Design of Proposed Auditorium-project Report

DESIG OF PROPOSED AUDITORIUM ACKOWLEDGEMET

We are delighted to express our hearty thanks to our honorable Principal, Dr.S.Joseph Sekhar, Ph.D for providing facilities to undertake this mini project work. We are grateful to Mrs.S.Judes Sujatha, B.E, M.Tech., Head of the Department, for extending all possible help in the execution of this work. We are extremely indebted to our internal guide,Mr.A.B.Danie Roy, M.E., who has suggested this topic, provided all the expertise, facilities and help in shaping this project into a successful one. We acknowledge the help rendered by Mr.A.Jinu Antony, Engineer associated with auditorium design We also express our thanks to all the staff members of the Civil Engineering department, for their support.

ABSTRACT

This project deals with the analysis and design of the Auditorium of St.Xavier’s Catholic College of Engineering with special emphasis on Slabs, Beams, Columns, Footing and Staircase. Analysis is carried out using Substitute Frame Analysis and preliminary analysis of Beams is carried out using Moment Distribution method. Concrete mix used for the RCC members is M20 and steel used is high yield strength deformed bars of grade Fe415. Limit State Method is adopted for the design of all structural members in the building. Safe bearing capacity of soil is taken as 200kN/m2. Footing is designed as Isolated type. Plan and detailing of reinforcement are enclosed in this report.

TABLE OF COTETS CHAPTER O.

TITLE

PAGE O.

ABSTRACT LIST OF SYMBOLS LIST OF FIGURES

1.

ITRODUCTIO 1.1 GENERAL

1

1.2

OBJECTIVES

2

1.3

DESIGN OF RC STRUCTURES

2

1.3.1 1.4

SLABS 1.4.1

1.5

1.7

2 3 3 4 4 5

1.6.1

SHORT COLUMN

5

1.6.2

SLENDER COLUMN

5

1.6.3

CLASSIFICATION OF COLUM

5

FOOTING TYPES OF COLUMN FOOTING

STAIRCASE 1.8.1

2.

DESIGN OF BEAMS

COLUMN

1.7.1 1.8

CLASSIFICATION OF SLABS

BEAMS 1.5.1

1.6

LIMIT STATE DESIGN

CLASSIFICATION OF STAIRS

PLAIG OF PROPOSED AUDITORIUM 2.1

LAYOUT OF SITE

2.2

PLANS

2.3

SECTION

2.4

ELEVATION

6 6 7 7

3

METHODOLOGY

4

3.1

LIMIT STATE DESIGN

3.2

PARTIAL SAFETY FACTOR

AALYSIS INTRODUCTION METHOD OF SUBSTITTE FRAME ANALYSIS ANALYSIS OF FRAMES

5

DESIG SLABS 5.1.1. DESIGN OF SLABS BEAMS 5.2.1

TYPES OF BEAMS

5.2.2

DESIGN OF L-BEAMS

5.2.3

DESIGN OF T-BEAMS

5.3

STAIRCASE 5.3.1

TYPES OF STAIRS

5.3.2

DESIGN OF DOGLEGGED STAIRCASE

5.4

COLUMN 5.4.1

TYPES OF COLUMN

5.4.2

DESIGN OF COLUMN

5.4.2.1 DESIGN OF AXIALLY LOADED COLUMN 5.4.2.2DESIGN OF UNIAXIALLY LOADED COLUMN 5.4.2.3DESIGN OF BI AXIALLY LOADED COLUMN 5.5

6

FOOTING 5.5.1

TYPES OF FOOTING

5.5.2

DESIGN OF FOOTING

COCLUSIO REFERECE

LIST OF FIGURES

Serial o. figure 1 figure 2 figure 3 figure 4 figure 5 figure 6 figure 7 figure 8 figure 9 figure 10 figure 11 figure 12 figure 13 figure 14 figure 15

Title

Page o.

analysis using substitute frame method - frame1 ................... 17 analysis using substitute frame method-frame2 ..................... 31 analysis using substitute frame method-frame3 ..................... 45 analysis using substitute frame method-frame4 ..................... 59 reinforcement details of two way slab-section ..................... 105 reinforcement details of two way slab- plan ......................... 105 reinforcement details of l-beams- longitudinal section ........ 111 reinforcement details of l-beams- cross section.................... 111 reinforcement details of t-beam-longitudinal design ............ 116 cross section of t-beam ......................................................... 116 reinforcement details of doglegged staircase........................ 122 reinforcement details of axially loaded column ................... 126 reinforcement details of uniaxially loaded column .............. 129 reinforcement details of biaxially loaded columns ............... 132 reinforcement details of axially loaded column ................... 137

LIST OF SYMBOLS

Mx

-

Moment in shorter direction

My

-

Moment in shorter direction

d

-

Effective depth

D

-

Overall depth

Ast

-

Area of Steel

P

-

Load

Wu (or) Pu

-

Design load

Mu

-

Design moment

Asc

-

Area of concrete

fy

-

Characteristic strength of steel

fck

-

Characteristic strength of concrete

B.M

-

Bending Moment

b

-

Breadth of beam

D

-

Overall depth

Vus

-

Strength of shear reinforcement

L

-

Clear span

Le

-

Effective span

N.A

-

Neutral Axis

MF

-

Modification factor

Q

-

Angle of repose of soil

M

-

Modular of rupture

τc

-

Permissible shear stress in concrete

τv

-

Nominal shear stress

CHAPTER 1 1. ITRODUCTIO

1.1 GEERAL Auditorium, Conference hall, Library and Indoor Games are necessary for an Engineering college. In St.Xavier’s Catholic College of Engineering, Library, Conference hall are located at different locations and also there is no special building for Auditorium. This project reports on the analysis and design of Auditorium, Library and Indoor Games hall in one separate block. All structural components for the building such as beams, columns, slabs, staircase etc are analysed and designed. Isolated footing is adopted for all columns. Safe bearing capacity is taken as 200kN/m2. The structure is designed by using limit state method, adopting M20 concrete and Fe415 HYSD bars. Site plan, plan showing various floors, section of plan, elevation of plan and detailing of reinforcements for Beam, Column, Slab, Staircase and Footing are also enclosed.

OBJECTIVES 2. To analyse the frames in the building. 3. To design the structural components of the five storey building. 4. To prepare the detailed drawing for the design carried out.

1.3 DESIG OF RC STRUCTURES Reinforced cement concrete members can be designed by the following methods: 1. Working stress method 2. Limit state method

1.3.1 Limit state design • Limit state method of design is based on elastic theory. • Partial safety factors are used in this method to determine the design loads and design strength of materials from their characteristics values. • The design aids to IS:456, published by the bureau of Indian standards. The design of limit state method is very simple and hence widely used in practice. • This method gives economical results when compared with the conventional working stress method.

1.4 SLABS • Slabs are primary members of a structure, which support the imposed load directly on them and transfer the same safety to the supporting elements such as beams, walls, columns etc. • A slab is a thin flexural member used in floor and roof of a structure to support the imposed loads.

1.4.1 Classification of slabs 1.4.1.1Solid slab 1.4.1.2Hollow slab 1.4.1.3Ribbed slab

1.5 BEAM • A beam has to be generally designed for the actions such as bending moments, shear forces and twisting moments developed by the lateral loads. • The size of the beam is designed considering the maximum moment in it and generally kept uniform throughout its length. • IS:456:2000 recommends that the minimum grade of concrete should not be less than M20 in RC works.

1.5.1 Design of beams • When there is a Reinforced concrete slab over a concrete beam, then the beam and the slab can be constructed in such a way that they act together. • The combined beam and slab are called as flanged beams. It may be ‘T’ or ‘L’ beams. Here both T-beams and L-beams are designed.

1.6 COLUMS • Vertical members in compression are called as columns and struts. • The term column is reserved for member which transfer load to the ground. Classification of column, depending upon slenderness ratio is 1.6.1Short columns 1.6.2Slender columns

1.6.1 Short column IS:456:2000 classifies rectangular column as short when the ratio of effective length(Le) to the least dimension is less than 12. This ratio is called slenderness ratio of the column.

1.6.2Slender columns The ratio of Le to the least dimension is less than 12 are called as slender column.

Classification of column 1. Axially loaded column 2. Eccentrically loaded column 3. Column subjected to axial load and moment

1.7 Footing • Foundation is the most important component of a structure. • It should be well planned and carefully designed to ensure the safety and stability of the structure. • Foundation provided for RCC columns are called as column base.

1.7.1Types of column base 1. Isolated footing 2. Combined footing 3. Strap footing 4. Solid raft foundation 5. Annular raft foundation

1.8 Staircase A staircase is a flight of steps leading from one floor to another. It is provided to afford the means of ascent and descent between various floors of the building. It should be suitably located in a building. In a domestic building the stair should be centrally located to provide easy access to all rooms. In public buildings stairs should be located near the entrance. In big building there can be more than one stairs. Fire protection to stairs is important too. Stairs are constructed using timber, bricks, stone, steel or reinforced cement concrete.

1.8.1Classification of stairs 1. Single flight stairs 2. Quarter turn stairs 3. Dog legged stairs 4. Open well type stairs 5. Biffurcated stairs 6. Circular stairs 7. Spiral stairs

CHAPTER 3 3.METHODOLOGY Various methods are available for the design of a structure. Limit state method is adopted in this project.

3.1 Limit state design The acceptable limit for safety and serviceability requirement before failure occur is called limit state. The aim of design is to achieve acceptable probabilities that the structure will not become unfit for use. All relevant limit state shall be considered in the design to ensure adequate degree of safety and serviceability.

3.2Partial safety factor The value of load which has a 95% probability of a structure of structural member for the limit state of collapse the following values of partial safety factor is applied for limit state of collapse. Ym = 1.5 for concrete Ym = 1.15 for steel

CHAPTER 4

4 AALYSIS 4.1 Introduction A multistoried frame is a complicated statically indeterminate structure. The analysis by moment distribution method is very lengthy and difficult. Hence substitute frame analysis is adopted for better and easier calculation.

4.2 Method of substitute frames In this method only a part of the frame is considered for the analysis. The part considered is called as substitute frame. The moments for each floor are separately computed. It is assumed that the moments transferred from one floor to another are small. Each floor is taken as connected to columns above and below with their far ends fixed. The frame taken this way is analysed for the moments and shears in the beams and columns. The column will carry the maximum bending moment when any one series of alternate spans should be loaded. The moment distribution for the substitute frame analysis is performed only for two cycles and hence, the method is sometimes referred to as, the two cycle method. When it is required to find the maximum negative moment at a joint, the spans meeting at the joint are loaded with dead and live load. The other spans are loaded with dead load alone.

