STRUCTURES PROJECT REPORT ON G+3 RESIDENTIAL BUILDING
STRUCTURES PROJECT REPORT ON G+3
RESIDENTIAL BUILDING
CANDIDA SILVA AGNELO
18031AA014
CANDIDA SILVA AGNELO
18031AA014
Church of South India - Medak Diocese
CHURCH OF SOUTH INDIA INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND PLANNING
(Affiliated to Jawaharlal Nehru Architecture & Fine Arts University, Hyderabad)
#145, Mcintyre Road, Wesley Degree & PG College Campus, Secunderabad- 500 003,
Telangana State, India.
STRUCTURES PROJECT REPORT ON G+3
RESIDENTIAL BUILDING
CANDIDA SILVA AGNELO
18031AA014
Church of South India - Medak Diocese
CHURCH OF SOUTH INDIA INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND PLANNING
(Affiliated to Jawaharlal Nehru Architecture & Fine Arts University, Hyderabad)
#145, Mcintyre Road, Wesley Degree & PG College Campus, Secunderabad- 500 003,
Telangana State, India.
Church of South India - Medak Diocese
CHURCH OF SOUTH INDIA INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND PLANNING
(Affiliated to Jawaharlal Nehru Architecture & Fine Arts University, Hyderabad)
#145, Mcintyre Road, Wesley Degree & PG College Campus, Secunderabad- 500 003,
Telangana State, India.
CERTIFICATE
This is to certify that the Structures Project Report entitled for
Structures report on G+3 Residential Building
Submitted by CANDIDA SILVA AGNELO bearing Roll Number 18031AA014 for the partial
fulfillment of the requirement for the award of the degree of the Bachelor of. Architecture from
Jawaharlal Nehru Architecture and Fine Arts University, Hyderabad is a bonafide work to the best
of our knowledge and may be placed before the examination board for consideration.
Approved by
Guide
H.O.D
External Examiner
Principal
TYPICAL FLOOR PLAN
S1
S4
S7
S2
S5
S8
S3
S6
S9
LOAD CALCULATIONS
Load: A structural load or structural action is a force, deformation, or acceleration
applied to structural elements. A load causes stress, deformation, and displacement
in a structure. Excess load may cause structural failure, so this should be
considered and controlled during the design of a structure. Structural loads are an
important consideration in the design of buildings. Building codes require that
structures be designed and built to safely resist all actions that they are likely to
face during their service life, while remaining fit for use. Minimum loads or
actions are specified in these building codes for types of structures, geographic
locations, usage and building materials.
Dead load: A dead load includes loads that are relatively constant over time,
including the weight of the structure itself, and immovable fixtures such as walls,
plasterboard or carpet. The roof is also a dead load. Dead loads are also known as
permanent or static loads. Building materials are not dead loads until constructed
in permanent position.
Live load: Live loads, or imposed loads, are temporary, of short duration, or a
moving load. These dynamic loads may involve considerations such as impact,
momentum, vibration, slosh dynamics of fluids and material fatigue. Live loads,
sometimes also referred to as probabilistic loads, include all the forces that are
variable within the object's normal operation cycle not including construction or
environmental loads. Roof and floor live loads are produced during maintenance
by workers, equipment and materials, and during the life of the structure by
movable objects, such as planters and people.
LOAD COMBINATIONS:
A load combination results when more than one load type acts on the structure. Building codes
usually specify a variety of load combinations together with load factors (weightings) for each load
type in order to ensure the safety of the structure under different maximum expected loading
scenarios. For example, in designing a staircase, a dead load factor may be 1.2 times the weight of
the structure, and a live load factor may be 1.6 times the maximum expected live load. These two
"factored loads" are combined (added) to determine the "required strength" of the staircase.
FORMULAE:
o Load on beam supporting one way slab
• ɭᵧ is longer span , ɭᵪ is span
ᴡɭᵪ2
2
• IF
≥2, then it is a one way slab
• load on beam =
o Load on beam supporting two-way slab
ᴡɭᵪ
2
• ɭᵧ is longer span, ɭᵪ is shorter span
ɭᵪ
• If ɭᵧ<2, then it is a two-way slab
o Equivalent UDL on beam (triangular beam)=
ᴡɭᵪ
3
o Equivalent UDL on beam (trapezoidal beam)=
ᴡɭᵪ
2
1
[1-3𝛽²]
o Total Dead load (DL) on slab= self-weight of slab (W) x floor finish
o Load from slab =
ᴡɭᵪ1
2
1
[1-3𝛽²1 ] +
ᴡɭᵪ2
2
1
[1－ 3𝛽²2 ]
• Total load = Sum Of Dead Loads + Live Load
• Total factored load = 1.5 X Total Load
REINFORCEMENT DETAILS:
CONSIDERATIONS
o Load on beam: Load on slab (DL + LL) + Load from wall + Self weight of beam
Practical data:
• Slab thickness= 150mm (0.15m)
• Floor finish= 1.5 KN/m2
• Brick masonry unit weight= 20 KN/m³
• Height of the floor= 3.0m
• Unit weight of concrete= 25 KN/m³
o W: Self weight of the slab = depth of slab x unit weight of concrete = 0.15 x 25 = 3.75 KN/m²
o Live load consideration for:
• Bedroom, Living, Dining & Kitchen = 2 KN/m2
as per IS 875 part 2 (1987) standards- clauses 3.1,3.1.1,4.1.1
o Live load consideration for:
•
Corridor, Lift & Staircase = 3 KN/m2
as per IS 875 part 2 (1987) standards- clauses 3.1,3.1.1,4.1.1
Total Dead load (DL) on slab = self- weight of slab (W) x floor finish
= 3.75 + 1.5= 5.25 KN/m2
Live Load Of Slab
= Thickness of slab x Density
0.15 x 25 = 3.75 KN/m
4
Dead Load Of Beam
Cross Sectional Area × Density
= 0.3×0.3×25
= 2.25 KN/M
3
S1
Weight Of Wall= 0.3×20×4
= 24 KN/M
Parapet Wall = 0.3×20×1
=6 KN/M
• ɭᵪ= 3
•
ᴡɭᵪ
6
,
ɭᵧ= 4
ɭᵪ
7.75×3
3
ɭᵧ
6
4
[3 -( )2 ] =
[3-( )2]
Beam Load =9.45 KN/m
Load On The Beam
Load On The Slab + Dead Load Of Beam + Parapet
Wall (Longer Side)
=9.45+2.25+24
=35.7 KN/M
Load On The Terrace Slab
Load On Slab + Dead Load Of Beam + Parapet Wall
=7.75+2.3+6
=16.05 KN/M
Since all the slabs sizes are similar ,
So load calculations will be the same for all
the slabs.
