INTRODUCTION 1.1 THE DESIGN PROCESS: The entire process of structural planning and design requires not only imagination and conceptual thinking but also sound knowledge of practical aspects, such as recent design codes and bye-laws, backed up by ample experience, institution and judgment. It is emphasized that any structure to be constructed must satisfy the need efficiency for which it is intended and shall be durable for its desired life span. Thus, the design of any structure is categorizes into following two main types:- 1. Functional design 2. Structural design 1.1.1 FUNCTIONAL DESIGN: The structure to be constructed should primarily serve the basic purpose for which it is to be used and must have a pleasing look. The building should provide happy environment inside as well as outside. Therefore, the functional planning of a building must take into account the proper arrangements of room/halls to satisfy the need of the client, good ventilation, lighting, acoustics, unobstructed view in the case of community halls, cinema theatres, etc. 1.1.2 STRUCTURAL DESIGN: Once the form of the structure is selected, the structural design process starts. Structural design is an art and science of understanding the behavior of structural members subjected to loads and designing them with economy and elegance to give a safe, serviceable and durable structure. 1
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INTRODUCTION
1.1 THE DESIGN PROCESS:
The entire process of structural planning and design requires not only
imagination and conceptual thinking but also sound knowledge of practical
aspects, such as recent design codes and bye-laws, backed up by ample
experience, institution and judgment.
It is emphasized that any structure to be constructed must satisfy the need
efficiency for which it is intended and shall be durable for its desired life span.
Thus, the design of any structure is categorizes into following two main types:-
1. Functional design
2. Structural design
1.1.1 FUNCTIONAL DESIGN:
The structure to be constructed should primarily serve the basic purpose for
which it is to be used and must have a pleasing look.
The building should provide happy environment inside as well as outside.
Therefore, the functional planning of a building must take into account the
proper arrangements of room/halls to satisfy the need of the client, good
ventilation, lighting, acoustics, unobstructed view in the case of community
halls, cinema theatres, etc.
1.1.2 STRUCTURAL DESIGN:
Once the form of the structure is selected, the structural design process starts.
Structural design is an art and science of understanding the behavior of
structural members subjected to loads and designing them with economy and
elegance to give a safe, serviceable and durable structure.
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1.2 STAGES IN STRUCTURAL DESIGN:
The process of structural design involves the following stages.
1) Structural planning.
2) Action of forces and computation of loads.
3) Methods of analysis.
4) Member design.
5) Detailing, Drawing and Preparation of schedules.
1.2.1 STRUCTURAL PLANNING:
After getting an architectural plan of the buildings, the structural planning of the
building frame is done. This involves determination of the following.
a. Position and orientation of columns.
b. Positioning of beams.
c. Spanning of slabs.
d. Layouts of stairs.
e. Selecting proper type of footing.
1.2.1.1 Positioning and orientation of columns:
Following are some of the building principles, which help in deciding the
columns positions.
1. Columns should preferably be located at (or) near the corners of a
building, and at the intersection of beams/walls.
2. Select the position of columns so as to reduce bending moments in
beams.
3. Avoid larger spans of beams.
4. Avoid larger centre-to-centre distance between columns.
5. Columns on property line.
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Orientation of columns:
1. Avoid projection of columns:
The projection of columns outside the wall in the room should be avoided as
they not only give bad appearance but also obstruct the use of floor space,
creating problems in placing furniture flush with the wall. The width of the
column is required to be kept not less than 200mm to prevent the column from
being slender. The spacing of the column should be considerably reduced so
that the load on column on each floor is less and the necessity of large sections
for columns does not arise.
2. Orient the column so that the depth of the column is contained in
the major plane of bending or is perpendicular to the major axis
of bending.
This is provided to increase moment of inertia and hence greater moment
resisting capacity. It will also reduce Leff/d ratio resulting in increase in the load
carrying capacity of the column.
1.2.1.2 POSITIONING OF BEAMS:
1. Beams shall normally be provided under the walls or below a heavy
concentrated load to avoid these loads directly coming on slabs.
2. Avoid larger spacing of beams from deflection and cracking criteria. (The
deflection varies directly with the cube of the span and inversely with the
cube of the depth i.e. L3/D3. Consequently, increase in span L which
results in greater deflection for larger span).
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1.2.1.3 SPANNING OF SLABS:
This is decided by supporting arrangements. When the supports are only on
opposite edges or only in one direction, then the slab acts as a one way
supported slab. When the rectangular slab is supported along its four edges it
acts as a one way slab when Ly/Lx < 2.
The two way action of slab not only depends on the aspect ratio but also on the
ratio of reinforcement on the directions. In one way slab, main steel is provided
along with short span only and the load is transferred to two opposite supports.
The steel along the long span just acts as the distribution steel and is not
designed for transferring the load but to distribute the load and to resist
shrinkage and temperature stresses.
A slab is made to act as a one way slab spanning across the short span by
providing main steel along the short span and only distribution steel along the
long span. The provision of more steel in one direction increases the stiffness of
the slab in that direction.
According to elastic theory, the distribution of load being proportional to
stiffness in two orthogonal directions, major load is transferred along the stiffer
short span and the slab behaves as one way. Since, the slab is also supported
over the short edge there is a tendency of the load on the slab by the side of
support to get transferred to the nearer support causing tension at top across
this short supporting edge. Since, there does not exist any steel at top across
this short edge in a one way slab interconnecting the slab and the side beam,
cracks develop at the top along that edge. The cracks may run through the
depth of the slab due to differential deflection between the slab and the
supporting short edge beam/wall. Therefore, care should be taken to provide
minimum steel at top across the short edge support to avoid this cracking.
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A two way slab is generally economical compare to one way slab because
steel along both the spans acts as main steel and transfers the load to all
its four supports. The two way action is advantageous essentially for large
spans (>3m) and for live loads (>3kN/m2). For short spans and light loads, steel
required for two way slabs does not differ appreciably as compared to steel for
two way slab because of the requirements of minimum steel.
FOOTING:
The type of footing depends upon the load carried by the column and the
bearing capacity of the supporting soil. The soil under the foundation is more
susceptible to large variations. Even under one small building the soil may vary
from soft clay to a hard murum. The nature and properties of soil may change
with season and weather, like swelling in wet weather. Increase in moisture
content results in substantial loss of bearing capacity in case of certain soils
which may lead to differential settlements. It is necessary to conduct the survey
in the areas for soil properties. For framed structure, isolated column footings
are normally preferred except in case of exists for great depths, pile foundations
can be an appropriate choice. If columns are very closely spaced and bearing
capacity of the soil is low, raft foundation can be an alternative solution. For a
column on the boundary line, a combined footing or a raft footing may be
provided.
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1.3 ASSUMPTIONS
The following are the assumptions made in the earthquake resistant design of structures:• Earthquake causes impulsive ground motions, which are complex and
irregular in character, changing in period and amplitude each lasting for small duration. Therefore resonance of the type as visualized under steady-state sinusoidal excitations, will not occur as it would need time to build up such amplitudes.
• Earthquake is not likely to occur simultaneously with wind or max. Flood or max. sea waves.
• The value of elastic modulus of materials, wherever required, maybe taken as per static analysis.
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2.1 DESIGN PHILOSOPHIES
• Working stress method (WSM)
• Ultimate load method (ULM)
• Limit state method (LSM)
2.1.1. Working stress method (WSM):-
This was the traditional method of design not only for reinforced concrete, but
also for structural steel and timber design. The method basically assumes that
the structural material behaves as a linear elastic manner, and that adequate
safety can be ensured by suitably restricting the stresses in the material
induced by the expected “working loads” on the structure. As the specified
permissible stresses are kept well below the material strength, the assumption
of linear elastic behavior is considered justifiable. The ratio of the strength of the
material to the permissible stress is often referred to as the factor of safety.
However, the main assumption linear elastic behavior and the tacit assumption
that the stresses under working loads can be kept within the ‘permissible
stresses’ are not found to be realistic. Many factors are responsible for this such
as a long term effort of creep and shrinkage, the effects of stress
concentrations, and other secondary effects. All such effects resulting
significant local increases in a redistribution of the calculated stresses. The
design usually results in relatively large sections of structural members, thereby
resulting in better serviceability performance under the usual working loads.
2.1.2. Ultimate load method (ULM):-
With the growing realization of the short comings of WSM in reinforced concrete
design, and with increased understanding of the behavior of reinforced concrete
at ultimate loads, the ultimate load of design is evolved and became an
alternative to WSM. This method is sometimes also referred to as the load
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factor methods are the ultimate strength. In this method, the stress condition at
the site of impending collapse of the structure is analyzed, and the non linear
stress-strain curves of concrete and steel are made use of.
The concept of ‘modular ratio’ and its associated problems are avoided entirely
in this method. The safety measure design is introduced by an appropriate
choice of the load factor, defined as the ratio of the ultimate load to the working
load. The ultimate load method males it possible for different types of loads to
be assigned different load factors under combined loading conditions, thereby
overcoming the related shortcoming of WSM.
This method generally results in more slender sections, and often economical
designs of beams and columns, particularly when high strength reinforcing steel
and concrete are used. However, the satisfactory ‘strength’ performance at
ultimate loads does not guarantee satisfactory ‘serviceability’ performance at
the normal service loads.
The designs sometimes result in excessive deflections and crack-widths under
service loads, owing to the slender sections resulting from the use of high
strength reinforcing steel and concrete. The distribution of stress resultants at
ultimate load is taken as the distribution at the service loads, magnified by the
load factor(s); in other words, analysis is still based on linear elastic theory.
2.1.3. Limit state method (LSM):-
The philosophy of the limit state method of design represents a definite
advancement over the traditional design philosophies. Unlike WSM
which based calculations on service load conditions alone, and unlike ULM,
which based calculations on ultimate load conditions alone, LSM aims for a
comprehensive and rational solution to the design problem, by considering
safety at ultimate loads and serviceability at working loads.
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The LSM philosophy uses a multiple safety factor format which attempts to
provide adequate safety at ultimate loads as well as adequate serviceability at
service loads, by considering all possible ‘Limit State’.
Limits States:-
A limit state is a state of impending failure, beyond which a structure ceases to
perform its intended function satisfactorily, in terms of either safety of
serviceability i.e. it either collapses or becomes unserviceable.There are two
types of limit states:
Ultimate limit states (limit states of collapse):- which deal with strength,
overturning, sliding, buckling, fatigue fracture etc.
