Design of G+3 considing earthquake with Etab .pdf

TABLE OF CONTENTS
S.No. Contents
1. DECLARATION
2. CERTIFICATE
3. ACKNOWLEDGEMENT
4. ABSTRACT
5. INTRODUCTION
6. NEED AND OBJECTIVE FOR STUDY
7. EARTHQUAKE AND IT’S CHARACTERISTICS
8. SOIL STRUCTURE INTERACTION
9. DESIGN FEATURES FOR SAFETY AGAINST
EARTHQUAKE
10. CASE STUDY : THE BHUJ EARTHQUAKE
11. LOAD CALCULATION FOR ANALYSIS OF G+3
BUILDINGUSING ETABS
12. DESIGN OF ISOLATED FOOTING
13. DESIGN OF SQUARE COLUMN
14. DESIGN OF BEAM
15. DESIGN OF STAIRCASE
16. REFRENCES

KITCHEN
3.99X3.24
COMBINED W/C
1.74X2.74
LIVING HALL WITH
DINNING ROOM
4.44X5.98
LIVING HALL WITH
DINNING ROOM
4.44X5.98
KITCHEN
3.99X3.24
COMBINED W/C
1.74X2.74
BALCONY
3.24X2.00
BEDROOM
3.24X2.79
PASSAGE
COMBINED W/C
1.74X2.74
COMBINED W/C
1.74X2.74
BEDROOM
3.99X4.74
BALCONY
3.24X2.00
BEDROOM
3.24X2.79
BEDROOM
3.99X4.74
D1
D1
D1
D1
D1
D1
D1
D1
D1
D1
D1
D1
D2
D2
D2
D2
W
W
W
W
W W
V
V
V
V
16.86
10.72

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ABSTRACT:
This study focuses on the comprehensive design and seismic analysis of a G+3 (Ground
plus three floors) building to enhance its earthquake resistance. Earthquakes pose
significant threats to structures, necessitating robust engineering solutions to mitigate
potential damages. The research employs state-of-the-art seismic design principles,
incorporating the latest building codes and standards to ensure the structural integrity
of the G+3 building.
The study begins with a thorough examination of the seismic hazard in the region,
considering factors such as local geological conditions and historical earthquake data.
Subsequently, the structural design process is detailed, encompassing material
selection, load calculations, and the application of advanced analysis techniques. The
G+3 building is designed to adhere to contemporary seismic design codes, with a focus
on achieving a balance between strength, ductility, and economy.
Finite Element Analysis (FEA) is employed to assess the structural response of the
building under seismic loading conditions. Various seismic performance parameters,
including base shear, inter- story drift, and modal analysis, are evaluated to ensure the
building's ability to withstand seismic forces. Sensitivity analyses are conducted to
identify critical elements and assess the effectiveness of different seismic design
strategies.
The research also explores retrofitting techniques to enhance the seismic performance
of existing structures, providing insights for practitioners involved in the modification
of older buildings to meet contemporary seismic standards.
The findings of this study contribute to the ongoing efforts in earthquake-resistant
design, providing valuable insights for engineers, architects, and policymakers involved
in ensuring the safety and resilience of buildings in seismically active regions. The
proposed design principles and analysis methodologies aim to establish a framework
for constructing buildings that can withstand the dynamic forces associated with seismic
events, ultimately fostering safer and more sustainable urban environments.

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INTRODUCTION:
Building construction is the engineering deals with the construction of building such as
residential houses.In a simple, building can be defined as an enclose space by walls with
roof, food, cloth and basic needs of human beings. In the early ancient times humans
lived in the caves, over trees or under trees, to protect to protect themselves from wild
animals, rain, sun, etc. As the times passed as human beings started livingin huts made
of timber branches. The shelters of those old have been developed nowadays into
beautiful houses. Buildings are the important indicator of social progress of the country.
Every human has desire to own comfortable homes on an average generally one spends
his two-third life times in the houses. The security civic sense of the responsibility.
These are some few reasons which are responsible that the person do utmost effort and
spend hard earned saving in owning houses. Nowadays the house building is the major
work of the social progress of the county. Daily new techniques are being developed
for the process of construction of houses economically, quickly and fulfilling the
requirementsof the community engineers and architects do the design work, planning
and layout, etc., of the buildings.
Draughtsman are responsible for doing the drawing works of building as for the
direction of engineers and architects. The draughtsman must know his job and should
be able to follow the instruction of the engineer and should be able to draw the required
drawing of the building, site plans and layout plans etc., as for the requirements. A
building frame consists of number of bays and story. A multi-story, multi-panelled
frame is a complicated statically intermediate structure. A design of R.C building of
G+3 story frame work is takenup. It is residential complex. The design is made using
software on structural analysis design (ETABS).
The building subjected to both the vertical loads as well as horizontal loads. The vertical
load consists of deadload of structural components such as beams, columns, slabs etc.
and live loads. The horizontal load consists of the wind forces thus building is designed
for dead load, live load and wind load as per IS 875. The building is designed as two-
dimensional vertical frame and analysed for the maximum and minimum bending
moments and shear forces by trial-and-error methods as per IS 456-2000.

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NEED FOR STUDY:
➢ Multi Storied Buildings have become a part of the day-to-day development. So, the
construction of the Multi Storied Buildings gained importance, their method of
constructions also gained importance.
➢ A multi-story building is a building that has multiple floors above ground in the
building.
➢ Multi-story buildings aim to increase the area of the building without increasing the
area of the land the building is built on, hence saving land and, in most cases, money
(depending on material used and land prices in the area).
➢ Buildings serve several needs of society – primarily as shelter from weather and as
general living space, to provide privacy, to store belongings and to comfortably live and
work. A building as a shelter represents a physical division of the human habitat and
the outside.
OBJECTIVE OF THE STUDY:
➢ This project describes a method of analysis and design of a multi storied residential
quarters. The scope behind presenting this project is to learn the concept of construction,
and to design an elegant, safe and durable structure with economy. The most prominent
convenient method of designing and analysing Multi Storied Building is ETABS.
➢ ETABS is one of the first software applications in the world made for the purpose of
helping the structural engineers to automate their work, to eliminate the tedious and
lengthy manual methods.
➢ ETABS is a general-purpose structural analysis and design program with applications
primarily in the building industry - commercial buildings, bridges and highway
structures, industrial structures,
➢ The interfaces with AutoCAD to provide design drawings are some of the highlighting
features this project. The Main advantage of displaying the drawing in auto cad is the
user has more flexibility to the detailing drawing Auto CAD as per his decision. The
total design and analysis is done by ETABS student version.