4.3AALYSIS OF FRAMES

A

B

C

D

E

F

FRAME 1 Figure 1-Analysis using substitute frame method - frame1

G

4.3.1DISTRIBUTIO FACTOR

Joint A

B

C

D

E

F

G

Member

Relative stiffness

AB

I/3.2

A1

I/4

A2

I/4

0.31

BA

I/3.2

0.28

BC

I/3.2

B1

I/4

0.22

B2

I/4

0.22

CB

I/3.2

0.32

CD

I/6.4

C1

I/4

0.26

C2

I/4

0.26

DC

I/6.4

0.32

DE

I/6.4

D1

I/4

0.31

D2

I/4

0.31

ED

I/6.4

0.32

EF

I/6.4

E1

I/4

0.31

E2

I/4

0.31

FE

I/6.4

0.32

FG

I/6.4

F1

I/4

0.31

F2

I/4

0.31

GF

I/6.4

0.24

G1

I/4

G2

I/4

4.3.2 LOAD CALCLATIO

Total stiffness

Stiffness for each member 0.38

0.8125I

1.125I

0.9688I

0.8125I

0.8125I

0.8125 I

0.656I

0.31

0.28

0.16

0.32

0.32

0.32

0.38 0.38

Beam name

AB

BC

CD

DE

EF

FG

8.25

8.25

8.25

8.25

8.25

8.25

15

15

15

15

15

15

2.56

2.56

7.99

7.99

7.99

7.99

Length m

3.2

3.2

6.4

6.4

6.4

6.4

Total DL kN/ m

6.6

6.6

10.3

10.3

10.3

10.3

Total LL kN /m

12

12

18.73

18.73

18.73

18.73

Dead load due to rib kN/m2

3.375

3.375

4.5

4.5

4.5

4.5

Total DL kN/m2

14.975

14.975

17.23

17.23

17.23

17.23

Total load kN/m2

26.975

26.975

35.96

35.96

35.96

35.96

DL kN / LL

m2

kN/m2

Area

m2

4.3.3 MOMET CALCULATIO AT JOITS JOINT-A joint Member

A AB

B BA

DF

0.38

0.28

FEM due to DL

BC 0.28 -12.78

FEM due to LL

-23.02

Distribution + Carryover

-1.4336

Distribution

-24.45 9.29

Net BM due to A

-15.16

+23.02

C CB CD 0.32

0.16

D DC 0.32

DE 0.32

JOINT-B joint Member

A AB

B BA

DF

0.38

0.28

C CB CD

BC 0.28

0.32

DC

0.16

FEM due to DL FEM due to LL

D DE

0.32

0.32

-58.81 -23.02

+23.02

-23.02

+23.02

Distribution + Carryover

4.37

5.726

Distribution

27.39 -2.827

-17.294 -2.827

Net BM due to A

24.563

-20.121

JOINT-C joint Member

B BA

DF

0.28

FEM due to DL

12.78

FEM due to LL

BC 0.28

C CB 0.32

D CD 0.16

DC 0.32

DE 0.32 -58.81

-122.74 +122.74 -122.74

Distributio n+ Carryover

15.39

-10.23

Distributio n

138.13 -1.6512

-132.97 -0.8256

Net BM due to A

136.48

-133.8

122.74

E ED EF 0.32

0.32

JOINT-D joint Member DF

B

C

BA BC CB CD 0.28

0.28

FEM due to DL

0.32

0.16

D DC 0.32

E DE

ED

0.32

0.32

12.78

FEM due to LL

EF 0.32 -58.81

-122.74 +122.74 -122.74 122.74

Distributi on + Carryove r

8.8

-10.23

Distributi on

131.54 0.46

-132.97 0.46

Net BM due to A

132

-132.51

JOINT-E joint Member

D DC

DF

0.32

FEM due to DL

+58.81

FEM due to LL

DE 0.32

ED 0.32

E EF

F FE

0.32

0.32

FG 0.32 -58.81

-122.74

122.74

-122.74 122.74

Distributi on + Carryove r

10.23

-10.23

Distributi on

132.97 0

-132.97 0

Net BM due to A

132.97

-132.97

G GF 0.24

JOINT-F joint Member DF

D DC 0.32

DE 0.32

FEM due to DL

ED 0.32

E EF

F FE

0.32

0.32

FG

G GF

0.32

0.24

-122.74

122.74

58.81

FEM due to LL

-122.74 122.74

Distributi on + Carryove r

10.23

-14.73

Distributi on

132.9 1.44

-132.97 1.44

Net BM due to A

134.41

-136.03

JOINT-G joint Member DF FEM due to DL FEM due to LL

D DC 0.32

DE 0.32

ED 0.32

E EF

F FE

0.32

0.32

FG

G GF

0.32

0.24

-122.74

122.74

58.81

Distributi on + Carryove r

10.23

Distributi on

132.97 -31.91

Net BM due to A

101.06

MID SPAN MOMENT AB joint Member DF

A AB

B BA

0.38

0.28

FEM due to DL FEM due to TL

-23.02

23.02

distribution moment

8.75

-2.87

carry over moment

-1.435

4.375

distribtion

0.545

-6.15

Net moment -15.16

C BC

CB

0.28

0.32

-12.78

12.78

D CD

0.16

0.32

-122.74

122.74

35.18 17.59

+18.375

Free BM at the centre of the span AB = Wl2/8 =(26.975 * 3.22) / 8 =34.53 kNm Net BM at centre of span AB =34.53-[ (15.16+18.375) / 2] =17.76 kNm

DC

DE 0.32

MID SPAN MOMENT OF BC joint

A AB

BA

DF

0.38

0.28

FEM due to DL

-12.78

12.78

Member

B

FEM due to TL

C BC 0.28

CB 0.32

-23.02

23.02

-2.87

11.45

-5.73

-1.43

distribtion

0.924

-2.816

Net moment

-30.696 30.224

distribution moment

4.86

carry over moment

2.43

Free BM at the centre of the span BC = Wl2/8 =(26.975 * 3.22) / 8 =34.53 kNm Net BM at centre of span BC =34.53-[ (30.696+30.224) / 2] =4.07 kNm

CD

D DC DE

0.16

0.32

-58.81

58.81

0.32

-122.74 20.46 10.23

MID SPAN MOMENT CD Joint member DF

B BA 0.28

FEM due to DL FEM due to TL distributio n moment carry over moment

BC 0.28

C CB CD 0.32

0.16

D DC 0.32

-12.78 12.78 23.02

E DE 0.32

ED 0.32

0.32

-58.81 58.81 -122.74 122.74

-2.86

EF

17.59

-1.43 -10.23

-122.74

-20.46

8.795

distributio n

1.86

Net moment

-95.923 104.99

20.46

10.23

-6.088

Free BM at the centre of the span CD = Wl2/8 =(35.96 * 6.42) / 8 =184.12 kNm Net BM at centre of span CD =184.12-[ (95.92+104.99) / 2] =83.66 kNm

MID SPAN MOMENT DE Joint member DF

B BA 0.28

FEM due to DL FEM due to TL

C BC 0.28

CB 0.32

D CD

0.16

DC 0.32

-58.81 58.81 122.74

distributio -20.46 n moment

E DE 0.32

ED EF 0.32

-58.81 58.81 -122.74 122.74

-20.46

carry over moment

20.46

-10.23 -10.23

-122.74

-20.46

10.23

distribtion

6.54

Net moment

-105.97 105.97

-6.54

Free BM at the centre of the span DE = Wl2/8 =(35.96 * 6.42) / 8 =184.12 kNm Net BM at centre of span DE =184.12-[ (105.97+105.97) / 2] =78.14 kNm

0.32

20.46

10.23

MID SPAN MOMENT EF joint

C

Member

D

DC 0.32

DF FEM due to DL

FEM due 122.74 to TL distributio n moment

DE

ED

0.32

0.32

-58.81

58.81

E EF

FE

0.32

0.32

G FG

GF

0.32

0.24

-58.81

58.81

-122.74 122.74 -20.46

20.46

-20.46

-10.23

10.23

Distribtion

6.55

-1.001

Net moment

-105.96 111.51

carry over moment

-10.23

Free BM at the centre of the span EF = Wl2/8 =(35.96 * 6.42) / 8 =184.12 kNm Net BM at centre of span EF =184.12-[ (105.97+111.51) / 2] =75.4 kNm

-14.11 -7.1

MID SPAN MOMENT FG joint

D

Member

DC 0.32

DF

E DE 0.32

ED 0.32

FEM due to DL FEM due to TL distributio n moment

F EF

FE

0.32

0.32

-58.81

58.81

122.74

G FG

0.32

GF 0.24

-122.74 122.74 -20.46

20.46

-29.46

-14.73

10.23

distribtion

7.98

-2.455

Net moment

-109.03 101 05

carry over moment

Free BM at the centre of the span FG = Wl2/8 =(35.96 * 6.42) / 8 =184.12 kNm Net BM at centre of span FG =184.12-[ (109.03+101.05) / 2] =79.08 kNm

-10.23

NEGETIVE MOMENT AT CENTRE OF DE Joint

C

member

CB

DF

0.32

FEM due to DL

12.78

D CD

0.16

DC 0.32

FEM due to TL

-122.74 122.74

distributio n moment

17.59

DE

E ED EF

0.32

0.32

-58.81

58.81

0.32

0.32

-122.74 122.74 -20.46

20.46

8.795

10.23

-10.23 -10.23

distribtion

-6.08

6.55

Net moment

-75.12

75.59

Free BM at the centre of the span DE = Wl2/8 =(17.23 * 6.42) / 8 =88.21 kNm Net BM at centre of span DE =88.21-[ (75.12+75.59) / 2] =12.86 kNm

FE

FG 0.32 -58.81

-20.46

carry over moment

F

20.46

-20.46

4.3.4 BENDING MOMENT IN COLUMN LOADING joint

A

B

C

D

E

F

G

Column DF Above floor

0.31

0.22

0.26

0.3

0.3

0.3

0.38

Below floor

0.31

0.22

0.26

0.3

0.3

0.3

0.38

Member

AB

BA

BC

CB

CD

DC

DE

ED

EF

FE

FG

GF

DF

0.38

0.28

0.25

0.32

0.16

0.19

0.19

0.19

0.19

0.19

0.19

0.24

-12.8

12. 8

-58.8

58.8

-58.8

58.8

FEM due to DL FEM due TL

-23.02

23.02

Distribution+

-1.435

4.37

17.59

-24.45

27.39

4.81

-122.7

122.7

-1.28

-6.07

8.79

6.07

11.5

-128.8

131.53

-52.7

-122.7

122.7

-6.07

-6.07

6.07

-7.06

6.07

52.74

-128.8

128.81

-65.9

64.88

carryover Total Distribution to column Above floor Distribution to column below floor Joint

7.58

7.084

30.5

-23.64

22.82

-18.882

24.65

7.58

7.084

30.5

-23.64

22.82

-18.882

24.65

A

B

C

D

E

F

G

Column DF Above floor

0.31

0.22

0.26

0.3

0.3

0.3

0.38

Below floor

0.31

0.22

0.26

0.3

0.3

0.3

0.38

Member

AB

BA

BC

CB

CD

DC

DE

ED

EF

FE

FG

GF

DF

0.38

0.28

0.25

0.32

0.16

0.19

0.19

0.19

0.19

0.19

0.19

0.24

FEM due to

-12.8

12. 8

-58.8

58.8

-58.8

58.81 -122.7

122.7

DL FEM due TL

-

23.02

-122.7

122.7

23.02 Distribution+

1.43

2.43

5.73

1.28

-6.07

2.86

-6.07

6.07

6.07

-6.07

-14.73

6.07

-11.4

15.21

-17.3

24.3

-64.9

61.7

-128.8

128.8

-52.7

52.7

-137.5

128.8

carryover Total Distribution to column Above floor Distribution to column below floor

