Inspiration - Hamasteel › wp-content › themes › franco...Provide4 - DIA25 +4-DIA12 =24.15 cm2 at bottom Provide 2 - DIA12 = 2.26cm 2 at top Designing for shear Provide dia 8

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Designer's H a n d b o o k

Hama Steel

Relevant portions of IS:456-:2000, IS1789-1985, SP-16 &SP-24,NS-191 have been extensively used for preparation of this handbook.

Compiled by: Hama Iron and Steel Industries 2062

A Designer's Handbook HAMA SG 500

Chapter 1 Economy Through Hama 500 RE-BARS Over Plain & CTD/TOR Bars 5

Chapter 2 Material Strength and Stress-Strain Relationships 3 7

Chapter 3 Fiexural Members 75

Chapter 4 Compression Members 95

Chapter 5 Shear and Torsion 113

Chapter 6 Development Length and Anchorage 119

Annexure I Conversion table 123

Annexure II Areas of Reinforcement Bars 124

Annexure III Fixed end moments 126

Annexure IV Substitution tables for Hama 500 129

Annexure V Guidlines for switching over from CTD/TOR to Hama 500 133

Table of Contents


CHAPTER - 1

Economy Through

Hama SG 500 RE-BARS

Over Plain & CTD/TOR Bars

5


6

It is evident that TMT rebars irrespective of grades are technically superior to conventional plain and cold twisted deformed bars. Besides, the replacement of conventional bars by TMT rebars will result in savings in terms of weight and there by the cost. However, the percentage saving will depend upon the type of structural member and the grade of steel.

A brief summary of probable range of savings arising due to the use of HAMA 500 quenched rebars is presented for structural members in the following paragraphs with a view to make the user feel about its cost effectiveness. This study is based on various charts and tables corresponding to CTD/TOR and TMT rebars with detailed discussions which will follow subsequently in this handbook.

i. Doubly Reinforced Beams

Use of TMT 500 rebars will result in the saving of reinforcement of about 44% to 47% over mild steel and 14% to 15% over CTD/TOR bars respectively and in terms of cost will be about 35% to 37% over plain bars and 6% to 8% over CTD/TOR bars.

If TMT 550 is used, the savings in weight will be 47% to 51 % over plain bars and

19% to 20% over CTD/TOR bars. If converted in cost, the savings will be 39% to 41% over plain and CTD/TOR bars respectively (refer table 1.2). If the cost of bending, binding and transportation are taken into consideration, it will result in further savings.

ii. Axially Loaded Columns

If TMT rebars are used instead of plain and CTD/TOR bars, the savings by weight will be about 44% respectively. Because, the cost of TMT 500 and CTD/TOR is the same, the cost saving will remain equal to weight-wise saving, i.e. 10 % (refer table 1.5).

iii. Columns with Uni-axial Banding

The saving by using TMT 500 reinforcing steel over plain bars will be about 39% by weight and 34% cost wise. However, the savings with respect of CTD/TOR bars could be summarised as following:

1.1 General


7

If the axial load on a column is comparatively more,TMT rebars have a distinct advantage over CTD/TOR bars between 8% to 10%. When the magnitude of moment is very high as compared to the axial load i.e. the column is subjected to more bending, the saving will be around 2% to 4%. In the following text, few model examples have been worked out to appraise the users about the economy which can be achieved in terms " of weight and cost by using TMT rebars in lieu of conventional plain/CTD/TOR bars-The results of these examples are summarised in tabular form.

1.2 Doubly Reinforced Beam

Design a Rectangular Beam with reinforcement grades offy 250, CTD/TOR. TMTSOOand 550. Grade of concrete fck= 15 N/mm2 and following input data.

M =189KN.muSF =137.5KN

Assume,B =300mmD =500d'/d =0.1

2 6 2M /Dd =(189x10 )/300x455 =3.0y

2 2f =15N/mrh f = 250N/mmck y2d'/d =0.1 M /bd = 3.0u

FromSP-16,T-452A = 1.71x0.3x45.5 = 2335cmt

2A = 0.403x0.3x45.5 = 5.5 cmsc2Provide 5 - dia 20 + 3 dia 18 = 23..33 cm at bottom

2Provide 5 - dia 12 = 5.65 cm at top

Designing for shear

Provide 8 dia @ 250 c/c 2L -Vertical stirrupArea of shear reinforcement = 11.6 cm2d = 0.875 kg/cm

Example -1

Case-1


8

20dia -5x6.0x2.466 = 74.0kg(CTD) 8-23x1592x0.395 = 14.0kg18dia -3x6.0x2.0 = 36.0kg12dia -5x6.0x0^88 = 27.0kgTotal steel = 151 kg

Cost of the reinforcement = Rs. 44070 x 0.151= Rs.6655

NB cost of deformed bar assumed to be Rs. 44070/ton

2f =15N/mm ck2d'/d = 0.1 M /bd =3.0u

2f = 415N/mm (CTD)y

FromSP-16T-49

2A = 1.003x0.3x45.5 = 13.69cmt2A = 0.299x0.3x45.5 = 4.08cmsc

2Provide 3 - (CTD) 18 + 3 - (CTD) 16 = 13.66 cm at bottom2Provide 2 - (CTD) 16 = 4.02 cm at top

Designing for shear

Provide (CTD) 8 @ 300 c/c 2L - vertical stirrup2Area of shear reinforcement = 9.6cm

Reinforcement requirement by weight

(CTD) 16 5x6x1.578 = 47.0kg(CTD) 8 19x1.592x0.395 = 12.0 kg

Total steel = 95.0kgSaving over mild steel =(151-95)/151%

=37%

Cost of the reinforcement = Rs.44070x0.095= Rs.4186.6

Saving in cost over mild steel = Rs. 2468.4= 37%

Class-II


9

Case-III

Case-IV

(TMT-500)