Serviceability limit states: - which deals with discomfort to occupancy and/ or
malfunction, caused by excessive deflection, crack width, vibration leakage etc.,
and also loss of durability etc.
2.2 PROPERTIES OF CONCRETE:
Grades of concrete:
Concrete is known by its grade which is designated as M15, M20 etc. in which
letter M refers to concrete mix and number 15, 20 denotes the specified
compressive strength (fck) of 150mm cube at 28 days, expressed in N/mm2.
Thus, concrete is known by its compressive strength. M20 and M25 are the
most common grades of concrete, and higher grades of concrete should be
used for severe, very severe and extreme environments.
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Compressive strength
Like load, the strength of the concrete is also a quality which varies
considerably for the same concrete mix. Therefore, a single representative
value, known as characteristic strength is used.
Characteristic strength
It is defined as the value of the strength below which not more then 5% of the
test results are expected to fall (i.e. there is 95% probability of achieving this
value only 5% of not achieving the same)
Characteristic strength of concrete in flexural member
The characteristic strength of concrete in flexural member is taken as 0.67
times the strength of concrete cube.
Design strength (fd) and partial safety factor for material strength
The strength to be taken for the purpose of design is known is known as design
strength and is given by
Design strength (fd) = characteristic strength/ partial safety factor for material
strength
The value of partial safety factor depends upon the type of material and upon
the type of limit state. According to IS code, partial safety factor is taken as 1.5
for concrete and 1.15 for steel.
Design strength of concrete in member = 0.45fck
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Tensile strength
The estimate of flexural tensile strength or the modulus of rupture or the
cracking strength of concrete from cube compressive strength is obtained by
the relations
fcr = 0.7 fck N/mm2
The tensile strength of concrete in direct tension is obtained experimentally by
split cylinder. It varies between 1/8 to 1/12 of cube compressive strength.
Creep
Creep is defined as the plastic deformation under sustain load. Creep strain
depends primarily on the duration of sustained loading. According to the code,
the value of the ultimate creep coefficient is taken as 1.6 at 28 days of loading.
Shrinkage
The property of diminishing in volume during the process of drying and
hardening is termed Shrinkage. It depends mainly on the duration of exposure.
If this strain is prevented, it produces tensile stress in the concrete and hence
concrete develops cracks.
Modular ratio
Short term modular ratio is the modulus of elasticity of steel to the modulus of
elasticity of concrete.
Short term modular ratio = Es / Ec
Es = modulus of elasticity of steel (2x10 5 N/mm2)
Ec = modulus of elasticity of concrete (5000√fck N/mm2)
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As the modulus of elasticity of concrete changes with time, age at loading etc
the modular ratio also changes accordingly. Taking into account the effects of
creep and shrinkage partially IS code gives the following expression for the long
term modular ratio.
Long term modular ratio (m) = 280/ (3fcbc)
Where, fcbc = permissible compressive stress due to bending in concrete in
N/mm2.
Poisson’s ratio:
Poisson’s ratio varies between 0.1 for high strength concrete and 0.2 for weak
mixes. It is normally taken as 0.15 for strength design and 0.2 for serviceability
criteria.
Durability:
Durability of concrete is its ability to resist its disintegration and decay. One of
the chief characteristics influencing durability of concrete is its permeability to
increase of water and other potentially deleterious materials.
The desired low permeability in concrete is achieved by having adequate
cement, sufficient low water/cement ratio, by ensuring full compaction of
concrete and by adequate curing.
Unit weight of concrete:
The unit weight of concrete depends on percentage of reinforcement, type of
aggregate, amount of voids and varies from 23 to 26KN/m2. The unit weight of
plain and reinforced concrete as specified by IS:456 are 24 and 25KN/m3
respectively.
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2.3 TYPES OF LOADS:
The loads are broadly classified as vertical loads, horizontal loads and
longitudinal loads. The vertical loads consist of dead load, live load and impact
load. The horizontal loads comprises of wind load and earthquake load. The
longitudinal loads i.e. tractive and braking forces are considered in special case
of design of bridges, gantry girders etc.
2.3.1 Dead load:
Dead loads are permanent or stationary loads which are transferred to structure
throughout the life span. Dead load is primarily due to self weight of structural
members, permanent partition walls, fixed permanent equipments and weight of
different materials.
2.3.2 Imposed loads or live loads:
Live loads are either movable or moving loads with out any acceleration or
impact. There are assumed to be produced by the intended use or occupancy
of the building including weights of movable partitions or furniture etc. The floor
slabs have to be designed to carry either uniformly distributed loads or
concentrated loads whichever produce greater stresses in the part under
consideration. Since it is unlikely that any one particular time all floors will not
be simultaneously carrying maximum loading, the code permits some reduction
in imposed loads in designing columns, load bearing walls, piers supports and
foundations.
2.3.3 Impact loads:
Impact load is caused by vibration or impact or acceleration. Thus, impact load
is equal to imposed load incremented by some percentage called impact factor
or impact allowance depending upon the intensity of impact.
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2.3.4 Wind loads:
Wind load is primarily horizontal load caused by the movement of air relative to
earth. Wind load is required to be considered in design especially when the
heath of the building exceeds two times the dimensions transverse to the
exposed wind surface.
For low rise building say up to four to five storeys, the wind load is not critical
because the moment of resistance provided by the continuity of floor system to
column connection and walls provided between columns are sufficient to
accommodate the effect of these forces. Further in limit state method the factor
for design load is reduced to 1.2 (DL+LL+WL) when wind is considered as
against the factor of 1.5(DL+LL) when wind is not considered. IS 1893 (part 3)
code book is to be used for design purpose.
2.3.5 Earthquake load:
Earthquake loads are horizontal loads caused by the earthquake and shall be
computed in accordance with S 1893. For monolithic reinforced concrete
structures located in the seismic zone 2, and 3 without more than 5 storey high
and importance factor less than 1, the seismic forces are not critical.
2.4 METHODS OF ANALYSIS OF FRAMES:
Elastic analysis deals with the study of strength and behavior of the members
and structure at working loads. Frames can be analyzed by various methods.
However, the method of analysis adopted depends upon the types of frame, its
configuration (portal bay or multibay) multistoried frame and Degree of
indeterminacy.
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It is based on the following assumptions:
1. Relation between force and displacement is linear. (i.e. Hook’s law is
applicable).
2. Displacements are extremely small compared to the geometry of the
structure in the sense that they do not affect the analysis.
The methods used for analysis of frame are:
1. Flexibility coefficient method.
2. Slope displacement method.
3. Iterative methods like
a. Moment distribution method(By Hardy Cross in 1930’s)
b. Kani’s method (by Gasper Kani in 1940’s)
4. Approximate methods like
a. Substitute frame method
b. Portal method
c. Cantilever method
2.4.1 FLEXIBILITY COEFFICIENT METHOD:
This method is called as force method or compatibility method. In this
Redundant forces are chosen as unknowns. Additional equations are obtained
by considering the geometrical conditions imposed on the formation of
structures. This method is used for analyzing frames of lower D.O.R.
• Limitations:
1. This method involves long computations even for simple problems with
small D.O.R.
2. This method becomes intractable for large D.O.R. (>3), when computed
manually especially because of simultaneous equations involved.
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This method is not ideal for computerizing, since a structure can be reduced to
a statically determinate form in more than one way.
2.4.2 SLOPE DISPLACEMENT METHOD:
It is displacement or equilibrium or stiffness method. It consists of series of
simultaneous equations, each expressing the relation between the moments
acting at the ends of the members is written in terns of slope & deflection. The
solution of slope deflection equations along with equilibrium equations gives the
values of unknown rotations of the joints. Knowing these rotations, the end
moments are calculated using slope deflection equations.
• Limitations:
1. This method is advantageous only for the structures with small Kinematic
indeterminacy.
2. The solution of simultaneous equation makes the method tedious for
annual computations.
The formulation of equilibrium conditions tends to be a major constraint in
adopting this method.
Hence flexibility coefficients & slope displacement methods have limited
applications in the analysis of frames. While other methods like iterative
or approximate methods are used for analyzing frames containing larger
indeterminacy.
2.4.3 APPROXIMATE METHODS:
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Approximate analysis of hyper static structures provides a simple means of
obtaining quick solutions for preliminary designs. It is a very useful process that
helps to develop a suitable configuration for final (rigorous) analysis of a
structure, compare alternative designs & provide a quick check on the
adequacy of structural designs. These methods make use of simplifying
assumptions regarding structural behavior so as to obtain a rapid solution to
complex structures. However, these techniques should be applied with caution
& not relied upon for final designs, especially complex structures.
The usual process comprises reducing the given indeterminate configuration to
a structural system by introducing adequate number of hinges. It is possible to
check the deflected profile of a structure for the given loading & there by locate
the points of inflection.
Since each point of inflection corresponds to the location of zero moment in the
structure, the inflection points can be visualized as hinges for purpose of
analysis. The solution of the structure is rendered simple once the inflection
points are located. In multistoried frames, two loading cases arise namely
horizontal & vertical loading.
The analysis is carried out separately for these two cases:
• VERTICAL LOADS:
The stress in the structure subjected to vertical loads depends upon the relative
stiffness of the beam & columns. Approximate methods either assumes
adequate number of hinges to render the structure determinate or adopt
simplified moment distribution methods.
• HORIZONTAL LOADS:
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The behavior of a structure subjected to horizontal forces depends on its height
to width ratio. The deformation in low-rise structures, where the height is
smaller than its width, is characterized predominantly by shear deformations. In
high rise building, where height is several times greater than its lateral
dimensions, is dominated by bending action. There are two methods to analyze
the structures subjected to horizontal loading.
2.4.3.1 PORTAL METHOD:
Since shear deformations are dominant in low rise structures, the method
makes simplifying assumptions regarding horizontal shear in columns. Each
bay of a structure is treated as a portal frame, & horizontal force is distributed
equally among them.
The assumptions of the method can be listed as follows:
1. The points of inflection are located at the mid-height of each column
above the first floor. If the base of the column is fixed, the point of
inflection is assumed at mid height of the ground floor columns as well;
otherwise it is assumed at the hinged column base.
2. Points of inflection occur at mid span of beams.
3. Total horizontal shear at any floor is distributed among the columns of
that floor such that the exterior columns carry half the force carried by
the inner columns.
2.4.3.2 CANTILEVER METHOD:
This method is applicable to high rise structures. This is based on the
simplifying assumptions regarding the Axial Force in columns.
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1. The basic assumption of the method can be stated as “the axial force in
the column at any floor is linearly proportional to its distance from the
centroid of all the columns at that level.