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EARTHQUAKE:
➢ Vibrations of earth’s surface caused by waves coming from a source of disturbance
inside the earth are described as earthquakes.
➢ Earthquake is a natural phenomenon occurring with all uncertainties.
➢ During the earthquake, ground motions occur in a random fashion, both horizontally
and vertically, in all directions radiating from epicentre.
➢ These cause structures to vibrate and induce inertia forces on them.
What Causes Earthquake:
➢ Tectonic activity
➢ Volcanic activity
➢ Land-slides and rock-falls
➢ Rock bursting in a mine
➢ Nuclear explosions
Characteristics Of Earthquakes:
Earthquakes are caused by the slippage of adjacent plates of the earth's crust and the
subsequent release of energy in the form of ground waves. Seismology is based on the
science of plate tectonics, which proposes that the earth is composed of several very
large plates of hard crust many miles thick, riding on a layer of molten rock closer to
the earth's core. These plates are slowly moving relative to one another, and over time
tremendous stress is built up by friction. Occasionally. the two plates slip, releasing the
energy we know as earthquakes. One of the most well-known boundaries between two
plates occurs between the Pacific plate and the North American plate along the coast of
California Earthquakes also occur in midpalates, but the exact mechanism, other than
fault slippage, is not fully understood. The plates slip where the stress is maximum,
usually several miles below the surface of the earth. Where this occurs is called the
hypocentre of the earthquake. The term heard more often is the epicentre, which is the
point on the earth's surface directly above the hypocentre. When an earthquake occurs,
complex actions set up. One result is the development of waves that ultimately produce
the shaking experienced in a building. There are three types of waves: P (pressure
waves), S (shear waves), and surface waves. Pressure wave cause a relatively small
movement in the direction of wave travel. Shear waves produce a sideways or up-and-

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down motion that shakes the ground in three directions. These are the waves that cause
the most damage to buildings. Surface waves travel at or near the surface and can cause
both vertical and horizontal earth movement. The ground movement can be measured
in three ways: by acceleration, velocity, and displacement. All three occur over time,
with most earthquakes lasting only a few seconds. It is the acceleration of the ground
that induces forces on a structure. The interaction of the various waves and ground
movement is complex. Not only does the earth move in three directions, but each
direction has a different, random acceleration and amplitude. In addition, the movement
reverses, creating a vibrating action.
The soil structure interaction:
It is conventionally considered to be beneficial for the seismic response of a structure.
The soft soil debris could remarkably extend the occurrence of seismic waves and that
increment in natural period of architecture might result to resonance with extended
surface vibration period. The perpetual deformity and degradation of soil may further
exasperate architectural seismic reaction. When Earthquake excitation happens in a
structure, it connects with the foundation and the soil and thus leads to a change in the
movement of the ground surface. Soil-Structure Interaction generally can be
distinguished into two phenomena: inertial and kinematic interaction. The ground
movement due to earthquake results in soil rearrangement which is called as free- field
motion. Nevertheless, the foundation fixed into the soil does not ensue the free surface
motion. This inefficiency of the foundation in matching the free surface motion causes
the kinematic interaction.
Contrarily, Inertial interaction is defined as the mass of the superstructure which imparts
the mechanical force to the soil leading to the further deformity in the soil. Kinematic
effect being more dominant at low level of ground shaking results in the extension of
period and increment in the emission damping. Nevertheless, it is inertial interaction
becomes predominant with the commencement of stronger vibration, the soil modulus
deterioration and soil pile gaping limit radiation damping causing bending strains and
enormous movement fixed near the ground level which results in pile damage
earthquake effects on deep and shallow foundations are accounted for by designing
them structurally to ensure serviceability and provide necessary strength.
Strength considerations primarily involves ensuring that the loads on foundation remain
well below the allowable bearing capacity specified under seismic conditions and the
serviceability of foundation is ensured by designing the substructure as per the
estimated permanent ground deformation. The responses of the structures during an
earthquake are usually analysed assuming that the foundations are rigidly fixed at their
base. Such analyzation generally anticipates overturning moment at the base that
transcends the maximum allowable overturning resistance because gravity force,
meaning that a part of mat foundation would occasionally exhilarate during an
earthquake.

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The nonlinear behaviour of shallow foundations during excessive amplitude
earthquake-induced loading can disperse the seismic energy by the soil yielding
mechanism underneath the foundation. The upliftment along with the yielding causes
extreme fugitive and enduring deformities such as sliding, rocking and settlement.
Structures that are sufficiently designed opposing the dynamic loads amid an
earthquake will have the momentous prospect of seismic failure because of enormous
perpetual ground movements due to surface fault wreckage. Subsidiary fractures also
add significantly to the comprehensive devastation due to enormous ground
movements, and these are placed at comparatively large distances from the position of
the central element of the fault fracture.
Design features of safety against earthquake:
In order to withstand the impacts of earthquake, a building must be able to redistribute
the forces that travel through the structures. There are a several important design
features that provide this stability:
Diaphragms:
A diaphragm is a structural element – typically horizontal – that transmits lateral loads
to the vertical resisting elements of a structure. Examples of diaphragms are the floors
and roofs. Earthquake-resistant buildings place these elements on their own deck and
are strengthened horizontally, allowing them to share force loads with vertical elements
of the structure.
Shear Walls-
These vertical design elements are used to resist in-plane lateral forces. These walls
help resist the swaying forces of earthquakes by stiffening the frame of the building.
Cross-Bracing-
A cross-bracing system features diagonal supports that intersect. This can be
accomplished by a variety of columns, braces, and beams that aim to transfer the seismic
loads back to the ground.
Trusses-
Trusses are used to add strength where the diaphragms are weakest. These are
commonly diagonal structures that fit into rectangular angles of the frame.

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Moment-Resisting Frames:
An assembly of beams and columns in which those beams are flexible, but are rigidly
connected to the columns. The resulting frame provides resistance to lateral forces
through the flexible movement in the columns and beams while the joints and
connectors remain rigid
The type of renovation and extent of the process will depend on the structure itself –
such as whether it’s a soft-story building or concrete. The process will likely include
the installation of a steel frame to prevent excessive swaying, which can lead to
collapse. These frames are installed not for weight-bearing support, but to stabilize the
building during an earthquake.
It’s important that the frames themselves be somewhat flexible, and strategic location
of the frames can enhance their ability to absorb some of the shock of the earthquake in
order to minimize damage. Importantly, the steel frames must be secured by
foundations, which means they must be firmly connected and rooted into the ground
beneath the structure.
A seismic retrofit renovation brings your building up to the latest enforcement codes.
More importantly, renovation reduces the risk of destruction, injury or death and around
your building when next quake strikes.