2f = 15N/mm f ck y2d'/d = 0.1 M /bd = 3.0u

(From Table 9 of handbook)2A = 0.8483x0.3x45.5 = 11.58 cmt

2A = 0.260x0.3x45.5 = 3.54 cmsc2Provide 6 -(TMT) 16 12.06 cm at bottom

Provide 3-(TMT) 12 3.39 cm2 at top

Designing for shearProvide (CTD) 8 @ c/c 2L - vertical stirrupArea of shear reinforcement = 11.07 cm2


(TMT) 16-6x6x1.578 = 56.81 kg(TMT) 12-3x6.0x0.888 = 16.0 kg(CTD) 8-22x1.592x0.395 = 14.0 kg

Total steel = 86.8 kgSaving over mild steel = 42%Saving over CTD/TOR = 8%

Cost of the reinforcement

Cost saving over mild steel = 45.6%Cost saving over CTD/TOR = 13.6%

(TMT-550)fck = 15N/mm2 f = 550 N/mm2y

2d'/d = 0.1 M /bd = 3.0u(FromTable 13 of handbook)

2A =0.7436x0.3x45.5 = 10.15cmt2Age =02466x0.3x45.5 = 3.36cm2Provide 5-(TMT) 16 = 10.05cm at bottom

2Provide 3-(TMT) 12 = 3.39 cm at top

2= 500N/mm (TMT)


10

Designing for shear

Provide (CTD) 8 @ 255 c/c 2L - vertical stirrupArea of shear reinforcement = 11.07cm2


(TMT) 16 5x6.0x1578 =47.0kg(TMT) 12 3x6.0x0.888 =16.0kg(CTD) 8 22x1.592x0395 =14.0 kgTotal sheet =77 kgSaving over mild steel =49%Saving over CTD/TOR =11%

Cost of the reinforcement = Rs. 44070 x 0.077

Cost saving over mild steel = 49%Cost saving over mild steel CTD/TOR = 18.9%

2a) Same as Example -1 with f = 20 N/mmck

(Ref.Sp.16)T-46

22F = 20 N/mm f =250 N/mm yck d'/d = 0.1 M /bd2 =3.0y

2A = 1.77x03x455 =24.16cmt 2A = 0.011x03x455 =0.15cmcs

2Provide4 - DIA25 +4-DIA12 =24.15 cm at bottom2Provide 2 - DIA12 = 2.26cm at top

Designing for shearProvide dia 8 @ 295 c/c 2L - vertical stirrup

2Area of shear reinforcement = 9.6 cmReinforcement requirement weight

Dia25 -4x6.0x3.854 = 92.0 kgDia12 -6x6.0x0.888 = 32.0 kgDia8 -19x1.592x0.395 = 12.0 kgTotal steel = 136 kg

Example -1

Case-1


11

Cost of the reinforcement = Rs.44070x0.136= Rs. 5993.5

(Ref.SP-16)T-50

2 2f =20N/mm f =415N/mm (CTD)ck y2d'/d =0.1 M /bd =3.0u

2A =1.029x0.3x45.5 =14.04cmt 2A =0.077x0.3x45.5 = 1.05cmsc

2Provide 4 - (CTD) 18+2-(CTD) 16 =14.19cm at bottom2Provide 2 - (CTD) 12 = 226 cm at top

Designing for shearProvide (CTD) 8 @ 310 c/c 2L - vertical stirrupArea of shear reinforcement = 9.6cm2

Reinforcement requirement by weight(CTD) 18 -4x6.0x2.0 = 48.0kg(CTD) 16 -2x6.0x1.578 = 19.0kg(CTD) 12 -2x6.0x0.888 = 11.0kg

(CTD) 18 -19x1.59x0.395 = 12.0 kgTotal steel = 90 kgSaving over mild steel = 34%

Cost of the reinforcement = Rs. 44070 x 0.09= Rs. 3966

Cost saving over f 250 =33.8%y

(Refer Table 10)

2f = 20N/mm2 f = 500 N/mm (TMT)ck y2d'/d = 0.1 M /bd =3.0u

2A = 0.8415x0.3x45.5 = 115cmt2A = 0.0885x0.3x45.5 =1.2 cmsc

2Provide 3 - (TMT) 22 = 11.4 cm at bottom2Provide 2 - (TMT) 12 =2.26 cm at top

Designing for shearProvide (CTD) 8 @ 275 c/c 2L - vertical stirrup

2Area of shear reinforcement = 10.06 cm

Case-II

Case-III


12


(TMT)22(TMT) 12 -2x6.0x0.888 =10.6 kg(CTD) 8 -21x1.592x0.395 =13.2 kgTotal steel =77 kgSaving over mild steel = 43.5%Saving over CTD/TOR = 14.5%

Cost of the reinforcement = Rs.44070x0.077=Rs. 3393.4

Cost saving over mild steel =43.3%Cost saving over CTD/TOR = 14.4%

(Ref.Table-14)

22F =20N/mm f = 550 N/mm (TMT) ck y 2d'/d =0.1 M /bd =3.0u2A =0.759x0.3x45.5 =10.4cmt2A =0.0937x0.3x45.5 =1.28cmsc

2Provide 2 - (TMT) 20 +2 - (TMT) 16 = 10.3 cm at bottom2Provide 2 - (TMT) 12 = 2.26 cm at top



Reinforcement requirement by weight(TMT) 20 -2x6.0x2.466 = 29.6 kg(TMT) 16 -2x6.0x1.578 = 18.9 kg(TMT) 12 -2x.6.0x0.888 = 10.7 kg(CTD) 8 -21x1.59x0.395 = 13.2 kg

Total steel = 72 kgSaving over mild steel = 47%Saving over CTD/TOR = 20%


Cost saving over mild steel = 47%Cost saving over CTD/TOR = 19.9%

-3x6.0x2.98 =53.6 kg

Case- IV


13

Design a Rectangular Beam with f - 250. CTD/TOR, TMT500 and TMT 550 y2 2N/mm . Grade of concrete f = 15 N/mm . Design by limit state method.ck