Assumptions 1&2 of the portal are also applicable to the cantilever method.
2.4.3.3 POINTS OF INFLECTION METHOD:
The frame is reduced to a statically determinate form by introducing adequate
number of points of inflection. The loading on the frames usually comprises
uniformly distributed dead loads & live loads.
The following are assumptions made:-
1. The beams of each floor act as continuous beams, with the points of
inflection at a distance of one-tenth of the span from the joints.
2. The unbalanced beam moment at each joint is distributed equally among
the columns at the joint.
3. Axial forces & deformations in beams are negligible.
2.4.3.4 SUBSTITUTE FRAME METHOD:
The method assumes that the moments in the beams of any floor are
influenced by loading on that floor alone. The influence of loading on the lower
or upper floors is ignored altogether. The process involves the division of multi-
storied structure into smaller frames. These sub frames are known as
equivalent frames or substitute frames.
The sub frames are usually analyzed by the moment distribution method, using
only one cycle of distribution. The substitute frames are formed by the beams at
the floor level under consideration, together with the columns above & below
with their far ends fixed. The distributed B.M are not carried over far ends of the
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columns in this process; the moments in the columns are computed at each
floor level independently & retained at that floor irrespective of further analysis.
2.4.4 ITERATIVE METHOD:
Iterative procedures form a powerful class of methods for analysis of
indeterminate structures. These methods after elegant & simple procedure of
analysis, that are adequate for usual structures.
These methods are based on the distribution of joint moments among members
connected to a joint. The accuracy of the solution depends upon the number of
iterations performed; usually three or five iterations are adequate for most of the
structures.
The moment distribution methods were developed by Hardy Cross in 1930’s &
by Gasper Kani in 1940’s. These methods involve distributing the known fixed
moments of the structural members to the adjacent members at the joints, in
order to satisfy the conditions of the continuity of slopes & displacements.
Though these methods are iterative in nature, they converge in a few iterations
to give correct solution.
2.4.4.1 MOMENT DISTRIBUTION METHOD:
This method was first introduced by Prof. Hardy Cross is widely used for the
analysis of intermediate structures. In this method first the structural system is
reduced to its kinematically determinate form, this is accomplished by assuming
all the joints to be fully restrained. The fixed end moments are calculated for this
condition of structure. The joints are allowed to deflect rotate one after the other
by releasing them successively. The unbalanced moment at the joint shared by
the members connected at the joint when it is released.
LIMITATIONS:
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1. This method is eminently suited to analyze continuous beams
including non-prismatic members but it presents some difficulties
when applied to rigid frames, especially when frames are
subjected to side sway.
2. Unsymmetrical frames have to be analyzed more than once to
obtain FM (fixed moments) in the structures.
3. This method can not be applied to structures with intermediate
hinges.
2.4.4.2 KANI’S METHOD:
This method was introduced by Gasper Kani in 1940’s. It involves distributing
the unknown fixed end moments of structural members to adjacent joints, in
order to satisfy the conditions of continuity of slopes and displacements.
ADVANTAGES:
1. Hardy Cross method distributed only the unbalanced moments at joints,
whereas Kani’s method distributes the total joint moment at any stage of
iteration.
2. The more significant feature of Kani’s method is that the process is self
corrective. Any error at any stage of iteration is corrected in subsequent
steps.
Framed structures are rarely symmetric and subjected to side sway, hence
Kani’s method is best and much simpler than pther methods like moment
distribution method and slope displacement method.
PROCEDURE:
1. Rotation stiffness at each end of all members of a structure is
determined depending upon the end conditions.
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a. Both ends fixed
Kij= Kji= EI/L
b. Near end fixed, far end simply supported
Kij= ¾ EI/L; Kji= 0
2. Rotational factors are computed for all the members at each joint it is
given by
Uij= -0.5 (Kij/ ΣKji)
{THE SUM OF ROTATIONAL FACTORS AT A JOINT IS -0.5}
(Fixed end moments including transitional moments, moment releases and
carry over moments are computed for members and entered. The sum of the
FEM at a joint is entered in the central square drawn at the joint).
3. Iterations can be commenced at any joint however the iterations
commence from the left end of the structure generally given by the
equation
M ij = Uij [(Mfi + Mי i) + Σ Mּיּי [(jiי
4. Initially the rotational components Σ Mji (sum of the rotational moments
at the far ends of the joint) can be assumed to be zero. Further iterations
take into account the rotational moments of the previous joints.
5. Rotational moments are computed at each joint successively till all the
joints are processed. This process completes one cycle of iteration.
6. Steps 4 and 5 are repeated till the difference in the values of rotation
moments from successive cycles is neglected.
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7. Final moments in the members at each joint are computed from the
rotational members of the final iterations step.
Mij = (Mfij + M ij) + 2 Mּיּי ij + Mי jiiּי
The lateral translation of joints (side sway) is taken into consideration by
including column shear in the iterative procedure.
8. Displacement factors are calculated for each storey given by
Uij = -1.5 (Kij/ΣKij)
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3.1 EARTHQUAKE:
An earthquake is vibration of earth surface by waves emerging from the source
of disturbance in the earth by virtue of release of energy in the earth’s crust. It is
essentially a sudden and transient motion or series of motions of the earth
surface originating in a limited under ground motion due to disturbance of the
elastic equilibrium of the earth mass and spreading from there in all directions.
REASONS FOR HIGH CASUALITY:
1) Urbanization is rapidly increasing and due to increase in land cost,
many multi storied buildings are being constructed.
2) Code is not mandatory.
3) Construction as such is governed by municipal bye-laws.
4) Seismic provisions are not incorporated.
5) Non enforceation of elaborated checks proper ways.
6) No checks even for simple ordinary design.
GENERAL GUIDE LINES:
Drift:
It is the maximum lateral displacement of the structure with respect to total
height or relative inter-storey displacement. The overall drifts index is the ratio
of maximum roof displacement to the height of the structure and inter-storey
drift is the ratio of maximum difference of lateral displacement at top and bottom
of the storey divided by the storey height.
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Non structural elements and structural non seismic members primarily get
damaged due to drift. Higher the lateral stiffness lesser is the likely damage.
The storey drift in any storey due to minimum specified design lateral force with
partial safety factor of unity shall not exceed 0.004 times the storey height.
Separation between adjacent units or buildings:
Two adjacent buildings or two adjacent units of the same building with
separation joint in between shall be separated by distance equal to the amount
R times the sum of the calculated storey displacements as specified above of
each of them to avoid damaging contact when the two units deflect towards
each other.
Soft storey:
Soft storey or flexible storey is one in which the lateral stiffness is less than 70%
of that in the storey above or less than 80% of the average lateral stiffness of
the three storeys above. In case of buildings with a flexible storey such as
ground storey consisting of open spaces for parking i.e. stilt buildings, special
arrangements are need to be made to increase the lateral strength and stiffness
of the soft storey.
For such buildings, dynamic analysis is carried out including the strength and
stiffness effects of infills and inelastic deformations in the members particularly
those in the soft storey and members designed accordingly. Alternatively, the
following design criteria are to be adopted after carrying the earthquake
analysis neglecting the effect of infill walls in other storeys.
When the floor levels of two similar adjacent buildings are at the same elevation
levels, factor R can be taken as R/2.
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a) The columns and beams of the soft storey are to be designed for 2.5
times the storey shear and moments calculated under seismic loads
specified.
b) Besides the columns designed and detailed for calculated storey
shears and moments, shear walls placed symmetrically in both
directions of the building as far away from the centre of the building as
feasible to be designed exclusively for 1.25 times the lateral storey
shear calculated.
Foundation:
The use of foundations vulnerable to significant differential settlement due to
ground shaping shall be avoided for structures in seismic zones-III, IV & V.
individual spread footings or pile caps shall be interconnected with ties except
when individual spread footings are directly supported on rock. All ties shall be
capable of carrying in tension and in compression an axial force equal to Ah/A
times the larger of the column or pile cap load in addition to the otherwise
computed forces where Ah is the design horizontal spectrum value.
Projections:
a) vertical projections:
Tanks, towers parapets, chimneys and other vertical cantilever projections
attached to buildings and projecting the above roof shall be designed and
checked for stability for 5 times the design horizontal seismic co-efficient Ah. In
the analysis of the building, the weight of these projecting elements will be
lumped with the roof weight.
b) horizontal projections:
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All horizontal projections like cornices and balconies shall be
designed and checked for stability for 5 times the design vertical co- efficient
equal to 10/3 Ah. These increased design forces either for vertical projection or
horizontal projection are only for designing the projecting parts and their
connection with the main structures.
This means that for the design of main structure such increase need not to be
considered.
Shape of the building:
Very slender buildings should be avoided. Large overhangs and projections
attract large earthquake forces. Heavy masses like large water tanks, etc., at
the top shall be avoided. Small water tanks, if provided, should be properly
connected with the framing system. Building should be sufficiently be away from
steep slopes. It should be built on filled up soil.
Asymmetry should be avoided as they undergo torsion and extreme corners are
subjected to very large earthquake forces.
Damping:
Damping is the removal of kinetic energy and potential energy from a vibrating
structure and by virtue of which the amplitude of vibration diminishes steadily.
Some vibrations are due to initial displacement or initial velocity. Due to
damping, these vibrations decay in amplitude.
1. When there is harmonic applied force and its period is nearly equal to
the natural period of the structure. The vibration will grow from zero
displacement and velocity. Damping limits the vibration maximum
amplitude.
2. More damping less is the amplitude.
3. Negative damping may arise while the vibration is small, followed by
positive damping at large amplitude vibrations. The code adopted for
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design of multistoried buildings considering seismic forces is IS 1893
(part I) – 2002. more than 60% area of India is earthquake prone.
According to IS 1893 (part I) – 2002, India is divided into several zones
to their magnitude of intensities.
3.2 NEED FOR SEISMIZ ZONATION:
a) There can not be entirely scientific basis for zonation in view of the scanty
data available.
b) Though the magnitudes are known there is little instrumental evidence for
comparing damage.
c) Hence, magnitudes and epicenters are used.
3.3 REVISION OF PAST CODES:
It is very difficult to predict the occurrence time and exact location of next
earthquake. More than 60% area is earthquake prone. Various problems are
generated after an earthquake. The magnitudes of these problems are very
severe. In order to reduce this effective counter measures are to be taken.
Enough steps should be taken by the concerned authorities for code
compliance so that the structures being constructed are earthquake resistant.
