interaction between braced and unbraced frames; (a) Characteristic
deformation shapes; (b) Variation of shear forces resulting from interaction.
Although the framed part of a high rise structure is usually more flexible in
comparison to the braced part, as the number of stories increases, its interaction with the
braced frame becomes more significant, contributing greatly to the lateral resistance of the
building. Therefore, when the frame part is fairly rigid by itself, its interaction with the
braced portion of the building can result in a considerably more rigid and efficient design.
4.4.1 Outrigger and Belt truss system:
Innovative structural schemes are continuously being sought in the design of high
rise structures with the intention of limiting the wind drift to acceptable limits without
paying a high premium in steel tonnage. The savings in steel tonnage and cost can be
dramatic if certain techniques are employed to utilize the full capacities of the structural
elements. Various wind-bracing techniques have been developed to this end; this section
deals with one such system, namely, the belt truss system, also known as the core-out-
30
31. trigger system in which the axial stiffness of the perimeter columns or the columns in line
with core bracing (outrigger system) is invoked for increasing the resistance to overturning
moments.
This efficient structural form consists of a central core, comprising of braced
frames, with horizontal cantilever "outrigger" trusses or girders connecting the code to the
outer columns. The core may be centrally located with outriggers extending on both sides
(fig 4.8 a) or it may be located on one side of the building with outriggers extending to the
building columns on one side (fig 4.8 b).
Fig 4.8 (a) Outrigger system with a central core (b) outrigger system with offset core.
When horizontal loading acts on the building, the column restrained outrigger resist
the rotation of the core, causing the lateral deflections and moments in the core to be
smaller than if the free-standing core alone resisted the loading. The resulting is to increase
the effective depth of the structure when it flexed as a vertical cantilever, by inducing
tension in the windward columns and compression in the leeward columns.
In addition to those columns located at the end of the outriggers, it is usual to also
mobilize other peripheral columns to assist in restraining the outrigger. This is achieved by
31
32. including a deep spandrel girder, or a "belt-truss", around the structure at the levels of the
outriggers.
To make the outriggers and belt truss adequately stiff in flexure and shear, they are
made at least one and often 2 stories deep. It is also possible to use diagonals extending
through several floor to act as outrigger as shown in (fig 4.8 c). And finally girders at each
floor may be transformed into outrigger system is very effective in increasing the structure
flexural stiffness; it does not increase its resistance to shear, which has to be carried mainly
by the core.
Fig 4.8 (c) Diagonals acting as outriggers;
In the flowing sub-section the stiffness effect of a single outrigger located at the top
of the structure is examined first. Next, the effect of lowering the truss along the height is
studied with the object of finding the most optimum location for minimizing the building
drift.
4.4.2 Behavior:
To understand the behavior of an outrigger system, consider a building stiffness by
a story high outrigger at top, as shown in (fig 4.9). Because the outrigger is at the top, the
system is often referred to as a cap or hat truss system. The tie-down action of the cap truss
generates a restoring couple at the building top, resulting in point of contra flexure in its
deflection curve. This reversal in curvature reduces the bending moment in the core and
hence, the bending drifts.
32
33. Although the belt truss shown in (fig 4.10) functions
as a horizontal stiffener mobilizing other exterior
column, for analytical simplicity we will assume that the
cumulative effect the exterior columns may be represent
by to equivalent columns, one at each end of the
outrigger (fig 4.9 c). This idealization is not necessary in
developing the theory, but the explanation simple.
The core may be considered as single-redundant
cantilever with rotation restrain at the top by stretching
and shorting of windward and leeward columns. The result of tensile and compressive
forces is equivalent to restoring couple opposing the rotation of core. Therefore, the cap
truss may be conceptualized as a restraining spring located at the top of the cantilever. Its
rotational stiffness may defined as the restoring couple due to a unit rotation of the core at
the top.
33
34. Fig4.9 Belt truss system (a)
Building plan with cap truss,
(b) cantilever bending of core;
(c) Tie-down action of cap
truss.