3.52

0.46

10.55

20.14

22.82

25.42

-48.9

3.52

0.46

10.55

20.14

22.82

25.42

-48.9

H

I

J

K

L

M

FRAME 2

Figure 2-Analysis using substitute frame method-frame2

N

4.3.5 DISTRIBUTIO FACTOR Joint H

I

J

K

L

M

N

Member

Relative stiffness

Total stiffness

Stiffness for each member

HI

I/3.72

H1

I/4

H2

I/4

0.33

IH

I/3.72

0.26

IJ

I/3.55

I1

I/4

0.24

I2

I/4

0.24

JI

I/3.55

0.3

JK

I/6.33

J1

I/4

0.27

J2

I/4

0.27

KJ

I/6.33

0.2

KL

I/6.43

K1

I/4

0.31

K2

I/4

0.31

LK

I/6.43

0.17

LM

I/3.55

L1

I/4

0.27

L2

I/4

0.27

ML

I/3.55

0.27

MN

I/3.72

M1

I/4

0.24

M2

I/4

0.24

NM

I/3.72

0.35

N1

I/4

N2

I/4

0.35 0.769I

1.05I

0.94I

0.81I

0.937I

1.05 I

0.769I

0.33

0.27

0.17

0.19

0.3

0.26

0.33 0.33

4.3. 6 LOAD CALCLATIO Beam name

HI

IJ

8.25

8.25

8.25

8.25

8.25

8.25

15

15

15

15

15

15

6.784

6.24

20.04

20.672

6.24

6.784

Length m

3.72

3.55

6.33

6.43

3.55

3.72

Total DL kN/ m

15.045

14.5

26.12

26.52

14.5

15.045

Total LL kN /m

27.35

26.37

47.49

48.22

26.37

27.35

Dead load due to rib kN/m2

3.375

3.375

4.5

4.5

3.375

3.375

Total DL kN/m2

18.42

17.875

30.62

31.02

17.875

18.42

Total load kN/m2

45.77

44.245

78.11

79.24

44.245

45.77

DL kN / LL

m2

kN/m2

Area

m2

JK

KL

LM

MN

4.3.7 MOMET CALCULATIO AT JOITS JOINT-H joint Member DF

H HI

I IH

IJ

0.35

0.26

0.27

FEM due to DL

J

-18.77

FEM due to LL

-52.78

Distribution + Carryover

-4.42

Distribution

-57.2 20.02

Net BM due to H

-37.18

+52.78

JI 0.3

K JK

KJ

0.17

0.2

KL 0.19

JOINT-I joint Member DF

H HI

I

J

IH

IJ

JI

JK

0.35

0.26

0.27

0.3

0.17

FEM due to DL FEM due to LL

K KJ 0.2

KL 0.19

-102.24 -52.78

+52.78

-46.47

46.47

Distribution + Carryover

9.237

8.366

Distribution

62.02 -6.22

-38.104 -6.46

Net BM due to I

55.8

-44.564

JOINT-J joint Member

I

J

K

IH

IJ

JI

JK

KJ

DF

0.26

0.27

0.3

0.17

0.2

FEM due to DL

102.24

FEM due to LL

L KL

0.19 -102.24

-46.47 46.47

-260.81

Distributio n+ Carryover

-7.53

-15.39

Distributio n

38.94 71.18

-276.2 40.33

Net BM due to J

110.12

-235.87

260.81

LK LM 0.17 0.3

JOINT-K joint Member DF

I

J

K

IH

IJ

JI

JK

KJ

0.26

0.27

0.3

0.17

0.2

FEM due to DL

L KL 0.19

LK

LM

0.17

0.3

18.77

FEM due to LL

-58.81 -260.81 260.81

-273.01 273.01

Distributi on + Carryove r

20.57

-21.61

Distributi on

281.38 2.648

-294.62 2.516

Net BM due to K

284.03

-292.10

JOINT-L joint Member

K KJ

DF

0.2

FEM due to DL

+102.2 4

FEM due to LL

KL

LK

L LM

0.19

0.17

0.3

M ML

MN

N NM

0.27

0.26

0.35

-21.24 -273.01

273.01

-46.47

Distributi on + Carryove r

16.22

-3.41

Distributi on

298.23 -40.67

-49.88 -71.77

Net BM due to L

248.56

-121.65

46.47

JOINT-M joint

K KL

LK

L LM

0.19

0.17

0.3

0.27

0.26

0.35

-46.47

46.47

-52.78

52.78

Distributi on + Carryove r

-9.06

-15.83

Distributi on

37.41 8.424

-68.61 8.112

Net BM due to M

45.834

-60.5

Member DF

KJ 0.2

FEM due to DL

M ML MN

N NM

106.88

FEM due to LL

JOINT-N joint Member DF FEM due to DL FEM due to LL

KJ 0.2

K KL 0.19

LK

L LM

0.17

0.3

M ML MN

N NM

0.27

0.26

0.35

-52.78

52.78

18.77

Distribution + Carryover

4.42

Distribution

57.2 -17.16

Net BM due to N

40.04

MID SPAN MOMENT HI joint Member DF

H HI

I IH

IJ

0.35

0.26

0.27

0.3

-18.77

18.77

FEM due to DL FEM due to TL

-52.78

52.78

distribution moment

18.47

-8.99

carry over moment

-4.495

9.235

distribution

1.573

-11.84

Net moment -37.23

J JI

JK

KJ

0.17

0.2

-260.81 72.6 36.3

41.18

Free BM at the centre of the span HI = Wl2/8 =(45.77 * 3.722) / 8 =79.2 kNm Net BM at centre of span HI =79.2-[ (37.23+41.18) / 2] =39.995 kNm

K

260.81

KL 0.19

MID SPAN MOMENT OF IJ joint

H HI

IH

IJ

DF

0.35

0.26

0.27

FEM due to DL

-102.24

102.24

Member

I

FEM due to TL

J JI 0.3

46.47

-15.06

16.73

8.36

-7.53

distribution

-7.09

-2.87

Net moment

-60.26

52.8

35.78

carry over moment

17.89

Free BM at the centre of the span IJ = Wl2/8 =(44.245 * 3.552) / 8 =69.699 kNm Net BM at centre of span IJ =69.7-[ (60.26+52.8) / 2] =13.2 kNm

JK

KJ

0.17

0.2

KL 0.19

-102.24 102.24 -46.47

distribution moment

K

-273.01 34.15 17.1

MID SPAN MOMENT JK Joint member DF

I

distribution moment

K

IH

IJ

JI

JK

KJ

0.26

0.27

0.3

0.17

0.2

FEM due to DL FEM due to TL

J

-18.77 18.77 52.78

KL LK 0.19

0.17

carry over moment

41.15

-4.59 -15.4

-46.47

-30.79

20.6

distribution

3.4

Net moment

-231.66 247.52

-3.1

Free BM at the centre of the span JK = Wl2/8 =(78.11 * 6.332) / 8 =391.22 kNm Net BM at centre of span JK =391.22-[ (231.7+247.52) / 2] =151.63 kNm

0.3

-106.9 106.9 -260.81 260.81

-9.18

L LM

-10.27

-5.135

MID SPAN MOMENT KL Joint

I

member DF

J

K

IH

IJ

JI

JK

KJ

0.26

0.27

0.3

0.17

0.2

FEM due to DL

-102.24 102.24

FEM due to TL

46.47

distribution moment

L KL LK

0.19

0.17

34.15

-43.22

-21.61

17.07

distribution

3.21

-3.68

Net moment

-257.26 243.18

carry over moment

4.74

Free BM at the centre of the span KL = Wl2/8 =(79.24 * 6.432) / 8 =409.52 kNm Net BM at centre of span KL =409.52-[ (257.26+243.18) / 2] =159.3 kNm

0.3

-18.77 18.77 -273.01 273.01

9.48

LM

-52.78 9.18

4.59

MID SPAN MOMENT LM joint

K

Member

KJ

DF FEM due to DL

0.2

FEM due to TL

260.81

distribution moment

L

M

N

KL

LK

LM

ML

MN

NM

0.19

0.17

0.3

0.27

0.26

0.35

-106.88

106.88

-21.24

21.24

-46.47 -29.25

46.47

-18.123 -6.812 -3.41

-9.06

Distribution

5.412

3.45

Net moment

-62.591 34.05

carry over moment

-14.63

Free BM at the centre of the span LM = Wl2/8 =(44.25* 3.552) / 8 =69.71 kNm Net BM at centre of span LM =69.71-[ (62.59+34.05) / 2] =21.39 kNm

-7.434 -3.717

MID SPAN MOMENT MN joint

K

Member

KJ

L

M

N

KL

LK

LM

ML

MN

NM

0.19

0.17

0.3

0.27

0.26

0.35

-18.77

18.77 -52.78

52.78

8.843

-18.5

-9.25

4.42

distribution

12.32

-1.55

Net moment

-40.87

37.15

0.2

DF FEM due to DL FEM due to TL distribution moment

273.01 -76.3

carry over moment

Free BM at the centre of the span MN = Wl2/8 =(45.77 * 3.722) / 8 =79.2 kNm Net BM at centre of span MN =79.2-[ (40.87+37.15) / 2] =40.19kNm

-38.15

NEGETIVE MOMENT AT CENTRE OF KL Joint

J

member

JI

JK

DF

0.3

0.17

FEM due to DL

KJ

K KL

LK

L LM

M ML MN

0.19

0.17

0.3

0.27

-106.9

106.9

0.2

18.77

FEM due to TL

-260.81 260.81

distributio n moment

41.15

-21.24 -41.47

41.47 -6.81

-30.79

-29.25

-10.27 -18.12

20.6

-9.06

-15.4

distribtion

-2.19

3.2

Net moment

-147.4

84.41

carry over moment

Free BM at the centre of the span KL = Wl2/8 =(31.02 * 6.432) / 8 =160.31 kNm Net BM at centre of span KL =160.31-[ (147.4+84.41) / 2] =44.61 kNm

0.26

-3.4

4.3.8 BENDING MOMENT IN COLUMN LOADING joint

H

I

J

K

L

Above floor

0.33

Below floor

0.33

Member

HI

IH

IJ

JI

JK

KJ

KL

LK

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

0.17

-18.8

18.8

-106.9

106.9

M

N

0.24

0.27

0.31

0.27

0.24

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Column DF

FEM due to

LM 0.3

ML

MN

0.27

NM

0.26

0.35

-21.24

21.24

DL FEM due TL

-52.78

52.78

Distribution+

-4.421

9.24

36.31

-57.2

62.02

17.51

-260.8

260.8

-4.56

-14.62

20.57

-5.13

14.18

-275.4

281.4

-112.0

-46.5

46.5

-14.6

-3.41

-9.06

-3.72

-3.28

92.26

-49.9

37.41

-24.96

17.96

carryover Total Distribution to column Above floor Distribution to column below floor