M = 352 KN.m SF = 187.5 knuAssume B = 300 D = 600d'/d = 0.1

2M /bd = (352 x 106) / (300 x 5502) = 3.9u

(Refer SP-16)T-452 2f =15 N/mm f = 250 N/mm ck y

2d'/d = 0.1 My/bd = 3.92A = 2.1697x0.3x55 = 35.8cmt

2A = 0.8776x0.3x55 = 14.5cmsc 2Provide 6 - dia 25 + 2 - dia 20 = 35.73cm at bottom2Pro vide 4- dia 18 + 4 - dia 12 = 14.69 cm at top

Designing for shearProvide 8 @ 170 c/c 2L - vertical stirrup


Reinforcement requirement by weightDia 25 - 6 x 8 x 3.854 = 1 85.0 kgDia20 - 2x8x2.466 = 39.5kgDia 18 - 4x8x2.0 = 64.0kgDia 12 - 4x8x0.888 = 28.5kgDia 8 - 45x.1.792x0.395 = 32.0kgTotal steel = 349 kg

Cost of the reinforcement = Rs. 44070 x 0.349= Rs. 15380.4

(Refer SP-16)T-492 2f =15 N/mm f = 415N/mm (CTD)ck y 2d'/d =0.1 M /bd = 3.9u

2A =1.28x0.3x55 = 21.12cmt2A =0.587x0.3x55 = 9.7cmsc

Case-I

Case-II


14

2Provide 3 - CTD 22+2 - CTD 25 = 2121 cm at bottom2Provide 2 -CTD 22+1-CTD 16 = 9.61cm at top

Designing for shear

Provide (CTD) 8 @ 260 c/c 2L - vertical stirrups2Area of shear reinforcement = 15.1 cm

Reinforcement requirement by weight(CTD) 25 - 2 x 8 x 3.854 = 61.7 kg(CTD) 22 - 5x8x2.98 = 119.2kg(CTD) 16 - 1x8x1.578 = 12.6kg(CTD) 8 - 30x1.792x0.395 = 21.2kgTotal steel = 215 kgSaving of steel over f 250 = 38.3%y


Cost Saving over f 250 = 38.3%y

(Refer Table 9)22f =15N/mm f = 500 N/mm (TMT)yck 2d'/d = 0.1 M /bd = 3.9u

2A = 1.0781x0.3x55 = 17.8cmt2A = 0.494x0.3x55 = 8.15cmsc

Provide 4 - (TMT) 22+2 - (TMT) 12 = 17.46 cm2 at bottom2Provide 4 - (TMT) 16 = 8.04 cm at top

Designing for shearProvide (CTD) 8 @ 230 c/c 2L - vertical stirrups


Reinforcement requirement by weight(TMT) 22 - 4x8x2.98 = 95.4 kg(TMT) 16 - 4x8x1.578 = 50.5 kg(TMT) 12 - 2x8x0.888 = 14.2kg(CTD) 8 - 34x1.792x0.395 = 24.1 kgTotal steel = 184 kgSaving over mild steel = 47.3%Saving over CTD/TOR = 14.5%

Cost of the reinforcement Rs. 44070 x 0.184 = Rs. 8108


Case-III


15

Case-IV

Example - 2

Case-I

(Refer Table 13)

2 2f = 15 N/mm f = 550 N/mm (TMT)ck y 2d'/d = 0.1 M /bd = 3.9u2A = 0.9526x0.3x55 = 15.72cmt

2A = 0.4585x0.3x55 = 756cmsc 2Provide 5 - (TMT) 20 = 15.72 cm at bottom

2Provide 3 - (TMT) l0 = 7.63 cm at top


2Area of shear reinforcements 17.1 cm

Reinforcement requirement by weight(TMT) 20 - 5x8x2.466 = 98.6 kg(TMT) 18 - 3x8x2.0 = 48kg(CTD) 8 - 34x1.792x0395 = 24.1 kg

Total steel = 170.70 kgSaving of steel over mild steel = 51%Saving of steel over CTD/TOR = 21%



a) Same as Example-2 with fck = 20 N/mm2

(Refer SP-16)T-42 2f = 20 N/mm f = 250 N/mmck y 2d'/d = 0.10 M /bd = 3.9u

2A = 223x0.3x55 = 39.8 cmt2A = 0.4901x0.3x55 = 8.1 cmsc 2Provide 6 - dia 25+ 6 - dia 12 = 363cm2Provide 4 - dia 16 = 8.04 cm at bottom

Designing for shearProvide dia 8 @ 220 c/c 2L - vertical stirrup



16

Reinforcement requirement by weightDia25 - 6x8x3.854 = 185.0 kgDia16 - 4x8x1.578 = 50.5 kgDia12 - 6x8x0.888 = 42.6kgDia8 - 35 x1.792x0.395 = 24.8 kgTotal steel = 303 kg

Cost of the reinforcement = Rs.44070 x 0.303= Rs.13353.2

(Refer SP-16)T-502F = 20N/mm2 f = 415N/mm (CTD)ck y

2d'/d = 0.1 M /bd = 3.9u2A = 1.306x0.3x55 = 2155cmt2A = 0.369x0.3x55 = 6.08 cm sc2Provide 4-(CTD) 25+2-(CTD) 12 = 21.9 cm at bottom2Provide 3 - (CTD) 16 = 6.03 cm at top




(CTD) 25 -4x8x3.854 = 123.3kg(CTD) 16 -3x8x1.578 = 37.9kg(CTD) 12 -2x8x0.888 =14.2kg(CTD) 8 - 29 x 1.792 x 0.395 = 20.5 kgTotal steel =196 kgSaving of steel over f 250 = 35.3%y


Cost of saving over f 250 = 35.3%y

(Refer table 10)2f = 20N/mm2 f = 500 N/mm (TMT)ck y

2d'/d = 0.1 Mu/bd = 3.92A = 1.0714x0.3x55 = 17.7cmt2A = 0.3232x0.3x55 = 5.33 cmsc 2Provide 4 - (TMT) 20+2 - (TMT) 18 = 17.64 cm at bottom

Case-II

Case-III


2Provide 2 - (TMT) 18 = 5.1 cm at topProvide (CTD) 8 @ 240 c/c 2L - vertical stirrupArea of shear reinforcement by = 16.1 cm2