Assuming the cap truss is
infinitely rigid, the axial
elongation and shortening of
columns is equal to the rotation
of core multiplied by their respective distances from the center of core. If the distance of
the equivalent column is d/2 from the center of the core, the axial deformation of the
column is than equal to d/2,where is d is the rotation of the core. Since the equivalent
spring stiffness is calculated for unit rotation of the core (i.e., θ=1), the axial deformation
of equivalent columns is equal to
1*d/2=d/2 units.
The corresponding axial load is given by
AEd
P=
2L
Where,
P = axial load in the columns.
A = area of columns.
E = modulus of elasticity.
d = distance between the exterior columns.
L = height of the building.
The resorting couple, that is, the rotational stiffness of the cap truss, is given by the
axial load in the equivalent columns multiplied by their distance from the center of the cre.
Using the notation K for the rotational stiffness, and noting that there are two equivalent
34
35. columns, each located at distance d/2 from the core, we get
d
K = P* * 2 = Pd
2
The reduction on drift depends on the stiffness K and the magnitude of rotation θ at
the top.
4.4.3 Calculation of displacements:
The cantilever bending and shear racking component can be easily determined
using the formulas and techniques mentioned in chapter-4 (Braced frames). The negative
displacement caused due to the presence of outrigger can be calculated using the procedure
mentioned below.
• The structural parameters for one outrigger-braced frame are obtained as follows.
The flexural stiffness associated with the columns of the braced frame is given by,
E * Aa * c2
EIt =
2
• The racking shear stiffness of the braced frames with 2 bays and 2 double diagonal
braced can be obtained from below equation,
2a2
* h * E * (Ad1+Ad2)
GAt =
d3
• The flexural stiffness of the outrigger structure is given by equation,
E * Ab * h2
EIo =
2
• The racking shear stiffness of outrigger with segment is given by,
a2
* h * E * (Ad1+Ad2+.........+Adn)
GAo =
d3
• The global 2nd moment of area of the exterior columns can be obtained from
equation,
EIc = 2 * E * Ac * l2
• The characteristic parameters Sv and Sh are given by equations,
H H 1 b 1 1
35
36. St = + ; Sh = + +
EIt EIc α2
24ΕΙο hGAo hGAt
• The characteristic non-dimensional parameters for the structure can now be
obtained from following equation;
αGAt
βH = H ;
√ EIt
Sh
ω =
Sv
Where,
E = Modulus Elasticity of steel
Aa = c/s area of the column attached to braced frame.
c = Total bay length of braced core.
Ab = c/s area of top and bottom chords of outriggers
h = Height of the outrigger.
Ac = c/s area of columns attached to outrigger.
Ad1 ..........Adn = c/s area of diagonals
l = Length of outrigger from center of braced core.
b = Length of outrigger from the face of BF.
a = Horizontal component of diagonal length.
d = Length of diagonal
H = Total height of the building
x = Location if mid-height of outrigger from top.
However, the practical optimum location of a single outrigger lie at the location
slightly higher than the value obtained from the above fig. The reason for this variation is
due to certain assumptions made during the derivation of the formulas discussed
previously. They are,
1. The lateral does not remain constant up the building height. It varies in a trapezoidal
or triangular manner, the former representative of wind loads and the later seismic
loads.
2. The c/s areas of both the exterior and interior columns typically reduce up the
36
37. building height. A linear variation is perhaps more representative of practical
building column.
3.
Fig. 4.10 Optimum location of outriggers
4. As the area of the core columns decreases the height, so does the moment of inertia
of core. Therefore, a linear variation M.I of the core, up the height is more
appropriate.
Incorporating the aforementioned modifications aligns the analytical model close to the
practical structure, but renders the hand calculation all but impossible.
4.4.4 Step wise Calculation:
E = 2 X 108
KN/m2
Aa = 8.712 X 10-3
m2
(designation - 2512)
c = 11m
Ab = 7.65 X 10-3
m2
(designation - 1716)
h = 3.3m
Ac = 7.92 X 10-3
m2
at16.5 and 7.16 X 10-3
m2
at 11m
37
38. (Note: Above values are avg. areas of all columns below the outrigger level)
l = 16.5m
a = 5.5m
d = 6.414m
H = 33m
x =?