ANALYSIS OF BEAM FRAME
A
16.05 KN/m
16.05 KN/m
16.05 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
35.7 KN/m
B
C
D
LOAD CALCULATIONS:
A load combination results when more than one load type acts on the structure. Building codes
usually specify a variety of load combinations together with load factors (weightings) for each load
type in order to ensure the safety of the structure under different maximum expected loading
scenarios. For example, in designing a staircase, a dead load factor may be 1.2 times the weight of
the structure, and a live load factor may be 1.6 times the maximum expected live load. These two
"factored loads" are combined (added) to determine the "required strength" of the staircase.
FORMULAE:
• ɭᵧis longer span , ɭᵪis span
o Load on beam supporting one way slab
ᴡɭᵪ2
2
• IF
≥2, then it is a one way slab
• load on beam =
ᴡɭᵪ
2
• ɭᵧ is longer span, ɭᵪ is shorter span
o Load on beam supporting two-way slab
ɭᵪ
• If ɭᵧ<2, then it is a two-way slab
o Equivalent UDL on beam (triangular beam)=
ᴡɭᵪ
3
o Equivalent UDL on beam (trapezoidal beam)=
ᴡɭᵪ
2
1
[1-3𝛽²]
o Total Dead load (DL) on slab= self- weight of slab (W) x floor finish
o Load from slab =
ᴡɭᵪ1
2
1
[1-3𝛽²1 ] +
ᴡɭᵪ2
2
1
[1－ 3𝛽²2 ]
• Total load = Sum Of Dead Loads + Live Load
• Total factored load = 1.5 X Total Load
LOAD CALCULATIONS
Three Moment Equation
Span AB, M = WL2/ 8
= 35.7 (4) 2/ 8
= 71.4 KN/m
35.7 KN/m
35.7 KN/m
4m
4m
A
B
Span BC, M
= WL2/ 8
= 35.7 (4) 2/ 8
= 71.4 KN/m
Applying moment equation for span AB and BC.
𝑎𝑥1
MA L1 + 2MB ( L1+ L2)+ MC L2 = -6 [
+
𝑙1
MA =? MB= ? MC=?
𝑎𝑥2
𝑙2
]
L1 = 4M,
L2= 4M
A1 = 2/3 x 4x 35.7 = 95.2
A2 = 2/3 x 4x 35.7 = 95.2
95.2 𝑋 2
0 x 4 + 2MB(4+4)+ MC x 4 = -6[
4
= -571.2
16MB + 4MC = -571.2
4MB+MC = -142.8 ------------------(1)
+
95.2𝑋 2
]
4
Span BC, MBC
= WL2/ 8
= 35.7 (4) 2/ 8
= 71.4 KN/m
Span CD, MCD
= WL2/ 8
= 35.7 (4) 2/ 8
= 71.4 KN/m
Applying ME for span BC and CD,
MB L2 + 2MC (L2+L3) + MDL3 = 6[
MB = ? MC = ? MD = ?
𝑎2𝑥2
𝑙2
35.7 KN/m
+
𝑎3𝑥 3
𝑙3
]
4m
C
D
a1= 96.32
a2= 96.32
x1 = 2
x3= 2
MB X 4 + 2MC ( 4+4) +0 x 4
4MB + 16 MC = - 571.2,
MB+ 4MC = - 142.8 ------------(2)
Solving equation 1 and 2,
4MB + MC = -142.8
MB+4MC = -142.8 x 4
4MB + MC
= -142.8
−4𝑀𝐵 − 16 𝑀𝐶 = 571.2
−15 𝑀𝐶 = 428.4
MC = -28.56
MB + 4( -28.56) = -142.8
MB= -28.56
Support reactions
RA + RB + RC = ( 35.7 x4 + 35.7 x4 + 35.7 x4 + 35.7 x4 )
=571.2
RA=RB=RC=RD=142.8
35.7 KN/m
35.7 KN/m
4m
35.7 KN/m
4m
A
4m
B
C
71.4 KN/m
D
71.4 KN/m
+
71.4 KN/m
+
+
BENDING MOMENT DIAGRAM
71.4 KN/m
35.7 KN/m
+
+
-
35.7 KN/m
+
-
35.7 KN/m
35.7 KN/m
SHEAR FORCE DIAGRAM
71.4 KN/m
Three Moment Equation
Span AB, M = WL2/ 8
= 16.05 (4) 2/ 8
= 32.1 KN/m
16.05 KN/m
16.05 KN/m
4m
Span BC, M
= WL2/ 8
= 16.05 (4) 2/ 8
= 32.1 KN/m
16.05 KN/m
4m
A
B
C
D
Applying moment equation for span AB and BC.
𝑎𝑥1
MA L1 + 2MB ( L1+ L2)+ MC l2 = -6 [
+
𝑙1
Ma =0 MB= ? MC=?
𝑎𝑥2
𝑙2
]
𝑙1
X1=[ = 2]
L1 = 4M,
L2= 4M
2
𝑙2
X2=[ = 2]
2
A1 = 2/3 x 4x16.05 = 42.8
A2 = 2/3 x 4x16.05 = 42.8
42.8 𝑋 2
0 x 4 + 2MB(4+4)+ MC x 4 = -6[
4
16MB + 4MC = - 256.8
4MB+MC = -64.2 ------------------(1)
+
42.8 𝑋 2
]
4
Span BC, MBC
= WL2/ 8
= 16.05 (4) 2/ 8
= 32.1 KN/m
Span CD, MCD
= WL2/ 8
= 16.05 (4) 2/ 8
= 32.1 KN/m
Applying ME for span AB and BC,
MB L2 + 2MC (L2+L3) + MDL3 = 6[
MB = ? MC = ? MD = 0
𝑎2𝑥2
𝑙2
+
𝑎3𝑥 3
𝑙3
]
𝑙1
L2 = 4M,
L3= 4M
A2 = 2/3 x 4x16.05 = 42.8
A3 = 2/3 x 4x16.05 = 42.8
MB X 4+ 2MC(4+4) +0 X4 = - 256.8
4MB+ 16MC = -256.8 ------------------(2)
Solving equation 1 and 2
4MB + MC = - 64.2
-4MB-16MC=+ 256.8
= -15MC = 192.6
MC = -12.84-------3
Equation 3 in 1
4MB + (-12.84) = -64.2
MB= - 12.84
Support reactions,
RA+RB+RC+RD
=(16.05 x4) + (16.05 x4) +(16.05 x4)+ (16.05 x4)
RA=RB=RC=RD
RA = (16.05 X 4 )
=64.2
RA=RB=RC=RD = 64.2
X2=[ = 2]
2
𝑙2
X3=[ = 2]
2
16.05 KN/m
16.05 KN/m
4m
16.05 KN/m
4m
A
B
16.05 KN/m
C
D
16.05 KN/m
4m
16.05 KN/m
4m
A
4m
B
C
32.1 KN/m
D
32.1 KN/m
+
32.1 KN/m
+
+
BENDING MOMENT DIAGRAM
32.1 KN/m
16.05 KN/m
+
16.05 KN/m
+
-
+
-
16.05 KN/m
16.05 KN/m
SHEAR FORCE DIAGRAM
32.1 KN/m
DESIGN OF SLABS
A slab is a flat two dimensional planar structural element having thickness small
compared to its other two dimensions. It provides a working flat surface or a
covering shelter in buildings. It primarily transfer the load by bending in one or
two directions.
