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“DESIGN OF PREFABRICATED MODULAR HOUSING FOR DIFFERENT OCCUPANCIES AT
PANCHESHWAR POWER PLANT”
BY: • FEBA MARY THOMAS (1010910068)• HARSHAL RASTOGI (1010910079)• JITHESH DHARMADAS (1010910087)
PROJECT GUIDE
Dr. M. LAKSHMIPATHY
OBJECTIVE
• For the inhabitants (about 5327 households ) displaced due to the implementation of the Pancheshwar Power Project on Mahakali river; housing is required to rehabilitate them
NECESSITY• Pancheshwar Power Project is proposed as a
Nepal-India bi-national scheme on the Mahakali river with a capacity of 6720 MW. With its implementation, a total of 41,330 persons from 5327 households have been displaced for which rehabilitation works has to be completed by 2012-2013 but as for now the progress is too slow to reach the deadline.
• For faster construction and as an approach to affordable homes , we provide a solution to mass housing using precast members.
SCOPE• The project envisages selection of a
suitable plan as per modular coordination and use of building architecture for proper functioning and orientation of the building.
• The houses are proposed to be classified on the basis of income groups (i.e. High Income Group, Medium Income Group and Low Income Group) which will then decide the corresponding plan areas.
METHODOLOGY• Selection of a realistic site.• Suggestion of a suitable plan for mass housing with grid
dimensions.• Selection of type of precast structural system.• Collection of necessary data and code books as required
for the project.• Design of foundation as per soil specifications of the site.• Selection of type of connection to be employed.• Design of precast members- Beams, columns and slabs.• Installation of the members as per design plan.• Provision for grid wise extension of the designed plan.
MAJOR DESIGN EXPERIENCE
• Planning and layout of a residential building.• Grid wise distribution of plan.• Design of structural and non- structural precast
members.• Design of connections between individual
precast members.
REALISTIC DESIGN CONSTRAINTS
Manufacturing constraints:
The design of functional plan and construction technology shall ensure that the project can be implemented in the shortest possible time with acceptable quality.
Safety constraints:
The design of all joints between prefabricated components shall meet the accepted procedures
Social constraints:
The compulsion to provide housing for people belonging to different status in society within the shortest possible time due to mass displacement.
REFERENCE TO CODES AND STANDARDS
• IS 10297:1982
Code for practice for design and construction of floors and roof using precast reinforced/ prestressed concrete.
• IS 875 :1987 Part (1&2)
Design loads for buildings and structures(Dead load & Imposed load).
• IS 456 :2000
Design co-efficient, Limit state design method.
APPLICATION OF EARLIER COURSE WORK
MULTIDISCIPLINARY COMPONENT AND TEAMWORK
• This project involves in interacting with the government officials of the Pancheshwar Project for getting necessary data.
SOFTWARE USED• AutoCAD
CONCLUSION (expected)• The project would successfully complete
the design of modular houses using advanced technology and a solution to quicker construction with economic advantages.
• Completion of the project will finally help in gaining vital and practical implementations in accordance with safety and serviceability of the designed units.
FUTURE SCOPE OF THE PROJECT (tentative)
• The implementation of the project will be of a great help to the rising need of quicker construction and in the field of mass housing techniques.
• It will be a boon for the weaker sections of society where owning a house is still a common dream and the economic advantage of the project would be effectively implemented.
• Provisions for extension of plan for other suitability issues is also included for satisfying different functional needs.
Distribution of Households as per Income Groups
• As per rehabilitation works at Pancheshwar Power Project, we need a total of 5327 households, out of which we assume as per guidance in Planning Commission, Government of India:
• 20% belonging to HIG i.e. 1066 households.• 50% belonging to MIG i.e. 2664 households.• 30% belonging to LIG i.e. 1597 households.
Allocation of Area for each Household
• The rehabilitation site being Pithoragarh and an available area of 200 acres as per Rehabilitation Proposal of the Pancheshwar Power Project.