Especially during the past 15 years there were severe earthquakes with a less
time gap and high intensity. Based on the technology advancement and
knowledge gained after earthquake occurrences, the seismic code is usually
revised. The fifth revision of IS 1893 with seven zones, was done in 2002 after
along gap of 18 years. According to the present revision, the latest map has
only 4 zones.
Fifth Revision in 2002:
• Code has been split into 5 parts:-
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Part 1: General provisions and buildings.
Part 2: Liquid retaining tanks-elevated and ground supported.
Part 3: Bridges and retaining walls.
Part 4: Industrial structures including stack like structures.
Part 5: Dams and embankment.
Part 1: General provisions and buildings:
• Zone map is revised and zone factors changed
• Response spectra for three types of founding strata
• Empirical expression for fundamental natural period
• Concept of response reduction factor
• Lower bound for design base shear
• Model combination rule is revised
• Other clauses revised and redrafted
Design philosophy:
The design approach in IS 1893 is…
• To ensure that the structure at least a minimum strength to with hand a minor
earthquake (< DBE) without damage,
• To resist moderate earthquake (DBE) without significant structural damage
through some non structural damage may occur, and
• To withstand a major earthquake (MCE) without collapse.
3.4 TERMINOLOGY:
Critical Damping:
The damping beyond which the free vibration motion will not be oscillatory.
Damping:
29
The effect of internal friction, imperfect elasticity of material, slipping, sliding
etc., in reducing the amplitude of vibration and is expressed as a percentage of
critical damping.
Design Acceleration Spectrum:
Design acceleration spectrum refers to an average smoothened plot of
maximum acceleration as a function of frequency or time period of vibration for
a specified damping ratio for earthquake excitations at the base of a single
degree of freedom system.
Design Basis Earthquake (DBE):
It is the earthquake which can reasonably be expected to occur at least once
during design life of the structure.
Design Horizontal Acceleration Co-efficient (Ah):
It is a horizontal acceleration coefficient that shall be used for design of
structures.
Design Lateral Force:
It is a horizontal seismic force prescribed by this standard that shall be used to
design a structure.
Ductility:
Ductility of a structure or its members is the capacity to undergo large inelastic
deformations without significant loss of strength or stiffness.
Importance Factor:
It is a factor used to obtain the design seismic force depending on the functional
use of the structure characterized by hazardous consequences of its failure, its
post earthquake functional need, historical value or economic importance.
Intensity of Earthquake:
The intensity of an earthquake at a place is a measure of the strength of
shaking during the earthquake and is indicated by number according to the
modified MERCALLIS SCALE or MSK scale of seismic intensities.
Natural Period (T):
Natural period of a structure is its time period of undamped free vibration.
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Response Reduction Factor:
It is the factor by which the actual base shear force that would be generated if
the structure were to remain elastic during its response design basis
earthquake (DBE) shaking, shall be reduced to obtain the design lateral force.
Seismic Mass:
It is the seismic weight divided by acceleration due to gravity.
Seismic Weight:
It is a total dead load plus appropriate amounts of specified impose load.
3.5 EARTHQUAKE AND VIBRATION EFFECT ON STRUCTURES:
BASIC ELEMENTS OF EARTHQUAKE RESISTANT DESIGN:
Introduction:
Structures on the earth are generally subjected to load of two types static and
dynamic. Static loads are constant with time while dynamic loads are time
varying. The majority of civil engineering structures are designed with
assumptions that all applied loads are static. The effect of dynamic loads is not
considered because the structure is rarely subjected to dynamic loads; more so,
its consideration in analysis makes the solution more complicated and time
consuming. This feature of neglecting the dynamic forces may some times
become the cause of disaster, particularly in the case of earthquake. There is a
growing interest in the process of designing civil engineering structures capable
to withstand dynamic loads, particularly, earthquake induced load.
The dynamic force may be an earthquake force resulting from rapid movement
along the plane of faults within earth’s crust. This sudden movement of fault
releases great energy in the form of seismic waves, which are transmitted to the
structures through their foundations, and cause to set the structure in motion.
These motions are complex in nature and induce abrupt horizontal and vertical
oscillations in structures, which result accelerations, velocities and
displacements in the structure. The induced accelerations generate inertial
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forces in the structure, which are proportional to the acceleration of the mass
and acting opposite to the ground motion.
The energy produced in the structure by the ground motion is dissipated
through internal friction within the structural and non-structural members. This
dissipation if energy is called damping. The structures always posses some
intrinsic damping, which diminishes with time once the seismic excitation stops.
These dissipative or damping forces are represented by viscous damping
forces, which are proportional to the velocity induced in the structure. The
constant of proportionality is called as linear viscous damping. The resisting
force in the structures is proportional to the deformation induced in the structure
during the seismic excitation. The constant of proportionality is referred to as
stiffness of structure. Stiffness greatly affects the structure’s uptake of
earthquake generated forces. On the basis of stiffness the structure may be
classified as brittle or ductile.
Brittle structure having greater stiffness proves to be less durable during
earthquake while ductile structure performs well in earthquakes.This behavior of
structure evokes an additional desirable characteristic called ductility. Ductility is
the ability of structure to undergo distortion or deformation without damage or
failure.
The basic equation of static equilibrium under displacement method of analysis
is given by
F(ext) = ky
Where, F(ext) is the external applied static force, k is the stiffness resistance,
and y is the resulting displacement. The restoring force (ky) resists the applied
force, F(ext).
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Now, if the applied static force changes to dynamic force or time varying force
the equation of static equilibrium becomes one of the dynamic equilibrium and
has the form
F(t) = my(t) + cy(t) + k(t)y(t)
Where,
my(t) = inertia forces acting in a direction opposite to that of seismic
motion applied to the base of the structure, whose magnitude is the mass of the
structure times its acceleration, m is the mass (kg) and y(t) is the acceleration
(m/sec2). Inertia forces are the most significant which depend upon the
characteristic of the ground motion and the structural characteristics of
structure. The basis characteristic of the structure and ground is its fundamental
or natural period.
The fundamental periods of structures may range from 0.05 sec for a well
anchored piece of equipment, 0.1 for a one storey frame, and 0.5 for a low
structure up to 4 storeys and between 1 to 2 seconds for a tall building of 20
storeys.
Natural periods of ground are usually in the range of 0.5 to 1 sec so that it is
possible for the building and ground to have the same fundamental period and
therefore, there is high probability for the structure to approach a state of partial
resonance called as quasi resonance. Hence, in developing a design strategy
for a building, it is desirable to estimate the fundamental periods both of the
structure and of the site so that a comparison can be made to see the existence
of the probability of quasi resonance.
Cy(t) = damping force acting in a direction opposite to that of the seismic
motion, c is the damping co-efficient (N sec/m) and y(t) the velocity (m/sec).
The value of damping in a structure depends on its components. The damping
effect is expressed as a percentage of the critical damping which is the greatest
damping value that allows vibratory moment to develop. The degrees of
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damping in common types of structures are reinforced concrete 5 to 10%, metal
frame 1 to 5%, and masonry 8 to 15%
k(t)y(t) = restoring force k(t) is the stiffness (N/m) or resistance is a function of
the yield condition in the structure which is in turn a function of time. y(t) is the
displacement in meters. F(t) is the externally applied force (N).
The equation above is a second order differential equation that needs to be
solved for the displacement y(t). The number of displacement components
required specifying the position of mass points is called the number of degrees
of freedom to obtain an adequate solution. For some structures, single degree
of freedom may be sufficient where as for others several hundred degrees of
freedom may be required.
3.6 LATERAL LOAD DISTRIBUTION OF FRAME BUILDING:
• In a two dimensional moment resisting frame each joint can have at the
most three degrees of freedom (displacement in horizontal and vertical
directions and rotation).
• Total number of degree of freedom is 3Nj where Nj is the number of
joints in the frame.
• In practice, beams carry very small axial force and undergo negligible
axial deformation. This means horizontal displacement at all joints located at
the beam level s same.
• In most buildings uptown moderate height, the axial deformation of
columns is negligible.
• Numbers of degrees of freedom are reduced to one rotation and one
horizontal displacement.
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• As the rotational inertia associated with the rotational degree of freedom
is insignificant, it is further possible to reduce, through static condensation,
the number of degrees to one per storey for carrying out dynamic analysis.
• In similar way, each joint of three dimensional frames can have at most
six degrees of freedom.
• Finally, there are three degrees of freedom per floor.
• Free vibration analysis of the building can thus be carried out by solving
(3N*3N) Eigen value problem, where N is the number of storeys in the
building.
• Once natural frequency and more shape is known it is possible to obtain
the maximum seismic force to be applied at each storey level due to given
earthquake ground motion.
3.7 LATERAL LOAD ANALYSIS OF MOMENT RESISTING FRAME:
• Once the design lateral loads are known on the two-dimensional frames,
one could analyze the frame for the member forces.
• One could carry out an accurate computer analysis or an approximate
analysis as per requirement.
• Approximate analysis is usually performed at preliminary design stage
and to assess the computer analysis.
• Two commonly used methods:-
A. Portal frame method: Consider the 2-D frame with m-base and n-storeys.
The degree of indeterminacy of the frame is 3mn. To analyze the frame, 3mn
assumptions are made;
• The point of contra-flexure in the column is at mid-height of the columns:
(m+1)n assumptions.
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• The point of contra-flexure in the beams is at the mid span of the beams:
mn assumptions.
• Axial force in the internal columns is zero (m+1)n assumptions.
• With the above assumptions, the frame becomes statically determinate
and member forces are obtained simply by considering equilibrium.
B. Cantilever method: In this method also, 3mn assumptions are to be made
to make the frame statically determinate; the point of contra-flexure in the
column is at mid-height of the columns: (m+1)n assumptions.
• The point of contra-flexure in the beams is at mod span of the beams:
mn assumptions.
• Axial force in the columns is approximated by assuming that the frame
behaves as a cantilever beam. Neutral axis of the frame is obtained using
the column area of cross section and the column location, axial stress in the
column is assumed to vary linearly from this neutral axis: (m-1)n
assumptions.
3.8 SEISMIC METHOD OF FRAMES:
Once the structural model has been selected, it is possible to perform analysis
to determine the seismically induced forces in the structures. There are different
methods of analysis, which provide different degrees of accuracy. The analysis
process can be categorized on the basis of three factors: the type of the
external applied loads, the behavior of structure and the type pf structural model
selected.