A concrete slab is a common structural element of modern buildings, consisting
of a flat, horizontal surface made of cast concrete. Steel-reinforced slabs,
typically between 100 and 500 mm thick, are most often used to construct floors
and ceilings, while thinner mud slabs may be used for exterior paving
Types of slabs based on support conditions
• One way spanning slab
• Two way spanning slab
• Flat slab resting directly on columns without beams
•
Grid slabs or waffle slabs
•
Circular slabs
Types of Loads on a Slab
• Dead load of the slab
• Live load
• Floor finish load
One- Way Slab
When the ratio of the longer to the shorter side (L/ S) of the slab is at least equal to
2.0, it is called one-way slab. Under the action of loads, it is deflected in the short
direction only, in a cylindrical form. Therefore, main reinforcement is placed in the
shorter direction, while the longer direction is provided with shrinkage
reinforcement to limit cracking. When the slab is supported on two sides only, the
load will be transferred to these sides regardless of its longer span to shorter span
ratio, and it will be classified as one-way slab.
Two-way slabs: A two-way slab has moment resisting reinforcement in both
directions. This may be implemented due to application requirements such as heavy
loading, vibration resistance, clearance below the slab, or other factors. However,
an important characteristic governing the requirement of a two-way slab is the ratio
of the two horizontal lengths. If the axial ratio is greater than two, a two-way slab is
required. (i.e., If Ly/ Lx > 2, where Ly is the longer span and Lx is the shorter span).
Anon-reinforced slab is two-way if it is supported in both horizontal axes.
Reinforcement details:
As per IS 456, clause 26.3.3.b as follows,
Spacing of Main Steel and Distribution Steel in Slab:
• Main Steel : Not more than 3d or 300 mm whichever is smaller. Where, d is effective
depth of slab.
• Distribution Steel : Not more than 5d or 450 mm whichever is smaller. Where, d is
effective depth of slab.
• Spacing between two bars is to be maintained so that maximum size of coarse
aggregate present in concrete to be used should pass between the bars. Also, it is
important to ensure compaction till the full depth of the beam.
Types of Slabs
Flat Slab:The flat slab is a reinforced concrete slab supported directly by concrete column or
caps. Flat slab doesn’t have beams so it is also called a beam-less slab. They are
supported on columns itself. Loads are directly transferred to columns. In this type of
construction, a plain ceiling is obtained thus giving an attractive appearance from an
architectural point of view. The plain ceiling diffuses the light better and is considered
less vulnerable in the case of fire than the traditional beam slab construction. The flat
slab is easier to construct and requires less form work . This is one of the types of
concrete slabs.
Advantages of Flat Slab:
1.It minimizes floor-to-floor heights when there is no
requirement for a deep false ceiling. Building height can be
reduced
2.Auto sprinkler is easier.
3.Less construction time.
4.It increases the shear strength of the slab.
5.Reduce the moment in the slab by reducing the clear or
effective span.
Disadvantages of Flat slab:
1.In a flat plate system, it is not possible to have a large
span.
2.Not suitable for supporting brittle (masonry) partitions.
3.Higher slab thickness.
Hollow core ribbed Slab or Hollow core slab:Hollowcore ribbed slabs derive their name from the voids or cores which run through
the units. The cores can function as service ducts and significantly reduce the selfweight of the slabs, maximizing structural efficiency. The cores also have a benefit in
sustainability terms in reducing the volume of concrete used. Units are generally
available in standard 1200 mm widths and in depths from 110mm to 400 mm. There
is total freedom in the length of units. These type of slabs are Pre cast and it is used
where the construction has to be done fast.
The hollow core ribbed slabs have between four and six longitudinal cores running
through them, the primary purpose of the cores being to decrease the weight, and
material within the floor, yet maintain maximal strength. To further increase the
strength, the slabs are reinforced with 12mm diameter steel strand, running
longitudinally. This is one of the types of concrete slabs.
Hollow core slab Advantages :
1.Hollow core ribbed slab not only reduces building costs it also
reduces the overall weight of the structure.
2.Excellent fire resistance and sound insulation are other attributes of
hollow core slab due to its thickness.
3.It eliminates the need to drill in slabs for electrical and plumbing
units.
4.Easy to install and requires less labour.
5.Fast in construction
6.No additional formwork or any special construction machinery is
required for reinforcing the hollow block masonry.
Hollowcore slab Disadvantages:
1.If not properly handled, the hollow core ribbed slab units may be
damaged during transport.
2.It becomes difficult to produce satisfactory connections between the
precast members.
3.It is necessary to arrange for special equipment for lifting and moving
of the precast units.
4.Not economic for small spans.
5.Difficult to repair and strengthen
Waffle Slab:Waffle slab is a reinforced concrete roof or floor containing square grids with deep
sides and it is also called as grid slabs. This kind of slab is majorly used at the
entrance of hotels, Malls, Restaurants for good pictorial view and to install artificial
lighting. This a type of slab where we find a hollow hole in the slab when the
formwork is removed. Firstly PVC trays (pods) are placed on shuttering then
reinforcement is provided between the pods and steel mesh is provided at top of the
pods and then concrete is filled. After concrete sets, the formwork is removed and
PVC pods are not removed. This forms a hollow hole in it in which hole is closed at
one end. The concrete waffle slab is often used for industrial and commercial
buildings while wood and metal waffle slabs are used in many other construction
sites. This is one of the types of concrete slabs.