• We adopt the carpet area of households according to the specifications provided by Planning Commission, Government of India, as follows:
• HIG- 150m2 (1615sqft)• MIG- 90m2 (968sqft)• LIG- 60m2 (646sqft)
ARCHITECTURAL INPUTS
• Orientation according to the sun-diagram• Anthropometrics • Space standards • Functional Planning and Circulation
ORIENTATION
• The orientation of a house is done according to the sun-diagram as shown in Fig. 3.1
Fig. 3.1 The sun diagram
ANTHROPOMETRICS• The dimensions of the human body as shown in Fig. 3.2 and the sizes of the
furniture help in deciding the space required in the design of a room. The size of the sofa in the living room, dining room in the dining room, bed in the bedroom, stove and fridge in the kitchen, the closet in the bath etc. help to decide the size of the rooms with proper clearances provided between the furniture for easy movement.
Fig. 3.2 Anthropometrics
SPACE STANDARDS
• Space is a specific volume which provides for a specific form of human activity. The common factor in buildings and areas in the concept of space. An architectural space is man-made. The space must be technically efficient and aesthetically satisfying.
• Every space accommodates an activity or a function, which decides the area and volume required. The activities determine the furniture requirements for the space.
FUNCTIONAL PLANNING AND
CIRCULATION• The design of a building depends upon the
nature of the building. Every building has a special character of its own. The function of the building is to be ascertained first. Then different blocks or units are to be planned. The units are then joined together to form a whole building. The sizes of various units depends upon the number
CONCEPT OF MODULAR COORDINATION EMPLOYED IN THE
PROPORTIONING OF PLAN• Modular coordination is a dimensional coordination
employing the basic module or a multi-module. A Module is the unit of size used in dimensional coordination. A multi module is a module whose size is a selected multiple of the basic module.
• The purposes of modular coordination are:
1. To reduce the variety of component sizes produced
2. To allow the building designer greater flexibility in the arrangement of components.
• Rules related to the basic elements according to modular coordination :
1. Planning grid in both directions of the horizontal plan shall be 3M. The centre lines of load bearing walls should preferably coincide with grid lines.
2. Planning module in the vertical direction shall be 1M.
3. Preferred increments for sill heights, doors, windows and other fenestration shall be 1M.
4. In case of internal columns, the grid lines shall coincide with the centre lines of columns.
5. In case of external columns and columns near the lift and stair, the grid lines shall coincide with centre lines of the column in the topmost storeys.
MODULAR COORDINATION ADOPTED IN COMPONENTS
• FLOORING AND ROOFING SCHEME: Precast slabs or other precast structural flooring units:
1. Length- multiples of 1M
2. Width- multiples of 0.5M
3. Overall thickness- multiples of 0.1M• BEAMS:
1. Length- multiples of 1M.
2. Width- multiples of 0.1M
3. Overall depth- multiples of 0.1M
• COLUMNS:
1. Height- multiples of 1M
2. Lateral dimensions- multiples of 0.1M• WALLS:
1. Thickness- multiples of 0.1M• LINTELS:
1. Length- multiples of 1M
2. Width- multiples of 0.1M
3. Depth- multiples of 0.1M• SUNSHADES:
1. Length- multiples of 1M
2. Projection- multiples of 0.5M
CONCEPT OF MODULAR COORDINATION
• Modular coordination is a concept of coordination of dimension and space, in which buildings and components are dimensioned and positioned in a term of a basic unit or module, known as 1M.
• The principal objective of implementing Modular Coordination is to improve productivity in the building industry through industrialization.
TERMINOLOGY• Module: A unit of size used as an increment in
dimensional coordination.• Modular size: A size that is a multiple of the
basic module.• Modular grid: A rectangular coordinate reference
system in which the distance between the consecutive lines is the basic module or a multi module. The multi module may differ for each of the two dimensions of the grid.
• Multi module: A module whose size is a selected multiple of the basic module.
BENEFITS OF MODULAR COORDINATION
• To obtain maximum economy in the production of components.
• Simplifies site operations by rationalizing setting out, positioning and assembly of building components.
• Ensures dimensional coordination between installation (equipment, storage units, other fitted furniture, etc.) as well as with the rest of the building.
• To allow the building design a greater flexibility in the arrangement of components.
Finalized LIG PlanThe plan for LIG having a carpet area of 60m2. All dimensions are in m.
Finalized MIG Plan
The plan for MIG having a carpet area of 90m2. All dimensions are in m.
Finalized HIG PlanThe plan for HIG having a carpet area of 150m2. All dimensions are in m.