Depending upon the nature of the considered variables, the method of analysis
can be classified. Based on the type of external action and behavior of structure
the analysis can be further classified as linear static analysis, dynamic analysis,
non linear analysis, or non linear dynamic analysis.
36
Linear static analysis or equivalent static analysis:
Linear static analysis or equivalent static analysis can only be used for regular
structure with limited height. Linear dynamic analysis can be performed in two
ways either by mode superposition method or response spectrum method and
elastic time history method.
This analysis will produce the effect of the higher modes of vibration and the
actual distribution of forces in the elastic range in a better way. They represent
an improvement over linear static analysis. The significant difference between
static and dynamic analysis is the level of force and their distribution along the
height of the structure.
Non-linear static analysis:
Non-linear static analysis is an improvement over the linear static or dynamic
analysis in the sense that it allows the inelastic behavior of structure. The
methods still assume a set of static incremental lateral load over the height of
the structure. The method is relatively simple to be implemented, and provides
information on the strength, deformation and ductility of the structure and the
distribution of demands.
This permits to identifying of critical members likely to reach limit stated during
the earthquake, for which attention should be given during the design and
detailing process. But this method contains many limited assumptions, which
neglect the variation of loading patterns, the influence of higher modes, ad the
effect of resonance.
This method, under the name of push over analysis has acquired a great deal
of popularity now-a-days and in spite of these deficiencies this method provides
37
reasonable estimation of the global deformation capacity, especially for
structures, which primarily respond according to the first mode.
A non-linear dynamic analysis or inelastic time history analysis is the only
method to describe the actual behavior of structure during an earthquake. The
method is based on the direct numerical integration of the motion differential
equations by considering the elastic-plastic deformation of the structure
element.
This method captures the effect of amplification due to resonance, the vibration
of displacements at diverse levels of a frame, an increasing of motion duration
and a tendency of regularization of movements as far as the level increases
from bottom to top.
Equivalent lateral force: Seismic analysis of most of the structures art still
carried out on the basis of lateral force assumed to be equivalent to the actual
loading. The base shear, which is the total horizontal force on the structure, is
calculated on the basis of structure mass and fundamental period of vibration
and corresponding mode shape. The base shear is distributed along the height
of structured in terms of lateral forces according to code formula. This method is
usually conservative for low to medium height buildings with a regular
conformation.
Response spectrum: This method is applicable for those structures where
modes other than the fundamental one affect significantly the response of the
structure. In this method the response of analysis multi-degree-of-freedom
system (MDOF) is expressed as the superposition of model response, each
modal response being determined from the spectral analysis of single degree-
of-freedom system, which are then combined to compute the total response.
38
Modal analysis leads to the history of the structure to a specified ground motion;
however, the method is usually used in conjunction with a response spectrum.
Elastic time theory: A linear time history analysis overcomes all the
disadvantages of modal response spectrum analysis, provided non-linear
behavior is not involved. This method requires greater computational efforts for
calculating the response at discrete times. One interesting advantage of such
procedure is that the relative signs of response quantities are preserved in the
response histories. This is important when interaction effects are considered in
design among stress resultants.
3.9 Seismic Design Methods:
Conventional civil engineering structures are designed on the basis of two main
criteria that are strength and rigidity. The strength is related to damageability or
ultimate limit state, assuring that the level developed in structures remains in
the elastic range, or some limited plastic deformation. The rigidity is related to
serviceability limit state, for which the structural displacements must remain in
some limits, which assures that no damage occurs in non-structural elements.
In case of earthquake resistant design, a new demand must be added to the
two above-mentioned ones, that is the ductility method.
Ductility is an essential attribute of a structure that must respond to strong
ground motions. Ductility serves as the shock absorbers in a building, for it
reduces the transmitted force to one that is sustainable. The resultant
sustainable force has traditionally been used to design a hypothetically elastic
representation of the building.
Therefore, the survivability of a structure under strong, seismic actions relies on
the capacity to deform beyond the elastic range, and to dissipate seismic
energy through plastic deformations, so the ductility check is related to the
39
control of whether the structure is able to dissipate the given quantity of seismic
energy considered in structural analysis or not. Based on three criteria rigidity,
strength and ductility the methods of seismic design are classified.
RESPONSE CONTROL CONCEPT:
Structural response control for seismic loads is a rapidly expanding field of
control systems, known as earthquake protection system. The aim of this
control system is the modification of the dynamic interaction between structure
and earthquake ground motion, in the order to minimize the structure damage
and to control the structural response. The family of earthquake protective
systems has grown to include passive, active and hybrid systems.
The control is based on two different approaches, either the modification of the
dynamic characteristics of the energy absorption capacity of the structure. In
the first case, the structural period is shifted away from the predominant periods
of the seismic input, thus avoiding the risk of resonance occurrence. It is clear
here that the isolation is effective only for a limited range of frequencies of
structures. The acceleration responses in the structure for some earthquakes
can be reduced at the same time,; for the other type of earthquake the
responses have proved to be much worse. Thus the effectiveness of isolation
depends upon the effectiveness of knowing in advance the kind of frequency
content that the earthquake will have. In the second case, the capacity of the
structure to absorb energy is enhanced through appropriate devices, which
reduces damage to the structure. Both the approaches are used in the
earthquake protection system.
IS 1893 (part I) 2002 suggests the following methods for seismic analysis:
Equivalent static analysis (ESA)
Dynamic
a) Response spectrum analysis
40
b) Time history analysis
3.9.1 EQUIVALENT STATIC ANALYSIS (ESA) :
Equivalent static analysis (ESA) is good enough for most of the buildings. It is
generally adopted for
Regular buildings of height less than 90m irregular buildings of
height less than 40m.
3.9.1.1 DETERMINATION OF DESIGN LATERAL FORCES:
The determination of lateral force in the code is based on the approximation
that effects of yielding can be accounted for by linear analysis of the building
using the design spectrum. This analysis is carried out by either modal analysis
procedure or dynamic analysis procedure (clause 7.8 of IS 1893 [part I]: 2002).
Lateral force procedure (clause 7.5 of IS 1893 [part I]: 2002) is also recognized
as equivalent lateral force procedures or equivalent static procedure. The main
difference between the equivalent lateral force and dynamic analysis procedure
lies in the magnitude and distribution of lateral forces over the height of the
buildings. In the dynamic analysis procedure, the lateral forces are based on
the properties of the natural vibration modes of the building which are
determined by distribution of mass and stiffness over height. In the equivalent
lateral force procedures the magnitude of forces is based on an estimation of
the fundamental period and on the distribution of forces given by simple
formulae.
EQUIVALENT LATERAL FORCE PROCEDURES:
The equivalent lateral force is the simplest method of analysis and requires less
computational effort because the forces depend on the code based
fundamental period of structures with some empirical modifier. The design base
shear shall first be computed as a whole, than be distributed along height of
buildings based on simple formulae appropriate for buildings with regular
distribution of mass and stiffness. The design lateral force obtained at each
41
floor level shall then be distributed to individual lateral load resisting elements
depending upon diaphragm action. The following are the major steps for
determining the forces by equivalent lateral force procedures.
3.9.2 DYNAMIC ANALYSIS:
IS 1893 (part I): 2002 has recommended the method of dynamic analysis of
buildings in the case of
(a) Regular building:
These are greater than 40m in height in zones IV and V and those greater than
90m in height in zones II and III.
(b) Irregular building:
(c) All framed buildings higher than 12m in zones IV and V and those greater
than 40m in height in zones II and III.
The purpose of dynamic analysis is to obtain the design seismic forces, with its
distribution to different levels along the height of the building and to the various
lateral load-resisting elements similar to equivalent lateral force method. The
procedure of dynamic analysis described in the code is valid only for regular
type of buildings, which are almost symmetrical in plan and elevation about the
axes having uniform distribution of lateral load resisting elements. It is further
assumed that all the masses are lumped at the storey level and only sway
displacement is permitted at each storey. The procedure of dynamic analysis of
irregular type of buildings should be based on 3D modeling of building that will
adequately represent its stiffness and mass distribution along the height of the
42
building so that its response to earthquake could be predicted with sufficient
accuracy.
3.10 DETERMINATION OF BASE SHEAR:
The total design force or design base shear along any principal direction shall
be determined by the following expression:
Vb = Ah * W
Where Vb = design base shear
Ah = design horizontal seismic co-efficient for a structure
W = seismic weight of building
Ah shall be determined by the following expression:
Ah = (Z/2)* (I/R) * (Sa/g)
Where, Z= zone factor
I= importance factor
R= response reduction factor
Sa/g= average response acceleration co-efficient
3.10.1 ZONE FACTOR (Z):
In factor z/2, Z is given in table-2 of IS 1893 [part 1]: 2002 for the Maximum
Considered Earthquake (MCE) and service life of structure in a zone. The factor
2 in the denominator of Z is used so as to reduce the Maximum Considered
Earthquake zone factor to the factor for Design Basis Earthquake (DBE). Z can
also be determined from the seismic zone map of India which segregates the
country in various areas of similar probable maximum intensity ground motion.
The maximum intensity is fixed in such a way that the lifeline/ critical structure
43
will remain functional and there is low probability of collapse for structures
designed with the provisions provided in the code even for an event of
occurrence of earthquake with higher intensity. The value of Z ranges from
0.102 to 0.36 corresponding to Zone II to Zone V. This map has divided the
whole country into 4 Zones starting from Zone II to V.
The intensity as per comprehensive intensity scale (MSK64) broadly associated
with the various zones is VI (or less), VII, VIII & IX (and above) for Zones II, III,
IV & V respectively. In Zone II, low seismic intensity zone where minor damage
could occur has a Z value 0.10.
Zone III (Z= 0.16), moderate intensity zone where moderate damage could
occur. Zone IV (Z= 0.24), severe intensity zone where major property damage
could occur and Zone V (Z= 0.36), where severe intensity zone that lie in close
proximity to certain prescribed major fault systems.
3.10.2 Importance factor (I):
It depends upon the fundamental use of the structure characterized by
hazardous consequences of its failure, post earthquake functional needs,
historic value or economic importance. The minimum values of importance
factor are given in table 6 of IS 1893 (part I) 2002. According to table 6
buildings are classified into two categories:
1) Importance service and community buildings
2) All other buildings
Importance service buildings have an I value of 1.5 and all other buildings are
assigned a value of 1.0. The value of I may be more than the assigned value
depending upon economy, strategy considerations like multi storied buildings,
hazardous consequences etc., essential facilities referred to those buildings of
structures that must be safe and usable for emergency purpose after a major
44
earthquake has occurred in order to preserve the peace, health and safety of
general public.