18.88

-19.09

70.54

-52.50

-11.44

-2.988

-5.93

18.88

-19.09

70.54

-52.50

-11.44

-2.988

-5.93

H

I

J

K

L

Above floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Below floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Member

HI

IH

IJ

JI

JK

KJ

KL

LK

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

0.17

FEM due to

-21.24

21.24

-

102.2

102.24

4

joint

M

N

Column DF

DL FEM due TL Distribution+

-46.5

46.5

-273

273

LM

ML

0.3

0.27

-18.77

18.77

MN

NM

0.26

0.35

-52.78

52.78

3.28

3.72

8.37

3.41

16.22

4.74

-21.61

16.22

4.59

-38.2

-9.24

4.42

-17.96

24.96

-38.1

49.88

-86.02

106.9

-294.6

289.2

-14.18

-19.4

-62.02

57.2

carryover Total Distribution to column Above floor Distribution to column below floor

5.93

3.15

9.76

58.17

-74.26

19.53

-18.9

5.93

3.15

9.76

58.17

-74.26

19.53

-18.9

O

P

Q

R

S

T

FRAME 3

Figure 3-Analysis using substitute frame method-frame3

4.3.9 DISTRIBUTIO FACTOR

U

Joint O

P

Q

R

S

T

U

Member

Relative stiffness

OP

I/3.72

O1

I/4

O2

I/4

0.33

PO

I/3.72

0.26

PQ

I/3.55

P1

I/4

0.24

P2

I/4

0.24

QP

I/3.55

0.3

QR

I/6.33

Q1

I/4

0.27

Q2

I/4

0.27

RQ

I/6.33

0.19

RS

I/6.43

R1

I/4

0.31

R2

I/4

0.31

SR

I/6.43

0.17

ST

I/3.55

S1

I/4

0.27

S2

I/4

0.27

TS

I/3.55

0.27

TU

I/3.72

T1

I/4

0.24

T2

I/4

0.24

UT

I/3.72

0.35

U1

I/4

U2

I/4

4.3.10 LOAD CALCLATIO

Total stiffness

Stiffness for each member 0.35

0.769I

1.05I

0.94I

0.81I

0.937I

1.05 I

0.769I

0.33

0.27

0.17

0.19

0.3

0.26

0.33 0.33

Beam name DL KN /

m2

OP

PQ

QR

RS

ST

TU

18.27

8.25

8.25

8.25

8.25

18.27

3

15

15

15

15

3

8.228

6.095

15.39

15.8

6.095

8.228

Length m

3.72

3.55

6.33

6.43

3.55

3.72

Total DL KN/ m

40.41

14.16

20.06

20.27

14.16

40.41

Total LL KN /m

6.64

25.75

36.47

36.86

25.75

6.64

Dead load due to rib KN/m2

3.375

3.375

4.5

4.5

3.375

3.375

Total DL KN/m2

48.085

22.045

27

27.19

22.045

48.085

Total load KN/m2

54.725

47.795

63.46

64.05

47.795

54.725

LL

KN/m2

Area

m2

4 .3.11 MOMET CALCULATIO AT JOITS

JOINT-O joint

O

Member

OP

PO

PQ

QP

QR

RQ

RS

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

P

FEM due to DL

Q

-23.15

FEM due to LL

-63.12

Distribution + Carryover

-5.2

Distribution

-68.32 23.912

Net BM due to O

-44.41

+63.12

R

JOINT-P joint

O

Member

OP

PO

PQ

QP

QR

RQ

RS

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

P

Q

FEM due to DL FEM due to LL

R

-90.16 -63.12

+63.12

-50.19

50.19

Distribution + Carryover

11.046

5.996

Distribution

74.166 -7.79

-44.194 -8.09

Net BM due to P

66.376

-52.284

JOINT-Q joint

O

Member

OP

PO

PQ

QP

QR

RQ

RS

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

FEM due to DL FEM due to LL

P

Q

R

55.45

-93.68 -50.19

50.19

-211.9

Distribution + Carryover

-0.71

-11.23

Distribution

49.48 52.095

-223.13 29.521

Net BM due to Q

101.575

-193.61

211.9

JOINT-R joint

Q

R

S

T

Member

QP

QR

RQ

RS

SR

ST

TS

TU

DF

0.3

0.17

0.19

0.19

0.17

0.3

0.27

0.26

FEM due to DL

23.15

FEM due to LL

-23.15 -211.9

211.9

-220.68

Distributio n+ Carryover

16.04

-16.79

Distributio n

227.944 -237.47 1.81 1.81

Net BM due to R

229.754 -235.66

+220.68

JOINT-S joint

Q

R

S

T

Member

QP

QR

RQ

RS

SR

ST

TS

TU

DF

0.3

0.17

0.19

0.19

0.17

0.3

0.27

0.26

FEM due to DL FEM due to LL

90.16

-55.45 -220.68 +220.68 -50.19

Distributio n+ Carryover

12.4

0.71

Distributio n

233.08 -31.212

-49.48 -55.08

Net BM due to S

201.87

-104.56

50.19

JOINT-T joint

R

S

T

U

Member

RQ

RS

SR

ST

TS

TU

UT

DF

0.19

0.19

0.17

0.3

0.27

0.26

0.35

-50.19

50.19

-63.12

63.12

Distributi on + Carryove r

-13.05

-11.05

Distributi on

37.14 9.99

-74.17 9.63

Net BM due to T

47.13

-64.54

FEM due to DL

93.68

FEM due to LL

JOINT U joint

R

S

T

U

Member

RQ

RS

SR

ST

TS

TU

UT

DF

0.19

0.19

0.17

0.3

0.27

0.26

0.35

-63.12

63.12

FEM due to DL FEM due to LL

23.15

Distributi on + Carryove r

5.2

Distributi on

68.32 -23.912

Net BM due to U

44.41

MID SPAN MOMENT OP joint

O

Member

OP

PO

PQ

QP

QR

RQ

RS

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

-23.15

23.15 -211.9

211.9

P

FEM due to DL FEM due to TL

-63.12

63.12

distribution moment

22.1

-10.39

carry over moment

-5.195

11.05

distribution

1.818

-10.23

Net moment -44.4

Q

R

56.6 28.3

53.55

Free BM at the centre of the span OP = Wl2/8 =(54.725 * 3.722) / 8 =94.66 kNm Net BM at centre of span OP =94.66-[ (44.4+53.55) / 2] =45.68 kNm

MID SPAN MOMENT OF PQ joint

O

Member

OP

PO

PQ

QP

QR

RQ

RS

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

FEM due to DL

-55.45

55.45

-90.16

90.16

P

FEM due to TL

Q

-50.19

50.19

-1.42

11.99

5.99

-0.71

distribution

-4.24

-3.5

Net moment

-49.86

57.97

distribution moment carry over moment

19.41 9.71

R

-220.68 20.46 12.35

Free BM at the centre of the span PQ = Wl2/8 =(47.79 * 3.552) / 8 =75.3 kNm Net BM at centre of span PQ =75.3-[ (49.86+57.97) / 2] =21.4 kNm

MID SPAN MOMENT QR Joint

P

Q

R

S

member

PO

PQ

QP

QR

RQ

RS

SR

ST

DF

0.26

0.27

0.3

0.17

0.19

0.19

0.17

0.3

FEM due to DL FEM due to TL

-23.15 23.15 -211.9

211.9

32.1

-22.46

-11.23

16.05

distributio n

2.83

-2.35

Net moment

-188.2

203.14

distributio n moment carry over moment

63.12

-93.68 93.68

-10.79

-5.4

-50.19 -7.4

-3.7

Free BM at the centre of the span QR = Wl2/8 =(63.46 * 6.332) / 8 =317.85 KNm Net BM at centre of span QR =317.85-[ (188.2+203.14) / 2] =122.18 KNm

MID SPAN MOMENT RS Joint

Q

R

S

T

member

QP

QR

RQ

RS

SR

ST

TS

TU

DF

0.3

0.17

0.19

0.19

0.17

0.3

0.27

0.26

FEM due to DL FEM due to TL distributio n moment

-90.16 90.16 50.19

-23.15 23.15 -220.68 220.68 24.8

-33.58

-16.79

12.4

distributio n

2.54

-3.03

Net moment

-210.13 196.25

carry over moment

6.8 3.4

-63.12 10.8 5.4

Free BM at the centre of the span RS = Wl2/8 =(64.05 * 6.432) / 8 =331.02 KNm Net BM at centre of span RS =331.02-[ (210.13+196.25) / 2] =127.8 KNm

MID SPAN MOMENT ST joint

R

S

T

U

Member

RQ

RS

SR

ST

TS

TU

UT

DF

0.19

0.19

0.17

0.3

0.27

0.26

0.35

-93.68

93.68

-55.45

55.45

FEM due to DL

FEM due to 211.9 TL -22.46 distribution moment

-50.19

50.19

13.05

1.42

0.71

6.53

Distribution

3.16

0.86

Net moment

-33.27

59

carry over moment

-11.23

Free BM at the centre of the span ST = Wl2/8 =(47.79 * 3.552) / 8 =75.3 kNm Net BM at centre of span ST =75.3-[ (33.27+59) / 2] =29.17 kNm

-19.41 -9.71

MID SPAN MOMENT TU joint

R

S

T

U

Member

RQ

RS

SR

ST

TS

TU

UT

DF

0.19

0.19

0.17

0.3

0.27

0.26

0.35

-23.15

23.15 -63.12

63.12

10.39

-22.1

-11.05

5.2

distribution

10.6

-1.82

Net moment

-53.18

44.4

FEM due to DL FEM due to TL distribution moment

220.68 -59.3 -29.65

carry over moment

Free BM at the centre of the span TU = Wl2/8 =(54.725 * 3.72) / 8 =94.66 kNm Net BM at centre of span TU =94.66-[ (53.18+44.4) / 2] =45.87 kNm

NEGETIVE MOMENT AT CENTRE OF RS Joint

Q

R

S

T

member

QP

QR

RQ

RS

SR

ST

TS

TU

DF

0.3

0.17

0.19

0.19

0.17

0.3

0.27

0.26

FEM due to DL

23.15

-93.68

93.68

FEM due to TL

-211.9 211.9

distributio n moment

32.1

-55.45 -50.19

50.19

-13.05

1.42

-22.46

22.46

-7.4

-16.05

-3.7

-11.24 0.71

Distributi on

-2.45

1.79

Net moment

-122.29

76.83

carry over moment

Free BM at the centre of the span RS = Wl2/8 =(27.19 * 6.432) / 8 =140.521 kNm Net BM at centre of span RS =140.521-[ (122.29+76.83) / 2] =40.96 kNm

4.3.12 BENDING MOMENT IN COLUMN LOADING

joint

O

P

Q

R

S

T

U

Column DF Above floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Below floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Member