PLAN INCLUDING LIG, MIG, HIG
IDENTIFICATION OF STRUCTURAL ELEMENTS
• Masonry wall- A wall made from materials which have traditionally been cemented together with the use of mortar.
• Reinforced Concrete Columns- They are structural members designed to carry compressive loads, composed of concrete with an embedded steel cage to provide reinforcement.
• Reinforced Concrete Beam- A beam is a structural element that is capable of withstanding load primarily by developing bending stresses and resisting it.
• Reinforced Concrete Slab - A structural member whose thickness is small compared to its plan dimensions, spanning between beams, girders, or columns, walls etc.
DESIGN OF SLAB SPAN: 3m*5m
STEP 1: TO DETERMINE THE TYPE OF SLAB
Lx = 3m
Ly = 5m
fck = 20 N/mm2
fy = 415N/mm2
Ly/Lx = 1.667< 2 (TWO WAY SLAB)
End condition = Four edges discontinuous
STEP 2: EFFECTIVE DEPTH OF SLAB
Span/depth ratio = 28
Effective depth = 107.14mm
Provide effective depth of 120mm, effective cover of 20mm.
Over all depth is 140mm
STEP 3: LOADS
Self weight of Slab = 0.14X 1 X 25 = 3.5 KN/m2
Live Load (IS 875 Part-2; Pg: 09) = 2 KN/m2
Floor Finish = 1 KN/m2
Total load = 6.5KN/m2
Design Ultimate Load, Wu = 1.5 x 6.5
Wu = 9.75 KN/m2 say 10KN/m2
STEP 4: ULTIMATE DESIGN MOMENT & SHEAR
Refer IS456 – 2000; Pg: 91 Table 26
a) SHORT DIRECTION
M = αxWuLx2
No Negative Moment due to absence of continuous edges.
Positive at Mid Span
αx = 0.0945
M = 0.0945x 10 x 32
M = 8.505 kNm
b) LONG DIRECTION
No Negative Moment due to absence of continuous edges.
Positive at Mid – Span
αy = 0.056
M = 0.056 x 10 x 52
M= 14 kNm
STEP 5: CHECK FOR DEPTH
Mu.lim = 0.138 x fck x bd2
d = 71.22mm < 120mm, Hence chosen depth is safe.
STEP 6: REINFORCEMENT (short & long span)
Min. Ast = 168mm2
Positive at mid span
Mu = 0.87 fy Ast d
14 x 106 = 0.87 x 415 x Ast x 120
Ast = 323.13mm2
Spacing should least of the following
Spacing = 459.3mm say 460mm
3d = 3(120) =360mm
300mm
Ast(pro) =392.7 mm2
Provide 10mm diameter bars @ 200mm c/c as main steel.
Distribution steel
As per minimum steel,
Ast = 168mm2
Provide 8mm diameter bars @ 300mm c/c as distribution steel.
STEP 7: CHECK FOR SHEAR
Considering the short span unit width of slab.
Vu = 0.5 x Wu x L x = 0.5 x 10 x 3
Vu = 15kN
v = 0.107 N/mm2
Pt = 0.28 (Refer table 19, IS456-2000; Pg: 73)
τc = 0.39 N/mm2 >v (0.107N/mm2)
Hence Shear Safe
STEP 8: CHECK FOR DEFLECTION
Basic = 20 For pt = 0.28, (IS456-2000, Pg: 38)
kt = 1.2
Max > Actual
Basic x kt >21.42
20 x 1.2 > 21.42
24 > 21.42, Hence Deflection are Safe
STEP 9: CHECK FOR ERECTION STRESSES
Hooks are provided at 1m offset from edge in longer span and .5m offset from edge in shorter span, at all four corners of slab.
Load on slab due to erection= self weight of slab= 52.5kN/m
Check for dimensions:
Negative moment at the edge due to cantilever= 52.5x0.5x0.5/2=6.56kNm
Positive moment at mid span= 52.5x2x2/8=26.25kNm
Net excess moment= 19.69kNm
Mexcess = 0.138 x fck x bd2
d = 84.27mm < 120mm, Hence chosen depth is safe
Thus slab is safe for erection stresses too.
