2_Madam Kumari Rai -15_final Report 12x12_ Column_ 2 Storey

ORIGINAL

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai

Submitted by: Home Plans Consultancy (P.) Ltd. Dharan-12, Tel: 527270, 8 September 2017

Table of Contents 1.

BACKGROUND .......................................................................................................3

ASSUMPTIONS ..........................................................................................................................3 1.1 DESCRIPTIONS OF THE BUILDING ..........................................................................3 2.

NUMERICAL MODEL ............................................................................................5

2.1 MODELING .........................................................................................................................5 2.2 ANALYSIS ...........................................................................................................................9 2.3 DESIGN ............................................................................................................................10 3.

SUMMARY ...........................................................................................................12

4.

REFERENCES .......................................................................................................13

Summary This report comprises the summary of the structure design of residential building of Mrs. Madam Kumari Raiat ward no.-15, Dharan Sub-Metropolitan. The Report consists of design procedures adopted, assumptions made, the inputs made in the design. During design it is assumed that the construction will be supervised by a professional engineer. The designer will not be responsible if any alteration or changes to the structural system is made by the client or contractor without the prior written permission from the designer, or the alternations to the non-structural system is made such that the weight of each individual floor or the weight of the whole building is altered by more than 10% of design weight of each floor and the total weight. The design calculations and derivations are limited to only a minimum to let the concerned people know the methodology adopted. However, the calculations may be provided to the client or concerned authorities when needed, upon request. The building is newly designed conforming to 1994 Nepal National Building code, and expects underlying intent of Life Safety performance under design earthquake.

……………………. Mr. Sudeep K.C., M.Sc. in Structural Engineering NEC No. 5691 Civil “A” Category

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

1. Background This report summarizes the structural analysis and design of residential building of Mrs. Madam Kumari Rai at ward no.-15. It has planned to utilize the building as a residential uses. The structural analysis in this building considers G+1 story with staircase cover. The aim of design is the achievement of an acceptable probability that structures being designed will perform satisfactorily during their intended life. With an appropriate degree of safety, they should sustain all the loads and deformations of normal construction and use and have adequate durability and adequate resistance to the effects of misuse and fire. Structural Analysis of the concerned building has been done in details with analysis and designs. The analysis and design has been based on the prevailing codes that are in practice in Nepal, the National Building code of Nepal (105:1994) and the IS code at places if required. This report consists of the design procedures adopted, the assumptions made, the inputs made in the design and the design output. Assumptions The following assumptions are taken into consideration in the seismic resistant analysis and design of structures: Adequate supervision and quality systems are provided during execution of the works. Construction is carried out by personnel having the appropriate skill and experience. Construction materials and products confirm to the pertinent codes and specifications. The structure is adequately maintained. The structure is used in accordance with the design brief. An earthquake is not likely to occur simultaneously with maximum flood, wind, waves or tides. Resonance as visualized under steady state sinusoidal excitation will not occur, as the small duration of earthquake is not enough to build up resonance amplitudes. Subsoil does not considerably settle or slide due to earthquake at the site of structure. This report is divided into three chapters. Chapter one begins with introductions and general description Chapter two comprises the numerical modeling, analysis and design; Chapter three presents the summary and recommendations 1.1 Descriptions of the building Following are the descriptions of the building based on architectural drawing study.

Page 3 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure: Conceptual Typical Architectural Floor Plan Table 1: General description Building Owner

Mrs. Madam Kumari Rai

Location

Ward no.-15,Dharan Sub-Metropolitan, Sunasari

Terrain type

Plain

Nos. of Blocks

One

Type of structure

Reinforced concrete frame building

No of stories

Two with stair case cover

Plan configuration

Regular

Vertical configuration

Regular

Position of the building block

Erected coinciding along property line at one side

Building dimension

Refer attached drawing

Storey height

10’ 5” all floors

Plinth Area

859.79 sq. ft.