Where to use Waffle Slab & Waffle slab details:
A waffle slab has a holes underneath, giving an appearance of waffles. It is usually
used where large spans are required (e.g. auditorium, cinema halls) to avoid many
columns interfering with space. Hence thick slabs spanning between wide beams (to
avoid the beams protruding below for aesthetic reasons) are required. The main
purpose of employing this technology is for its strong foundation characteristics of
crack and sagging resistance. Waffle slab also holds a greater amount of load
compared with conventional concrete slabs.
Types of Waffle slabs:
Based on the shape of Pods (PVC Trays) waffle slabs are classified into the
following types:
1.Triangular pod system
2.Square pod system
Advantages of Waffle slabs:
1.Waffle slabs are able to carry heavier loads and span longer distances than flat slabs as
these systems are light in weight.
2.Waffle slab can be used as both ceiling and floor slab.
3.Suitable for spans of 7m – 16m; longer spans may be possible with post-tensioning.
4.These systems are light in weight and hence considerable saving is ensured in the
framework as the light framework is required
Disadvantages of Waffle slabs:
1.Waffle slab is not used in typical construction projects.
2.The casting forms or moulds required for precast units are very costly and hence only
economical when large scale production of similar units are desired.
3.Construction requires strict supervision and skilled labour.
Dome Slab:This kind of slab is generally constructed in temples, Mosques, palaces etc. And
Dome slab is built on the conventional slab. The thickness of Dome slab is 0.15m.
Domes are in the semi-circle in shape and shuttering is done on a conventional
slab in a dome shape and concrete is filled in shuttering forming dome shapes. This
is one of the types of concrete slabs.
Pitch roof slab:
Pitch roof is an inclined slab, generally constructed on resorts for a natural
look. Compared to traditional roofing materials Tile-sheets used in pitch
roof slab are extremely lightweight. This weight saving reduces the timber
or steel structural requirements resulting in significant cost savings. Tilesheets are tailor made for each project offering labour cost savings and
reduced site wastage. And the thickness of the slab depends on the tiles we
using it maybe 2″-8″. This is one of the types of concrete slabs.
Post tension slab:
The slab which is tensioned after constructing a slab is called Post tension slab.
Reinforcement is provided to resist the compression. In Post tension slab the
reinforcement is replaced with cables/ steel tendons.
Post-Tensioning provides a means to overcome the natural weakness of concrete in
tension and to make better use of its strength in compression. The principle is easily
observed when holding together several books by pressing them laterally.
In concrete structures, this is achieved by placing high-tensile steel tendons/cables in
the element before casting. When concrete reaches the desired strength the tendons are
pulled by special hydraulic jacks and held in tension using specially designed
anchorages fixed at each end of the tendon. This provides compression at the edge of
the structural member that increases the strength of concrete for resisting tension
stresses. If tendons are appropriately curved to a certain profile, they will exert in
addition to compression at the perimeter, a beneficial upward set of forces (load
balancing forces) that will counteract applied loads, relieving the structure from a
portion of gravity effects. This is one of the types of concrete slabs.
In this type of slab, cables are tied instead of reinforcement. In Steel reinforcement, the
spacing between bars is 4inch to 6inch whereas in Post tension slab the spacing is more
than 2m.
Advantages of Post tension slab:
1.It allows slabs and other structural members to be thinner.
2.It allows us to build slabs on expansive or soft soils.
3.Cracks that do form are held tightly together.
4.Post tension slabs are excellent ways to construct stronger structures at an affordable
price.
5.It reduces or eliminates shrinkage cracking-therefore no joints, or fewer joints, are
needed
6.It lets us design longer spans in elevated members, like floors or beams.
Disadvantages of Post tension slab:
1.The Post tension slab can be made only by skillful professionals.
2.The main problem with using Post tension slab is that if care is not taken while making
it, it can lead to future mishaps. Many times, ignorant workers do not fill the gaps of the
tendons and wiring. These gaps cause corrosion of the wires which may break untimely,
leading to some failures unexpectedly.
Pre Tension Slab :
The slab which is tensioned
before placing the slab is
called Pre tension slab. The
slab has the same features of
Post-tensioning slabs.
DESIGN OF SLABSRoom Size = 4Τ3=1.3< 2 → two way slab.
For M15 concrete ; fck = 15 N/mm2
HYSD steel bars, fy = 415 N/mm2
Assume thickness of slab are 100 mm
Clear cover 15mm X 10 ∅ bars
𝐶
Lx= of supports
𝐶
= 3+0.2=3.2m
10
Overall depth, D = 100+15+ 2 = 120 mm
𝐶
Efficient length on shorter span
Lx = clear span + effective span
= 3+1=3.1m⇒ lx = 3.1m
Lx=4m (least of the two values)
Efficient length of longer span
Ly = 4+1=0.1m⇒ ly = 4.1m
(least of the two values)
Calculation of loads
Dead loads = 2.25 KN/m2
Live load = 3.75KN/m2
Floor Finish = 1KN/m2
Total load = 7 KN/m2
Factored load = (WU ) = 1.5 X 7= 10.5KN/m2
Ratio of spam
𝐿𝑦
𝐿𝑥
3.1
= 4.1 = 0.75
Assuming the value as
Longer span coefficient = 𝛼y (+ve)
𝛼y = 0.057
𝛼x = 0.044
Binding moment calculation
-
Shorter side
-
𝑀𝑥 = 𝛼𝑥 𝑤𝑦 𝑙𝑥 2
= 0.044 X 10.5 X (3.1)2
= 4.43 KN/m
Ly= of supports
𝐶
= 4+0.2=4.2m
-longer side
𝑀𝑦 = 𝑥𝑦 𝑤𝑢 𝑙𝑥 2
= 0.057 X 10.5 X (4.1)2 = 10.06 KN/m
check for depth
D=
𝑀𝑦
0.138𝑓𝑐𝑘 𝑏
=
10.06×106
=
0.138×15×1000
69.71 < 100 ∴ safe
∴ provide overall depth of slab as 120 mm
Area of steel in shorter side
𝐴5𝑡 =
0.36𝑓𝐶𝑘 𝑏𝑥𝑢 𝑚𝑎𝑥
0.86𝑓𝑦
Spacing =
1000𝐴∅
717.9
=
0.36×15×1000(0.48×100)
0.86×415
= 726.25mm2
= 109.4, say 105 mm c/c
Area of steel in longer side
1 − 𝐴𝑠𝑡 + 𝑓𝑦
𝑀𝑦 = 0.87𝑓𝑦 𝐴𝑠 ⅆ
𝑏ⅆ 𝑓𝑐𝑘
1−415𝐴𝑠𝑡
15×1000×90
10.06𝑥 𝑋 106 = 0.87 X 415 Ast X 90
10.06𝑥 𝑋 106 = 0.87 X 415 X 𝑥X 90
𝟏𝟓 × 𝟏𝟎𝟎𝟎 ×𝟗 −𝟒𝟏𝟓𝐴𝑠𝑡
15×1000×90
Ast = 𝑥 = 210.86 m2
alternate bars are cracked at 0.12 distanced from the support in which direction extent at 50 % of
positive steel at near top support to resist bending movement.