PLINTH BEAM DESIGN5m span
STEP 1: ADOPT A PRELIMINARY BREADTH AND DEPTH
d=L/20= 5000/20= 250mm
D=d+effective cover= 250+30= 280mm
b =150mm
STEP 2: LOAD CALCULATIONS
Self weight= .15*.28*25=1.05kN/m
Weight of brick masonry wall above plinth =.15*2.6*19= 7.41kN/m
Total Load= 8.46kN/m
Factored Load= 1.5*8.46=12.69~=13kN/m
STEP 3: MOMENT CALCULATIONS
Mu=Wu*leff*leff/30= 13*5*5/30= 10.83kNm
Mu,lim= .138fckbd2 =.138*20*150*250*250= 25.875kNm
Mu<Mu,lim Hence adopted dimensions are safe.
STEP 4: REINFORCEMENT DETAILS
Mu=0.87fyAstd(1-(Astfy/bdfck))
Ast=129.22mm2
Ast, minimum= (.85/fy)*b*D=(.85/415)*150*280=86.02mm2
Ast, cal>Ast, min
Adopt 10mm dia bars.
No.of bars= 129.22/78.5=2
Hence providing 3Y10 as tension steel.
STEP 5: DESIGN OF STIRRUPS
Shear force Vu=Wu*L/2= 13*5/2= 32.5kN
Nominal shear stress= Vu/bd= 32500/(150*250)=.87N/mm2
Permissible Shear Strength of concrete as per Table 19 IS 456 for M20 and Ast=235.5mm2 =.5N/mm2
Nominal shear stress> Permissible Shear Strength, stirrups are provided for Nominal shear stress= Permissible Shear Strength.
Vus=.87*fy*Asv*d/sv
32500=.87*415*Asv*250/300
Asv=108.01mm2
For a two legged 10 dia stirrup, 2*78.5=157mm2>Asv
Hence provide 2LY10@300c/c for shear reinforcements
STEP 6: CHECK FOR DEFLECTION
Basic = 20
For Pt = 0.628, (IS456-2000, Pg: 38)
Kt = 1.8
20 X 1.8 > 20
36 > 20
Hence Deflection is Safe.
STEP 7: CHECK FOR ERECTION STRESSES
Hooks are provided at 0.3m offset from both edges.
Load on beam due to erection= self weight of beam= 1.05kN/m
Check for dimensions:
Negative moment at the edge due to cantilever= 1.05x0.3x0.3/2=0.047kNm
Positive moment at mid span= 1.05x4.4x4.4/8=2.541kNm
Net excess moment= 2.494kNm
Moment adopted for design=10.83 kNm
Moment adopted for design> Net excess moment due to erection
Thus beam is safe for erection stresses too.
INTERIOR COLUMN DESIGNSTEP 1: LOAD CALCULATIONS
Load on column= 120 KN. Design constant a) Grade of concrete =M20 b) Grade of steel = Fe415. L = Unsupported length of the column in mm = 4650mm Design load Pu = 1.5 x120 =180 kN.
STEP 2: COLUMN DIMENSIONS
The cross-sectional dimensions required will depend on the percentage of reinforcement.
Assume percentage of comp. steel between 0.8 to 6% of gross c/s area
Assuming 1.0 percent reinforcement and referring to Chart 25 SP16 Design Aids,
Ag= 500cm2
Adopting square column, hence providing 250*250mm
STEP 3: TYPE OF COLUMN
Leff/b= 1*4650/250=18.6>12, hence long column.
STEP 4: ADDITIONAL MOMENT DUE TO BUCKLING IN LONG COLUMN
Max=May=(Pu*D/2000)*(Leff/D)2
=186000*250/2000*(1*4650/250)2 = 8.04kNm
Puz = 0.45fck Ac + 0.75fy As =751.40kN
Pu/Puz=.2, αn=1
Mux=Muy= 15.028kNm,
Interaction equation=.958 <1.0 as per SP16 Design Aids
STEP 3: LONGITUDINAL REINFORCEMENTSAsc = 1.0 % Ag= 625mm2 For = 12 No of Bar = N =5.52~=6∅
STEP 4: SHEAR REINFORCEMENTSa) Select diameter of lateral ties least of 6 mm or 1/4 diameter of the largest longitudinal bar not less than 16 mm diameter. Diameter of the lateral ties / link =8 mmb) Spacing of lateral ties / link Least of i) Least lateral dimension of column =250mm ii) Sixteen times the smallest dia. of bar = 16 x 12=192mm and iii) 300 mm Provide 8 mm dia. @ 150 C/c
STEP 7: SUMMARY OF DESIGN 1. Column size: 250x250 mm 2. Longitudinal Steel: 6Y123. Lateral Steel: 2LY8@150c/c
STEP 8: CHECK FOR ERECTION STRESSES
Hooks are provided at L/3m i.e. 1.55m offset from both edges.