Foundation, Column, Beam, Slab etc.,

Refer to table 2, Under the heading Member Properties

Page 4 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

2. Numerical Model 2.1 Modeling The analysis has been carried out with the most popular and reliable structural analysis software “ETABS 2016”. All the models are built up in 3-Dimensions and actual 3-D analysis is performed ETABS 2016 is based on Finite Element Method. Modulus of elasticity and poison’s ratio for the materials used are taken accordingly. Beams and columns are modeled as frame (line) elements with sufficient and appropriate meshing. The section properties used are based on preliminary section sizing with consideration for deflection, minimum sizing specified and serviceability. The buildings are modeled as a series of load resisting elements. The lateral loads to be applied on the buildings are based on the Indian standards. The study is performed for seismic zone V as per IS 1892:2002. The building sadopted consist fo reinforced concrete and brick masonry elements. The frames are assumed to be firmly fixed at the bottom and the soil-structure interaction is neglected. Table : Model data of the buildings Structure

SMRF

Number of stories

G+1 with staircase cover

Type of building use

Residential

Foundation type

Isolated, strap

Material Properties Young’s modulus of M20 concrete, E

22.36x 105 KN/m2

Grade fo concrete

For all structural elements M20

Grade fo steel

Fe 500 for all

Density of reinforced concrete

25 KN/m3

Density of brick masonry

20.0 KN/m3

Menber Properties Thickness of floor slab

130mm

Beam size

230mm x 350mm

Column size

300mm x 300mm

Thickness of wall

230mm and 115mm

Deaed Load Intensities Floor finishes and other

2 kN/m2

Live Load Intensities Staircase, Room, Roof

3.0 kN/m2 , 2.0 kN/m2 , 1.50 kN/m2

Page 5 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Base shear calculation As per NBC 105: 1994 Seismic zone

Dharan

Seismic Zone factor

Z

cl 8.1.6, fig 8.2

I

cl 8.1.7, table 8.1

Type of Building

1 All other

Importance factor Lateral load resisting system

cl 8.1.8, table 8.2

1.0 Ductile Moment Resisting Frame

Structural performance factor

K

Height of the building

h

12.192

Dimension of the building Along X

Dx

7.480

Dimension of the building Along Y Time period of the building along X,

Dy Tx= 0.09h/√Dx

9.970 0.401

Time period of the building along Y

Ty= 0.09h/√Dy

cl 7.3 cl 7.3

Soil type Cx

Basic seismic coefficient along Y Design Horizontal Seismic Coefficient along X

Cy

Seismic Wt of the Building

0.348 Sub Soil Type II

Basic seismic coefficient along X

Design Horizontal Seismic Coefficient along Y

1.0

cl 8.1.4, fig 8.1 cl 8.1.4, fig 8.1

0.080

Cdx = CZIK

cl 8.1.1

0.080

Cdy = CZIK W

cl 8.1.1

Base Shear

VB

Load combination are used as per NBC 105:1994

Page 6 of 31

0.080

0.080 2439.60

Cl 7.5.3 Ah W

195.17

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Fig: 3-D view of the building in ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Fig: 2-D (Plan) view of the building in ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Fig: 2-D (Elevation) view of the building in ETABS 2016

2.2 Analysis Three dimensional Response Spectrum Analysis has been carried out using the standard software ETABS 2016.The structure is assumed to be fixed at the foundation level. The brick wall is considered as the filler wall only. The beams are modeled as rectangurlar beams. The flange effect of the beams has been neglected. Center to center dimension of the structure has been considered in the analysis. The rigid end effect has also been considered in the analysis. Following tables summarizes the analysis output of the modelled structure. Table: Base shear after scaling Load Case/Combo

FX kN

EQX EQY RSAX Max RSAY Max Table: Model Load Participation ratio Case

Item Type

FY kN

-195.17

0

0 195.17 0.11

-195.17 0.11 195.17

Static %

Item

Dynamic %

Modal

Acceleration

UX

100

99.98

Modal

Acceleration

UY

100

99.99

Modal

Acceleration

UZ

47.25

24.99

Table: Model Participation Mass Ratios Page 9 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Case