(TMT) 20 - 4x8x2.466 = 79.0 kg(TMT) 18 - 4x8x2.0 = 64.0kg(CTD) 8 - 32x1.792x0.395 = 22.7 kgTotal steel = 166 kgSaving over mild steel = 45.2%Saving over CTD/TOR = 15.3 %

Cost of the reinforcement Rs.44070x0.166 =Rs.7315.6Cost saving over mild steel = 45.2%Cost saving over CTD/TOR = 15.3%

(Refer Table-14)2 2f = 20N/mm f = 550 N/mm (TMT)ck y

2d'/d = 0.1 Mu/bd = 3.92A = 0.9682x0.3x55 = 16.0 cmt

2A = 0.3067x0.3x55 = 5.06cmsc2Provide 2 - (TMT) 25+2 - (TMT) 20 = 16.09 cm at bottom

2Provide 2 - (TMT) 18 = 5.10 cm at top


2Area of shear reinforcement =17.1 cm

Reinforcement requirement by weight(TMT) 25 ' - 2x8x3.854 = 61.7kg(TMT) 20 - 2x8x2.466 = 39.5 kg(TMT) 18 - 2x8x2 = 32.0kg(CTD) 8 - 34x1.79x0.395 = 24.0 kgTotal steel = 157 kgSaving over mild steel = 48.2 kgSaving over CTD/TOR = 20%

Cost of the reinforcement Rs. 44070 x 0.157 = Rs. 6919Cost saving over mild steel = 48%Cost saving over CTD/TOR = 19.8%

The above information are presented in tables 1.1 and 1.2

Case-IV

5


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0

TO

R 8

@2

56

TO

R 8

@2

40

TO

R 8

@2

30

30

3

19

6

16

6

15

7

Rs.

13

35

3.2

Rs.

86

37

.72

Rs.

73

15

.6

Rs.

69

19

- 35

.3%

45

.2%

48

.2%

- 35

.3%

42

.2%

48

%

- - 15

.3%

19

.8%

- - 15

.3%

20

%


19

Ta

be

l 1

.1 -

Su

mm

ary

of

Qu

an

tity

an

d c

os

t o

f D

iffe

ren

t G

rad

e o

f C

on

cre

te a

nd

Se

ll

Se

ctio

nE

xam

ple

Gra

de

of

Co

ncr

ete

Gra

de

of

Ste

el

QT

Y.

in K

g.

% s

avi

ng

in w

t. w

i th

re

spe

ct to

fy-2

50

CT

D-4

15

Co

st in

Rs.

% s

avi

ng

in c

ost

w

ith r

esp

ect

to

fy-2

50

CT

D-4

15

Do

ub

ly

Re

info

rce

d

Be

am

1 1.(

a)

15

15

15

15

fy 2

50

CT

D 4

15

TM

T 5

00

TM

T 5

00

15

1

95

87

77

-

37

%

42

%

49

%

6%

19

%

Rs.

66

55

Rs.

41

86

.6

RS

. 3

61

3.7

Rs.

33

93

.4

- 37

%

45

.6%

49

%

- - 13

.6%

18

.9%

2

20

20

20

20

fy 2

50

CT

D 4

15

TM

T 5

00

TM

T 5

00

13

6

90

77

72

-

34

%

43

.5%

47

%

14

5%

20

%

Rs.

59

93

.5

Rs.

39

66

RS

. 3

39

3.4

Rs.

31

73

.04

- 37

%

45

.6%

49

%

- - 14

.4%

19

.9%

2.(

a)

15

15

15

15

fy 2

50

CT

D 4

15

TM

T 5

00

TM

T 5

00

34

9

21

5

18

4

17

0

-

38

.3%

47

.3%

51

.2%

14

.55

%

21

%

Rs.

15

38

0

Rs.

94

75

.05

RS

. 8

10

8.9

Rs.

74

91

.9

- 38

3%

47

.2%

51

.2%

- - 14

.4%

20

.9%

20

20

20

20

fy 2

50

CT

D 4

15

TM

T 5

00

TM

T 5

00

30

3

19

6

16

6

15

7

-

35

.3%

45

.2%

48

.2%

15

.3%

20

%

Rs.

13

35

3.2

Rs.

86

37

.72

RS

. 7

31

5.6

Rs.

69

19

- 35

3%

45

.2%

48

.2%

- - 15

.3%

19

.8%


20

Fig 1.1 gives the percent saving in usingTMT415 rebars instead of CTD/TOR bars of Mu/bd2 different values of d7d and also the average savings. It can be seen that there is maximum saving of about 3.8% and average saving of about 1.5%. These curves are plotted for M20 concrete. The percentage saving is more if we useTMT 500 rebars and TMT 550 rebars instead of CTD/TOR bars. The percentage saving is indicated in Fig 1.2 & 13.The maximum saving is about 19.7% in case of TMT 500 rebars and about 27.0% in case of TMT 550 rebars. The average saving is about 17.5% and 24.5% respectively. The above figures are in tonnage only. In terms ofcosuhese figures will be slightly more since TMT 500 and TMT 550 rebars are the same if not less costlier than CTD/TOR bars.