Area of distribution steel
𝐴𝑠𝑡𝑦 = 0.12% of B
0.12
× 1000 × 120 = 144𝑚2
100
Spacing of 6mm ∅ bars
1000 =
𝐴∅
𝐴𝑠𝑡𝑦
=
𝜋
1000× 6 2
4
144
= 193.34 mm
≈190 mm
∴Provide 6 m ∅ HYSD bars@ 190mm c/c as distribution steel
Carc of reinforcement
3ൗ 𝐴 = 3 × 210.86 = 158.145 𝑚2
4 𝑠𝑡𝑥 4
Spacing of 10 m ∅ bars =
1000×𝜋Τ4 10 2
=
158.145
198.5 m2m
≈144.07
= 140 mm
∴ provide 10 mm ∅ bars @ 140 mm c/c as 4 covers at top and bottom as mech of site.
DESIGN OF COLUMNS
Introduction:
Introduction in a building, columns play extremely significant role. Columns are the
vertical support members to which the other elements such as beams, slabs and walls
are rigidly connected. Failure of the column can lead to the collapse of the entire
structure. In a framed structure, where the columns are rigidly connected to other
structural elements, besides the direct loads large bending moments are imposed on
the columns. Reinforced columns are reinforced with the help of longitudinal bars are
meant to carry the tensile stresses besides sharing the compressive forces with the
concrete.
Arrangement of lateral ties & links in a column:
1. Single tie
2. Two ties
3. Single tie & link
4. Two ties
5. single tie & two link
6. Three
REINFORCEMENT DETAILS:
• Generally, concrete columns consist of square, rectangular or circular
cross- sectional area. Columns are essentially required with the
primary longitudinal reinforcement and lateral ties to avoid buckling
of the primary bars.
• The details of minimum and maximum limits of reinforcements,
minimum no. of bars, the size of bars, cover requirements, diameter,
and spacing are given in the picture.
• In case of rectangular column, the minimum longitudinal reinforcement should be 4
nos. The minimum dia of bars should not be less than 12 mm, and the dia of a
stirrup should not be less than 8 mm. Stirrup should be placed at a distance of 150
mm (center to center distance).
DESIGN OF COLUMN
Column size – 300 x 300 mm
Load Calculation on Column
o Volume of concrete = 0.3x0.3x3 = 0.27
o Weight if concrete = 0.27x2400 = 648 kg
o Weight of steel (1%) in concrete = 0.27 x 0.01 x 7850
= 21.19 ≃ 21kg
o Total weight load of Column
= 648+21
= 669 KN
•
Load (p) = 669 KN
o
Factored load (Pu) = 1.5 x 669
= 1003.5 KN = 1003x103 N
o
Grade of Concrete M20 (fck) = 20N/mm
o
For mild steel (fy) = 250N/m2
o
Size of Column = 300x300 mm
o
Longitudinal area of steel = Pu = 0.4fck Ac + 0.67 fy Asc
1003x 103 = 0.4 x 20(300x300 - Asc) + 0.67 x 250 Asc
1003x 103 = 72x 104 –8 Asc+167.5Asc
283000 = 175.5 Asc
Asc = 1612.5 mm2
•
o
Using 16 mm ∅ bars
No . of bars = 1612.5 / π/4 (16) 2 = 8 bars
∴ assume 6 bars
Provide 6-16 mm ∅ longitudinal bars
Design of lateral bars
Diameter of ties ∅t < ∅l/4 = 16/4 =4mm
∴ assume 6mm
say 6mm > 4mm as spacing should be more
Pitch of lateral ties, P ≤ LLD = 300 mm
≤ 16 x ∅L = 16x16 = 256mm
≤ 300 mm
∴ Pitch of 300mm c/c
Longitudinal
bar 6 - 16 ∅
R.C.C column
300 x 300 mm
( M20 )
Lateral ties
6mm ∅ @230
c/c spacing
t =300 mm
Mild steel
6 ∅ 16 mm
b =300 mm
Ties ∅ 6 ∅ 230 mm
DESIGN OF FOOTINGS
FOUNDATION
Introduction to Foundations:Foundation is an important part of the
structure which transfers the load of the
structure to the foundation soil. The
foundation distributes the load over a large
area. So that pressure on the soil does not
exceed its allowable bearing capacity and
restricts the settlement of the structure within
the permissible limits. Foundation increases
the stability of the structure. The settlement
of the structure should be as uniform as
possible and it should be within the tolerable
limits.
Why we provide Foundations or Footings?
In simple words, Consider 1m3 of concrete
weight i.e., 2400 Kgs to 2600 Kgs depending
on mix. Think for a Two storeyed building
how much concrete needed? How much
quantity of bars needed? to construct a
building. Foundation is to be strong enough
to bear that all loads without any settlement,
So for spreading the vertical load to large
area footings are constructed.
Different types of Foundations:Foundations are mainly classified into two
types:
1. Shallow Foundations
2. Deep foundations
If depth of the footing is equal to or greater
than its width, it is called deep footing,
otherwise it is called shallow footing.
37
I. Isolated footing:Footings which are provided under
each column independently are called
as Isolated footings. They are usually
square, rectangular or circular in
section. Footing is laid on PCC.
Before laying PCC, termite control
liquid is sprayed on top face of PCC to
restrict the termites to damage the
footing. Isolated footings are provided
where the soil bearing capacity is
generally high and it comprises of a
thick slab which may be flat or stepped
or sloped. This type of footings are
most economical when compared with
the other kind of footings.
(i) Flat or Pad or Plain footing:These kind of footings are generally
square or rectangular or circular in
shape which are provided under
each column independently. Flat or
Pad Footing is one of the Shallow
Foundations. It is circular, square or
rectangular slab of uniform thickness.