Period

Mode

sec

UX

UY

UZ

Sum UX

Sum UY

Sum UZ

Modal

1

0.523

0.90

0.00

0.00

0.90

0.00

0.00

Modal

2

0.51

0.00

0.88

0.00

0.90

0.88

0.00

Modal

3

0.441

0.00

0.03

0.00

0.90

0.91

0.00

Modal

4

0.202

0.07

0.00

0.00

0.97

0.91

0.00

Modal

5

0.195

0.00

0.07

0.00

0.97

0.97

0.00

Modal

6

0.166

0.00

0.01

0.00

0.97

0.98

0.00

Modal

7

0.155

0.00

0.02

0.00

0.97

1.00

0.00

Modal

8

0.155

0.03

0.00

0.00

1.00

1.00

0.00

Modal

9

0.144

0.00

0.00

0.00

1.00

1.00

0.00

Modal

10

0.069

0.00

0.00

0.11

1.00

1.00

0.11

Modal

11

0.066

0.00

0.00

0.01

1.00

1.00

0.12

Modal

12

0.065

0.00

0.00

0.13

1.00

1.00

0.25

2.3 Design The aim of structural design is the achievement of an acceptable probability that structures being design will perform satisfactorily during their intended life with an appropriate degree of safety, they should sustain all the loads and deformations of normal construction and use and have adequate durability and adequate resistance to the effect of misuse and fire. Therefore, Limit state method is used for the design of RCC elements. The design is based on IS: 456-2000, SP16, IS: 1893-2002, and Reinforced Concrete Designer’s Handbook are extensively used in the process of design. Foundation design is carried out to satisfy strength and stability requirements. The space frame is considered as a special moment resisting frame (SMRF) with a special detailing to provide ductile behavior at every joint between beams and columns and in other parts to get ductility and comply with the requirements given in IS 13920:1993, Hand book on Concrete Reinforcement and Detailing SP: 34 and NBC201:1994. The provision of shear reinforcement is sufficient so that shear failure mode is avoided moreover there will be failure in flexure since this is more ductile. Hence the design philosophy of “Strong Column and weak beam”. Bearing capacity of the soil was assumed to be 150 kN/m2. Raft foundation is adopted. Durable M20 concrete has been used in the foundation which is in contact with the soil. Ductile detailing has been extensively adopted while detailing. The design out put has been presented in the form of structural drawing. 2.3.1 Summary of Design For all Floor Slab Provide the Thickness of the Slab = 130 mm Bottom Main bar in X-direction = 8 mm Ø @ 150 mm c /c Bottom Main bar in Y-direction= 8 mm Ø @ 150 mm c /c Top Main bar in X-direction = 8 mm Ø @ 150 mm c /c Top Main bar in Y-direction= 8 mm Ø @ 150 mm c /c Page 10 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Section of columns & Reinforcement Details S.N.

COLUMN SIZE

1

300mm X300mm

COLUMN NAME

Column (All)

Stirrups

Ground Floor

Remaining upper floor to roof

4#16mmØ + 4#12mmØ

4#16mmØ + 4#12mmØ

Ties 4 legged 8mmØ@ 100mm and 150 mm at centers (refer Structural Drawings)

Ties 4 legged 8mmØ@ 100mm and 150 mm at centers (refer Structural Drawings)

For all details, Refer submitted Structural Drawing It is recommended that the mix design of concrete should be carried out to conform the desired strength as per IS 456-2000. Details of Floor Beams

Floor name

Size (BXD)

Grid

Top bar

Bottom bar

(mm) additional bars Foundation /Plinth beam

230x230

All

Ground Floor Beams and First floor Beams

230X350

All

Second Floor Beams

230X350

All

Staircase cover Beams

230X350

All

main bars

additional bars

main bars

3# 12mmØ

3# 12mmØ

1# 12mmØ

2# 16mmØ

2# 16mmØ

1# 12mmØ

2# 12mmØ

2# 12mmØ

2# 12mmØ

2# 12mmØ

Stirrups 2 legged, 8mmØ@ 100mm and 150 mm at centers (refer Structural Drawings) For all details, Refer submitted Structural Drawing It is recommended that the mix design of concrete should be carried out to conform the desired strength as per IS 456-2000. Page 11 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Summary of Details of Foundation

S.N .

Foundation Symbol/ Grid

d (mm)

D (mm)

Depth of LxXLy Foundati (mm) on (mm)

Reinforcement

1.

F-1

200

450

2000

1900x1900

12mmØ@150mm C/C both ways

(C-1, C-2,C-3) 2.

F-2 (A-4,B-4, A-1,B-1)

200

450

2000

2000x1500

12mmØ@150mm C/C both ways

3.