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CASE STUDY:
THE BHUJ, INDIA EARTHQUAKE OF 26th JANUARY 2001:
The powerful earthquake that struck the Kutch area in Gujarat at 8:46 am on 26 January
2001 has been the most damaging earthquake in the last five decades in India. The M7.9
quake caused large loss of life and property. Over 18,600 persons are reported to be
dead and over 167,000 injured; the number of deaths is expected to rise with more
information coming in. The estimated economic loss due to this quake is placed at
around Rs.22,000 Crores (~US$5 billions).
The earthquake was felt in most parts of the country and a large area sustained damage.
About 20 districts the state of Gujarat sustained damage. The entire Kutch region of
Gujarat, enclosed on three sides by the Great Runn of Kutch, the Little Runn of Kutch
and the Arabian Sea, sustained highest damage with maximum intensity of shaking as
high as X on the MSK intensity scale. Several towns and large villages, like Bhuj,
Anjaar, Vondh and Bhachau sustained widespread destruction. The other prominent
failures in the Kutch region include extensive liquefaction, failure of several earth dams
of up to about 20m height, damage to masonry arch and RC bridges, and failure of
railroad and highway embankments. Numerous recently-built multistorey RC frame
buildings collapsed in Gandhidham and Bhuj in the Kutch region, and the more distant
towns of Morbi (~125km east of Bhuj), Rajkot (~150km southeast of Bhuj) and
Ahmedabad (~300km east of Bhuj). At least one multistorey building at Surat (~375km
southeast of Bhuj) collapsed killing a large number of people. The strong motion
records obtained from the region at the Passport Office Building under construction in
Ahmedabad city, indicate a peak ground acceleration of about 0.11m/s.
Seismological aspects and tectonic setting:
The region of Kachchh is a seismically active region lying in the western continental
margin of the Indian subcontinent. It can be viewed as a transition zone between the
stable continental region of peninsular on the south and active plate margins on the
north and east. Along the northern plate boundary, the Indo-Australian plate is pushing
against the Eurasian plate. The boundary between the Arabian plate and the Indo-
Australian plate lies to the east. The epi-centre of the January 26 earthquake is located
at a distance of about 400 km from the junction of the three plates.
The Kachchh region is traversed by a number of east–west tending faults, including the
Katrol Hill fault, Kachchh Mainland fault, Banni fault, Island Belt fault, and the Allah
Bund fault. Historically, a number of earthquakes of varying magnitudes have occurred
along or in the vicinity of these faults (Malik et al. 2000). The largest of these was the
earthquake of June 16, 1819, having a moment magnitude Mw 7.8. That earthquake

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caused the formation of an east– west alluvial scarp, about 90 km long and 9 m high. It
dipped quite steeply south face, but more gently along the north face. The scarp blocked
the southeast flowing tributary of Indus known as Nara and was given the name Allah
Bund, or the Dam of the God, by the local people. Allah Bund earthquake took place in
a sparsely populated and caused the death of between 1500 and 2000 people. The other
large earthquake in the Kachchh region occurred in 1956. This earthquake, known as
the Anjar earthquake, had a moment magnitude Mw 6.1, and its epicentre was located
along the Katrol Hill fault.
Performance of reinforced concrete frame buildings:
A large number of reinforced concrete frame buildings located in Ahmedabad suffered
serious damage or collapsed. As stated earlier, Ahmedabad is about 300 km from the
epi-centre. At such a distance the intensity of ground motion would not be expected to
be large. The fact that a number of buildings in Ahmedabad suffered damage could be
attributed to several factors. Many buildings were founded on deep sediments deposited
by the Sabarmati River. This may have amplified the ground motion experienced by
such buildings.
Another important factor contributing to the damage was the use of open first story
combined with poor detailing and in- different quality of construction. Almost all
buildings with open first story suffered some damage. In some cases, the buildings
collapsed, while in some others the damage was so severe that the buildings had to be
written off. At the time of our visit, which is about 7 weeks after the earthquake, the
rubble from the collapsed building had been cleared but the severely damaged buildings
had not been pulled down.
Repair work was in progression some of the private buildings that had suffered
repairable damage. A typical example of a framed building with open first story is
shown in Fig , which shows what was once a complex of four identical five-story blocks.
Each block had a reinforced concrete frame construction with an open first story and
brick infill walls in upper stories. Two of the four blocks, which were located in the
foreground the picture, completely collapsed killing several residents. The other two
blocks that are seen standing the picture suffered severe damage. The owners have
decided pull them down. Temporary supports have been provided to the buildings in
their lowest story so that the useful contents of the buildings could be salvaged. Figures
show details of the damage suffered by the first-story columns.

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Codal Provisions For Structural Planning:
with respect to, IS 456: 2000 and IS 13920:2016
Sizing of elements; as per
For Floor Slabs: Clause 23 and 24 of 456: 2000
For Beams: Clause 6 of 13920: 2016 and Clause 23 of 456: 2000
For Columns: Clause 7 of 13920: 2016
Slab – Preliminary Sizing
Slab, Preliminary Dimensions as per Deflection Point of view by
𝑙
𝑑
ratio as per Cl.24.1
Lx= 40× 0.8
3.24
𝑑
=32
d = 0.102 m = 102 mm (effective depths)
D = d +
∅
2
+ clear cover
Hence, Providing Preliminary Sections for Analysis and Design
Floor Slab (D) = 125 mm;
Staircase Waist Slab (D) = 250 mm

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Beam – Preliminary Sizing:
Beam, Preliminary Dimensions as per Clause 6 of 13920: 2016 and Clause 23 of 456:
2000
Clause 23 of 456: 2000
𝑙
𝑑
=26
4.74
𝑑
=26
d = 0.183 m
Clause 6 of 13920: 2016
as per Cl.6.1.1 :
𝑏
𝑑
> 0.3
as per Cl.6.1.2 : Width (b), should not less than 200 mm
as per Cl.6.1.3 : D <
1
4
× Clear Span
Primary Beam=240mm×325 mm (b×D); Secondary Beam=240mm×250mm(b×D);
Plinth Beam = 240 mm×250 mm (b×D);
Column – Preliminary Sizing:
Column, Preliminary Dimensions as per Clause 7.1.1 of 13920: 2016
Minimum Dimension of a Column shall not be less than,
(1) 20×db =20×12 = 240 mm
(2) 300 mm
Columns = 350 mm × 350 mm (b×D) &
375 mm × 375 mm (b×D)
Structural Planning:
Preliminary Sizing of elements with M25 Grade Concrete
Floor Slab = 125 mm; Staircase Waist Slab = 250 mm
Primary Beams = 240 mm × 325 mm (b ×D); Secondary Beams = 240 mm × 250 mm (b ×D)
Plinth Beam = 240 mm × 250 mm (b ×D)
Columns = 350 mm × 350 mm (b ×D) & 375 mm × 375 mm (b ×D)

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LOAD CALCULATIONS:
(1) Dead Load (Load Pattern: Dead)
Dead Load of Columns, Beams, Slabs are considered by software ETABS itself because
we input material properties with respect to unit weight & density and assigned Dead
load Pattern as self-weight multiplier 1 & property modifier of weight is 1.
(2) Super -Imposed Dead Load (Load Pattern: Super Dead) as per IS 875-Part1: 1987
1. Load intensity for 10 mm thick mortar is 0.21 KN/m2
but for 50 mm thick mortar
is to be; 0.21×5=1.05 KN/m2
for below flooring.
2. Ceiling plaster (6 mm) =0.21×0.61=0.126 KN/m2
3. Clay floor Tiles of 12.5 mm =0.12 KN/m2
for floor tiles excluding terrace SIDL
is, 1.05+0.126+0.12=1.296 KN/m2
4. Thickness of water proofing =125 mm, Density of water proofing course =22
KN/m2
. Load intensity of Water proofing course =0.0125×22=2.75 KN/m2
∴For terrace SIDL is:
2.75+0.125=2.876 KN/m2
5. Unit weight of concrete =25 KN/m3
6. Unit weight of floor finish =23.5 KN/m3
7. Load of steps=1/T× (R×T)/2× Unit weight of concrete
=1/291.11×(0.162×29.11)/2×25
=2.03 KN/m3
8. Load of floor finish step=(thickness of floor finish ×T)/T× Unit weight of floor
finish
= (0.020×0.2911×23.5)/0.2911
= 0.47 KN/m2
For steps of stairs: 2.03+0.47=2.50 KN/m2