(ii) Stepped footing:These types of footings are constructed
in olden days now they are outdated.
As from the name its resembling that,
footings are stacked upon one another
as steps. Three concrete cross sections
are stacked upon each other and forms
as a steps. This type of footings are
also called as a Step foundation.
Stepped footing is used generally in
residential buildings.
38
(iii) Sloped Footing:Sloped footings are trapezoidal
footings. They are designed and
constructed with great care to see that
the top slope of 45 degree
is
maintained from all sides. When
compared the trapezoidal footing
with the flat footing, the usage of
concrete is less. Thus, it reduces the
cost of footing in concrete as well as
reinforcement.
(iv) Shoe or eccentric footing –
Shoe footing is the half cut-out from
the original footing and it has a shape
of shoe. They are constructed on
property boundary, where there is no
provision of setback area. It is
constructed at the corner of the plot
when the exterior column is close to
the boundary or property line and
hence there is no scope to project
footing much beyond the column
face.. Column is provided or loaded
at the edges of shoe footing. Shoe
footings are constructed when the
soil bearing capacity is 24KN/m2
(v) Combined footing:A footing which has more than one
column is called as combined
footing. This kind of footing is
adopted when there is a limited
space. Due to lack of space we
cannot cast individual footing,
Therefore footings are combined in
one footing. They are classified into
two types based on their shape:
1. Rectangular combined footing.
39
2.Trapezoidal combined footing.
II. Raft or Mat Foundation or footing:When the column loads are heavy or when the safe bearing capacity of soil is
very low, The required footing area become very large. As mentioned this
footing is in shallow foundation. So in order to spread the load over large area
with less depth then we have to increase the footing area. If we increase footing
area the footings are overlapped each other, instead of providing each footing
on each column all columns are placed in common footing. A raft
foundation is a solid reinforced concrete slab covering entire area beneath the
structure and supporting all the columns. Such foundation due to its own
rigidity minimizes differential settlements.
It is provided in a places like seashore area, coastal area area where the water
table is very high and soil bearing capacity is very weak.
When number of column in more than one row, provided with a combined
footing, the footing is called mat or raft foundation.
III. Strip foundation:
Strip foundation is also called as Wall footing. As name itself showcasing that,
it is a strip type footing which follows the path of Superstructure Wall. This
type of footing is constructed for Load bearing walls. It is a continuous strip of
concrete that serves to spread the weight of a load-bearing wall across an area
of soil. The strip footing foundation width is decided by considering bearing
capacity of soil. Greater the bearing capacity of soil lesser is the width of the
Strip footing.
40
Deep foundations or Pile Foundations:If the depth of a foundation is greater than its width, the foundation laid
is known as deep foundation. In deep foundation, the depth to width
ratio is usually greater than 4 to 5. Deep foundations as compare to
Shallow foundations distribute the load of the super structure vertically
rather than laterally. Deep foundations are provided when the expected
loads from superstructure cannot be supported on shallow foundations
.
Pile footings:A pile is a long vertical load transferring member made of timber, steel
or concrete. In pile foundations, a number of piles are driven in the base
of the structure.
They are constructed where excessive settlement is to be eliminated and
where the load is to be transferred through soft soil stratum, where the
Soil bearing capacity is sufficient. These types of footings are provided
when the Soil bearing capacity of soil is very weak and the Ground
water table (level) is high. These types of the footings are generally
designed on sea shore areas, bridges to construct pillars, etc.
The main objective of providing piles under the footing is to prevent
structure from settlement. If we don’t provide pile under the footing,
then the building will have settlement. Piles are hammered in to the
ground till hard strata (in compressible) layer of earth is found.
Pile foundations are divided into two types they are:1. Pre cast Piles.
2. Cast-in-situ piles.
41
Types of Loads on Footings
1. Dead load
1. Self-Weight of the elements
2. Superimposed loads such as finishes, partitions, block work,
services.
2. Live load
3. Impact load
4. Snow load
5. Wind load
6. Earthquake force
7. Soil pressure
8. Rain loads
9. Fluid loads
Load Transfer Mechanism in Footing
Soil is the root support of the footing. All the forces that come in contact
with the footings will be transferred to the soil. The soil shall bear these
loads by the aspect known as bearing capacity. The bearing capacity
changes from one type of soil to another and it is the key factor in
estimating the size of footings.
Transfer of loads from structural elements to the
ground through footing
Dissipating loads of footing in underlying
soil
42
DESIGN OF FOOTING
A Definition Footings are structural members used to support columns and walls
and to transmit and distribute their loads to the soil in such a way that the load
bearing capacity of the soil is not exceeded, excessive settlement, differential
settlement, or rotation are prevented and adequate safety against overturning or
sliding is maintained.
DEFNITIONS:
TYPES OF FOOTING’S:
Wall footings : Wall footings are used to support for other floors or to support
nonstructural walls.
⚫
Isolated or single footings: They are used to support
single columns. This is one of the most economical
types of footings and is used when columns are spaced
at relatively long distances. These footings essentially
consist of a bottom slab.
⚫
There are three basic types:
1.
Pad footing (with uniform thickness)
2.
Stepped footing (with non- uniform thickness)
3.
Sloped footing (trapezoidal section)
⚫
Combined footings : They usually support two columns, or three columns not
in a row. Combined footings are used when tow columns are so close that
single footings cannot be used or when one column is located at or near a
property line.
⚫
Cantilever or strap footings : They consist of two single footings connected with a beam or a strap
and support two single columns. This type replaces a combined footing and is more economical.
⚫
Continuous footings : They support a row of three or more columns. They have limited width and
continue under all columns.
⚫
Rafted or mat foundation : They consists of one footing usually placed under the entire
building area. They are used, when soil bearing capacity is low, column loads are heavy single
footings cannot be used, piles are not used and differential settlement must be reduced.
⚫
Pile caps: They are thick slabs used to tie a group of piles together to support and
transmit column loads to the piles.
DISTRIBUTION OF SOIL PRESSURE:
When the column load P is applied on the centroid of the footing, a uniform pressure is assumed
to develop on the soil surface below the footing area. However the actual distribution of the soil
is not uniform, but depends on may factors especially the composition of the soil and degree of
flexibility of the footing
DESIGN CONSIDERATIONS OF FOOTINGS:
Footings must be designed to carry the column loads and transmit them to the soil safely while
satisfying code limitations.
•
The area of the footing based on the allowable bearing soil capacity
•
Two-way shear or punching shear.