OP

PO

PQ

QP

QR

RQ

RS

SR

DF

0.35

0.26

0.27

0.3

0.17

0.19

0.19

0.17

-23.2

23.2

-93.68

93.68

FEM due to

ST 0.3

TS

TU

UT

0.27

0.26

0.35

-55.45

55.45

DL FEM due TL

-63.12

63.12

Distribution+

-5.2

11.05

28.31

-68.32

74.17

-5.16

-211.9

211.9

-5.4

-11.23

16.04

-3.7

17.75

-223.1

227.9

-97.38

-50.19

50.19

-11.2

0.71

-6.52

-9.7

0.68

82.45

-49.48

43.67

-65.15

56.13

carryover Total Distribution to column Above floor Distribution to column below floor

joint

22.55

-16.56

55.45

-40.47

-8.9

5.15

-18.5

22.55

-16.56

55.45

-40.47

-8.9

5.15

-18.5

P

Q

R

O

S

T

U

Column DF Above floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Below floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Member

OP

PO

PQ

DF

0.35

0.26

0.27

FEM due to

-55.45

55.45

QP 0.3

QR

RQ

RS

SR

0.17

0.19

0.19

0.17

-90.16

90.16

ST

TS

TU

UT

0.3

0.27

0.26

0.35

-23.2

23.2 -63.12

63.12

DL FEM due TL Distribution+

-50.2

50.2

-220.7

220.7

-0.68

9.7

5.6

-0.71

12.4

3.4

-16.79

12.4

5.4

-29.6

-11.05

5.2

-56.13

65.15

-44.2

49.48

-77.76

93.56

-237.5

233.1

-17.75

-6.48

-74.17

68.32

carryover Total Distribution to column Above floor Distribution to column below floor

18.52

-5.03

7.63

44.61

-58.14

19.36

-22.6

18.52

-5.03

7.63

44.61

-58.14

19.36

-22.6

A1

B1

C1

D1

E1

F1

G1

H1

I1

J1

K1

L1

M1

N1

O1

P1

Q1

FRAME 4

Figure 4-Analysis using substitute frame method-frame4

R1

S1

T1

U1

4.3.13 DISTRIBUTIO FACTOR

Joint A1 B1

C1

D1

E1

F1

G1

H1

I1

J1

Member A1B1 A11 A12 B1A1 B1C1 B11 B12 C1B1 C1D1 C1 1 C1 2 D1C1 D1E1 D11 D12 E1D1 E1F1 E1 1 E1 2 F1E1 F1G1 F11 F12 G1F1 G1H1 G11 G12 H1G1 H1I1 H11 H12 I1H1 I1J1 I11 I12 J1I1 J1K1 J1 1 J1 2 K1J1

Relative stiffness I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2

Total stiffness 0.8125I 1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

Stiffness for each member 0.38 0.31 0.31 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28

K1

L1

M1

N1

O1

P1

Q1

R1

S1

T1

U1

K1L1 K11 K12 L1K1 L1M1 L11 L12 M1L1 M1N1 M1 1 M1 2 N1M1 N1O1 N11 N12 O1N1 O1P1 O11 O12 P1O1 P1Q1 P1 1 P1 2 Q1P1 Q1R1 Q11 Q12 R1Q1 R1S1 R1 1 R1 2 S1R1 S1T1 S1 1 S1 2 T1S1 T1U1 T1 1 T1 2 U1T1 U11 U12

I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/3.2 I/4 I/4 I/3.2 I/6.4 I/4 I/4 I/6.4 I/8.16 I/4 I/4 I/8.16 I/4 I/4

4.3.14 LOAD CALCLATIO

1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

1.125I

0.9688I

0.7788I

0.6225I

0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.28 0.28 0.22 0.22 0.32 0.16 0.26 0.26 0.2 0.16 0.32 0.32 0.2 0.4 0.4

Beam name

Live load kN/m2 15

Area m2 5.12

Length slab DL m kN/m 3.2 13.2

Total LL kN/m 24

Rib DL kN/m 3.375

Total DL kN/m 16.575

Total load kN/m 40.575

1

A1B1

Dead load kN/m2 8.25

2

B1C1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

3

C1D1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

4

D1E1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

5

E1F1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

6

F1G1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

7

G1H1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

8

H1I1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

9

I1J1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

10

J1K1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

11

K1L1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

12

L1M1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

13

M1N1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

14

N1O1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

15

O1P1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

16

P1Q1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

17

Q1R1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

18

R1S1

8.25

15

5.12

3.2

13.2

24

3.375

16.575

40.575

19

S1T1

8.25

15

16.2

6.4

20.88

37.97

4.5

25.38

63.35

20

T1U1

8.25

15

13.74

8.16

13.89

25.26

4.5

18.39

43.65

No

JOINT-A1 joint

A1

B1

C1

D1

Member

A 1B 1

B 1A 1

B1C1

C1B1

C1D1

D1C1

D1E1

DF

0.38

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

-12.78

FEM due to LL

-34.624 34.624

Distributio n+ Carryover

-2.868

Distributio n

-37.492 14.247

Net BM due to A1

-23.245

JOINT-B1 joint

A1

B1

C1

D1

Member

A 1B 1

B 1A 1

B1C1

C1B1

C1D1

D1C1

D1E1

DF

0.38

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

-14.14 -34.624 34.624

-34.624 34.624

Distribution + Carryover

6.58

-2.87

Distribution

41.204 -37.494 -1.0388 -1.0388

Net BM due to B1

40.165

-38.533

joint

JOINT-C1 C1

B1

D1

E1

Member

B 1A 1

B1C1

C1B1

C1D1

D1C1

D1E1

E1D1

E 1F 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.14

FEM due to LL

-14.14 -34.62

+34.62 -34.62

Distributio n+ Carryover

2.868

-2.868

Distributio n

37.49 0

-37.49 0

Net BM due to C1

37.49

-37.49

+34.62

JOINT-D1 joint

B1

C1

D1

E1

Member

B 1A 1

B1C1

C1B1

C1D1

D1C1

D1E1

E1D1

E 1F 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-58.81 -34.624 +34.62 -34.624 +34.62 4 4

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to D1

37.492 -37.492

JOINT-E1 joint

D1

F1

E1

G1

Member

D1C1 D1E1

E1D1

E 1F 1

F 1E 1

F 1G 1

G 1F 1

G1H1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.1 4

FEM due to LL

0.28

-14.14 +34.62 34.624 4

-34.624 +34.624

Distributio n+ Carryover

2.868

-2.968

Distributio n

37.492 0

-37.492 0

Net BM due to E1

37.492

-37.492

JOINT-F1 joint

D1

F1

E1

G1

Member

D1C1

D1E1

E1D1

E 1F 1

F 1E 1

F 1G 1

G 1F 1

G1H1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-14.14 -34.624 +34.62 -34.624 +34.62 4 4

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to F1

37.492 -37.492

JOINT-G1 joint

F1

H1

G1

I1

Member

F 1E 1

F 1G 1

G 1F 1

G1H1

H1G1

H1I1

I1H1

I 1J 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.14

FEM due to LL

-14.14 +34.624 -34.624 +34.624 34.624

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 0

-37.492 0

Net BM due toG1

37.492

-37.492

JOINT-H1 joint

F1

H1

G1

I1

Member

F 1E 1

F 1G 1

G 1F 1

G 1H 1

H1G1

H1I1

I1H1

I 1J 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-14.14 -34.624 +34.62 -34.624 +34.62 4 4

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to H1

37.492 -37.492

JOINT-I1 joint

H1

J1

I1

K1

Member

H1G1

H1I1

I1H1

I 1J 1

J 1I 1

J 1K 1

K 1J 1

K1L1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.14

FEM due to LL

-14.14 -34.624 34.624

-34.624 34.624

Distributio n+ Carryover

2.868

-2.968

Distributio n

37.492 0

-37.492 0

Net BM due to I1

37.492

-37.492

JOINT-J1 joint

H1

J1

I1

K1

Member

H1G1

H1I1

I1H1

I 1J 1

J 1I 1

J 1K 1

K 1J 1

K1L1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-14.14 -34.624 +34.62 -34.624 +34.62 4 4

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to J1

37.492 -37.492

JOINT-K1 joint Member

J1 J 1I 1

J 1K 1

L1

K1 K 1J 1

K1L1

L1K1

M1 L1M1

M1L1

M 1N 1

DF

0.28

FEM due to DL

14.14

FEM due to LL

0.28

0.28

0.28

0.28

0.28

0.28

0.28

-14.14 -34.624 34.624 -34.624 34.624

Distributio n+ Carryover

2.868

-2.968

Distributio n

37.492 -37.492 0 0

Net BM due to K1

37.492 -37.492

JOINT-L1 joint

J1

L1

K1

M1

Member

J 1I 1

J 1K 1

K 1J 1

K 1L 1

L1K1

L1M1

M1L1

M1N1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-14.14 -34.624 34.624 -34.624 34.624

Distributio n+ Carryover

2.868

-2.968

Distributio n

37.492 -37.492 0 0

Net BM due to L1

37.492 -37.492

JOINT-M1 joint

L1

N1

M1

O1

Member

L1K1

L1M1

M1L1

M1N1

N1M1

N1O1

O1N1

O 1P 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.14

FEM due to LL

-14.14 -34.624 34.624 -34.624 34.624

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to M1

37.492 -37.492

JOINT-N1 joint

L1

N1

M1

O1

Member

L1K1

L1M1

M1L1

M1N1

N1M1

N1O1

O1N1

O 1P 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-14.14 -34.624

34.624 -34.624

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to N1

37.492 -37.492

34.624

JOINT-O1 joint

N1

P1

O1

Q1

Member

N1M1

N1O1

O1N1

O 1P 1

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.14

FEM due to LL

-14.14 -34.624 34.624 -34.624 34.624

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to O1

37.492 -37.492

JOINT-P1 joint

N1

P1

O1

Q1

Member

N1M1

N1O1

O1N1

O 1P 1

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to LL

14.14

-14.14 -34.624

34.624 -34.624

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to P1

37.492 -37.492

34.624

JOINT-Q1 joint

P1

R1

Q1

S1

Member

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

R1Q1

R1S1

S1R1

S 1T 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.32

0.16

FEM due to DL

14.14

FEM due to LL

-14.14 -34.624 34.624 -34.624 34.624

Distributi on + Carryove r

2.868

-2.968

Distributi on

37.492 -37.492 0 0

Net BM due to Q1

37.492 -37.492

JOINT-R1 joint

P1

R1

Q1

S1

Member

P 1 O 1 P 1 Q 1 Q 1P 1

Q1R1

R1Q1

R1S1

S1R1

S 1T 1

DF

0.28

0.28

0.28

0.28

0.32

0.16

FEM due to DL FEM due to LL

0.28

0.28 14.14

-86.63 -34.624 34.624

-34.624

Distributi on + Carryove r

2.868

8.32

Distributi on

37.492 -3.13

-26.304 -3.13

Net BM due to R1

34.362

-29.434

34.624

JOINT-S1 joint

R1

S1

Member

R1Q1

R1S1

S 1T 1

S 1T 1

T 1S 1

DF

0.28

0.28

0.32

0.16

0.2

FEM due to DL

14.14

FEM due to LL

U1

T1 T1U1 0.16

U1T1 0.2

-102.04 -34.624

34.624

-216.23 216.23

Distributi on + Carryove r

2.868

-11.42

Distributi on

37.492 60.85

-227.65 30.43

Net BM due to S1

98.342

-197.22

JOINT-T1 joint

R1

S1

T1

U1

R1Q1

R1S1

S 1T 1

S 1T 1

T 1S 1

DF

0.28

0.28

0.32

0.16

0.2

0.16

0.2

-216.23

216.23

-242.2

242.2

Distributio n+ Carryover

16.167

-24.22

Distributio n

232.397 6.81

-266.42 5.44

Net BM due to T1

239.207

-260.98

FEM due to DL FEM due to LL

T1U1

U1T1

Member

14.14

JOINT-U1 joint

R1

S1

T1

Member

R1Q1

R1S1

S 1T 1

S 1T 1

T 1S 1

DF

0.28

0.28

0.32

0.16

0.2

FEM due to DL FEM due to LL

U1 T1U1

U1T1

0.16

0.2

-242.2

242.2

86.63

Distributio n+ Carryover

12.45

Distributio n

254.65 -50.93

Net BM due to U1

203.72

MID SPAN MOMENT A1B1 B1 C1

joint

A1

Member

A 1B 1

B 1A 1

B 1C 1

C1B1

C1D1

D1C1

D1E1

DF

0.38

0.28

0.28

0.28

0.28

0.28

0.28

-14.14

14.14 -34.624

34.624

FEM due to DL FEM due to TL

-34.624

34.624

distribution moment

13.16

-5.74

carry over moment

-2.87

6.58

distribution

1.09

-2.65

Net moment -23.24

D1

5.74 2.87

+32.814

F ree BM at the centre of the span A1B1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span A1B1 =51.936-[ (23.24+32.814) / 2] =23.909 kNm