21

Fig

1.1

- %

Sa

vin

g in

Us

ing

TM

T 4

15

O

ve

r C

TD

/TO

R in

Do

ub

ly R

ein

forc

ed

Be

am

4 3 2 1 02

34

56

78

% Saving (wt)

On

ly m

ain

re

info

rce

me

nt h

as

be

en

ta

ken

into

co

nsi

de

ratio

n.

d'/d

=0

.05

d'/d

=0

.20

d'/d

=0

.10

d'/d

=0

.15

Ave

rag

e


22

Fig

1.2

- %

Sa

vin

g in

Us

ing

TM

T 5

00

Ov

er

CT

D/T

OR

in

Do

ub

ly R

ein

forc

ed

Be

am

On

ly m

ain

re

info

rce

me

nt h

as

be

en

ta

ken

into

co

nsi

de

ratio

n.

d'/d

=0

.05

d'/d

=0

.20

d'/d

=0

.10

d'/d

=0

.15

Ave

rag

e

21

20

19

18

17

16

15

14

13

23

45

67

8

% Saving (wt)


23

Fig

1.3

- %

Sa

vin

g in

Us

ing

TM

T 5

50

Ov

er

CT

D/T

OR

in

Do

ub

ly R

ein

forc

ed

Be

am

On

ly m

ain

re

info

rce

me

nt h

as

be

en

ta

ken

into

co

nsi

de

ratio

n.

d'/d

=0

.05

d'/d

=0

.20

d'/d

=0

.10

d'/d

=0

.15

Ave

rag

e

% Saving (wt)

21

20

19

18

17

16

15

14

13

23

45

67

8


24

2.3 Axially Loaded Columns

Example 3

Case-I:

Case-II:

Case-III:

Axially Loaded Column DesignGiven:

Factored loaded P = 5000KNuGrade of concrete M20Unsupported length of column = 3.0 m

Reqd:Cross-section of column and reinforcementAssuming: Column size 800 mm x 500 mm

Column with reinforcement off =250 N/mm2y25Area of concrete = A = 800 x 500 = 4 x 10 mmg

For given values of P ,A , and f = 20cku g Corresponding to Chart 1 (or Ch. 24 of SP-16)P =2.9%Required Area of reinforcementAge =2.9x(80x50)/100

2=116cm2Provide (12-dia 32 +4-dia 25) Eq. area = 116014 cm

Column with CTD/TOR reinforcement.

As per chart 25 of SP -16: for given loading.Column area & grade of concrete: P = 1.67%Required area of reinforcement

2= A = 1.67 x (80x50)7100 = 66.8cmsc 2Provide (12-dia 32 + 6-CTD 10) Eq. area = 6630 cm

Column with TMT 415 reinforcementFrom chart 1 of handbookP =1.45%Therefore area of reinforcement required

2A = 1.45 x (50x80)/100 = 58.0cmsc 2Provide (8-TMT 25 + 8-TMT 18) Eq. area = 59.62cm

This information is summarized in Table 1.3 and 1.5


25

2.4 Uniaxial Bending

Example-4

Case-I:

Case-II:

Rectangular Column with Uniaxial BendingGiven:

Factored Load P = 500 KNuFactored Moment My = 250 KNm (along longer direction)Concrete grade M20Unsupported length of column = 3.0 M

Required: Cross-section of column & reinforcement

Assumptions:1) Columnsize = 250mmx5002) Dia.ofbar = 20 mm3) Clear cover to main reinforcement = 40 mm

d' =40+20/2 = 50mmd'/d =50/500 = 0.1P /f bd =500x103/(20x250x500) = 0.2u ck

2M /f bd =250x103x103/20x250x500x500=0.2u ck

Column with reinforcement f = 2501 N/mm2yReferring Ch.28 of SP-16p/f =0.172ck P =0.172x20 = 3.44%

2Area of steel reqd. Ag = 3.44 x 25 x 50 /100 = 43 cm2Provide (4 - dia 28 + 4-dia 25) A = 44.26 cms

Column with CTD/TOR reinforcementAsper Ch.32 of SP-16p/f =0.11ck

P =0.11x20 = 2.2%2Area of steel A =22x25x50/100 = 27.5cms

2Provide (4 - CTD 22+4 - CTD 20) A = 27.76 cms


26

Case-III:

Column with TMT 415 reinforcementAs per Ch. 3 of handbookp/f = 0.10ck P = 0.10x20 = 2.0%

2Area of steel A = 2x25x50/100 = 25 cms2Provide (8 -TMT 20):A = 25.13 cms

This information is presented in Table 1.4 & 1.5

In Fig 1.5 to 1.7 the interaction diagrams of CTD/TOR bars are superimposed on the TMT rebars of different grades and d'/d =0.10. Also, the interaction curves for CTD/TOR bars are superimposed on TMT 500 for comparison Fig 1.6a. It is explicit that in case of TMT rebars, as the reinforcement percentage increases the curves tend to bulge out For the same percentage of steel and P /f bd, the section can cku

2resist a higher moment In other words, for a particular P /f bd and M /f bd , u ckck up/fck values are less in case of TMT rebars. For same concrete grade, reinforcement percentage will be less forTMT rebars which are used and this results in savings-The percentage savings will vary depending

2on the P /f bd and M /f bd values.u c u ckk


Dim

esn

ion

of th

eS

ect

ion

(M

M)

Mu

(KN

)

fck

N/

sqm

i

Gra

de

of

Ste

el

Are

a o

f st

ee

l

As

Lin

ks

No

. a

nd

Dia

. o

f B

ars

Co

mp

ress

ion

Sh

ea

r

% S

avi

ng

with

re

spe

ct to

fy -

25

0 &

fy

- 4

15

in w

t.

27

Ta

be

l 1

.3 -

Ec

on

om

y in

us

ing

TM

T 4

15

in

Pla

ce

of

fy 2

50

an

d C

TD

/TO

R

Fo

r A

xia

lly

Lo

de

d C

olu

ms

Pu

=5

00

0K

N2

0

Tota

l W

t.in

Kg

Tota

l cc

of R

/F%

pf S

avi

ng

with

re

spe

ct to

fy -

25

0 &

fy

- 4

15

in R

s.

fy-2

50

116

.22

.01

12

-dia

32

+4

-dia

25

dia

8@

25

0 c

/c3

02

Rs.

13

30

9.1

__

CT

D-4

15

66

.62

.01

10

-CT

D 2

8+

6-C

TD

10

CT

D 8

@2

50

c/c

18

8R

s. 8

28

53

7.7

% o

ver

ty-2

50

37

.7%

ove

r ty

-25

0

(Exa

mp

le)

TM

T-4

15

58

2.0

18

-T2

0+

8-T

MT

18

CT

D-8

@2

50

c/c

16

9R

s. 7

44

7.8

44

% o

ver

ty-2

50

44

% o

ver

ty-2

50

10

% o

ver

CT

D-4

15

10

.1%

ove

r ty

-25

0

Dim

esn

ion

of th

eS

ect

ion

(M

M)

Pu

(KN

)

fck

N/

mm

2

% S

avi

ng

with

re

spe

ct to

fy-2

50

& C

TD

-41

5 in

wt.