•
•
One-way bearing
Bending moment and steel reinforcement required
Footings must be designed to carry the column loads and transmit them to the soil safely while
satisfying code limitations.
•
Bearing capacity of columns at their base
•
Dowel requirements
•
Development length of bars
•
Differential settlement
FORMULAS:
The area of footing can be determined from the actual
external loads such that the allowable soil pressure is
not exceeded.
⚫
Area of footing = Total load ( including self-weight)
⚫
allowable soil pressure Strength design requirements q of
u = p of u
area of footing For two-way shear in slabs (& footings) Vc is
smallest of
⚫
⚫
The shear force Vu acts at a section that has a length b0 =
4(c+d) or 2(c1+d) +2(c2+d) and a depth d; the section is
subjected to a vertical downward load Pu and vertical upward
pressure qu .
The Allowable
For one way shear:
footings with bending action in one direction thr critical section is located in a distance d from
face of column
REINFORCEMENT DETAILS
1.The concrete cover of Reinforcements:
According to IS 456-200, the minimum thickness to main reinforcement in footing should not be
less than 50 mm if the footing is in contact with the earth surface directly, and 40 mm for the
external exposed face such as surface leveling PCC. If surface leveling is not used, then it is
required to specify a cover of 75 mm to cover the uneven surface of excavation.
2.Minimum reinforcement and bar diameter:
Minimum reinforcement shall not be less than 0.12 percent of the total cross sectional area. The
minimum diameter for the main reinforcement should not be less than 10 mm.
short side of the footing.
3-. Reinforcement Distribution in Footing:
In one-way RCC footing, the reinforcement is distributed uniformly across the ful
width of footing. In two-way square footings, the reinforcement extending in both
directions is distributed uniformly across the full width of the footing. But in the
case of two-way rectangular footings, reinforcement is distributed across the ful width
of footing in a long direction. However, for short direction, the reinforcement is
distributed in the central band as per the calculations below. The res reinforcement in
a short direction is distributed equally on both sides of the centra band.
Reinforcement in central band/Total reinforcement in short direction= 2/(x/y)+1
Where y is the long side and x is the short side of the footing.
I.
o
o
Size of Footing:
Size of the footing is determined based on the service load working loads.
Take 10% of the load as self-weight.
Permissible Stress:
o
o
o
As per IS:456-2000for M20 grade concrete ,
σcbc = 7 N/mm2
for HYSD steel σst = 230 N/mm2
Design Criteria: for M20 grade concrete and Fe -415 steel
o
M= => => 13.33
o
K= => => 0.28
o
j= 1- => 1- => 0.905
o
Q = σcbc X kj
 X 7 X 0.28 X 0.905 => 0.88
o
o
o
As per IS: 456-2000 (Table 23)
τc = 0.21 N/mm
τv ≤ k τc
As per IS: 456-2000, for 300 mm or more thick slab
o K=1
o k τc = 1 x 0.21 = 0.21 N/mm > τv
Safe
DESIGN OF FOOTING
o
o
Cloumn size = 300 x 300 mm
Axial load (W) = 675 KN
Assume 𝑀15 grade concrete and mild steel.
o
Safe bearing capacity of soil = 200kN/𝑀2
o
𝑀 = 3𝑎𝑏 𝜎 = 3×5 = 18.6
o
𝑐
𝑘 = 𝑀𝜎+𝜎
= 18.6×5+14 = 0.399 = 𝑂. 4
280
280
𝑐
𝑀𝜎 𝑏𝑐
186×5
𝑐𝑏𝑐𝑠𝑡
𝑘
0.4
3
o
𝐽 = 1−3 = 1−
o
𝑄=
o
LOAD CALCULATION
•
•
•
Axial Load (W) = 675 KN
10% Sectional Load = 10/100 x 675 = (10/100 x W) = 67.5
Total Load = W +10% Of sectional Load
= 67.5 + 657
= 742.5
𝑘𝐽𝑐𝜎 𝑏𝑐
2
=
𝜎
𝐶𝑏𝑐
𝜎
= 5 , 𝑠𝑡 = 190
= 0.867
0.87×0.4×5
2
= 0.87
o AREA OF FOOTING
•
𝑇𝑜𝑡𝑎𝑙 𝑙𝑜𝑎𝑑
𝑆𝑎𝑓𝑒 𝑏𝑎𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑜𝑖𝑙
=
742.5
200
= 3.7 𝑚2
• Area = L x B
3.7
= L = 1.92 = 1.94 m
• Therefore Provide a footing of size = 1.94 x 1.94 m
𝑊
675
• Net Upward Pressure (q) = 𝐿 𝑥 𝐵 = 1.9 𝑥 1.9 = 186.9 KN/ 𝑚2
o CRITICAL SECTION FOR MAXIMUM BENDING MOVEMENT OF THE COLUMN,
• M = (qB(B−𝑏 2 )) /8
= 186.9 x 1.92 (1.92− 0.32 ) / 8
= 98. 67 KN m
𝑀
107.88 𝑥 106
o
Effective Depth from BM – (d) = √𝑄𝐵 = √ 0.87 𝑥 1920 = 254.13
o
Effective Depth from Shear Consideration (On way Shear) – (𝛾) =
o
Shear force of critical section @ a distance from face of column
𝐵 −𝑏
𝛾 = 𝑞𝐵 ( 2 - d )
•
𝛾 = Net upward pressure x width of footing (
= 186.9 x 1.92
= 183
1.92 −0.3
( 2
𝑀
𝑉
3𝑑
𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑓𝑜𝑜𝑡𝑖𝑛𝑔 −𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑐𝑜𝑙𝑢𝑚𝑛
)
2
– Depth of column
- 0.3)
98.67 𝑥 106
o Area of Steel (𝐴𝑠𝑡 ) = 𝜎𝑠𝑡 𝑗𝑑 = 190 𝑥 0.86 𝑥 254.13 = 2371.35
o Percentage (%) of steel =
=
100 𝑥 𝐴𝑠𝑡
1920 𝑥 𝑐𝑜𝑙𝑢𝑚𝑛 𝑤𝑖𝑑𝑡ℎ (300 )
100 𝑥 2371.35
1920 𝑥 300
= 0.4 %
300 mm c/c
16 mm ∅ Bars
3m
1.94 m
1.94 m
DESIGN OF STAIRCASE
INTRODUCTION
A stair, or a stair step, is one step in a flight of stairs. In buildings, stairs is a term
applied to a complete flight of steps between two floors. A stair flight is a run of
stairs or steps between landings .A staircase or stairway is one or more flights of
stairs leading from one floor to another, and includes landings, newel posts,
handrails, balustrades and additional parts. A stairwell is a compartment extending
vertically through a building in which stairs are placed. A stair hall is the stairs,
landings , hallways, or other portions of the public hall through which it is necessary
to pass when going from the entrance floor to the other floors of a building . Box
stairs are stairs built between walls, usually with no support except the wall strings .