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(3) Live Load (Load Pattern: Live) as per IS 875 Part-2 :1987
Live Load intensity as per type of room for residential building as;
Living Room = 2 KN/m2
Table 1-1. a.1
Kitchen = 2 KN/m2
Table 1-1. a.1
WC & Bath = 2 KN/m2
Table 1-1. a.2
Balcony = 3 KN/m2
Table 1-1. a.3
Bed Room = 2 KN/m2
Table 1-1. a.1
Passage = 3 KN/m2
Table 1-1. a.3
Stairs = 3 KN/m2
Table 1-1. a.3
Terrace = 1.75 KN/m2
Table 1-1. i. a
Terrace = 0.75 KN/m2
Table 1-1. i. b
(access not provided for maintenance)
(4) Wind Load (Load Pattern: Wind) as per IS 875 Part-3 :2015
Here in software ETABS we are not defining load pattern directly as per directly IS
875(Part 3):2015 because by inputting Cpi and Cpe values we don’t get to know what
is wind load before analysis so here we are calculating wind load as per IS 875(Part
3):2015 & apply the load as per story height w.r.t. different conditions & parameters.
Dimensions of Building:
a) Length of building in x direction =17.105 m
b) Length of building in y direction =10.965 m
Design wind speed (Vx)=VbxK1xK2xK3
Where Vb=44 m/s … Annex A
K1=Risk coefficient =1.0 Cl.6.3.18 & Table 1 (General Building)
K2=Height factor Cl.6.3.2 & table 2
K3=Topography factor =1.0 (plain terrain)
K4=Importance factor, for cyclonic regions = 1.0 Cl.6.3.4
For each story Vx is calculated as
Vx= VbxK1xK2xK3K4
Vx=(44)×(1)×(K2)×(1)×(1)
Vx=44×K2
Design Wind pressure (pz)=0.6×Vz2
Wind pressure (pd)=Kd×Ka×Kc×pz
Were,
Kd=Wind directionality factor =0.9 (for regular shape) cl.7.2.1
Ka=Area averaging factor = 0.8 (for RCC Frame structure) cl.7.2.2
Kc=Combination factor =0.9 (for RCC Frame structure) cl.7.2 & cl.7.3.3
The value of Pd however shall not be less than 0.70 pz cl.7.2

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Pd= Kd×Ka×Kc×pz
Pd=0.9×0.8×0.9pz = 0.648 pz ≥ 0.70pz
The value of Pd is calculated for each story
Calculating the value of CF …
Here our building dimensions;
a) for wind in x-direction
a/b ratio is 1.55
where h/b ratio is1.57≥1
hence, we are using 4.a of IS 875:2015(part 3)
cf=1.15
b) for wind in y direction
a/b ratio is 0.64
where h/b ratio is1.008≥1
hence, we are using 4.a of IS 875:2015(part 3)
∴cf =1.3
Wind force=F=cf.Pd.B.H
Were,
B=Dimension along wind need to
H=effective height
Similarly, for all story wind load is calculated in both directions.
(5) Earthquake Load (Load Pattern: Seismic) as per IS 1893 (Part 1)-2016
Location of structure: Mumbai
a) Seismic Zone: III
b) Soil type Medium or stiff soil
c) Site type II
d) Zone factor =0.16 (Zone III)
e) Response Reduction factor of a building System: RC Building with special
moment resisting frame (SMRF); R=5… Table 9.i.b
f) Percentage of imposed Load to be considered in calculation of seismic weight.
LL is up to 3 KN/m2
hence 25% imposed load is considered in seismic weight
cl.7.3.1 and table 10.
g) Approximate fundamental translation natural period (Ta) of oscillation cl.7.6.2.c

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H=16.250 m
Dx=17.105 m
Dy=10.965 m
a) Ta along x direction: natural period
Tax=0.09h/√d
Tax =0.09x16.25/√17.105
Tax=0.3536 s
b) Ta along y-direction: natural period
Tay=0.09h/√d
Tay=0.09×16.25/√10.965
Tay=0.4417 s
h) Importance factor =1.2
(6) Wall Load -SIDL(Super Imposed Dead Load):
here, structural details
story height = 3.25 m
primary beam = 240mm×325mm -M25
secondary beam = 240×250 mm - M25
width of wall = 240 mm of masonry wall
for construction we will use AAC Block
∴Properties of Material:
Unit weight of AAC block =6 kN/m
Compressive strength of AAC block=4N/mm2
Unit weight of plaster =20 KN/m3
1. Internal wall under primary beam:
Depth of wall =3.25-0.325=2.925 m
Weight per meter run AAC block=0.24×2.925×6=4.212 KN/m
Weight per meter run for plaster=2×0.020×2.925×20=2.34 KN/m
Total weight of wall per meter run =4.212+2.34=6.552 KN/m
2. Internal wall under secondary beam:
Depth of wall =3.25-0.25=3 m
Weight per meter run AAC block=0.24×3×6=4.32 KN/m
Weight per meter run for plaster=2×0.020×3×20=2.4 KN/m

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3. Wall under staircase secondary beam:
Depth of wall =3.25/2 -0.25=1.375 m
Weight per meter run for plaster= (0.020+0.025)1.375×20
=1.2375 KN/m
∴Total weight of wall per meter run =1.98+1.2375
=3.218 KN/m
4. Wall under staircase primary beam:
Depth of wall =3.25/2-0.325=1.3 m
Weight per meter run for plaster=(.020+0.25)1.3×20=1.17KN/m
5. External wall:
Depth of wall =3.25-0.325=2.925 m
Weight per meter run for plaster= (0.0025+0.020) ×2.925×20=
2.63 KN/m
6. Wall for Head Room:
Depth of wall =3.25-0.325=2.925 m
plaster= (0.0025+0.020) ×2.925×20=2.63 KN/m
7. Parapet wall on Terrace:
Depth of wall =1.25 m
Weight per meter run for plaster= (0.025+0.020) ×1.25×20=
1.125 KN/m
Total weight of wall per meter run =2.925 KN/m