MID SPAN MOMENT OF B1C1 joint

A1

Member

A 1B 1

B 1A 1

B 1C 1

C1B1

C1D1

D1C1

D1E1

DF

0.38

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

-14.14

14.14

-14.14

14.14

B1

FEM due to TL distribution moment

C1

-34.624 34.624 5.74

-5.74

2.87

-2.87

distribution

0.052

-1.61

Net moment

-31.702 30.14

carry over moment

D1

5.37 2.685

-34.624 5.74 2.87

Free BM at the centre of the span B1C1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span B1C1 =51.936-[ (31.702+30.14) / 2] =21.015 kNm

MID SPAN MOMENT C1D1 Joint

B1

C1

D1

E1

member

B 1A 1

B1C1

C1B1

C1D1

D1C1

D1E1

E1D1

E 1F 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distributio n moment carry over moment

-14.14 14.14 34.62 4

-14.14 14.14 -34.624 34.624

-5.74

5.74

-2.87 -2.87

-34.624

-5.74

2.87

distributio n

-1.6

1.6

Net moment

-33.35

33.35

5.74

2.87

Free BM at the centre of the span C1D1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span C1D1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT D1E1 Joint

C1

D1

F1

E1

member

C1B1

C1D1

D1C1

D 1E 1

E1D1

E 1F 1

F 1E 1

F 1G 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74

-2.87

Free BM at the centre of the span D1E1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span D1E1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

-34.624 5.74

2.87

MID SPAN MOMENT E1F1 Joint

D1

F1

E1

G1

member

D1C1

D1E1

E1D1

E 1F 1

F 1E 1

F 1G 1

G 1F 1

G1H1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

Free BM at the centre of the span E1F1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span E1F1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

-34.624 5.74 2.87

MID SPAN MOMENT F1G1 Joint

F1

E1

H1

G1

member

E1D1

E 1F 1

F 1E 1

F 1G 1

G 1F 1

G1H1

H1G1

H1I1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span F1G1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span F1G1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT G1H1 Joint

F1

H1

G1

I1

member

F 1E 1

F 1G 1

G 1F 1

G1H1

H1G1

H1I1

I1H1

I 1J 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74

-2.87

Free BM at the centre of the span G1H1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span G1H1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

-34.624 5.74

2.87

MID SPAN MOMENT H1I1 Joint

H1

G1

J1

I1

member

G 1F 1

G1H1

H1G1

H 1I 1

I1H1

I 1J 1

J 1I 1

J 1K 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span H1I1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span H1I1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT I1J1 Joint

H1

J1

I1

K1

member

H1G1

H1I1

I1H1

I 1 J1

J 1I 1

J 1K 1

K 1J 1

K1L1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

Free BM at the centre of the span I1J1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span I1J1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

-34.624 5.74 2.87

MID SPAN MOMENT J1K1 Joint

J1

I1

L1

K1

member

I1H1

I 1J 1

J 1I 1

J 1K 1

K 1J 1

K1L1

L1K1

L1M1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

Free BM at the centre of the span J1K1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span J1K1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

-34.624 5.74 2.87

MID SPAN MOMENT K1L1 Joint

J1

L1

K1

M1

member

J 1I 1

J 1K 1

K 1J 1

K1L1

L1K1

L1M1

M1L1

M1N1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span K1L1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span K1L1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT L1M1 Joint

L1

K1

N1

M1

member

K 1J 1

K1L1

L1K1

L 1M 1

M1L1

M1N1

N1M1

N1O1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span L1M1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span L1M1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT M1N1 Joint

L1

N1

M1

O1

member

L1K1

L1M1

M1L1

M1N1

N1M1

N1O1

O1N1

O 1P 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span M1N1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span M1N1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT N1O1 Joint

N1

M1

P1

O1

member

M1L1

M1N1

N1M1

N 1O 1

O1N1

O 1P 1

P 1O 1

P 1Q 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span N1O1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span N1O1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT O1P1 Joint

N1

P1

O1

Q1

member

N1M1

N1O1

O1N1

O 1P 1

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

Free BM at the centre of the span O1P1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span O1P1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

-34.624 5.74 2.87

MID SPAN MOMENT P1Q1 Joint

P1

O1

R1

Q1

member

O1N1

O 1P 1

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

R1Q1

R1S1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

1.6

Net moment

-33.35

33.35

carry over moment

-5.74 -2.87

-34.624 5.74 2.87

F ree BM at the centre of the span P1Q1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span P1Q1 =51.936-[ (33.35+33.35) / 2] =18.586 kNm

MID SPAN MOMENT Q1R1 Joint

P1

R1

Q1

S1

member

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

R1Q1

R1S1

S 1T 1

S 1T 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.32

0.16

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

-14.14 14.14 -34.624 34.624 5.74

-5.74

-2.87

2.87

distribution

-1.6

5.33

Net moment

-33.35

37.084

carry over moment

-5.74 -2.87

-216.23 32.33 16.16

F ree BM at the centre of the span Q1R1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span Q1R1 =51.936-[ (33.35+37.084) / 2] =16.719 kNm

MID SPAN MOMENT R1S1 Joint

R1

Q1

S1

T1

member

Q 1P 1

Q1R1

R1Q1

R 1S 1

S 1T 1

S 1T 1

T 1S 1

DF

0.28

0.28

0.28

0.28

0.32

0.16

0.2

FEM due to DL FEM due to TL distribution moment

-14.14 14.14 34.624

5.74

16.64

8.32

2.87

distribution

1.526

5.896

Net moment

-19.038 60.03

carry over moment

-2.87

-242.2 31.11 15.55

Free BM at the centre of the span R1S1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span R1S1 =51.936-[ (19.038+60.03) / 2] =12.402 kNm

0.16

-86.63 86.63 -34.624 34.624

-5.74

T1U1

MID SPAN MOMENT S1T1 joint Member DF

R1 R1Q1 0.28

FEM due to DL FEM due to TL distribution moment

R1S1

S1

T1

U1

S1R1

S1T1

T1S1

T1U1

U1T1

0.28

0.32

0.16

0.2

0.16

0.2

-14.14

14.14

34.624

-102.04 102.04 -216.23 216.23

-5.74

32.33

-22.838

-11.42

16.165

distribution

-2.29

1.19

Net moment

-197.61 210.75

carry over moment

-2.87

F ree BM at the centre of the span S1T1 = Wl2/8 =(216.23 * 3.22) / 8 =276.77 kNm Net BM at centre of span S1T1 =276.77-[ (197.61+210.75) / 2] =72.594kNm

MID SPAN MOMENT T1U1 joint Member

R1

U1

S1T1

T1S1

T1U1

U1T1

0.32

0.16

0.2

0.16

0.2

-86.63

86.63 -43.65

43.65

-688

-8.73

-4.37

-3.44

Distribution

0.48

-0.688

Net moment

-54.42

30.792

0.28

R1S1

T1

S1R1

DF

R1Q1

S1

0.28

FEM due to DL FEM due to TL

40.575

distribution moment

14.74

carry over moment

7.37

F ree BM at the centre of the span T1U1 = Wl2/8 =(43.65 * 8.162) / 8 =363.3kNm Net BM at centre of span T1U1 =363.3-[ (54.42+30.79) / 2] =320.69kNm

MID SPAN MOMENT K1L1 Joint

J1

L1

K1

M1

member

J 1I 1

J 1K 1

K 1J 1

K1L1

L1K1

L1M1

M1L1

M1N1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to DL

14.14

-14.14 14.14

FEM due to TL

-34.624 34.624

distribution moment

5.74

-14.14 -34.624 34.62 4

-5.74

-5.74

5.74

5.74

2.87

2.87

-2.87

-2.87

distribution

-1.61

1.67

Net moment

-18.62 18.62

carry over moment

Free BM at the centre of the span K1L1 = Wl2/8 =(40.575 * 3.22) / 8 =51.936 kNm Net BM at centre of span K1L1 =51.936-[ (18.62+18.62) / 2] =33.316 kNm

-5.74

4.3.15 BENDING MOMENT IN COLUMN LOADING joint

A1

B1

C1

D1

E1

F1

G1

Above floor

0.31

0.22

0.22

0.22

0.22

0.22

0.22

Below floor

0.31

0.22

0.22

0.22

0.22

0.22

0.22

Member

A1 B1

B1A1

B1 C1

C1 B1

C1 D1

D1 C1

D1 E 1

E 1D 1

E1 F1

F1E1

F1 G1

G1F1

G 1H 1

DF

0.39

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

-14.2

14.2

-14.2

14.2

-14.2

14.2

Column DF

FEM due to DL FEM due TL

-34.62

34.62

Distribution+

-2.87

6.75

2.87

-37.49

41.37

-11.3

-34.62

34.62

-2.87

-2.87

2.87

2.87

11.3

-37.49

37.49

-11.3

-34.62

34.62

-34.62

-2.87

-2.87

2.87

2.87

-2.87

-2.87

11.3

-37.49

37.49

-11.3

11.3

-37.49

carryover Total Distribution to column Above floor Distribution to column below floor joint