F-3 (A-3,B-3, A-2, B-2)

200

450

2000

2000x2000

12mmØ@150mm C/C both ways

Floor name

Size (BXD)

Grid

Top bar

Bottom bar

(mm) additional bars Strap Beams

300x550

Refer drawing

main bars

additional bars

main bars

2#16mmØ 3#16mmØ, 2#16mmØ 3# 16mmØ

Stirrups 3 legged, 8mmØ@ 150mm at centers (refer Structural Drawings)

3. Summary This report is outcome of structural analysis and design of the residential building of Mrs. Madam Kumari Rai at ward no.-08, Dharan Sub-Metropolitan. Three dimensional Response Spectrum Analysis has been carried out using the standard software ETABS 2016. The design of the members has been done as per philosophy of limit state method. For the design of the members IS 456: 2000 and aid SP 16 has been extensively used. Ductile detailing has been extensively adopted while detailing. The design out put has been presented in the form of structural drawing. Building which are properly planned, designed and constructed has a good capacity to withstand earthquakes. Past earthquakes have shown that well designed buildings have withstood earthquakes well. Earthquake resistant design of the building costs money. The total cost of the building may be increase. The owners of the building should bear this in mind and be mentally prepared to invest this extra cost.

Page 12 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

4. References IS : 456-200 : Code of Practice for Plain and Reinforced Concrete IS 875n(Parts 1-5) : Code of Practice for Design Loads (Other than Earthquake) for Buildings and Structures (second revision) o Part 1 – Dead Loads o Part 2 – Imposed Loads NBC 105 : 1994 : Seismic Design of Buildings in Nepal IS : 1893- 2002 : Criteria for Earthquake Resistant Design of Structures IS 13920 – 1993: Ductile Detailing of Reinforced Concrete Structures Subjected to Seismic Forces – Code of Practice SP: 16- 1980 : Design Aids for Reinforced Concrete to IS : 456-1978 SP : 34- 1987: Handbook on Concrete Reinforcement Detailing Jain, A.K. Reinforced Concrete, Limit State Design, fifth edition, Nem Chand and Bros, Roorkee,1999 Sinha, S.N. Reinforced Concrete Design, Second edition, Tata McGraw Hill Publishing Company Ltd, New Delhi, 1996 Pillai, U.C. and Menon,.D. Reinforced Concrete Design, Second edition, Tata McGraw Hill Publishing Company Ltd, New Delhi,2003.

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Annex A: Typical Design Software Design Out put

Page 14 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid A-A, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid B-B, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid C-C, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid 1-1, ETABS 2016

Page 18 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid 2-2, ETABS 2016

Page 19 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid 3-3, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars along grid 4-4, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars in beams at First floor level, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars in beams at Second floor level, ETABS 2016

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Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Figure showing rebars in beams at Staircase Cover floor level, ETABS 2016

Page 24 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Strap footing analysis and design

FEM model of Strap footing with pad

Loading (area load) (left column 250kN, right column 350kN)

Page 25 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

M11- stress (max 13.00 kN-m/m)

M22- stress (max -42.00 kN-m/m)

Page 26 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Bending moment diagram on strap beam

Shear force diagram on strap beam

Page 27 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Strap beam design area of steel (Provide 3 # 16 mm dia top regular bars plus 2# 16 mm dia bars at extra bars at top and bottom) (Stirrups 4 legged 8 mm dia @ 100 mm c/c) Area of steel in footing slab Over all depth D = 250 mm Effective depth d = 250 – 15 – 12/2 = 229 mm

Mu = 42. 00 kN-m/m Fy = 500 MPa, b = 1000 mm Ast = 443.05 mm2 Provide 12 mm dia @ 150 mm at centers (Provided Ast = 113 mm2* 1000mm/150mm = 904 mm2 > 443.05 mm2 (ok) Page 28 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

ETABS 2016 Concrete Frame Design IS 456:2000 Beam Section Design

Beam Element Details Type: Ductile Frame (Summary) Level

Element

Unique Name

Section ID

Combo ID

Station Loc

Length (mm)

LLRF

Base

B1

1

Strap Beam

DCon10

2000

4280

1

Section Properties b (mm)

h (mm)

bf (mm)

ds (mm)

dct (mm)

dcb (mm)

300

550

300

0

33

33

Material Properties Ec (MPa)

fck (MPa)

Lt.Wt Factor (Unitless)

fy (MPa)

fys (MPa)

22360.68

20

1

500

500

Design Code Parameters ɣC

ɣS

1.5

1.15

Factored Forces and Moments Factored Mu3 N-mm

Factored Tu N-mm

Factored Vu2 N

Factored Pu N

-152344159

0.17

107661.15

0

Design Moments, Mu3 & Mt Factored Moment N-mm

Factored Mt N-mm

Positive Moment N-mm

Negative Moment N-mm

-152344159

0.28

0

-152344159

Design Moment and Flexural Reinforcement for Moment, Mu3 & Tu Design -Moment N-mm Top