3.10.3 Response reduction factor (R):
It depends upon the perceived seismic damage performance of the structure,
characterized by ductile or brittle deformations. This characteristic represents
the structures ductility, damping as well as the past seismic performance of
structure with various structural framing structure. The need for incorporation of
factor R in base shear formulae is an attempt to consider the structures in
elastic characteristics in linear analysis method since it is undesirable as well as
uneconomical that a structure will be designed on the basis that it will remain in
elastic range for all major earthquakes. The base shear equation produces
force levels that probably or more representative of those occurring in an actual
structure. It is achieved by applying those base shears for linear design that are
reduced by a factor I/R from those that would be obtained from fully elastic
response.
The value of R increases with the increase of structural ductility and its energy
dissipation capacity and degree of redundancy. The value of R is prescribed in
table 7 of IS 1893 (part I) 2002 for different types of building system. A low
value of R approaching 1.5 is assigned to an extremely brittle building i.e.,
unreinforced masonry wall buildings and a high value of 1.5 is assigned to a
more ductile structure like special moment resisting frame reinforced concrete
or shear wall building.
3.10.4 Average response acceleration co-efficient (Sa/g):
Sa/g for rock or soil sites for different soil conditions based on appropriate
natural periods of the structure is given by fig 2 of IS 1893 (part I) 2002.
45
These values are given for 5% of damping of the structure; for other value of
damping it is modified according to table 3 of IS 1893 (part I) 2002. These
curves represent free field ground motion.
The fundamental natural period for buildings are given in clause 7.6 of IS 1893
(part I) 2002 and is summarized below
Ta = 0.075* ho.75
Moment resisting RC frame buildings without brick in fill walls.
Ta = 0.085* ho.75
Moment resisting steel frame buildings without brick in fill walls. Ta = 0.09/d0.5
All other buildings including moment resisting RC frame building without brick in
fill walls. (h is the height of building in meters and d is the base dimension of
building at plinth level in meter, along the considered direction of lateral force).
W = seismic weight of building which is the sum of the seismic weight of
floors. The seismic weight at any floor level would be equal to dead weight of
the floor system plus weight of column and walls in inverse proportion to its
distance from the floors plus appropriate amount of imposed load as specified
in clause 7.3 of IS 1893 (part I) 2002. Imposed load on roof level need not to be
considered. The basic reasons for considering the percentage of live load are
1. Only a part of the maximum live load will probably be existing at the time of
earthquake.
2. Non rigid mounting of the live load absorbs part of the earthquake energy.
3.11 Lateral Distribution of Base shear:
The computer base shear is now distributed along the height of the building.
The shear force, at any level, depends on the mass at that level and deforms
shape of the structure. Generally, a structure has a continuous system with
infinite degree-of-freedom. From structural idealization we convert an infinite
degree-of-freedom to finite degree of freedom system. Multi storied building has
46
been idealized into lumped mass model by assuming the mass of the building
lumped at each floor levels (called node); with one degree of freedom in the
direction of lateral displacement in which the structure is being analyzed per
floor, resulting in as many degree of freedom as of freedom system with many
possible patterns of deformations.
The magnitude of the lateral force at a particular floor (node) depends on the
mass of that node, the distribution of stiffness over the height of structure, and
the nodal displacement in a given node. The actual distribution of base shear
over the height of the building is obtained as the superposition of all the nodes
of vibration of the multiple degree of freedom system.
In equivalent force procedure, the magnitude of lateral forces is based on
fundamental period of vibration, the other periods and shapes of natural nodes
are not required. IS 1893 (part I): 2002 uses a parabolic distribution (Paz, 1994)
of lateral force along the height of building as per the following expression.
n
Q= VB* (W1-h12) / Σ Wig* h1
2
j=1
Where, Q= Design lateral force at floor i,
W= Seismic weight of floor i,
h1= Height of floor I measured from base, and
n= Number of storeys in the building is the number of levels at which
masses are located.
47
4.1 PRESENT PROBLEM:
We have considered a proposed multi storied building in HYDERABAD. The structure is designed for (G+4) as per requirements. The complete building has been idealized using STAAD software. The structure is designed as per requirements and specifications.
Why only STAAD Pro.?
STAAD Pro is widely used software for structural analysis and integral steel, concrete, timber, aluminum, design from research engineering international. STAAD Pro consists of a core package and an extension component. The STAAD Pro core package consists of the following component THE STAAD PRO GRAPHICAL USER INTERFACE. It is used to generate the model, which can then be analyzed using the STAAD Pro.
STAAD ENGINEERING:
It is general purpose calculation engineering structural analysis and integrated steel, concrete, timber and aluminum design. The STAAD Pro extension program consists of the following. This package consists of several modules for very specific structures engineering tasks such as analysis and design of base plate, footings, cantilever retaining wall, bolt group, pile group, one way and two way slabs etc.
48
4.2 DESIGN CONSIDERATIONS
• The design of reinforced concrete members have been carried out in accordance with IS 456-2000 using limit state.
• Live load on floors and roofs have been considered as per IS 875 part 2 1987 as 2kN/m2 and 1.5kN/m2.
• Floor finishes on floors and roofs have been considered as per IS 875 part 1 1987 as 1.5kN/m2 and 1.75kN/m2.
• Concrete of M20 grade is considered for all concrete members.• High yield strength deformed bars confirming to IS 1786 is considered for all
R.C.C members.• As per soil reports, the safe bearing capacity is considered as 250kN/m2 for
design of footings.• IS 1893 part 1 2002 has been used for calculation of base shear.• Zone factor is taken as 0.1(zone 2)• Importance factor is taken as 3• Average response acceleration coefficient is taken as 2.5 (from curves)
49
5.1 LOAD CALCULATIONS
5.1.1 DEAD LOADS:
WALL LOADS:
EXTERNAL WALLS : Thickness*height * unit wt
=0.23*(3.05-0.3)*19
= 12.018 KN/m
INTERNAL WALLS : Thickness * height *unit wt
= 0.115*(3.05-0.3)*19
=6.009 KN/m
FLOOR LOADS:
self weight of the slab = 0.125*25 = 3.125 KN/Sq.m
weight of the floor finish = 0.75 KN/Sq.m
weight of unknown partitions = 0.5 KN/Sq.m
total floor load 4.375 KN/Sq.m
LOADS ON CANTILEVER:
cantilever load = floor load*length
= 4.375 * 1.56
= 6.825 KN/m
PARAPET WALL:
50
Parapet wall load = thickness*height*unit wt
= 0.23*0.75*19
= 3.2775 KN/m
(height of parapet wall taken as 0.75m)
5.1.2 LIVE LOADS:
for first 5 floors live load = 2 KN/Sq.m
for terrace live load = 1.5 KN/Sq.m
5.2 SEISMIC EQUIVALENT METHOD
Seismic equivalent method involves
Converting the dynamic seismic loads into equivalent static loads. The base shear, which is total horizontal force on the structure is calculated
on the basis of structure mass and fundamental period of vibration. The base shear is distributed along the height of structure in terms of lateral
forces according to IS:1893-2002
Design seismic base shear
Seismic base shear = VB =Ah *W
Ah = (Z*I*Sa/g)/(2*R)
where W = seismic weight of the buildingZ = zone factorR = response reduction factor
Sa/g = Avg. response acceleration coefficient.
Values according to IS:1893 :2002
Zone Factor Z= 0.10 (Zone 2) Importance factor I =1.0 Response reduction factor R = 3.0
1.00/T 0.40<T<4.00 (from graphs of Rocky/hard soil sites)
DISTRIBUTION OF BASE SHEAR TO DIFFERENT FLOOR LEVELS:
Qi = VB * Wi*hi^2 SUM(Wj*hj^2)
Qi = design lateral force at floor i Wi = seismic weight of floor i
hi = height of floor i measured from base
52
5.3 RESPONSE SPECTRUM METHOD
Response spectrum method involves
In this method the response of analysis of multi degree of freedom system is expressed as the superposition of modal response, each model response being determined from the spectral analysis of single degree of freedom system, which are then combined to compute the total response.
In this method peak ground accelerations are given as input (from the response spectrum, a graph between acceleration and time period).
ratio a/b = 0.23/0.3 = 0.383 Area = B*L = 0.383*L2 5.764 = o.383*L2 L = 3.88m B = 1.5m Therefore, provide 2*3m2 Area provided = 2*3 = 6m2 Net factored soil pressure = (1.5*1310)/6 = 327.5kN/m2 ONE WAY SHEAR :Critical section is at ‘d’ from the face,
Hence the assumed column size and % of steel are O.K.
Reinforcement
Asc = 860 mm2
Assuming 12 mm bars,
Hence Provide 8- 12 mm bars
Lateral ties
Provide lateral ties of dia 8 mm
Provide 8mm# bars @ 250mm c/c
74
6.3 DESIGN OF BEAMS
75
L1= Length of the beam B1= 3.61mL2= Length of the beam B2= 3.67mL3= Length of the beam B3= 2.5mL4= Length of the beam B4= 3.61mL5= Length of the beam B5= 3.67m
DATA:Live load on slab =2kN/m2
Floor finishes= 1.5kN/m2
Self weight of slab= 0.125*25= 3.125kN/m2
Cross section of beam= 230*360mmSelf weight of beam= 0.23*0.6*25= 3.45kN/mInternal wall weight= 0.115*19*(3.05-0.3)= 6.009kN/mTotal triangular dead load on slab= 3.125+1.5= 4.625kN/m2
Total live load= 2kN/m2
Beam B1:UD live load= (W*Lx)/3 = (2*3.61)/3= 2.41kN/mTotal UD live load= 2*2.41= 4.82kN/m [load is acting from two slabs on the beam since we have to multiply with 2].Total UD live load approximately= 4.82kN/m.Converting triangular load to uniformly distributed load= (W*Lx)/3 Triangular dead load to UD load= (W*Lx)/3 = (2*(4.625*3.61))/3 = 11.13kN/m.Total dead load= 11.13+6.009+3.45 = 20.59kN/m.L.L= 4.82kN/m and D.L= 20.59kN/m.