To

tal

Wt.

in K

gTo

tal c

c o

f R

/F%

pf S

avi

ng

with

re

spe

ct to

fy-2

50

& C

TD

-41

5 in

Rs.

Ta

be

l 1

.4 -

Ec

on

om

y in

us

ing

TM

T in

Pla

ce

of

fu 2

50

an

d C

TD

/TO

R

Fo

r U

nia

xia

l b

en

din

g w

ith

Co

mp

res

sio

n

Mu

(KN

-m)

Gra

de

of

Ste

el

Are

a o

f st

ee

lsq

. cm

As

Lin

ks

No

. &

Dta

. o

f b

ars

Co

mp

ress

ion

Sh

are

fy-2

50

43

6.5

44

-dia

28

+4

-dia

25

dia

-8@

25

0c/

c11

5R

s. 5

06

8

Pu

=5

00

Mu

=2

50

20

CT

D-4

15

27

.56

.54

4-C

TD

22

+4

-CT

D2

20 C

TD

-8@

25

0c/

c7

5.9

Rs.

33

44

.93

4%

ove

r fy

-25

03

3.9

% o

ver

fy-2

50

(Exa

mp

le-4

)T

MT-4

15

25

6.5

48

-TM

T 2

0C

TD

-8@

25

0c/

c6

9.7

Rs.

30

71

.63

9%

ove

r fy

-25

03

9.9

% o

ver

fy-2

50

8%

ove

r C

TD

-41

58

.1%

ove

rCT

D-4

15


28

Se

ctio

nE

xam

ple

Gra

de

of

Co

ncr

ete

Gra

de

of

Ste

el

QT

Y.

in K

g.

% o

f S

evi

ng

in

fy-2

50

CT

D-4

15

Co

st in

Rs.

% o

f S

evi

ng

inco

st o

ver

fy-2

50

CT

D-4

15

AX

IAL

LY

LO

AD

ED

CO

LU

MN

S

3

20

20

20

fy-2

50

CT

D-4

15

TM

T-4

15

30

2

18

9

16

9

- 37

.7%

44

%

- - 10

.1%

Rs.

27

18

Rs.

18

47

Rs.

16

55

- 37

.7%

44

%

- - 10

.1

UN

IAX

IAL

BE

ND

ING

WIT

H

CO

MP

RE

SS

ION

4

20

20

20

fy-2

50

CD

T-4

15

TM

T-4

15

115

76

70

- 34

%

39

%

- - 8%

Rs.

10

33

Rs.

74

4

Rs.

68

4

- 33

.4%

39

.3%

- - 8%

Ta

be

l 1

.5 -

Su

mm

ary

of

Qu

an

tity

an

d c

os

t o

f D

iffe

ren

t G

rad

e o

f C

on

cre

te a

nd

Ste

el


29

12.9

12.8

12.7

12.6

12.5

12.4

12.3

12.2

10 15 20 25 30 35 40 45

Grade of Concrete, fck (N/sq. mm)

Only Main reinforcement is taken into consideration

Fig 1.4 - % Saving in Using TMT 415 CTD 415 for Axially Loded Coluns


30

2fy = 415N/mm d'/D=0.10

As=pbD/100b

D

dAxis of banding

Pu

/ f

ck

bD

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5

2Mu / fck bD

Fig. 1.5 - Comparative Chart for Compression with Bending for TMT 415 andCTD/TOR (Rectangular Section-Reinforcement Distributed equally on two sides)

TMT

CTD

0

0

02.1

0.02

P Lc 1=128


31

2fy = 415N/mm d'/D=0.10

As=pbD/100b

D

dAxis of banding

Pu

/ f

ck

bD

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5

2Mu / fck bD


TMT

CTD

0

0

02.1

0.02

P Lc 1=128


32

2fy = 415N/mm d'/D=0.10

As=pbD/100b

D

dAxis of banding

Pu

/ f

ck

bD

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5

2Mu / fck bD


TMT

CTD

0

0

02.1

0.02

P Lc 1=128


33

2fy = 415N/mm d'/D=0.10

As=pbD/100b

D

dAxis of banding

Pu

/ f

ck

bD

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.6

2Mu / fck bD

Fig. 1.7 - Comparative Chart for Compression with Bending for TMT 550 andCTD/TOR (Rectangular Section-Reinforcement Distributed equally on two sides

TMT

CTD

0

0

02.1

0.02

P Lc 1=128

0.5


34

Characteristics Mild Steel CTD 415 HAMA TMT 500

HAMA TMT 550

Design Strength 250N/mm2 415N/mm2 500N/mm2 550N/mm2

Quantity Required 1.000 M. T. 0.637 M.T. 0.544 M.T. 0.515 M.T.

% Saving in Weight Over

fy-250

36.3% 45.5% 48.5%

% Saving in Weight

14.60% 19.15%

Cost of Reinforcement

Per M.T.Rs. 44070

Cost of Reinforcement

Excluding Fabrication

Rs. 44070 Rs. 44070 Rs. 44070

Rs. 44070 Rs. 28072 Rs. 23974 Rs. 22696

Saving in cost WithRespect to Fy -250

Per 1 M.T.Reinforcement

Rs. 15998 Rs. 20096 Rs. 21374

% of Cost Savingwith Respect to

Fy - 25036.3% 54.6% 48.5%

Saving in Cost withRespect to CTD/TOR

Per 1M.T.Reinforcement

Rs. 4098 Rs. 5376

% of Cost SavingWith Respect to

CTD-41514.5% 19.1%

Note: 1. Cost towards cutting, bending, binding, fixing and placing not included. If this cost is staken into consideration then There will be further savings.