E * Aa * c2
EIt = = 2 x 108
x 8.712 x 10-3
x112
/2 = 105.42 x 106
Kn-m2
2
2a2
* h * E * (Ad1 + Ad2)
GAt = = 2 x 5.52
x 3.3 x 2 x 108
x (10.1+5.8) x10-3
x 6.414-3
d3
=2.41 x 106
Kn
E * Ab * h2
EIo = = 2 x 108
x 7.65 x 10-3
x 3.32
/2 = 8.33 x 106
Kn-m2
2
a2
* h * E * (A1 + A2+....... An)
GAo =
d3
= 2 x 5.52
x 3.3 x 2 x 108
x (14.9+6.6+2x6.4) x10-3
x 6.414-3
=2.6 x 106
Kn
EIc = 2 * E * Ac * l2
= 2 x 2 x 108
x (7.92 x 16.52
+ 7.16 x 112
) x 10-3
= 1209.83 x 106
Kn-m2
Sv = 33 x ((105.42 x 106
)-1
+ (1209.83 x 106
)-1
) = 3.4 x 10-7
Sh = 1.5-2
(11 x (24x8.33x106
)-1
+ (3.3x2.6x106
)-1
+ (3.3x2.41x106
)-1
= 1.32 x 10-7
Therefore, from fig 4.10, optimum location of outrigger is X = 11.55m
38
40. 8 57.45 315.66
7 65.22 242.09
6 71.15 178.31
5 79.45 125.65
4 85.97 79.97
3 85.97 45.23
2 92.49 20.11
1 101.98 5.07
The above table shows the moment of inertia and lateral load values of 10 storey
model of moment frame building ,here we observe that MI decreases the height of the
building increases and shear force increases with the increases in the height of building.
TABLE -5.2 Chord Drift Component of 10 Storey Moment Frame Building
Storey d. (mm)
10 0.81
9 0.69
8 0.57
7 0.46
6 0.35
5 0.25
4 0.17
3 0.09
2 0.04
1 0.01
From the above table it can be observe that the chord drift values are insignificant.
TABLE-5.3 Column and Beam ROTATION Components Due To ELY
Storey c. (mm) b. (mm)
10 69.15 57.26
9 63.76 53.36
8 56.67 47.43
7 48.06 40.91
6 38.88 33.87
5 30.79 26.80
4 23.02 20.00
3 16.59 13.63
2 10.02 7.78
1 5.72 2.56
40
41. The above table shows column and beams rotation components due to earthquake
loading in Y direction, while comparing it can be seen that the rotation due to beams
members is lesser than column members.
TABLE-5.4 % CONTRIBUTION OF EACH COMPONENT DUE TO ELY
Storey C.B. % CR % BR % Total (mm) Limit
10 0.64 55.36 45.01 127.23 132
9 0.59 55.12 45.3 117.83 118.8
8 0.55 55.13 45.31 105.69 105.6
7 0.52 53.74 45.74 89.45 92.4
6 0.49 53.18 46.33 73.11 79.2
5 0.44 53.23 46.33 57.86 66
4 0.4 53.3 46.31 43.21 52.8
3 0.33 55.71 45.96 30.33 39.6
2 0.25 56.17 43.57 17.86 26.4
1 0.16 65.68 35.16 7.31 13.2
AVG. 0.44 55.16 45.4
From the above table, we can see that from all the models the deflection values due to
earthquake load is in the limits as per IS code.
Table- 5.5 Chord Drift Components of single diagonal braced frame.
Storey M.I. (m4) ELY (KN)
10 0.20 371.65
9 0.24 391.78
8 0.51 310.39
7 0.48 238.23
6 0.86 175.42
5 0.84 122.00
4 1.24 78.21
3 1.22 45.09
2 1.57 19.62
1 1.67 5.92
From the above table shows the moment of inertia and earthquake loading in y
direction for 10 storey model, it can be seen that the lateral load caused due to earthquake
41
42. is maximum in top storey.