18 | P a g e
DESIGN OF BEAM:
Beam at 1st Floor
ETABS Label No. B1 and B6
Beam No :1
From analysis we have,
For label B1
Mu1=44.2625 KNm
Mu2=25.0931 KNm
SFma×=54.4429 KN
For label B6
Mu1=44.2739KNm
Mu2=25.0621 KN-m
Mu3=54.4281KN-m
∴For Beam No.1 ;we consider
Mu1 =44.2739 KN-m
Mu2 =25.0931 KN-m
Negative B.M. (Hogging)
Positive B.M. (Sagging)
Max. Shear Force
Where,
Beam No.1 :
Size=240 mm × 325 mm
Concrete:M25 ∴fck =25 N/ mm2
Steel: Fe 415 ∴fy =415 N/ mm2
Finding Ast
From, Annex G-G.1.1.(b) of IS 456:2000
Mu = 0.87 fyAstd [1-
𝑓𝑦𝐴𝑠𝑡
𝑓𝑐𝑘 𝐵𝑑
]
For UR Section
Where,
d=effective depth of beam
d=325-25-8-12/2
d=286 mm
Mu2=25.0931 KN-m
25.0931=0.87×415×Ast ×286(1-(Ast × 415)/(240×325×25))
∴Ast=257.07 mm2
Xulim/d=0.48 (CL.38.Note of IS 456:2000)
But,
Xu/d=0.87fyAst/0.36fckbd AnnexG:G.1.1.a
Xu/d=0.87×415×257.07/0.36×25×240×286
Xu/d=0.15
Xu/d<Xulim/d ∴Ok
Section is UR

19 | P a g e
Astmin=0.85×bd/fy Cl.26.5.1.1 of IS 456:2000
Astmin=0.85×240×286/415
Astmin= 140.5879 mm2
∴Astmin <Ast ∴Ok
No of bars of 12 mm dia. =Ast/(π/4)122
=257.07/(π/4)122
No. of bars of 12 mm dia. =2.27~=3
∴Provide 3# 12 mm dia. bars
∴Ast provided=π/4×122 ×3 =339.29 mm2
Finding Shear Reinforcements:
Tv =Vu/bd Cl.40.1 of IS 456:2000
Tv= 54.4429 ×103
/240 ×286
Tv=0.79 N/mm2
∴Nominal shear stress coming on the beam is 0.79 N/mm2
From table 19 of IS 456:2000
Design shear strength of concrete (Tc):
100 Ast/bd= 100×339.29/240×286 =0.49 %
From table we obtain the value of Tc = 0.4848 N/mm2
Here, Tv> Tc
∴need to design the shear reinforcements From cl.40.4
Vus=0.87fy.Asv.d/Sv
Where,
Vus=Vu- Tc.bd
=54.4429×103-(0.4848×240×286)
=21151.328 N
=21.151 kN
Considering,2 legged stirrups of 8 mm dia.
21151=0.87×415×(π/4×82×2)×339.29/Sv Sv=582.23 mm
But as per Cl.26.5.1.5 of IS 456:2000 Max. spacing of Shear reinforcement
Svmax=0.75d or 300 mm Svmax=0.75×(286) or 300 mm
Svmax= 214.5 mm or 300 mm
Provide 2 legged stirrups of 8 mm dia. @ 200 mm c/c distance

20 | P a g e
Finding Area of steel at support
From, Annex G-G.1.1.(b) of IS 456:2000
Mu = 0.87 fyAstd [1-
𝑓𝑦𝐴𝑠𝑡
𝑓𝑐𝑘 𝐵𝑑
]
For UR Section d=286 mm
Mu1=44.2652 kN-m
44.2652×106=0.87×415×Ascs×286×(1-Ascs×415/240×325×25)
Ascs=477.123 mm2
Xulim/d=0.48 (CL.38.Note of IS 456:2000) But,
Xu/d=0.87fyAscs/0.36fckbd AnnexG:G.1.1.a
Xu/d=0.87×415×477.123/0.36×25×240×286 Xu/d=0.269
Xu/d<Xulim/d ∴Ok
Section is Under-Reinforced
Astmin=0.85×bd/fy Cl.26.5.1.1 of IS 456:2000
Astmin=0.85×240×286/415
Astmin= 140.5879 mm2
Astmin <Ast Hence Ok
No of bars of 12 mm dia. =Ascs/(π/4)122
=477.123/(π/4)122
No. of bars of 12 mm dia. =4.21~=5 Provide 5# 12 mm dia. bars
Ast provided=π/4×122 ×5 =565.46 mm2
Detailing:

21 | P a g e
fy 415 N/mm2
Moment(Mu kNm) Shear(kN) Torsion(kNm) Slab Torsion = 0 kNm
fck 25 N/mm2
44.2739 54.4429 0 Axial Force = 0.0 kN
240 mm Area of Steel = 0.0 mm
2
325 mm
25 mm 12 mm
8 mm 232.6663611 mm
1 4.297999914
12 mm
1
12 mm Ast 486 Asc 0
286 mm Ast (mm2) = 486 →pt= 0.71%
SINGLY
REINFORCED
Rebar Dia. 12 12
39 mm Asc (mm2) = 0 →pc= 0.00% No of Bars 4.295810966 0
0.136 Extra Asc (mm2) = 0 Spacing 44.22913427 #DIV/0!
2.255 Ast (min) = 140.5879518
44 kNm EXACT by Area
68 kNm Ast Provided 486 mm2 100.5312
Sv = 171 mm 16
(C/S Area 2 Legged
Closed Hoop) Asv
0 mm2 654.0206257
(Total Area of Shear
Reinforcement) Asv
mm2 214.5
Design of Beam as per IS 456:2000
Breadth of Section b =
Depth of Section D =
Clear Cover = Dia of Bar =
Spacing =
Dia. of Strirrup ds =
No. of Tension Reinf. Layers = No of Bars =
Dia of Tension Rebar =
No. of Comp. Reinf. Layers
Vertical Stirrups by Spacing
Area of Stirrup Legs, Asv
Dia of Comp Rebar =
Effective Depth, d =
d' =
d'/d =
Mu/bd2 =
Me1 =
Mu,lim =
Vus (kN)
Sv Required
Sv Provided

22 | P a g e
DESIGN OF ISOLATED FOOTING:
ETABS Label No. : 1 and 8
Footing No. 1
Factored Load (Pu)
For label No. 1 =446.6087 KN
For label No. 8=450.3779 KN
Hence, here for Footing No. 1 taking
Pu=450.3779 KN
SBC of Soil=400 KN/m2
(qc)
Depth of Footing=1 m
Diameter of bar=12 mm
Grade of concrete =M 25 ∴ fck=25 N/mm2
Grade of steel=Fe 415 ∴fy=415 N/mm2
Area of Footing Required (Afreq.)
= (P+10% of P)/qc
= 300.25+(0.1×300.25)/400
=0.8275 m2
Size of Footing : (Dimensions)
∴Af=B×L
0.8257=L×L
L=0.9086 m
Area of footing provided = 0.95 m × 0.95 m
i.e., 0.9025>0.8257
∴Ok
Depth of Footing (Based on One-way Shear):
Factored Soil Pressure=q=Pu/Area of footing provided
=450.3779/0.95×0.95
=0.499033 N/mm2
Design shear strength of concrete:
Tc=0.36 N/mm2
assuming Pt=0.25% ((Ast/bd)×100))
from table 19 of IS 456:2000