Stairs may be in a "straight run", leading from one floor to another without a tum or
change in direction. Stairs may change direction, commonly by two straight flights
connected at a 90 degree angle landing. Stairs may also return onto themselves with
180 degree angle landings at each end of straight flights forming a vertical stairway
commonly used in multistory and highrise buildings. Many variations of geometrical
stairs may be formed of circular, elliptical and irregular constructions.
The Various Parts of a Staircase are as Follows:
1. Step :This is a portion of a stair which is comprised of the tread and riser, and
permits ascending or descending transitions from one floor to another.
2. Curtail Step :It is the starting step of the staircase, which projects out of the string.
The curtail step can be constructed in a variety of designs
3. Tread : It's a top horizontal part of a step on which foot is placed, while transiting
in ascending or descending order
.4. Riser :This is a vertical member between two treads. Riser provides a support to
the treads.
5. Rise : Rise is a vertical distance between the upper faces of any two consecutive
steps.
6.Going Going is the width of the tread between two successive risers. In other
words, it is horizontal distance between the faces of any two consecutive risers.
7. Flight A continuous series of steps without any break or landing is known as flight.
8. Landing : Landing is a platform provided between two flights. A landing extending
to full width of staircase is known as half spaced landing and the landing extending
to only half across a staircase is called as quarter space landing.
09. Nosing : Nosing is the outer projecting edge of a tread. This is generally made
rounded to give more pleasing appearance and makes the staircase easy to negotiate
10. Line of Nosing : An imaginary line touching the nosing of each treads parallel to
the slope of the stair is known as line of nosing.
11. Winders : Winders are the tapering steps used for changing the direction of the
stair.
12. String or Stringers : String is a sloping member which supports the steps in a
stair.
13. Newel Post : Newel post is a vertical post placed at the top and bottom ends of
flights supporting the handrails.
14. Soffit : Soffit is the underside of a stair
15. Baluster/Spindle : Baluster is a vertical member or filling in between handrail
and base rail. It is provided for safety and aesthetic purpose.
16. Balustrade : The combined framework of handrail and baluster is known as
balustrade.
17. Railing : This is a framework of enclosure supporting a handrail and serves as a
safety barrier.
18. Handrail : This is a protective bar placed at a convenient distance above the stairs
for support. Elderly people can rest their hands on handrail to climb stairs easily .
The whole staircase is the assembly of all the aforementioned parts. The various
parts of a staircase can vary according to the type and material of the staircase.
TYPES OF STAIRCASE:
STRAIGHT STAIRCASE
If the space available for stair case is narrow and long,
straight stairs may be provided. Such stairs are commonly
used to give access to porch or as emergency exits to cinema
halls.
DOG-LEGGED STAIRCASE
It consists of two straight flights with 180° turn between the two.
They are very commonly used to give access from floor to floor.
OPEN WELL OR NEWEL STAIRCASE
It differs from dog legged stairs such that in this case there is
0.15 m to 1.0 m gap between the two adjacent flights.
GEOMETRICAL STAIRCASE
This type of stair is similar to the open newel stair except that
well formed between the two adjacent flights is curved . The
hand rail provided is continuous.
BIFURCATED STAIRCASE
Apart from dog legged and open newel type turns, stairs may turn
in various forms. They depend upon the available space for stairs.
Quarter turned, half turned with few steps in between and
bifurcated stairs are some of such turned stairs.
SPIRAL STAIRCASE
These stairs are commonly used as emergency exits. It consists of
a central post supporting a series of steps arranged in the form of
a spiral . At the end of steps continuous hand rail is provided .
Such stairs are provided where space available for stairs is very
much limited.
STAIRS OF DIFFERENT MATERIALS
BRICK STAIRS
• May be built of solid masonry construction or arches may be
provided in a lower portion.
METAL STAIRS
• The external fire-escape stairs are generally made of metal.
• The common metals used are cast iron, bronze and mild steel.
R.C.C. STAIRS
• commonly used in all type of constructions for residential,
public, and industrial buildings ,in case of framed structures,
R.C.C. stairs is perhaps only choice.
• are very good fire resistance.
• can be easily molded to the desired shape. (σcbc)
DESIGN CALCULATIONS
Modular ratio : M =
K=
280
3σcbc
= 13.33
𝑚σcbc
𝑚σcbc +σs𝑡
=
13.33×7
13.33×7+230
j = 0.905
Q = 0.88
Size of the room = 5×3.5×3
Provide 2 flights
Height of the flight = 3/2 = 1.5m
Number of risers in each flight = 1.5/0.15 = 10
Number of treads = 10-1 = 9
= 0.28
Assuming 270mm width of tread = 0.27×9= 2.43m
Effective span = 2.43 + 1.4 + 0.15/2 = 3.905m
Load calculations
(i)
Self weight of steps = 1×0.15/2×25 = 1.875
(ii) Self weight of waist slab on sloped area = 1×0.17×25 = 4.25 KN/m
(iii) Self weight of waist slab plain area =4.25
𝑅 2 +𝑇2
𝑅
= 4.25
2702 +1502
270
=4.86 KN/m
Live load = 4×1= 4KN/m
(iv) Finish (assume ) = 0.5KN/m
Total = 15.48KN/m
Maximum Bending Moment : M =
𝑀
Qb
Effective depth : d = √
=√
15.48×3.9052
6
39.34×106
0.88×1000
= 39.34KN-m
= 211.43mm ~ 215mm
M
39.34×106
Area of main steel Ast =
=
= 1058.28mm
σ𝑠𝑡𝑗𝑑 190×0.91×215
Spacing of 12mm ∅ bars =
1000×𝜋/4(122)
1058.28
= 106.86 mm ~ 110mm
Therefore , provide 12mm ∅ bars @ 110mm c/c.
Distribution steel = mm 0.12/100× 1000 × 215 = 258m2
Spacing of 8mm ∅ bars =
1000×𝜋/4(82)
258
= 194.82mm = 200mm
Therefore , provide 8mm ∅ bars @ 200mm c/c .