Table - 5.6 Displacement values obtained using E-tabs.
Storey CB (mm)
10 61.95
9 51.67
8 41.72
7 32.45
6 25.11
5 16.86
4 10.84
3 6.09
2 2.66
1 0.65
The above table value of deflection for the cross brace building model can be
viewed, as the deflection is maximum in the top storey when compared with other stories.
Table - 5.7 Displacement values of 10 storey-braced frame model.
Storey M.I. (MF) m4 M.I. (BF) m4 ELY (KN)
10 29.75 0.17 368.82
9 39.76 0.26 388.54
8 48.23 0.48 309.54
7 56.58 0.64 237.88
6 65.06 0.87 175.94
5 68.15 1.1 121.82
4 72.4 1.13 79.25
3 71.76 1.4 45.6
2 77.16 1.67 19.86
1 77.16 1.67 5.98
The above table reflects the value of moment of inertia, for moment frame building
model, braced frame building model, while comparing both we can see the moment of
inertia is maximum in moment frame model, then the earthquake load in y direction can
also be viewed for the same 10 storied building models.
42
44. 8 2.06 18 14.43 5.98 52.19 41.84 34.5 52.8
7 1.6 15.27 12.13 5.52 52.67 41.81 29 46.2
6 1.19 12.73 9.88 5.01 53.47 41.52 23.8 39.6
5 0.84 10.13 7.84 4.46 53.86 41.68 18.8 33
4 0.54 8.06 6 3.72 55.19 41.09 14.6 26.4
3 0.31 5.95 4.24 2.95 56.66 40.38 10.5 19.8
2 0.14 4 2.56 2.1 59.64 38.26 6.7 13.2
1 0.04 2.01 0.96 1.19 66.96 31.84 3 6.6
AVG % 7.42 51.74 40.84
From the above table all models is compared for the wind loading in x direction
which has increased from 0.44% to 7.42%. The remaining displacement is shared almost
equally by both beam and column.
It is observed that in case of most moment frame, the building undergoes double
curvature i.e., the inter storey displacements decreases as we move away from the base. It
can be said that the efficiency of moment frames is more in top floors when compared to
the bottom floors.
44
46. direction, it is observed that contribution of chord drift has further increased to 9.49%
compared to previous value of 7.42%. Also the beam rotation contributes almost twice
when compared to column rotation.
Table - 5.11 Displacement and % contributions of single diagonal braced frame
Storey Flexural Shear Flexure % Shear % Total Total % Limit
10 58.08 24.52 70.32 29.68 82.60 62.58 132.00
9 48.55 23.25 67.62 32.38 71.80 60.44 118.8
8 39.37 21.33 64.86 35.14 60.70 57.48 105.6
7 30.78 18.42 62.57 37.43 49.20 53.25 92.40
6 23.02 16.48 58.27 41.73 39.50 49.87 79.20
5 16.25 13.25 55.08 44.92 29.50 44.70 66.00
4 10.55 11.15 48.61 51.39 21.70 41.10 52.80
3 6.02 7.48 44.58 55.42 13.50 34.09 39.60
2 2.70 5.50 32.99 67.01 8.20 31.06 26.40
1 0.70 2.00 25.86 74.14 2.70 20.45 13.20
AVG % 53.08 46.92 45.5
From the above table it is observed that the avg. % contribution of both flexure and
shear components is approximately same and the pattern in which the flexure component
vary is reverse of that observed in shear.
DISPLACEMENT ELY
DISPLACEMENT (mm)
46
47. Chart 5.1 - Displacement component in a single diagonal braced frame
The chart shows storey vs. displacement for the avg. % contribution of both
flexure and shear components. We can see that shear is lesser than flexure.