Load on beam due to erection= self weight of column= 1.5625kN/m
Check for dimensions:
Negative moment at the edge due to cantilever= 1.5625x1.55x1.55/2=1.87kNm
Positive moment at mid span= 1.5625x2.325x2.325/8=1.05kNm
Net excess moment= 0.814kNm
Mexcess = 0.138 x fck x bd2
d = 34.35mm < 170mm, Hence chosen depth is safe
Check for shear:
Vu = 0.5 x Wu x L = 0.5 x 1.5625 x 1.15
Vu = .898kN
v = 0.014 N/mm2
Pt = 1.0
(Refer table 19, IS456-2000; Pg: 73)
τc = 0.62 N/mm2 >v (0.014N/mm2)
Hence Shear Safe
Thus column is safe for erection stresses too.
FOOTINGData:
SBC of soil = 200 kPa
Unit weight of soil = 18 kNm3
Ø= 30°
Grade of concrete = M20
Steel bars used = Fe 415
Load from column = 258 kN
Step 1: Determination of depth of foundation:
Depth of foundation = qsΥs[1-sinØ1+sinØ]2
= 20018[1-sin301+sin30]2
= 1.3 m
Hence we have to excavate soil upto 1.3 m below ground level
Step 2: Determination of plan area:
Area = A = loadqs
= W+Wfqs
= 258+0.1×258200
= 1.419 m2
Step 3: Determination of width of foundation:
Assuming a square footing:
Width of the square footing = B = A = 1.419 = 1.19 m
Lets us assume the width of the footing = 1.2 m
Hence, we have to provide a square footing of size 1.2 m×1.2 m
Step 4: Determination of maximum bending moment:
Maximum bending moment = wa22
Where,
w= upward soil pressure in kNm
a= B2-b2
B= width of foundation = 1.2 m
B = width of column = 300 mm = 0.3 m
w = load from columnplan area×B
= [2581.22]×1.2
= 215 kNm
Ultimate bending moment = Mu = 1.5×215×.4522
= 32.65 kN-m
Step 5: Calculation of effective depth:
Mu=.36fckbd2k(1-.42k)
d=Mu.36fckbk1-.42k
d=32.65×106.36×20×1200×.48(1-.42×.48) = 99.305 mm
Hence, let us adopt a depth of 175 mm.
Step 6: Calculation of Ast:
Mu= .87fyAstd1-fyAstfckbd
32.65 × 106 = .87×415×Ast×1751-415Ast20×1200×175
From the above equation: Ast = 546.22 mm2
Ast,min= .0012×(b×D)
= .0012×(1200×230) = 331.2 mm2
Hence, Ast>Ast,min
Step 7: Check for one way shear:
For one way shear the critical section will take place at a distance, “d” from one face of column.
Upward shear force = V=upward soil pressure×area
= 1.5×2581.22×.275×1.2
= 88.68kN
Nominal shear stress = ƫv = Vbd
= 88.68×10001200×175
= .422 mPa
As per IS 456: 2000:
ƫv≤ k×ƫc
From IS 456: 2000, table number 19:
percentage of tension steel=p=100Astbd = .26
For,
p = .26 and fck= 20 mPa
ƫc= .36 mPa
k=1
Hence,
ƫv>(k×ƫc)
The depth chosen is not adequate as per one way shear criteria and the depth has to be redesigned.
1.5×2581.22×.275-d×1.2= .36×1.2×d
From the above equation; d = 274 mm
Adopting the depth to be 300 mm
Step 8: Check for two way shear/ punching shear:
The punching shear occurs at a distance of half of the effective depth from all the faces of column.
Fig. 7: Critical section for punching shear
Shear force = V = soil pressure ×area
= 215 [1.22-.2+.32]
= 255.85 kN
ƫv= Vbd
= 2558504×600×300
= .355 mPa
ƫc = .25fck= .25×20 = .64 mPa
ks=1
ƫv< ks×ƫc
Hence, the design is safe.