(+2 Axis)

Bottom (-2 Axis)

Design +Moment N-mm

-152344159 0

-Moment Rebar mm²

+Moment Rebar mm²

Minimum Rebar mm²

Required Rebar mm²

776

0

776

354

194

0

0

194

Page 29 of 31

Structural Analysis and Design Report of the Residential Building of Mrs. Madam Kumari Rai at ward no.-15, Dharan Sub-metropolitan

Shear Force and Reinforcement for Shear, Vu2 & Tu Shear Ve N

Shear Vc N

Shear Vs N

Shear Vp N

Rebar Asv /s mm²/mm

157735.54

74472.97

83262.57

50074.39

0.45

Torsion Force and Torsion Reinforcement for Torsion, Tu & VU2 Tu N-mm

Vu N

Core b1 mm

Core d1 mm

Rebar Asvt /s mm²/mm

0.17

107661.15

254

504

0

Page 30 of 31

ISOLATED FOOTING DESIGN

FORCES DETAILS :

Axial Load = P1 = Moment along Major axis = Mx = Moment along Minor axis = Mz =

25 T 1 T-m 1 T-m G.L

COLUMN DETAILS :

Length = ( Larger Dimension of Column ) Width = ( Smaller Dimension of Column )

0.3 m 0.3 m

FOOTING DETAILS :

Length = L = Width = B = Depth = D =

1.9 m 1.9 m 0.25 m

Cover to Main R/f = Diameter of R/f in Footing =

0.05 m 12 mm

1.75

0.25 SOIL DETAILS :

Density of Soil = g = Depth of foundation below G.L = H =

3 1.7 T/m 2.0 m

1.90 X

MATERIAL CONSTANT :

M - 20 N/mm2 Fe - 415 N/mm2 1.5

Concrete Grade = R/f Grade = Load Factor = gf =

1.90 Z

Z

DESIGN FORCES :

Axial load = P = Self Weight of Footing =

25.00 T 2.26 T

X

1.90

Total Vertical Load =

27.26 T

Moment along Major axis Moment along Minor axis

1 T-m 1 T-m

PRESSURE CALCULATION :

SBC = 15 T/m2 1.25 x FOR EARTHQUAKE CONDITION ALLOWABLE S.B.C =

P=

P A

+ -

Mx Zx

+ -

\ Pmax =

7.55 +

0.87 +

0.8748 =

9.30

T/m2

\ Pmin =

7.55 -

0.87 -

0.8748 =

5.80

T/m2

15 =

18.75 T/m2

Mz Zz

< S.B.C

SAFE

TENSION NOT CREATED

R/F CALCULATION FROM BENDING CONSIDERATION :

1900

800

1900

300 300 800

5.8 T/M2

9.3 T/M2

MOMENT AT CRITICAL SECTION ALONG WIDTH :

M = Pmax x 0.8 x 0.8 / 2 M= 2.98 T-m Mu = 44.64 KN-m 2 Ast = 664.27 mm 2 Min Req = 300 mm

( To be distributed in 1.9 m Length ) ( Ast = 0.12 x b x D )

PROVIDE 12 # @ 150 C/C ALONG WIDTH \ Ast =

753.98

mm2

MOMENT AT CRITICAL SECTION ALONG LENGTH :

M = Pmax x 0.8 x 0.8 / 2 M= 2.98 T-m Mu = 44.64 KN-m 2 Ast = 664.27 mm 2 Min Req = 300 mm

( To be distributed in 1.9 m Length ) ( Ast = 0.12 x b x D )

PROVIDE 12 # @ 150 C/C ALONG WIDTH \ Ast =

753.98

mm2

CHECK FOR ONE WAY SHEAR ALONG LENGTH : Critical Section is at diatance of ' d ' from face of column

0.8 1.90

0.8

0.6

1.90 \ Shear force at critical section = V = \ Actual Shear stress tv =

= = Pt =

\

tc

100 x As b x d

=

0.28 <

=

N / mm2

tv HENCE UNSAFE

9.30 x 5.58

0.6 T

Vu bxd 1.5 x 1000 x 0.418 100 x 1000 x

5.58 200

x 10000

N / mm2 753.98 200

=

0.38

Pt 0.15 0.2

tc 0.28 0.33

CHECK FOR ONE WAY SHEAR ALONG WIDTH : Critical Section is at diatance of ' d ' from face of column