Table 5.12 Displacements and % contributions of double diagonal braced frame
Storey Flexural Shear Flexure % Shear % Total Total % Limit
10 61.95 12.55 83.16 16.84 74.5 56.44 132.00
9 51.67 12.42 80.61 19.39 64.09 53.95 118.8
8 41.72 11.68 78.13 21.87 53.39 50.56 105.6
7 32.45 10.54 75.48 24.52 42.99 46.53 92.40
6 24.11 9.28 72.21 27.79 33.39 42.16 79.20
5 16.86 8.13 67.47 32.53 24.99 37.86 66.00
4 10.84 6.55 62.32 37.68 17.39 32.94 52.80
3 6.09 5.1 54.39 45.61 11.19 28.26 39.60
2 2.66 3.43 43.69 56.31 6.09 23.07 26.40
1 0.65 1.74 27.02 72.98 2.39 18.1 13.20
AVG % 64.45 35.55 38.99
From the above table it is observed that due to presence of double diagonals the
shear displacements due to diagonal deformation has reduced considerably and so has the
overall displacement. Also the percentage average of the displacements from all the
floors has reduced to 38.99% compared to 45.5% observed in single diagonal frame.
DISPLACEMENT ELX
DISPLACEMENT (mm)
47
48. Chart 5.2 displacement components of 10 storey double diagonal braced frame
The above chart shows storey vs. displacement in which shear displacements have
been reduced.
Table- 5.13 displacements and % contributions of double diagonal braced frame
along X direction.
Storey Flexure Shear Flexure % Shear % Total Limit
30 117.69 16.11 91.69 8.31 193.8 198
29 169.72 16.18 91.3 8.7 185.9 191.4
28 161.76 16.14 90.93 9.07 177.9 184.8
27 153.79 16.01 90.57 9.43 169.8 178.2
26 145.84 15.66 90.3 9.7 161.5 171.6
25 137.91 15.19 90.08 9.92 153.1 165
24 129.99 14.71 89.84 10.16 144.7 158.4
23 122.12 14.08 89.66 10.34 136.2 151.8
48
50. Chart 5.3 Displacement components of 30 storey’s DDBF in X-direction.
DISPLACEMENT WLY
Chart 5.4 Displacement components of 30 storeys DDBF in Y-direction.
The above charts show
storey vs. displacement.
In case of 30 storey braced
frame the cantilever
effect is observed to huge and a
single braced core placed at the
center of the building is
found to be inefficient. A
single braced core causes huge
moments to be concentrated at the base and requires very large sections.
Table-5.14 displacements and % contributions of double diagonal braced framed
along Y direction.
Storey Flexure Shear Flexure % Shear % Total Limit
30 177.69 12.91 93.23 6.77 190.6 198
50
52. 1 0.02 0.69 1.91 0.57 26.53 72.9 2.62 19.83 13.2
AVG 1.32 65.84 32.85 33.9
The above table gives the complete set of displacements along with their %
contributions to overall displacement. From the above table it is clear that it is clear that
the chord drift offered by the moment frame is negligible, whereas, that offered by the
braced frame from the significant part of the overall displacement.
DISPLACEMENT ELY
Chart 5.5 Displacement components in 10 storey integrated system the chart shows.
The chart shows storey vs. displacement. It is observed that overall displacements
are much lesser
compared to both
moment and
braced frame.