Step 9: Check for bearing stress:
Bearing stress = wcolAg
= 258×1033002
= 2.867 mPa
.45fckA1A2 = .45×20×2 = 12.47 mPa
=>2.867<12.47
Hence, the design is safe against bearing.
Step 10: Spacing of reinforcement:
Assuming 10 mm bars for main reinforcement, the spacing = s = .785×102×1200546.22 = 172 mm ≅ 150 mm
Hence, 10 mm dia Fe 415 bars will be provided @ 150 mm c/c distance as main reinforcement.
Spacing of transverse reinforcement:
Assuming 8 mm diameter bars, spacing = s = .785×64×1200.0012×356×1200 = 117.6 mm ≅ 100 mm
Hence, 8 mm dia Fe415 bars will be provided @ 100 mm c/c distance as transverse reinforcement.
JOINTS AND CONNECTIONS
• Connections are among the most essential parts in precast structures. Their performance relates to the structural limit states, as well as to manufacture, erection and maintenance of the structure itself. Proper design of connections is one major key to a successful prefabrication.
• The main purpose of the structural connections is to transfer forces between the precast concrete elements in order to obtain a structural interaction when the system is loaded.
• By the ability to transfer forces, the connections should secure the intended structural behavior of the superstructure and the precast subsystems that are integrated in it.
• This could for instance be to establish diaphragm action in precast floors and walls, or cantilever action in precast shafts. For this reason the structural connections should be regarded as essential and integrated parts of the structural system and they should be designed accordingly and with the same care as for the precast concrete elements. It is insufficient just to consider the connections as details for site erection.
• The advantages that normally are obtainable with prefabrication can be lost with an inappropriate design and detailing of the structural connections.
FLOOR TO BEAM CONNECTIONS
• Details of typical bearing of a floor unit over the precast beam are shown in Fig. 1 the stirrups of the precast beams are protruded and function as shear connectors
• The reinforcing bars of the in-situ screeding concrete are extended over the beam supports so as to ensure continuity.
Fig. 1 – Precast slab to beam joint
BEAM TO COLUMN CONNECTIONS
• The bracket support for the beam over the column is shown in Fig. 2.
• A tolerance of 2-3 cm is allowed at the seating of the beam over the bracket.
• A dowel bar inserted through the holes provided in the bracket and the beam ensures an effective connection between them.
• The top reinforcing bars of the precast beams are connected to thecolumn joint by welding. Since only a few number of bars are welded, it is assumed that the connection between the beam and the column is a rigid one at the serviceability stage, but behaves as a hinged one at the ultimate stage
Fig. 2 – Precast beam to column joint
FOUNDATIONS
• The foundations usually cast as in-situ isolated footings as the local soil conditions warrant.
• The bottom end of the precast column is connected to the foundation as shown in Fig. 3
Fig. 3 – In-situ footing to precast column connection
PRODUCTION AND ERECTION
• The method of production depends on the total number of prefabricated elements that are to be produced. The components may be produced either in a factory on mass scale or in casting yards located near the site and equipped with the necessary plant and machinery.
• For facilitating erection, lifting hooks are provided in the precast floors and beams. Erection eyes as given in Fig.4 provided in the structural elements help in lifting them during transportation and erection using temporary bracing.
• For transportation and erection purposes the hook placements adopted are shown in Fig. 5, Fig. 6 and Fig. 7.
Fig. 4 – Hook details
Fig. 5 – Hook placements for slab
Fig. 6 – Hook placements for beam
Fig. 7 – Hook placements for column
REFERENCES
• Various authors (2008), ‘Principles of Architecture’, Oxford University Press, New Delhi, Vol.7, pp. 154-167
• Nicholson Peter (2009), ‘Principles of Architecture: Comprising Fundamental Rules of the Art, with Their Application to Practice’, H. G. Bohn, Cambridge, Vol.6, pp. 38-42
• Venugopal M.S. (1981), Structural Engineering Research Centre, Madras, Vol.1, pp. 1-23
• Ramakrishna(1982), ‘Precast concrete- cost implications and future’ , SERC,
• Madras, Vol.1, pp.1-8• National Building Code of India(2005), Bureau of Indian Standards• Raju Krishna (2009), ‘Concrete technology’ Tata McGraw-Hill
Education, New Delh, Vol5, pp. 603-631
THANK YOU