0.8 1.90

0.8

0.6 1.90 \ Shear force at critical section = V = \ Actual Shear stress tv = = = Pt = \

tc

100 x As b x d

=

0.28 <

= N / mm2

tv HENCE UNSAFE

9.30 x 5.58

0.6 T

Vu bxd 1.5 x 1000 x 0.418 100 x 1000 x

5.58 200

x 10000

N / mm2 753.98 200

=

0.38

CHECK FOR TWO WAY SHEAR : Critical Section is at distance of 'd/2' from face of column 1.90

0.5 1.90

0.5

d/2 d/2

\ Shear force at Critical Section =

9.30 x

= = Critical Perimeter = =

Area of Shadeded Portion

9.30 x

3.36

31.25 T

2 x

0.5

+

2 x

2.00 m

\ Actual Shear stress tv =

Vu bxd

=

1.5 x 31.25 2000.00 x 200

=

1.172

( CLAUSE 31.3.3 IS 456 : 2000 )

where, ks = ( 0.5+b ) Short Side of Column = 0.3 Long Side of Column = 0.3

ks = 1.50

but not greater than 1.0

x 10000

N / mm2

Allowable Shear stress = ks.tc

b=

0.5

=

1.00

Where,

tc = 0.25  fck tc = 0.25  M - 20

=

Allowable Shear stress = ks.tc =

1.12

1.12

N/mm2

N/mm2

UNSAFE

CHECK FOR OVERTURNING : ALONG LENGTH : Rm

Restoring Moment = Rm = Applied Moment =

F.O.S. = P

=

25.00

x 0.95

23.75

T.m

1.0

T.m

Restoring Moment Applied Moment 23.75 1

= >

23.75 2.2 SAFE

0.95

Architectural descriptio of staircase Dog-legged staircase Floor to floor height Height/flight Riser Tread No. fo riser in one flight No. fo tread in one flight Eff. Span, L

𝑇𝑟𝑖𝑎𝑙 𝑑𝑒𝑝𝑡ℎ =

3.048 1.524 0.17 0.30 11 10 3.13

m m m m NO. NO. m

𝑒𝑓𝑓. 𝑠𝑝𝑎𝑛 𝑆 𝐷 𝑟𝑎𝑡𝑖𝑜 ∗ 𝑀. 𝐹.

𝑆 𝐷

20 1.4

M.F. 3.6

d reqd= 20∗1.4.

Assume, D d=D-clear cover-dia/2

0.11 m

0.2 m 0.165 m

Provided

Load calculation on step portion a)

Dead load of waist slab, D*25*sqrt(R^2+T^2)/T

5.74 kN/m^2

b)

D.L. of steps, R/2*25

2.12 kN/m^2

c)

F.F.

1.25 kN/m^2

d)

L.L.

3 kN/m^2

Total Factored load, W'

12.11 kN/m^2 18.16 kN/m^2

Load calculation on landing portion a)

D.L. of slab, 25D

b)

F.F.

1.25 kN/m^2

c)

L.L.

3 kN/m^2

Total Factored load Factored load, W'

1)

5 kN/m^2

9.25 kN/m^2 13.88 kN/m^2 18.16 kN/m^2

Bending moments, Shear Forces and corresponding checks Calculation of design moments (Find maximum bending either by drawing shear force and bending moment diagram or by considering it equal to (0.125 W'*L^2), Mu

22.24 kN

2) Reinforcement calculation 2.1) Main rebars

fck fy

20 MPa 500 MPa

Ast

341.30 mm^2

Provided steel, 12mm dia @ 150 mm c/c Ast, provided, main and distribution Ast min, 0.15%bD

753.33 mm^2 300.00 mm^2

OK

3) Check for shear 3.1) max. design shear force, Vud = W'*L/2 Calculate shear resisted by concrete, Vuc = k 3.2) ζc*b*d k 100As/bd ζc Vuc Vuc>Vud

4)

Check for deflection fs = 0.58*fy(Desgin steel/Provided steel) Pt M.F. d

28.42 kN kN 1.2 0.457 0.46 90.95 kN safe

131.38 Mpa 0.457 1.5 0.10 < d provided

Ok