23 | P a g e
V=q×L×[(L-a)/2-d] -(i)
V=Tc×d×L -(ii)
Equating eq (i) and (ii),we get
d=q[(L-a)/2]/(Tc+q)
d=0.499033[(0.95-0.35)/2]/(0.36+0.499033)
d=0.176 m
∴effective depth of footing is 176 mm
Check for Two-way shear:
Factored SF=q[L2
-(a+d)2
]
=0.499033[9502
-(350+176)2
]
=312.30682 KN
Shear stress of concrete=0.25√fck
(As per cl.31.6.3.1 of IS 456:2000)
Tc=0.25√25
Tc=1.25 N/mm2
∴Shear resistance of concrete:
=4(a+d)×d×Tc
=4(350+176)×176×1.25
=462.88 KN
∴Shear resistance of concrete>Factored shear force
∴footing is safe in Two-way Shear
Thickness of Footing= Effective depth of footing +clear cover +dia. of cover +dia. of
bar +dia.of bar/2
= 176 +50+12+12/2
=244 mm ~= 250 mm Area of steel Reinforcement:
Mu at X-X = q[(L×(L-a)/2×(L-a)/2)/2)]
= q[L×(L-a)2/8]

24 | P a g e
= 0.499033[950×(950-350)2/8]
= 21.33366 KNm
And,
Mu=0.87fy.Ast.d(1-(Ast.fy)/(b.d.fck))
Where, Mu=max BM
Fy=steel grade=415 N/mm2
Ast=Area of steel
d=effective depth of footing=176 mm fck=25 N/mm2
b=width of footing=950 mm
21.333×106=0.87×415×Ast ×176(1-(Ast × 415)/(176×950×25)) Ast=347.731 mm2
Where as per clause 26.5.2.1 of IS 456:2000 For HYSD bars
Astmin=0.12%bD Astmin=0.12/100×950×250 Astmin=285mm2
Ast taken into consideration is 347.731 mm2
Spacing=L-2×clear cover-dia.of cover/(No. of bars-1)
=950-2×50-12/(347.731/π/4×122)-1
=403.92 mm >300 mm
But as per cl.26.3.3.b.1 of IS 456:2000
Spacing ≤300mm
Spacing ≤3 × effective depth of slab Hence spacing provided =300mm
∴provide reinforcement
12 mm dia. bar @ 300 mm c/c
Detailing:

25 | P a g e
Load: P (Factored) 450.3779 KN
Servce Load: P 300.25
Concrete Fck 25 N/mm2
Steel Fy 415 N/mm
2
Dia. Of Rebar 12 mm
Width of Column for Foorting 350 mm
qc (SBC) 400 KN/m2
Depth of Footing 1 m
Footing Size 0.9100 × 0.9100 m
Footing size(Provided) 0.95 × 0.95 m
0.50 N/mm2
Assume p=0.25%
𝜏c 0.36 N/mm2
Effective depth of footing 174.28 mm
Factored SF 313.2101436 kN
Shear strength of concrete 1.25 N/mm
2
Shear Resistance 456.8483004 kN
Safe
Gross bearing pressure 318.93 kN
Safe
Mu 21.33369 kN.m
a= 172225
b= -1717721030
c= 582676408125.00
solution= 9622.09279
351.6103903
Area of Steel 351.61 mm
2
Min. Ast 285 mm
2
Area of Steel(Provided) 351.61 mm2
Spacing 397.30 mm
Spacing(Provided) 300 mm
Thickness of Footing 242.28 mm
Thickness of Footing (Provided) 250 mm
Bending Moment
(From IS 456, 26.5.2.1)
should not be greater than 300mm
Isolated Square Footing Design as per IS 456:2000
Check for Two Way Shear
Gross Bearing Capacity
Assuming unit weight of concrete and soil as 24 kN/m3
and 20 kN/m3
Assuming wt. for footing+backfill = 10% of P
Check for Depth Based on One Way Shear
Factored soil pressure
(From IS 456, Table 19)

26 | P a g e
Footing No. Dimensions (in meter) Thickness (in milimeter) Reinforcements in Both Directions
1 0.95 × 0.95 250 12mm dia. @300mm c/c
2 1.00 × 1.00 275 12mm dia. @300mm c/c
3 1.15 × 1.15 300 12mm dia. @250mm c/c
4 1.15 × 1.15 300 12mm dia. @250mm c/c
5 0.90 × 0.90 250 12mm dia. @300mm c/c
6 1.25 × 1.25 350 12mm dia. @200mm c/c
7 1.50 × 1.50 425 12mm dia. @150mm c/c
8 1.25 × 1.25 350 12mm dia. @200mm c/c
9 1.15 × 1.15 300 12mm dia. @250mm c/c
10 1.00 × 1.00 275 12mm dia. @300mm c/c
11 1.50 × 1.50 400 12mm dia. @150mm c/c
12 1.55 × 1.55 425 12mm dia. @150mm c/c
13 1.15 × 1.15 300 12mm dia. @250mm c/c
14 1.15 × 1.15 325 12mm dia. @250mm c/c
Concrete Grade M25 Depth of footing 1 meter
Steel Grade Fe415 Clear Cover 50 mm
Diameter of Rebar 12 mm
Design of Footings
Notes
Reinforcement Type: Two Way Reinforcement

27 | P a g e
DESIGN OF SQUARE COLUMN:
Column at Ground Floor (From plinth level to 1st floor)
ETABS Column Label No: C1 and C6
Assign column as: Column No. 1
∴Label C1
Pu=375.4304 KN
Mux=24.5050 KNm
Muy=14.3102 KNm
Label C6
Pu=377.6548 KN
Mux=23.8559 KNm
Muy=13.3323 KNm
∴For Column No.1
Pu=377.65 KN Mux=24.5050 KNm
Muy=14.3102 KNm
Column Size= 350×350 mm Dia. of longitudinal bar=16 mm Dia. of lateral ties= 8
mm
Grade of concrete =M 25 fck=25 N/mm2
Grade of steel=Fe 415 fy=415 N/mm2
Let us assume that ,we are using # 8 bars of 16 mm dia. bars
P=π/4×162×8/(350×350)=1.31%
d’=clear cover+dia.of lateral ties+dia.of main bar/2
d’=40+8+16/2
d’=56 mm
d’/D=56/350=0.16 d’/b=56/350=0.16 p/fck=1.31/25=0.0524
Pu/(fck.b.D)=377.65×103/(25×350×350)=0.1233
From SP16;
Using chart 45: d’/D=0.15 and chart 46:d’/D=0.20
By linear interpolation:
d’/d Mu/(fck.b.d2)
0.15 0.105
0.20 0.120
For 0.16 we get 0.108
Mu×1=0.108×25×350×3502 Mu×1=115.7625 KNm
Muy1=0.108×25×350×3502 Muy1=115.7625 KNm
From section 3.3 of SP 16 Puz=0.45fckAc+0.75fyAs
Puz=[0.45×25×(350×350-π/4×162×8)]+[0.75×415×(π/4×162×8)] Puz=1860.64 KN
Pu/ Puz=377.65/1860.64=0.203