11.62

-6.62

5.77

-5.77

5.77

-5.77

5.77

11.62

-6.62

5.77

-5.77

5.77

-5.77

5.77

H1

I1

J1

K1

L1

M1

N1

Column DF Above floor

0.22

0.22

0.22

0.22

0.22

0.22

0.22

Below floor

0.22

0.22

0.22

0.22

0.22

0.22

0.22

Member

H1 G1

H1 I 1

I 1 H1

I1 J 1

J 1 I1

J 1 K1

K1 J 1

K1 E 1

L1 K1

L1 M1

M1 L1

M 1 N1

N 1M 1

N 1O 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

-14.2

14.2

-14.2

14.2

-14.2

14.2

FEM due to

-14.2

DL FEM

due

34.62

-

TL Distribution

34.62

-

34.62

34.62

-

34.62

34.62

34.62

2.87

2.87

-2.87

-2.87

2.87

2.87

-2.87

-2.87

2.87

2.87

-2.87

-2.87

2.87

2.87

37.5

-11.3

11.3

-37.5

37.5

-11.3

11.3

-37.5

37.5

-11.3

11.3

-37.5

37.5

-11.3

+ carryover Total Distribution to column Above floor Distribution to column below floor

-5.77

5.77

-5.77

5.77

-5.77

5.77

-5.77

-5.77

5.77

-5.77

5.77

-5.77

5.77

-5.77

joint

O1

P1

Q1

R1

S1

T1

U1

Above floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Below floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Column DF

Member

O 1N 1

O 1P 1

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

R1Q1

R1S1

S1R1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.32

FEM due to

14.2

-14.2

14.2

-14.2

14.2

S1T1 0.16

T1S1

T 1U 1

U 1T 1

0.2

0.16

0.2

-102.1

102.1

DL FEM due TL Distribution+

-34.62

34.62

-2.87

-2.87

2.87

2.87

11.3

-37.5

37.5

-11.3

-34.62

34.62

-2.87

-2.87

2.87

32.33

11.3

-37.5

37.5

-11.3

-216.2

216.2

-2.87

-11.42

16.17

-10.2

-9.14

11.3

227.65

232.4

-112.2

92.9

carryover Total Distribution to column Above floor Distribution to column below floor

joint

5.77

-5.77

5.77

-12.25

-62.12

-38.45

-37.2

5.77

-5.77

5.77

-12.25

-62.12

-38.45

-37.2

A1

B1

C1

Above floor

0.31

0.22

Below floor

0.31

0.22

Member

A1 B1

B1A1

B1 C1

C1 B1

C1 D1

D1 C1

D1 E 1

E 1D 1

E1 F1

F1E1

F1 G1

G1F1

G 1H 1

DF

0.39

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to

-14.2

14.2

-14.2

14.2

-14.2

14.2

D1

E1

F1

G1

0.22

0.22

0.22

0.22

0.22

0.22

0.22

0.22

0.22

0.22

Column DF

-14.2

DL FEM due TL Distribution+

-34.6

34.62

-34.62

34.62

-34.62

34.62

-34.62

2.87

2.76

-2.87

2.87

2.87

-2.87

-2.87

2.87

2.87

-2.87

-2.87

2.87

2.87

11.3

16.9

-37.5

37.49

-11.3

11.3

-37.49

37.49

-11.3

11.3

-37.49

37.49

-11.3

carryover Total Distribution to column Above floor Distribution to column below floor

-3.49

4.53

-5.77

5.77

-5.77

5.77

-5.77

-3.49

4.53

-5.77

5.77

-5.77

5.77

-5.77

joint

H1

I1

J1

K1

L1

M1

N1

Column DF Above floor

0.22

0.22

0.22

0.22

0.22

0.22

0.22

Below floor

0.22

0.22

0.22

0.22

0.22

0.22

0.22

Member

H1 G1

H1 I 1

I 1 H1

I1 J 1

J 1 I1

J 1 K1

K1 J 1

K1 E 1

L1 K1

L1 M1

M1 L1

M 1 N1

N 1M 1

N 1O 1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

FEM due to

14.2

-14.2

14.2

-14.2

14.2

-14.2

14.2

DL FEM

due

-

TL

34.62

-

34.62

Distribution

34.62

-

34.62

34.62

-34.62

34.62

-2.87

-2.87

2.87

2.87

-2.87

-2.87

2.87

2.87

-2.87

-2.87

2.87

2.87

-2.87

-2.87

11.3

-37.5

37.5

-11.3

11.3

-37.5

37.5

-11.3

11.3

-37.5

37.5

-11.3

11.3

-37.5

+ carryover Total Distribution to column Above floor Distribution to column below floor

5.77

-5.77

5.77

-5.77

5.77

-5.77

5.77

5.77

-5.77

5.77

-5.77

5.77

-5.77

5.77

joint

O1

P1

Q1

R1

Above floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

Below floor

0.33

0.24

0.27

0.31

0.27

0.24

0.33

S1

T1

U1

Column DF

Member

O 1N 1

O 1P 1

P 1O 1

P 1Q 1

Q 1P 1

Q1R1

R1Q1

R1S1

S1R1

DF

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.28

0.32

-14.2

14.2

-14.2

14.2

FEM due to

S1T1

T1S1

T 1U 1

U 1T 1

0.16

0.2

0.16

0.2

-86.63

86.63 -242.2

242.2

DL FEM due TL

34.62

Distribution+

2.87

2.87

37.5

-11.3

-34.6

34.62

-2.87

-2.87

2.87

2.87

11.3

-37.5

37.5

-11.3

-34.62

34.62

-2.87

8.32

2.87

15.56

4.16

-24.22

12.45

11.3

-26.31

37.5

-71.1

90.79

-266.4

254.7

carryover Total Distribution to column Above floor Distribution to column below floor

-5.77

5.77

-5.77

3.31

8.73

56.2

-102

-5.77

5.77

-5.77

3.31

8.73

56.2

-102

CHAPTER 5 5.DESIG

5.1SLABS The most common type of structural element used to cover floors and roofs of building are reinforced concrete slabs of different types. One way slabs are those supported on the two opposite sides so that the loads are carried along one direction only. Two way slabs are supported on all four sides with such dimensions such that the loads are carried to the supports along both directions. If Ly/Lx < 2, then the slab is designed as two way slab If Ly/Lx >2, then the slab is designed as one way slab. Where, Ly = longer span dimension of the slab. Lx = shorter span dimension of slab. Restrained slabs are referred to as slabs whose corners are prevented from lifting. They may be supported on continuous or discontinuous edges.

5.1.1 DESIG OF SLAB

Dimensions Lx

=3.2

Ly

=5.5

Span ratio =5.5 /3.2 =1.1 τv k*τc=1.3*0.43 =0.5616 0.398 > 0.5616N/mm2 Hence it is safe. Check for deflection (L/d) basic Pt

=20 =100 Ast pro/bd =100*523.59/1000*130 =0.4

Fs

=0.58*415*523.59/465.86 =270

kc

=1

kf

=1

kt

=1.2

(L/d)max =(L/d)basic*kt*kc*kt =20*1.3*1*1 =26 (L/d)act

=3200/130=24.16

(L/d)act < (L/d)max Hence safe against deflection.

Check for control Reinforcement provided is more than, the minimum % of c/s area Ast

=(0.12/100)*1000*150 =180mm2

Spacing of main reinforcement should not be greater than 3d ie, 3*130 =390mm Diameter of reinforcement should be less than D/8 150/8 =18.75 Hence cracks will be with in safe permissible limits Torsion reinforcement at corner Area of torsion steel at each of the corners in 4 layers is computed as =0.75* Ast along shorter span =0.75*523.59 =393mm2 Length cover which torsion steel is provided =1/5*shorter span =1/5*3200 =640mm Using 6mm dia bars Spacing =1000ast/ Ast =(1000*π*62/4)393 =71.9mm Provide 6mm bars at 100mm c/c for length and 640mmat all corners in 4 layers

Reinforcement in end strips Ast =0.12% of c/s =180mm2 Assume 10mm dia bars Spacing =(1000*π/4*102)/180 =436 > 300 As per code spacing should not exceed 300mm Provide 10mm dia bars at 300mm c/c Ast =(1000*π/4*102)/300 Ast =262mm2

10mm dia bars @ 150mm c/c 6mm dia bars @ 100mm c/c 150

Figure 5-Reinforcement details of two way slab-section

ly/8 437.5

3500

6mm dia @ 100mm c/c 10mm dia bars @ 150mm c/c

3ly/4 2625

10mm dia bars @ 250mm c/c ly/8 437.5 lx/8 400

3lx/4 2400

lx/8 400

3200

REINFORCEMENT DETAILS OF TWO WAY SLAB

Figure 6-Reinforcement details of two way slab- plan

5.2 BEAMS Beams are defined as structural members subjected to transverse load that caused bending moment and shear force along the length. The plane of transverse loads is parallel to the plane of symmetry of the cross section of the beam and it passes through the shear centre so that the simple bending of beams occurs. The bending moments and shear forces produced by the transverse loads are called as internal forces. 5.2.1Types of beams Depending upon the supports and end condition, beams are classified as below. 5.2.1.1simply supported beams 5.2.1.2over hanging beams 5.2.1.3cantilever beam 5.2.1.4fixed beam The reinforced concrete beams, in which the steel reinforced is placed only on tension side, are known as singly reinforced beams, the tension developed due to bending moment is mainly resisted by steel reinforcement and compression by concrete. When a singly reinforced beam needs considerable depth to exist large bending moment, then the beam is also reinforced in the compression zone. The beams having reinforcement in compression and tension zone is called as doubly reinforced beam.

5.2.2 DESIG OF L-BEAMS

Dimensions c/c of support = 3.2+(0.3/2)+(0.3/2) = 3.5m Thickness of slabs = 150 mm fy = 20 N/mm2 fck = 415 N/mm2 Width of beam = 300 mm Overall depth = 300 mm Effective cover = 25 mm Effective depth = 300-25-10=265mm Effective span a) c/c of supports = 3.2 +(0.3/2) +(0.32/2) = 3.5 m b) Clear span + d = 3.2 +0.265 = 3.465m Hence, l = 3.465 m Load calculation Dead load of slab = (3.465/2)*0.15*25 = 6.5 kN/m Floor finish

= 0.75*(3.465/2) = 1.3 kN/m

Self weight of rib = 0.3 *0.15 *25 = 1.125 kN/m Live load

= 4*(3.465/2) = 6.93 kN/m

Total load

= 16.855 kN/m

Effective flange width a)bf = (Lo/12)+bw+3Df = 952.125 mm b) bf = bw +0.5 times spacing b/w ribs = 1900 mm

Ultimate BM and SF At support, Mu = 1.5 * wl2/12 = 25.3 kNm Vu = 1.5 * wl / 2 = 43.8 kN At centre of span section, Mu = 1.5 * wl2 / 24 = 12.65kNm Vu = 1.5 * wl / 2 = 43.8 kN Torsion moment produced due to dead load of span and live load on it = working load parameter-rib wt = 16.855-1.125=15.73 kN/m Ultimate load on slab = 15.73 *3.465 * 1.5 = 81.8 kN Total ultimate load

= 82/2 =41 kN

Distance of centroid of SF from the centre line of the Beam=(952.125/2)150 = 326.06mm Ultimate tortional moment = 4 * 103 *326.06= 13.37 kNm Equivalent BM and SF According to IS456 2000 clause 41.4.2 Mel = Mu +Mt Mt = Tu*(1+D/b)/1.7 = 15.73 kNm Mel = 13.37 + 15.73 = 29.09 kNm Equivalent SF Ve = Vu + 1.6(Tu/b) =115.1 kN Main reinforcement Mu (lim) = 0.138*fck*bd2 = 58.15 kNm Mel < Mu (lim) Hence the section is under reinforced