Table-5.16
comparison of
lateral
displacements
Storey MF BF MBF Limit
52
53. 30 193.6 193.8 191.76 198
29 190.9 185.9 186.52 191.4
28 186 177.9 180.13 184.8
27 178.8 169.8 172.56 178.2
26 169.3 161.5 163.75 171.6
25 158.7 153.1 154.34 165
24 151 144.7 146.37 158.4
23 142.6 136.2 138.01 151.8
22 133.9 127.8 129.54 145.2
21 124.9 119.4 120.93 138.6
20 115.9 111.1 112.37 132
19 108.9 102.9 104.84 125.4
18 101.5 94.7 97.12 118.8
17 93.7 86.7 89.3 112.2
16 86 78.8 81.58 105.6
15 78.2 71.2 73.95 99
14 71.8 63.7 67.07 92.4
13 65.2 56.5 60.24 85.8
12 58.4 49.5 53.41 79.2
11 51.9 42.8 46.88 72.6
10 45.4 36.5 40.54 66
9 40 30.6 34.95 59.4
8 34.5 25.1 29.5 52.8
7 29 20 24.26 46.2
6 23.8 15.4 19.4 39.6
5 18.8 11.4 14.95 33
4 14.6 7.9 11.14 26.4
3 10.5 4.9 7.62 19.8
2 6.7 2.6 4.6 13.2
1 3 0.9 1.93 6.6
0 0 0 0 0
The above table gives the comparison between moment frame, braced frame and
moment braced frame. The moment braced frame is having less displacement and is more
efficient when compared to the other two frames.
COMPARISION OF LATERAL DISPLACEMENT
53
54. Chart 5.6
Comparison of lateral
displacements
between MF, BF and
MBF
Chart 5.6
comparison of lateral
displacements shows MBF has less displacement and it is preferable than the other two.
TABLE-5.17 Displacement components of different models
Storey CB DD OTD Total Total% Limit
10 84.71 18.29 -48.99 54.01 40.92 132
9 71.21 12.39 -37.19 46.41 39.07 118.8
8 58.08 7.5 -27.02 38.55 36.51 105.6
7 45.58 4.39 -19.58 30.4 32.9 92.4
6 33.93 2.33 -12.3 23.96 30.25 79.2
5 23.55 1.62 -2.59 22.57 34.2 66
4 14.95 0.83 1.03 16.82 31.85 52.8
3 8.26 0.37 2.43 11.07 27.95 39.6
2 3.6 0.15 3.14 6.89 26.11 26.4
1 0.92 0.03 1.43 2.37 17.99 13.2
AVG% 31.78
From the above table it can be observed that an outrigger reduces the total displacement
by pushing the structure in opposite direction to that of lateral loads. This is achieved by
generating a restoring moment which can be calculated as below.
DISPLACEMENT ELX
54
55. Chart 5.7-Displacement components in a single outrigger structure
From the above graph it can be see that the structure undergoes sudden change in
displacement at the level of outrigger. A part from that it can be seen that the total
displacements at all floors are further reduced when compared to the outrigger placed at
top level.
Table 5.18 displacements for outrigger at different location.
Storey Top Middle Bottom
10 55.85 56.01 77.9
9 53.7 46.11 66.5
8 46.83 38.55 55.9
7 40.11 30.4 43
6 32.62 23.96 33.2
5 25.9 32.57 23.3
4 18.53 16.82 15.9
3 11.85 11.07 8.4
2 7.33 6.89 3.6
1 2.56 2.37 2.6
0 0 0 0
The table 5.18 gives the comparison of final displacements for outrigger placed at top,
middle and bottom location. We can observe that displacement at top is less than middle
and bottom.
DISPLACEMENT ELX
55
56. DISPLACEMENT (mm)
Chart 5.8 Displacements due to outrigger at top, middle and bottom location
Given in chart 5.10 is the comparison of displacements for various outrigger
locations. From the chart it can be seen that there is sudden change in displacement at the
outrigger location in all three cases. This is due to the restoring effect caused by the
presence of outrigger.
56
58. DISPLACEMENT (mm)
Chart 5.9 Displacement components in 30 storey outrigger model.
The above chart shows storey vs. displacement for 30 storey outrigger model in
case of belt truss system it is found that by addition of few diagonals at outrigger level
the lateral displacements at all floors are reduced considerably, with little change in the
weight of the structure. The reduction in lateral displacement is due to increased flexural
rigidity to the structure when compared to simple outrigger system.
Table-5.20 lateral displacements due to wind load in OBT model.
Outrigger Outrigger
58
60. DISPLACEMENT (mm)
Chart 5.10 displacements in simple outrigger and outrigger belt truss system in X
direction.