28 | P a g e
From section 3.3 of SP 16 Pu/ Puzán
≤0.2 1
≥0.8 2
By linear interpolation for 0.203 we get án =1.005 From section 3.3 of SP 16
(Mux/Mux1) án +(Muy/Muy1) án
=(24.5050/115.7625)1.005+(14.3102/115.7625)1.005
=0.3323<1
Hence OK Design is safe
Detailing Details:
Column Size (b×D)=350×350 mm Main bar= 16 mm dia. 8#
From cl.26.5.3.2.C of IS 456:2000
Pitch should not be more than the following:
(1) 350 mm
(2) 16×dia. of bar=16×16= 256 mm
(3) 300mm
Pitch of transverse reinforcement is 230 mm Dia. of ties = 8mm ≥
1
4
×16
Clear cover=40 mm
Detailing:

29 | P a g e
Data Input Data Geometry and X-axis Data Input Data Geometry and X-axis
Column No. Y-Axis, Curve d'/d; Mu/fck.b.d.d Column No. Y-Axis, Curve d'/d; Mu/fck.b.d.d
1 0.1460, 0.0526 0.20, 0.095 1 0.123, 0.0524 d'/d = 0.16; 0.108
2 0.1620, 0.0526 0.20, 0.108 2 0.147, 0.0524 d'/d = 0.20; 0.105
3 0.2110, 0.0526 0.20, 0.106 3 0.182, 0.0524 d'/d = 0.20; 0.109
4 0.1990, 0.0526 0.20, 0.103 4 0.175, 0.0524 d'/d = 0.20; 0.107
5 0.1330, 0.0526 0.20, 0.098 5 0.115, 0.0394 d'/d = 0.20; 0.090
6 0.2680, 0.0526 0.20, 0.107 6 0.235, 0.0525 d'/d = 0.20; 0.105
7 0.3070, 0.0458 0.15, 0.095 7 0.276, 0.0524 d'/d = 0.15; 0.104
8 0.2310, 0.0458 0.15, 0.106 8 0.212. 0.0524 d'/d = 0.15; 0.112
9 0.2130, 0.0526 0.20, 0.106 9 0.189, 0.0524 d'/d = 0.20; 0.109
10 0.1740, 0.0526 0.20, 0.097 10 0.164, 0.0524 d'/d = 0.20; 0.103
11 0.3040, 0.0458 0.15, 0.098 11 0.289, 0.0456 d'/d = 0.15; 0.100
12 0.3600, 0.0458 0.15, 0.085 12 0.334, 0.0456 d'/d = 0.15; 0.089
13 0.1880, 0.0458 0.15, 0.108 13 0.176, 0.0340 d'/d = 0.15; 0.088
14 0.2190, 0.0526 0.20, 0.124 14 0.193, 0.0393 d'/d = 0.20; 0.095
1 0.0880, 0.0394 0.20, 0.059 1 0.0540, 0.0394 0.20, 0.071
2 0.1070, 0.0526 0.20, 0.097 2 0.0680, 0.0394 0.20, 0.073
3 0.1330, 0.0526 0.20, 0.098 3 0.0840, 0.0394 0.20, 0.079
4 0.1290, 0.0526 0.20, 0.100 4 0.0820, 0.0394 0.20, 0.079
5 0.0850, 0.0394 0.20, 0.089 5 0.0550, 0.0394 0.20, 0.070
6 0.1720, 0.0394 0.20.0.095 6 0.1090, 0.0526 0.20, 0.098
7 0.2020, 0.0458 0.15, 0.108 7 0.1280, 0.0458 0.15, 0.099
8 0.1570, 0.0458 0.15, 0.106 8 0.1020, 0.0458 0.15, 0.097
9 0.1390, 0.0526 0.20, 0.099 9 0.9000, 0.0394 0.20, 0.079
10 0.1270, 0.0526 0.20, 0.097 10 0.0880, 0.0394 0.20, 0.078
11 0.2100, 0.0458 0.15, 0.108 11 0.1210, 0.0458 0.15, 0.098
12 0.2260, 0.458 0.15, 0.107 12 0.1280, 0.0458 0.15, 0.100
13 0.1350, 0.0458 0.15, 0.099 13 0.0940, 0.0458 0.15, 0.094
14 0.1430, 0.0526 0.20, 0.097 14 0.0920, 0.0394 0.20, 0.079
1 0.0220, 0.0394 0.20, 0.062 10 0.0200, 0.0394 0.20, 0.060
2 0.0290, 0.0394 0.20, 0.064 12 0.0230, 0.0343 0.15, 0.055
3 0.0350, 0.0394 0.20, 0.065 13 0.0160, 0.0343 0.15, 0.052
4 0.0350, 0.0394 0.20, 0.065
5 0.0240, 0.0394 0.20, 0.063
6 0.0460, 0.0394 0.20, 0.068
7 0.0550, 0.0343 0.15, 0.065
8 0.0470, 0.0343 0.15, 0.064
9 0.400, 0.0394 0.20, 0.068
10 0.530, 0.0394 0.20, 0.070
11 0.0490. 0.0343 0.15, 0.063
12 0.0630, 0.0343 0.15.0.069
13 0.0560, 0.0343 0.15, 0.067
14 0.0410, 0.0394 0.20, 0.069
Column at Footing to Plinth Level Column at Ground Floor to 1st Floor
Column at 1st Floor to 2nd Floor Column at 2nd Floor Floor to 3rd Floor
Column at 3rd Floor Floor to Terrace Column at Terrace to Head Room

30 | P a g e
Pu (KN) Mux (KNm) Muy (KNm) Fy (N/mm2)
377.6548 24.505 14.3102 415
Steel % (Assume) 1.31 % Fck 25
p/Fck 0.0526 d' 56
d 350 in mm
d'/d and d'/b 0.16 0.16 b 350 in mm
Pu/fckbd 0.1230
Mu/fck bdd 0.1080 Chart 1 Chart for d'/D = 0.16
Mu/fck dbb 0.1080 Chart 2 Chart for d'/b = 0.16
Mux1 0.1080 1071.875 115.7625 I
Muy1 0.1080 1071.875 115.7625 II
puz 1861.0434
pu/puz 0.20292638
0.0048773 &n = 1.0048773 &n = 1 if pu/puz <=0.2
&n = 2 if pu/puz >=0.8
0.21 0.12
0.210086420743885 0.122362853887357 0.3324 Ast
O.K. 1609.728 mm2
Dia of bar 16 Numbers
Number of bar 8 mm
Ast 1609.728 mm
2
Square Column Design as per IS 456 and SP 16
Clear Cover = 40mm
(SP16 Pg.130 and 131)
(SP16 Pg.130 and 131)
Noumber of Rebars and Diameter of Bar Provided