To find Ast Mu = 0.87*fy* Ast *d[1-( Ast *fy/bd*fck)] Ast = 332.83mm2 20mm dia rods are used Ast pro = 628.32 mm2 Ast min = 0.85*bw*d/ fy = 162.83 mm2 Assume 20mm dia bars, Ast pro = 628 mm2 Provide 2 nos of 20mm dia bars @ side face

Reinforcement Shear reinforcement τve =Ve/ bw *d = 1.45 N/ mm2 Pt= (100* Ast)/( bw *d) = 0.79 Ref table 19 of IS456 2000 τc=0.56N/ mm2 Hence shear reinforcement are required using 10mm dia 2 legged stirrups with side cover 25mm top+ bottom cover of 25mm b1= 300-25-25 = 250mm d1= 300-25-25 = 250mm Asv= 157 mm2 σc = Asv *0.87*fy/ (τv – τc)*b = 214.6 Provide 10mm dia 2 legged stirrups @200mm spacing

Check for deflection (L/d)max = (L/d)basic *kt * kc* kf (L/d)basic = 20 [for simply supported] (L/d)max = 20*1*1*1.04 = 20.8 (L/d)actual = 3200/300 = 10.66 (L/d)max > (L/d)actual Hence the design is safe

2 nos of 20mm dia bars 3 nos of 20mm dia bars 10mm dia 2 legged stirrups @ 200mm c/c

3500 LONGITUDINAL SECTION OF L-BEAM

Figure 7-Reinforcement details of L-beams- longitudinal section

2 bars of 20mm dia

2 bars of 20mm dia

150

150

10mm dia 2 legged stirrups @ 200mm c/c

10mm dia 2 legged stirrups @ 200mm c/c

3 bars of 20mm dia

3 bars of 20mm dia

SUPPORT SECTION

MID SECTION

CROSS SECTION OF L-BEAM Figure 8- Reinforcement details of L-beams- cross section

5.2.3 DESIG OF T- BEAM Dimensions Slab thickness

=150mm

c/c of support

=3.2+(0.3/2)+(0.3/2) =3.5m

fy

=20N/mm2

fck

=415N/mm2

Cross sectional dimension Width of beam

=300mm

Overall depth

=300mm

Effective cover

=25mm

Effective depth

=300-2-10 =265mm

Effective span 1. c/c of support

=3.2+(0.3/2)+(0.3/2) =3.5m

2. clear span+depth

=3.2+0.265 =3.465m

Load calculation Dead load of slab

=(3.465/2)*0.15*25 =6.5kN/m

Floor finish

=0.75*(3.465/2) =1.3kN/m

Self weight of rib

=0.3*0.15*25 =1.125kN/m

Live load

=4*(3.465/2)

=6.93kN/m Light partition

=1kN/m

Total load

=16.855kN/m

Ultimate moment and shear =1.5wl2/8

Mu

=(1.5*16.855*3.4652)/8 =37.935kN/m Vu

=wl/2 =(16.855*3.465)/2 =43.8kN/m

Effective width of flange Refer page no 36 clause 23, 1.

bf

=L0/b+bw+6Df =(3.465*0.7)/6+300+(6*150) =1604.25mm

2.

c/c of rib

=3000-(300/2)-(300/2) =2700mm

Ie,

bf

=1604.25mm

Moment capacity of flange Assume N.A lies with in the flange Xu(max)=Df ,

b=bf

Mu(limit) =(0.36*Xu(max))/d *(1-(0.42Xu(max)/d))*(bd2fck) =0.36*(150/265) *[1-(0.42*150)/26]*(1604.25*2652*20) =349.98kNm Mu < Mu(limit) Hence the section is under reinforced. Since the section should design as a singly reinforced beam.

Find Ast Mu =0.87fy Ast d [1-( Ast fy /bf d fck)] 37.935*106=0.87*415* Ast *265*[1-( Ast *415/1604*265*20)] Ast =404.46mm2 Check for Ast min Ast min/bw d

=0.85/fy

Ast

=(0.85*300*265) /415 =162.83mm2 Ast > Ast min Ast =404.46mm2

N*πd2/4 =404.46 N

=2 nos.

Ast provide, Provide 2 nos of 20mm dia bars =2*π202/4 =628mm2 And two longer bars of 12mm dia on the compression face . Shear reinforcement τv

=Vu/bw d =43.8*103/300*265 =0.55

Pt

=100 Ast /bw d =(100*π/4*202*2)/300*265 =0.79

τc

=0.56+((0.62-0.56)/(1-0.75))*(0.79-0.75) =0.57 τv166.7

Hence ok.

Check for depth for waist slab D

=√Mu/(0.138fckb) =√76.699*106/(0.138*20*1000) =166.7mm

But D

=200mm

D

=200-20 =180>166.7

Hence ok.

12mm dia bars @ 100mm c/c 8mm dia bars @ 200mm c/c Tread = 300mm Riser =125mm Thickness of flight = 200mm

12mm dia bars @ 100mm c/c 8mm dia bars @ 200mm c/c

DETAILING OF DOG LEGGED STAIRCASE Figure 11-Reinforcement details of doglegged staircase

5.4 COLUMS A column is defined as a structural member subjected to compressive force in a direction parallel to its longitudinal axis. The columns are used primarily to support compressive load. When the compression members are over loaded then their failure may take place in direct compression (crushing), excessive bending combined with twisting. Failure of column depends upon slenderness ratio. 5.4.1 Types of columns 1) Short column 2) Long column When slenderness ratio (lex/b) is less than 12, the compression member (lex/b) is said to be short column and if the slenderness ratio is greater than 12, it is called as long column.

5.4.2DESIG OF COLUM 5.4.2.1 DESIG OF AXIALLY LOADED COLUM

Dimensions Factored load

=1200kN

Concrete grade

=M20

Characteristic strength of reinforcement =415N/mm2 Unsupported length of column

=3.55m

Cross sectional area of column

=400*300

Leff

=k*L

k

=0.65(effectively held in position at both ends)

Leff

=0.65*3550 =2307mm

Slenderness ratio Leff /D

=2307/400 =5.814.6 ie, codal formula for axially compressed column can be used.

Longitudinal reinforcement Pu

=[0.4fck Ac+0.67fy-0.4fck)Ast]

1200*103 =[(0.4*20*400*300)+[(.67*415)-(0.4*20)]Asc Asc

=888.7mm2

Minimum reinforcement provided =0.008*400*300=960mm2 ie, Provide 6 nos of 20 mm dia bars of longitudinal reinforcement Lateral ties Tie diameter >6mm 16*20=320mm ie, provide 8mm dia ties @ 300mm c/c

Lateral ties 8mm dia bars @ 300mm c/c 6 nos of 20mm dia bars

AXIALLY LOADED COLUMN

Figure 12-Reinforcement details of axially loaded column

5.4.2.2 DESIG OF UIAXIALLY LOADED COLUM

Dimensions Size of column = 400mm×300mm = 650 kN

Load, Pu

Factored moment= 127 kNm Eccentricity

= 127/650 = 0.19

fck

= 20 N/mm2

fy

= 415 N/mm2

D

=400mm

b

=300mm

Assuming cover, d`=50mm d`/D = 50/400 =0.125 Pu/ fck bD = (650*103)/(20*300*400) = 0.27 Mu/ fck bD2 = (127*106)/ (20*300*4002) = 0.132 From graph 45 of SP16, p/ fck = 0.07 percentage of steel = 1.4 As = pbD/100 = (1.4*400*300)/100 =1800mm2 nπd2/4 = 1800mm2 n = 6 nos

Provide 8 nos. of 20mm dia bars and they are equally arranged on all four sides Spacing = 400-(50+50+20) = 280mm < 300mm Hence safe

Design of lateral ties Dia of lateral ties not less than 6mm and not greater than 16mm Take 8mm dia ties Spacing should not be greater than 300mm or 16φ=16*20= 320mm Hence provide 8mm φ bars @ 250mm c/c

Lateral ties 8mm dia bars @ 250mm c/c 8 nos of 20mm dia bars

UNIAXIALLY LOADED COLUMN

Figure 13-Reinforcement details of uniaxially loaded column

5.4.2.3 DESIG OF BI AXIALLY LOADED COLUM

Dimension b = 450mm D = 600mm fck =20 N/mm2 fy = 414 N/mm2 Pu = 590.6 kN Mux= 150 kN Muy= 106 kN Reinforcements Reinforcements are distributed equally on four sides As a trial adopt percentage of reinforcement in the CS as p =1% As = pbD/100 = 1*450*600/100 = 2700mm2 Provide 10 bars of 20mm dia on each face As = 10*π*202/4 = 3141.6mm2 P = (100*3141.6)/(450*600) = 1.16 p/ fck = 1.16/20 =0.058 d`= 40+10 = 50mm Pu/ fck bD = (590.6*103)/(20*450*300) = 0.12 d`/D = 50/600 =0.08 from chart 44 of SP16

Mu/ fck bD2 = 0.09 For moments about minor axis yy b= 450mm d`=40+10=50mm d`/D = 50/450 =0.111 Pu/ fck bD = 0.12 From chart 44 for d`/D=0.15 Mu/ fck bD2 = 0.09 Muy1=0.09*20*600*4502 = 218.7 kNm Puz= 0.45 fck Ac+0.75 fy As =0.45*20[(600*450)-314.6]+[0.75*415*3141.6*10-3] = 3379.55kN Pu/ Puz = (590.6/3379.55)=0.175 According to IS456 clause 39.6 αn =1.04 (Mux/ Mux1) αn +( Muy/ Muy1) αn = 0.970.25 Assuming 60mm dia bars, Spacing = 1000ast/ Ast =1000*π*162/(4*1970.4) =105mm Hence, provide 16mm dia bars @100mm c/c in both directions.

GL Column Reinforcement

16mm dia bars @ 100mm c/c (both ways)

FOOTING FOR AXIALLY LOADED COLUMN Figure 15-Reinforcement details of axially loaded column

CHAPTER 6 6. COCLUSIO The analysis and design of the structural components of the college auditorium envisaged planning for each floor of the building with detailed analyses of Beams, Columns, Slabs and Stairs. Isolated footings for Columns were considered. This work throws an insight into the structural components of the proposed college auditorium which will be constructed soon.

REFERECES 1.

“Advanced Reinforced Concrete Design”, by N.Krishna Raju.

2.

“Strength of Materials”, by Ramamirtham and Narayanan.

3.

“Reinforced Concrete Design”, by P.P.Vargheese

4.

IS:875 part , “Code of Practice for design loads for buildings and structures – Dead Loads”.

5.

IS:875 part , “Code of Practice for design loads for buildings and structures – Live Loads”.

6.

IS:875 part , “Code of Practice for design loads for buildings and structures – Wind Loads”.

7.

IS:456: 2000, “Plain and Reinforced Concrete - Code of Practice”.

8.

“Design of Concrete Structures”, by Shah