2. Price of steel may increase, but percentage savings will be same


35

Typ

e o

f L

ap

La

p L

eg

th r

eq

dn

Ma

teria

lR

eq

uire

me

nt

Co

stP

erc

en

tag

e c

ost

sa

vin

g p

er

join

t o

fsi

ng

le b

ar

Co

nve

ntio

na

l

ba

sed

on

con

cre

te-s

tee

l

bo

nd

ing

Fo

r w

eld

ed

La

p jo

ints

Av.

50

dia

=1

00

0m

m

1w

=6

.3d

ia

6.3

dia

=1

26

mm

1w

=6

.3d

ia

dw

=0

.2d

ia o

r 4

mm

bw

=0

.7d

ia o

r 1

0m

mb

w

2.7

4 K

g. o

f b

ar

@ R

s. 4

40

70

pe

r to

nn

e

Rs.

10

8.8

0.3

1 K

g. o

f b

ar

@ R

s. 4

40

70

p

er

ton

ne

2.5

ele

ctro

de

so

f 4

mm

dia

& 4

50

mm

lon

g

Rs.

13

.66

Rs.

5

Rs.

11

Rs

.72

%

Re

com

me

nd

ed

we

ldin

g le

ng

th

Fo

r

TM

T 4

15

1w

= 6

.3d

ia

TM

T 5

00

1w

= 7

.0 d

ia

TM

T 5

50

1w

= 7

.0 d

ia

Incl

ud

ing

co

st o

f e

lect

rod

es.

02

, D

a &

oth

ers

Ta

ble

1.6

a -

Ad

dit

ion

al C

os

t S

av

ing

by

Us

ing

TM

T b

ars

Wit

h W

eld

en

La

p J

oin

ts


26

CHAPTER - 2

Material Strength and

Stress-Strain

Relationships


38

2.1 Grade of Concrete

The grade of concrete used in this hand book M15,M20,25&M30

2.2 Types and Grades of Steel

The reinforcement steel used in this handbook conform to 15:432 in case of mild steel bus and IS: 1786/NS191 in case of re-bars.

2.3 STRESS-STRAIN RELATIONSHIP FOR CONCRETE

The stress-strain relationship for concrete is shown in Fig 2.1

2.4 STRESS-STRAIN RELATIONSHIP FOR STEEL

The stress-strain relationship for CTD/TOR and TMT Rebars is shown inFigs. 2.2 to 2.5

2.5 Typical stress-strain relationship for 12mm, 16mm, 20mm and 25mm

TMT bars as shown in Figs 2.6 and 2.7.

2.6 The actual stress-strain relationship for 8mm to32mm HAMA 500 rebars

along with theirtypical values of mechanical properties are indicated inFigs. 2.8 to 2.15.

Figs. I and II are copies of test certificates from SAIL indicating typicalchemical properties.

Fig. Ill shows a typical test certificate issued with each dispatch.


37

ParabolicCurve

0.446 fck

0.002 0.0035

Strain

Str

es

s

Fig 2.1 - Stress-Strain Curve for Concrete


40

500

450

400

350

300

150

200

150

100

50

0

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

(0.06-fy for stress 0.002)

Characteristic Curve

CTD 415

2 2Es=2.10 N/mm

2S

tre

ss

,10

mm

Strain

Fig 2.2 - Stress-Strain Curve for CTD 415


41

500

450

400

350

300

150

200

150

100

50

0

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007


CTD 415

2 2Es=2.10 N/mm

2S

tre

ss

,10

mm

Strain

Fig 2.3 - Stress-Strain Curve for TMT 415

415

361TMT 415

Design Curve


42

550

500

450

400

350

300

250

200

150

100

50

0

0.001 0.002 0.003 0.004 0.005 0.006 0.007


TMT 500

2 2Es=2.10 N/mm

2S

tre

ss

,10

mm

500

435TMT 415

Design Curve

0



43

550

500

450

400

350

300

250

200

150

100

50

0

0.001 0.002 0.003 0.004 0.005 0.006 0.007


TMT 550

2Es=2.10 N/Sq. mm

2S

tra

in,N

/mm

550

478TMT 550

Design Curve

0

600

Strain



44

80

70

60

50

40

20

10

30 0

05

10

15

20

+

+

+

2S

tre

ss

(K

g/m

m)

Strain

Fig. 2.6


45

80

70

60

50

40

20

10

30 0

05

10

15

20

++

2S

tre

ss

(K

g/m

m)

Strain

Fig. 2.7

++

+


46

Fig. 2.8a


47

Fig. 2.8b


48

Fig. 2.8c


Fig. 2.9a

49


50

Fig. 2.9b


51

Fig. 2.9c


52

Fig. 2.10a


53

Fig. 2.2.10b


54

Fig. 2.2.10c


55

Fig. 2.2.11a


56

Fig. 2.2.11b


57

Fig. 2.2.10cc


58

Fig. 2.2.12a


59

Fig. 2.2.12b


60

Fig. 2.2.12c


61

Fig. 2.2.13a


62

Fig. 2.2.13b


63

Fig. 2.2.13c


64

Fig. 2.2.14a


65

Fig. 2.2.14b


66

Fig. 2.2.14c


67

Fig. 2.2.15a


68

Fig. 2.2.15b


69

Fig. 2.2.15c


70


71


72

Fig. I


73

Fig. II


74

Fig. III

CHAPTER - 3

Flexural Members


75


76

3.1 Assumptions:

The basic assumptions in design offlexural members for limit state of collapse are as given below (in accordance with Clause 37.1 of Code.

a) Plane sections normal to the axis remain plane after bending.

b) The maximum strain in concrete at the outermost compression fiber is taken as 0.0035.

c) The design stress-strain relationship for concrete is as given in Fig 2.1

d) The tensile strength of concrete is ignored.

e) The stresses for reinforcement are derived from the curves given in Fig 2.3,2.4, & 2.5 (for bars ofTMT415,TMT 500 and TMT 550)

f) Maximum strain in tension reinforcement is less than (fy/1.15Es)+0.002 to ensure ductile failure.