31 | P a g e
Staircase Architectural Calculation For Planning & Comfortability
Checks:
Storey Height = 3250 mm
Height of one flight = 3250/2=1625 mm Here, considering 10 no. of risers in one
flight Riser depth=height of one flight/no. of risers
=1625/10
=162.5 mm
No. of tread=No. of risers -1
=10-1
=9
Tread length=clear distance/no. of tread
=2620/9
=291.1 mm ~=290 mm Riser =162.5 mm (R) Tread=291.11 mm (T)
For comfort; check
2R+T should be in between 550 mm & 700 mm Here,2R+T =(2×162.5)+291.11
=616.11 mm
Hence, 550 mm <616.11 mm <700 mm
i.e., it indicates that normal relationship in R & T
Angle of stair = height of one flight / clear distance between two flights
=1625 / 2620
=31.81‫﮲‬
Hence, angle of stair is in between 30‫﮲‬ to 35‫﮲‬ which is most preferable and
comfortable.
DESIGN OF STAIRCASE:
General Details:
Floor to floor height=3.25 m Height of one flight=1.625 m Depth of Riser=162.5 mm
Length of tread=291.11 mm
Materials used:
Grade of concrete =M 25 fck=25 N/mm2
Grade of steel=Fe 415 fy=415 N/mm2
No. of Risers=10 No. of Treads=9
Depth of waist slab=250 mm (D); d=224 mm Width of one flight=1200 mm
Effective span=4.74 m Loading:

32 | P a g e
(i) Dead Load
Computed by software itself for analysis. DL=(WB)×(unit wt. of RCC)/T
=(0.33339×0.25×25)/0.29111
=7.157 KN/m/m width
(ii) Super imposed dead load SIDL=RT/2× (unit wt. floor finish)/T
=(0.1625×0.2911)/2×23.5/0.29111
=1.909 KN/m/m width (iii)Live load
LL=3KN/m/m width of stairs (as per IS 875 Part 2: 1987 Table 1-1.0.3)
Design load=1.5(DL+LL+SIDL) Wu=1.5(7.15+3+1.907)
Wu=18.096 KN/m/m width of stairs Bending Moment:
Max. BM(Mu)= Wul2/8=(18.096 ×4.742)/8
=50.8217 KNm
Mulim=0.138fck.b.d2
cl.38.1.Note of IS 456:2000
Mulim=0.138×25×1000×2502
Mulim=215.625×106 Nmm
Here,Mulim>Mu
Therefore section is under-reinforced
i.e. value of xu/d is less than the limiting value as per cl.38.1 Note of IS 456:2000
From Annex G-G.1.1.(b) of IS 456:2000 Mu=0.87fy.Ast.d(1-(Ast.fy)/(b.d.fck))
50.8217×106=0.87×415×Ast ×250(1-(Ast × 415)/(1000×224×25))
Ast=588.7 mm2
Where as per clause 26.5.2.1 of IS 456:2000 For HYSD bars
Astmin=0.12%bD ×Astmin=0.12/100×1000×250 × Astmin=300 mm2
As per cl.26.3.3.b.1 of IS 456:2000 (i)Spacing ≤300mm
(ii)Spacing ≤3 × effective depth of slab=3×(250-20-12/2)=3×224=672 mm
Hence spacing provided =300mm
Spacing for Main steel
Dia. of bar used for main steel=12 mm
Spacing for main steel = =(
𝜋
4
×122×1000)/588.7)
=192.11 mm ≈175 mm Ast provided
=(
𝜋
4
×122×1000)/175)=646.27 mm2
Pt = (646.27×100)/(1000×224)
=0.2885

33 | P a g e
Distribution Steel:
Astmin is provided as distribution steel =300 mm2
Spacing for distribution steel:
12 mm dia. bars are provided as distribution steel Spacing=(
𝜋
4
×122×1000)/300)
=376.99 mm ≈350 mm.
Check for spacing for distribution steel :(Cl.26.3.3.b.2)
Max. spacing is lesser of:
(i) 5d=5×224=1120 mm
(ii) 450mm
Provided spacing is less then the maximum spacing Hence OK
Check for shear:
Vu=Wul/2 Vu=(18.096×4.74)/2 Vu=42.88 KN
As per Cl.40.1 of IS 456:2000
Nominal shear stress=Tv Tv=Vu/bd Tv=42.88×103/1000×(250-12/2-20) Tv=0.19143
N/mm2
As per clause cl.40.4 and Table 19 Pt=0.2885
Concrete Grade =M25
Pt Tc
0.25 0.36
0.50 0.49
By linear interpolation for Pt=0.2585 ,the value of Tc is 0.38002 Tv<Tc
0.19143<0.38002
Check for shear is O.K.
Check for Deflection:
Here ,L=4.74 m
d=0.25m L/d=4.74/0.25=18.96
Pt=0.2585
As per clause 23.2.1 of IS 456:2000 For continuous slab; L/d=26
From fig.4 of IS456:2000 fs=0.58×(Ast req/Ast prov.)×fy×fs=0.58×585/646.27×415

34 | P a g e
fs=217.88 N/mm2
for fs =217.88 N/mm2
& Pt=0.2585 Modification factor =1.85 Allowable L/d=MF×26
Allowable L/d=1.85×26 Allowable L/d=48.1 Hence ,18.96<48.1
Provided L/d<Allowable L/d
Safe, Hence check for deflection is OK
All Checks are satisfied codal provisions and requirements Hence for a staircase
provide
Main Steel: 12 mm dia. @ 175 mm c/c Distribution Steel: 12 mm dia. @ 300 mm c/c
Materials used:
Grade of concrete =M 25
fck=25 N/mm2
Grade of steel=Fe 415
fy=415 N/mm2
Width of Flight :1200 mm
Depth of Waist Slab : 250 mm.
END OF REPORT.

35 | P a g e
MAX MOMENT
MAX SHEAR

36 | P a g e
MAX DEFLECTION
STRESS DISTRIBUTION

37 | P a g e
REFRENCES:
1. Books:
• "ETABS Users' Manual" by Computers and Structures, Inc.
• "Design of Earthquake Resistant Buildings" by S.K. Duggal & B.N. Krishna
2. Websites:
• Bureau of Indian Standards (BIS): https://www.bis.gov.in/?lang=en
• Indian Institute of Technology Delhi (IIT Delhi): https://home.iitd.ac.in/
• Computers and Structures, Inc.: https://www.csiamerica.com/
• National Disaster Management Authority (NDMA): https://ndma.gov.in/
3. IS Codes and Standards:
• IS 456:2000 - Code of practice for plain and reinforced concrete
• IS 1893:2016- Code of Practice for Earthquake Resistant Design of structures
• IS 13920:2016 - Ductile detailing of reinforcement steel in concrete structures
• NBC 2016 - National Building Code of India

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