DISPLACEMENT WLY
DISPLACEMENT (mm)
Chart 5.11 Disp in simple outrigger and outrigger belt truss system in Y- direction.
From the above charts 5.10 and 5.11 the storey vs. displacement charts it is
concluded that among two outrigger system it is preferable to use combined outrigger and
belt truss
System as it also reduces the forces at the base of core which otherwise may yield to
complications in the foundation design.
60
61. Table-5.21 comparison of lateral displacements obtained with each system
Storey MF BF MBF OT OBT Limit
30 193.6 193.8 193.6 195.62 171.43 198
29 190.9 185.9 190.9 191.38 169.49 191.4
28 186 177.9 186 182.18 165.41 185.8
27 178.8 169.8 178.8 178.14 160.76 178.2
26 169.3 161.5 169.3 175.53 155.44 171.6
25 158.7 153.1 158.7 165.42 149.67 165
24 151 144.7 151 157.93 143.34 158.4
23 142.6 136.2 142.6 151.14 136.43 151.8
22 133.9 127.8 133.9 145.09 129.07 145.2
21 125.9 119.4 125.9 135.85 121.43 138.6
20 115.9 111.1 115.9 127.57 113.67 132
19 108.9 102.9 108.9 119.36 106.2 125.4
18 101.5 94.7 101.5 111.3 99.16 118.8
17 93.7 86.7 93.7 103.57 92.67 112.2
16 86 78.8 86 96.29 86.63 105.6
15 78.2 71.2 78.2 89.69 81.14 99
14 71.8 63.7 71.8 87.2 79.42 92.4
13 65.2 56.5 65.2 80.5 73.75 85.8
12 58.4 49.5 58.4 73.11 67.49 79.2
11 51.9 42.8 51.9 65.25 60.63 72.6
10 45.4 36.5 45.4 57.08 53.38 66
9 40 30.6 40 48.82 46.04 59.4
8 35.5 25.1 35.5 40.68 38.93 52.8
7 29 20 29 52.86 32.13 46.2
6 23.8 15.4 23.8 25.62 25.7 39.6
5 18.8 11.4 18.8 19.02 19.75 33
4 15.6 7.9 15.6 13.45 15.3 26.4
3 10.5 4.9 10.5 8.64 9.54 19.8
2 6.7 2.6 6.7 5.7 5.44 13.2
1 3 0.9 3 1.73 2.23 6.6
From the above table it can be seen that most efficient system with respect to reduction in
lateral displacement is a combined outrigger and belt truss system. However, in case of
both outrigger and belt truss system two outriggers are used, one at top level and another
at mid level, requiring at least two service floors. It should also be kept in mind that the
level at which the outriggers are placed are not the optimum locations.
DISPLACEMENT ELY
61
62. DISPLACEMENT (mm)
Chart 5.12 comparisons of displacements from all 30 storey models.
The chart 5.12 gives the comparison of all the lateral systems used in the present study.
The above chart storey vs. displacement gives the comparison of lateral systems from 30
storey models. It is conclude that outrigger system is preferable from all.
DISCUSSIONS:
• These are from the analyses result of models using Etabs.
• MI decreases as the height of the building increases and shear force increases with
the increase in height of the building.
• The chord values are insignificant in case of 10 storey moment frame building the
moment of inertia and earthquake loading in Y direction for 10 storey model, it
can be seen that the lateral load caused due to earthquake is maximum in top
storey when compared with other stories.
• The efficient of moment frames is more in top floors when compared to the
62
63. bottom floors. Due to the diagonal deformation has reduced considerably in
DDBF.
• That contribution of chord drift has further increased to 9.49% compared to
previous value of 7.42%. Also the beam rotation contributes almost twice when
compared to column rotation in single diagonal frame.
• In case of 30 storey braced frame the cantilever effect is observed to b huge and a
single braced core placed at the center of the building is found to be insufficient.
• For 30 storey outrigger model in case of belt truss system it is found that by
addition of few diagonals at outrigger level the lateral displacement at all floors
are reduced considerably, with little change in weight of the structure.