Beam B2:UD live load= (W*Lx)/3 = (2*3.67)/3= 2.45kN/mTotal UD live load= 2*2.45= 4.9kN/m [load is acting from two slabs on the beam since we have to multiply with 2].Converting triangular load to uniformly distributed load= (W*Lx)/3 Triangular dead load to UD load= (W*Lx)/3 = (2*(4.625*3.67))/3 = 11.31kN/m.Total dead load= 11.31+6.009+3.45 = 20.77kN/m.L.L= 4.9kN/m and D.L= 20.77kN/m.Beam B3:UD live load= (W*Lx)/3
76
= (2*2.5)/3= 1.67kN/mTotal UD live load= 2*1.67= 3.34kN/m [load is acting from two slabs on the beam since we have to multiply with 2].Converting triangular load to uniformly distributed load= (W*Lx)/3 Triangular dead load to UD load= (W*Lx)/3 = (2*(4.625*2.5))/3 = 7.71kN/m.Total dead load= 7.71+6.009+3.45 = 17.17kN/m.L.L= 3.34kN/m and D.L= 17.17kN/m.
Beam B4:UD live load= (W*Lx)/3 = (2*3.61)/3= 2.41kN/mTotal UD live load= 2*2.41= 4.82kN/m [load is acting from two slabs on the beam since we have to multiply with 2].Converting triangular load to uniformly distributed load= (W*Lx)/3 Triangular dead load to UD load= (W*Lx)/3 = (2*(4.625*3.61))/3 = 11.13kN/m.Total dead load= 11.13+6.009+3.45 = 20.59kN/m.L.L= 4.82kN/m and D.L= 20.59kN/m.
Beam B5:UD live load= (W*Lx)/3 = (2*3.67)/3= 2.45kN/mTotal UD live load= 2*2.45= 4.9kN/m [load is acting from two slabs on the beam since we have to multiply with 2].Converting triangular load to uniformly distributed load= (W*Lx)/3 Triangular dead load to UD load= (W*Lx)/3 = (2*(4.625*3.67))/3 = 11.31kN/m.Total dead load= 11.31+6.009+3.45 = 20.77kN/m.L.L= 4.9kN/m and D.L= 20.77kN/m.
= 0.138 * 20* 230 * (600-50)2 [cover=50] = 192.03kN-m.Maximum bending moment developed at the support of the beam= 29.91kN-m.Mulimit> Maximum bending moment.But we have to provide Ast for the maximum bending moment.Ast= (0.36* fck* b* Xumax)/(0.87* fy) = (0.36* 20* 230* 0.48* 550)/(0.87* 415) = 1210.86mm2.Additional steel for 29.92kN-m by a couple of Ast and Asc,Asc= M/[(fsc- fcc)* (d-d’)]d= effective depth= 550mmd’= effective cover= 50mmd’/d= 50/550 = 0.09Asc= (29.91*106)/[(352-(0.446*20)) * (550-50)] = 174.36mm2.From IS 456-2000, fsc for 0.09 is 352Mpa. 0.87* 415* Ast2= fsc* Asc 0.87* 415* Ast2 = 352* 174.36 Ast2= 170mm2.The maximum positive bending moment for span EF is 29.91kN-m.The maximum positive bending moment for span DE is 28.64kN-m.According to IS 456-2000, clause 22.5, the average of the bending moments can be taken. i.e., (29.91+28.64)/2 = 29.275kN-m.for span DE and EF,Xu = (0.87* fy* Ast)/(0.36* fck* b) = (0.87* 415* Ast)/(0.36* 20* 230)Xu= 0.218* Ast
Provide 2no’s of 16mm diameter bars.So, provide Ast= 2* 201 = 402mm2
In addition to this, provide 4no’s of 16mm diameter bars at the top.Total steel at top of the support is, = (4* 201) + (402) = 1286mm2 > 1210.86mm2.Maximum shear force at support E= 55.05kN.P= (100* Ast)/(b* d) = (100* 1286)/(230* 550) = 1.016Allowable shear stress for M20 grade of concrete is 0.62Mpa.Nominal shear stress= V/(bw* d) = (55.05* 103)/(230* 550) = 0.435Mpa.Nominal shear stress is less than design shear stress.Provide 8mm diameter 2legged stirrups @ 250mm c/c throughout.Spacing not more than 0.75*d = 0.75* 550 = 412.5mm.Provided spacing is within the limit Hence safe.
6.4 DESIGN OF SLABS
DATA:
Slab NO:S1
Grade of concrete= M20
81
Grade of steel= Fe415
Dimensions : 3.93*5.25m
EFFECTIVE DEPTH OF SLAB:
Assuming overall depth of slab= 125mm
Let effective cover of slab= 20mm
Effective depth of slab= 105mm
EFFECTIVE SPAN OF THE SLAB:
As per clause no.22.2 (b) of IS: 456-2000, if the width of the support is
less than 1/12 of clear span, the effective span shall be
Clear span + effective depth of slab
(OR) } whichever is less
Clear span + c/c of supports
Effective span in short direction:
3930/12= 327.5 > 230mm
3.93 + 0.1= 4.03m
3.93 + 0.23= 4.16m
Lx= 4.03m
Effective span in long direction:
5250/12= 437.5 > 230mm
5.25 + 0.1= 5.35m
5.25 + 0.23= 5.48m
Ly= 5.35m
Aspect ratio= Ly/Lx= 5.35/4.03= 1.33 (<2)
Hence the slab is designed as two-way slab with two adjacent
edges discontinuous
The bending moment coefficients from table.26 of IS: 456-2000 as follows
82
αx αy
-ve moment at continuous edge 0.067 0.047
+ve moment at mid span 0.051 0.035
LOADS ON SLABS:
Considering unit weight of slab= 25
Dead load= 4.375 kN/m2
Live load= 2kN/m2
Total load= 6.375kN/m2
Factored load intensity= Wu= 6.375*1.5= 9.56kN/m2
CALCULATION OF BENDING MOMENT:
Short span direction
-ve moment at continuous edge= αX w LX2
= 0.067*9.56*4.03*4.03
= 10.4 kN-m
+ve moment at mid span= αX w LX2
= 0.051*9.56*4.03*4.03
= 7.92 kN-m
Long span direction
-ve moment at continuous edge= αy w Lx2
= 0.047*9.56*4.03*4.03
= 7.3kN-m
+ve moment at mid span= αy w Lx 2
= 0.035*9.56*4.03*4.03
= 5.43 kN-m
CHECK FOR DEPTH:
M= 0.138*fkc*b*d2
83
10.4X106= 0.138X20X1000Xd2
d= 62mm
Overall depth required= 62 + 25= 87mm
Overall depth provided= 125mm
Hence, satisfied
Dx= 125-25-8/2= 96mm
Dy= 125-25-8-8/2= 88mm
CALCULATION OF STEEL:
Mu= 0.87*fy*Ast*d*(1-((Ast*fy)/(b*d*fck)))
Short span
Ast –ve= 310mm2
Ast +ve= 230mm2
Long span
Ast –ve= 210mm2
Ast +ve= 155mm2
Minimum steel @ 0.12%= (0.12/100)*1000*125
= 150mm2
Use 8mm diameter bars
Aø= (3.14/4)*82= 50.26mm2
SHORT SPAN:
Spacing s1= (Aø /Ast )*1000
= (50.26/307.69)*1000
= 160mm
S2= 210mm
LONG SPAN:
S3= 230mm
84
S4= 320
Dx = 125-25-(8/2)
= 96mm
Dy= Dx-8
= 88mm
Maximum spacing Sx= 3d or 300mm
= 3*96 or 300mm
= 288 or 300mm
Sy= 3*88 or 300mm
= 264 or 300mm
Select whichever is less
Therefore, Sx =280mm
Sy =250mm
TORSIONAL REINFORCEMENT:
Torsional steel= (3/4)*Ast max
= 230mm2
Use 6mm diameter bars
Spacing= (28.3/230)*1000
= 120mm
use 6mm diameter bars @ 120mm c/c spacing
CHECK FOR STIFFNESS:
fs= 0.58*fy*(Ast req/Ast prov)
IS 456-2000
Modification factor, k= 2.24
85
Allowable l/d= 26*2.24
= 58.24mm
Actual l/d= 4030/100
= 40.3mm
Hence satisfied
DATA:
Slab NO:S2Grade of concrete= M20Grade of steel= Fe415Dimensions : 3.05*3.93m
86
EFFECTIVE DEPTH OF SLAB:Assuming overall depth of slab= 125mmLet effective cover of slab= 20mmEffective depth of slab= 105mm
EFFECTIVE SPAN OF THE SLAB:As per clause no.22.2 (b) of IS: 456-2000, if the width of the support is less than 1/12 of clear span, the effective span shall be
Clear span + effective depth of slab (OR) } whichever is lessClear span + c/c of supportsEffective span in short direction: 3050/12= 327.5 > 230mm 3.05 + 0.1= 3.15m 3.05 + 0.23= 3.28m Lx= 3.15mEffective span in long direction: 3930/12= 327.5 > 230mm 3.93 + 0.1= 4.03m 3.93 + 0.23= 4.16m Ly= 4.03mAspect ratio= Ly/Lx= 4.03/3.15= 1.28 (<2)Hence the slab is designed as two-way slab with two adjacentedges discontinuousThe bending moment coefficients from table.26 of IS: 456-2000 as follows αx αy-ve moment at continuous edge 0.05 0.037+ve moment at mid span 0.037 0.028
LOADS ON SLABS:Considering unit weight of slab= 25
Lx= 2.40+0.1= 2.5mLy= 17.06+0.1= 17.16mAspect ratio= 17.16/2.5 = 6.86.> 2Hence, the slab is designed as one way slab.Loads on slabs:Total load= 6.375kN/m2
Factored load= 6.375*1.5 = 9.56 kN/m2
Bending moment:Maximum bending moment= wl2/10 = 5.98kN-mCheck for depth:M= 0.138*fck*bd2
Use 8mm diameter bars.Aø= (3.14*64)/4 = 50.26mm2 No. of bars= Ast/Aø = 11bars.Spacing= 50.26/420 = 100mmMaximum spacing= 3d or 300mm = 3*100 or 300Therefore, provide 8mm ø bars at 100mm c/c spacing.
Distribution steel:
Ast= (0.12/100)*1000*125 = 150mm2
Use 6mm diameter bars Spacing= 180mmTherefore, provide 6mm diameter bars at 180mm c/c spacing.Check for stiffness:
2.5 0.4; 2.75 0.4; 3.00 0.35; 3.25 0.3; 3.5 0.3; 3.75 0.25; 4.00 0.25 LOAD 3 WL IN X DIRECTIONWIND LOAD X 1 TYPE 1LOAD 4 WL IN - X DIRECTIONWIND LOAD X -1 TYPE 1LOAD 5 WL IN Z DIRECTIONWIND LOAD Z 1 TYPE 1LOAD 6 WL IN - Z DIRECTIONWIND LOAD Z -1 TYPE 1*DEAD LOADLOAD 7 DLSELFWEIGHT Y -1*WALL LOADMEMBER LOAD1 TO 3 6 10 12 15 18 29 TO 31 34 38 40 43 46 57 TO 59 62 TO 65 78 79 -83 TO 86 99 100 104 109 120 125 TO 129 132 136 138 141 144 155 TO 157 160 -164 166 169 172 183 TO 185 188 TO 191 204 205 209 TO 212 225 226 230 233 -
121
244 249 TO 253 256 260 262 265 268 279 TO 281 284 288 290 293 296 -307 TO 309 312 TO 315 328 329 333 TO 336 349 350 354 357 368 373 TO 377 380 -384 386 389 392 403 TO 405 408 412 414 417 420 431 TO 433 436 TO 439 452 -453 457 TO 460 473 474 478 481 492 497 TO 501 504 508 510 513 516 -527 TO 529 532 536 538 541 544 555 TO 557 560 TO 563 576 577 581 TO 584 597 -598 602 605 616 621 622 UNI GY -12.0184 5 8 9 11 13 14 32 33 36 37 39 41 42 66 67 70 71 87 88 91 92 105 108 112 -113 116 117 130 131 133 TO 135 137 139 140 158 159 161 TO 163 165 167 168 -186 187 192 TO 194 196 197 213 TO 215 217 218 231 232 236 237 240 241 254 -255 257 TO 259 261 263 264 282 283 285 TO 287 289 291 292 310 311 -316 TO 318 320 321 337 TO 339 341 342 355 356 360 361 364 365 378 379 381 -382 TO 383 385 387 388 406 407 409 TO 411 413 415 416 434 435 440 TO 442 444 -445 461 TO 463 465 466 479 480 484 485 488 489 502 503 505 TO 507 509 511 -512 530 531 533 TO 535 537 539 540 558 559 564 TO 566 568 569 585 TO 587 -589 590 603 604 608 609 612 613 UNI GY -6.009*CANTILEVERMEMBER LOAD78 79 99 100 204 205 225 226 328 329 349 350 452 453 473 474 576 577 597 598 -700 701 721 722 UNI GY -6.825*FLOOR LOADFLOOR LOADYRANGE 0 15 FLOAD -4.375 GY*PARAPET WALLMEMBER LOAD623 TO 625 628 632 634 637 640 651 TO 653 656 660 662 665 668 679 TO 681 684 -685 TO 687 700 701 705 TO 708 721 722 726 729 740 745 746 UNI GY -3.2775*LIVE LOADLOAD 8 LLFLOOR LOADYRANGE 0 12.3 FLOAD -2 GYYRANGE 12.3 15.6 FLOAD -1.5 GY*floor loadMEMBER LOAD132 136 160 164 256 260 284 288 380 384 408 412 504 508 532 536 628 632 656 -660 UNI GY -5.75188 TO 191 209 TO 212 230 233 249 250 312 TO 315 333 TO 336 354 357 373 374 -436 TO 439 457 TO 460 478 481 497 498 560 TO 563 581 TO 584 602 605 621 622 -684 TO 687 705 TO 708 726 729 745 746 UNI GY -7.6204 205 225 226 328 329 349 350 452 453 473 474 576 577 597 598 700 701 721 -722 UNI GY -7.4192 TO 195 213 TO 216 316 TO 319 337 TO 340 440 TO 443 461 TO 464 564 TO 567 -585 TO 588 688 TO 691 709 TO 712 UNI GY -15236 237 240 241 360 361 364 365 484 485 488 489 608 609 612 613 732 733 736 -737 UNI GY -13
LOAD COMB 47 (1.0 DL+ 0.8 LL+ 0.8 WLX)7 1.0 8 0.8 3 0.8LOAD COMB 48 (1.0 DL+ 0.8 LL- 0.8 WLX)7 1.0 8 0.8 4 0.8LOAD COMB 49 (1.0 DL+ 0.8 LL+ 0.8 WLZ)7 1.0 8 0.8 5 0.8LOAD COMB 50 (1.0 DL+ 0.8 LL- 0.8 WLZ)7 1.0 8 0.8 6 0.8LOAD COMB 51 (0.9 DL+ 1.0 ELX)7 0.9 1 1.0LOAD COMB 52 (0.9 DL- 1.0 LLX)7 0.9*LOAD COMB 53 (0.9 DL+ 1.0 ELZ)*7 0.9*LOAD COMB 54 (0.9 DL- 1.0 ELZ)*7 0.9LOAD COMB 55 (0.9 DL+ 1.0 WLX)7 0.9 3 1.0LOAD COMB 56 (0.9 DL- 1.0 WLX)7 0.9 4 1.0LOAD COMB 57 (0.9 DL+ 1.0 WLZ)7 0.9 5 1.0LOAD COMB 58 (0.9 DL- 1.0 WLZ)7 0.9 6 1.0PERFORM ANALYSISLOAD LIST 34 TO 36 39 TO 44 47 TO 52PRINT SUPPORT REACTIONLOAD LIST 9 TO 11 14 TO 19 22 TO 27 30 TO 33PERFORM ANALYSIS PRINT ALLSTART CONCRETE DESIGNCODE INDIANUNIT MMS NEWTONFC 20 ALLFYSEC 415 ALLMAXMAIN 25 ALLMAXSEC 12 ALLMINMAIN 12 ALLMINSEC 8 ALLCLEAR 40 ALLDESIGN COLUMN 16 17 19 TO 28 44 45 47 TO 56 72 TO 77 80 TO 82 93 TO 98 101 -102 TO 103 110 111 114 115 118 119 122 123 142 143 145 TO 154 170 171 173 -174 TO 182 198 TO 203 206 TO 208 219 TO 224 227 TO 229 234 235 238 239 242 -243 246 247 266 267 269 TO 278 294 295 297 TO 306 322 TO 327 330 TO 332 343 -344 TO 348 351 TO 353 358 359 362 363 366 367 370 371 390 391 393 TO 402 418 -
125
419 421 TO 430 446 TO 451 454 TO 456 467 TO 472 475 TO 477 482 483 486 487 -490 491 494 495 514 515 517 TO 526 542 543 545 TO 554 570 TO 575 578 TO 580 -591 TO 596 599 TO 601 606 607 610 611 614 615 618 619 638 639 641 TO 650 -666 667 669 TO 678 694 TO 699 702 TO 704 715 TO 720 723 TO 725 730 731 734 -735 738 739 742 743CLEAR 25 ALLTORSION 1 ALLDESIGN BEAM 1 2 4 5 9 11 29 30 32 33 37 39 57 66 67 78 79 87 88 99 100 112 -113 116 117 120 127 128 130 131 133 135 137 155 156 158 159 161 163 165 183 -192 TO 195 204 205 213 TO 216 225 226 236 237 240 241 244 251 252 254 255 -257 259 261 279 280 282 283 285 287 289 307 316 TO 319 328 329 337 TO 340 -349 350 360 361 364 365 368 375 376 378 379 381 383 385 403 404 406 407 409 -411 413 431 440 TO 443 452 453 461 TO 464 473 474 484 485 488 489 492 499 -500 502 503 505 507 509 527 528 530 531 533 535 537 555 564 TO 567 576 577 -585 TO 588 597 598 608 609 612 613 616 623 624 626 627 629 631 633 651 652 -654 655 657 659 661 679 688 TO 691 700 701 709 TO 712 721 722 732 733 736 -737 740DESIGN BEAM 3 6 8 10 12 TO 15 18 31 34 36 38 40 TO 43 46 58 59 62 TO 65 70 -71 83 TO 86 91 92 104 105 108 109 125 126 129 132 134 136 138 TO 141 144 -157 160 162 164 166 TO 169 172 184 TO 191 196 197 209 TO 212 217 218 230 -231 TO 233 245 248 TO 250 253 256 258 260 262 TO 265 268 281 284 286 288 290 -291 TO 293 296 308 TO 315 320 321 333 TO 336 341 342 354 TO 357 369 -372 TO 374 377 380 382 384 386 TO 389 392 405 408 410 412 414 TO 417 420 -432 TO 439 444 445 457 TO 460 465 466 478 TO 481 493 496 TO 498 501 504 506 -508 510 TO 513 516 529 532 534 536 538 TO 541 544 556 TO 563 568 569 581 -582 TO 584 589 590 602 TO 605 617 620 TO 622 625 628 630 632 634 TO 637 640 -653 656 658 660 662 TO 665 668 680 TO 687 692 693 705 TO 708 713 714 726 -727 TO 729 741 744 TO 746*CHECK CODE ALLCONCRETE TAKEEND CONCRETE DESIGNFINISH
126
7.2 CONCLUSION:
Different types of Analysis can be employed for multiple design assessments. In the present theses, the analysis of the 5-storey building is done taking the seismic forces into considerations, using Static equivalent method and Response spectrum method. According to IS: 1893 2002, the analysis results are compared and it is found that Response spectrum method gives more conservative values for the design parameters, like bending moments, stresses, thus leading to more economic design. The reason for this is, the Dynamic analysis is done using accelerations-response spectrum than equivalizing the dynamic forces into static forces.
The approximate economy achieved using Response spectrum method over equivalent seismic method is 70 % in concrete quantity & 72 % in steel quantity.
The design of structural members (foundations, columns, beams, slabs) is done according to IS: 456 200
127
7.3 DRAWINGS
TYPICAL FLOOR PLAN
128
FLOOR OUTLINE
129
BEAMS LAYOUT
130
COLUMN LAYOUT
131
GRID LAYOUT
132
FRAME
133
REINFORCEMENT DETAILS ::
FOOTINGS
134
BEAMS:
135
SLABS
136
STAIR CASE
137
7.4 REFERENCES:
1. ILLUSTRATED R.C.DESIGN BY V.L.SHAH & H.J.SHAH
138
2. REINFORCED CONCRETE DESIGN BY S.UNNIKRISHNA PILLAI
3. REINFORCED CONCRETE DESIGN BY RAMCHANDRA
4. REINFORCED CONCRETE DESIGN BY A.K.JAIN
CODES:
I.S 456 2000 PLAIN AND REINFORCED CONCRETE
I.S 875 1987 DESIGN LOADS PART 1 – DEAD LOADS PART 2 – LIVE LOADS
I.S 1893 2002 EARTHQUAKE RESISTANT DESIGN OF STRUCTURE