• The reduction in lateral displacements is due to increased flexural rigidity of the
structure when compared to simple outrigger system.
• Among two outrigger systems it is preferable to use combined outrigger and belt
truss system as it also reduces the forces at the base of core which otherwise may
yield to complications in foundation design.
• From all the models outriggers belt truss system has less displacement and more
control over drift moment frame and braced has displacements nearly equal.
Moment-braced frame has less displacement than the two.
CHAPTER -6
CONCLUSION
1. The most efficient system with respect to steel tonnage once again works out be
“integrated rigid-braced frame systems”, however the differences this time is much more
significant when compared to simple double diagonal braced frame system.
2. The 30 storey rigid brace frame in the present study is subjected to much rigorous
optimization, hence the least steel tonnage achieved. However, rigorous optimization
means that the sections used are not consistent.
63
64. 3. It should be kept in mind that a moment frame involves a more detail design of the
joints to achieve the required portal frame effect. The additional steel required for the
joints is much more when compared to the amount of steel required for simple shear
connections used in braced and outrigger systems.
4. The most efficient system with respect to reduction in lateral displacement is a
combined outrigger and belt truss system . However, in case of both outrigger and belt
truss system two outriggers are used , one at top level and another at mid level, requiring
at least two service floors. It should also be kept in mind that the level at which the
outriggers are placed are not the optimum locations.
5. From the above discussion it can be concluded that even though integrated systems has
least steel tonnage, it requires additional steel for rigid joint, which will bring the steel
tonnage close to that of outrigger systems. Among two outrigger systems it is preferable
to use combined outrigger and belt truss system as it also reduces the forces at the base of
core which otherwise may yield to complications in the foundation design.
SCOPE FOR THE FUTURE WORK
Future work can be carried out for across earthquake response of the tall buildings
with respect to structural systems. The different type of systems may be introduces for
resisting the lateral forces
Lateral systems along with the different type of combinations may be used for
resisting the lateral forces. Analysis using better techniques, a detail dynamic analysis can
be carried out, collecting the response of the tall building at every mode. A study can be
done to these lateral systems for making more effective in earthquake as well as wind
forces resisting designs. Any how many new techniques are now available to make the
structures stiff against the lateral forces. A study can be done by providing the base
64
65. isolation techniques with these lateral system or the springs may to provided with these
systems, also we can make an investigation of dampers with these systems.
REFERENCES
Literature & Books:
1. Zhixin Wang, Haitao Fan and Haungjuan, “Analysis of the seismic
performance of RC frame structure with different types of bracing” Applied
mechanics and material vols, 166-169, pp 2209-2215, May 2012.
2. Huanjun jiang, Bo Fu and Laoer Liu, “Seismic performance evolution of a
steel concrete hybrid frame-tube high-rise building structure” Applied Mechanics
and materials vol. 137, pp 149-153, Oct 2011.
3. Paul W. Richards, P.E., M.ASCE, “Seismic column demands in ductile braced
frames” Journal of structure engineering, vol. 135,No.1, ISSN 0733-9445/2009/1-
65
66. 33-41, January 2009.
4. Mir M. Ali and Kyoung Sun Moon, “Structural development in tall building;
current trends and future prospects” architectural science review, Vol. 50.3, pp
205-223, June 2007.
5. Jinkoo Kim, Hyunhoon Choi, “ Response modification factors of chevron-
braced frames” Engineering structures, Vol. 27, pp 285-300, October-2004.
6. Mahmood R. Maheri, R. Akbari, “Seismic behavior factor, R for steel X-braced
and Knee-braced RC buildings” Engineering structure, Vol. 25 pp 1505-1513,
May 2003.
7. V. Kapur and Ashok K. Jain, “Seismic response of shear wall frame versus
braced concrete frames” university of Roorkee, Roorkee, 247 672, April 1983.
8. Taranth B.S., “Structural analysis and design of tall buildings” McGraw-Hill
Book company, 1988.
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