3.2 Under Reinforced Sections:

3.2.1 Under reinforced sections are those single reinforcement sections in which the amount of reinforcement percentage does not exceed the values given in Table E of SP-16. Here steel fails first. At collapse, the strain in steel will be more than that given in code i.e. (0.002+fy/I.ISEs) so the depth of neutral axis is less than Xu.max. and it could be calculated by equating the forces in tension and compression. The expression for

2M /bd can be written as:u2M /bd 0.87 f Cpt/100) x [1 -1.005(f /f ) (p /100)]y y ty ck

3.2.2 One worksheet was developed and the same was used to prepare tables by only varying different variable parameters. Tables show the variation of

2P .I.e percentage reinforcement with the change in M /bd and for t udifferent values of fy. In worksheet the formula was fed for Pt for the

22corresponding value of M /bd i.e. P = f (M /bd ). The limiting condition is u ualso introduced so that it returns for the values of Pt above the balanced section. Thus after preparing one worksheet only value of fck had to be changed to obtain different worksheets.

3.2.3 Tables 1 to 4 give the values percentage of steel for different values of2M / bd and grade of concrete.u


76

3.1 Assumptions:

The basic assumptions in design offlexural members for limit state of collapse are as given below (in accordance with Clause 37.1 of Code.

a) Plane sections normal to the axis remain plane after bending.

b) The maximum strain in concrete at the outermost compression fiber is taken as 0.0035.

c) The design stress-strain relationship for concrete is as given in Fig 2.1

d) The tensile strength of concrete is ignored.

e) The stresses for reinforcement are derived from the curves given in Fig 2.3,2.4, & 2.5 (for bars ofTMT415,TMT 500 and TMT 550)

f) Maximum strain in tension reinforcement is less than (fy/1.15Es)+0.002 to ensure ductile failure.

3.2 Under Reinforced Sections:

3.2.1 Under reinforced sections are those single reinforcement sections in which the amount of reinforcement percentage does not exceed the values given in Table E of SP-16. Here steel fails first. At collapse, the strain in steel will be more than that given in code i.e. (0.002+fy/I.ISEs) so the depth of neutral axis is less than Xu.max. and it could be calculated by equating the forces in tension and compression. The expression for

2M /bd can be written as:u2M /bd 0.87 f Cpt/100) x [1 -1.005(f /f ) (p /100)]y y ty ck

3.2.2 One worksheet was developed and the same was used to prepare tables by only varying different variable parameters. Tables show the variation of

2P .I.e percentage reinforcement with the change in M /bd and for t udifferent values of fy. In worksheet the formula was fed for Pt for the

22corresponding value of M /bd i.e. P = f (M /bd ). The limiting condition is u ualso introduced so that it returns for the values of Pt above the balanced section. Thus after preparing one worksheet only value of fck had to be changed to obtain different worksheets.

3.2.3 Tables 1 to 4 give the values percentage of steel for different values of2M / bd and grade of concrete.u


77

3.3 Doubly Reinforced Section

33.1 Doubly reinforced section is generally adopted when the dimensions of the beam is predetermined form various considerations and the design moment exceeds the moment of resistance of the singly reinforced sections. The additional moment of resistance needed is obtained by providing compression reinforcement and additional tensile reinforcement. The moment of resistance of a doubly reinforced section is thus the sum of the limiting moment of resistance M . ulm of singly reinforced section and the additional moment u

2 2Mu . Given the values of M which is greater than M lim. the values of Mu uucan be calculated.

2Mu = M -M .limu u

3.3.2 The equations for the moment of resistance may be written as follows: M = M , lim + P d . 87(d-d') u u t2

100

M =-M ,lim+P (0-87f ) d-d')u yu t2

2 2 bd bd 100 d

Where P is the additional percentage of tensil reinforcementt2

P =P lim+Pt2 t. t2 P =P t(0.87f )/(f -t )]sc ccc t2 y

3.3.3 The values of P and P for four values of d'/d form 0.05 to 0.20 have been t tc tabulated in the tables 45 to 56.The tabulation is done by changing the values of the variables like f and the starting values of the tables with correspond to y the balanced singly reinforced section.


78

Table - 1 Flexure Reinforcement Percentage Pt for Singly Reinforced Sections

2fy (N/mm ) 2fy (N/mm )

2Mu/bd2N/mm

250 415 500 550* 2Mu/b d

2N/mm250 415 500 550

0.30

0.35

0.40

0.45

0.50

0.1413

0.1655

0.1900

0.2146

0.2395

0.0851

0.0997

0.1144

0.1293

0.1443

0.0706

0.0828

0.0950

0.1073

0.1197

0.0642

0.0752

0.0863

0.0976

0.1089

1.50

1.52

1.54

1.56

1.58

0.7957

0.8083

0.8209

0.8336

0.8464

0.4793

0.4868

0.4945

0.5022

0.5099

0.3979

0.4041

0.4105

0.4168

0.4232

0.3617

0.3674

0.3731

0.3789

0.3847

Note: "-"indicates inadmissible reinforcement percentage

0.55

0.60

0.65

0.70

0.75

0.2646

0.2899

0.3155

0.3414

0.3674

0.1594

0.1747

0.1901

0.2056

0.2214

0.1323

0.1450

0.1578

0.1707

0.1837

0.1203

0.1318

0.1434

0.1552

0.1670

1.60

1.62

1.64

1.66

1.68

0.8593

0.8723

0.8853

0.8984

0.9116

0.5177

0.5255

0.5333

0.5412

0.5492

0.4297

0.4361

0.4427

0.4492

0.4558

0.3906

0.3965

0.4024

0.4084

0.4144

0.80

0.82

0.84

0.86

0.8

0.3938

0.4044

0.4151

0.4258

0.4365

0.2372

0.2436

0.2500

0.2565

0.2630

0.1960

0.2022

0.2075

0.2129

0.2183

0.1203

0.1318

0.1434

0.1552

0.1670

1.70

1.72

1.74

1.76

1.78

0.9249

0.9383

0.9517

0.9653

0.9789

0.5572

0.5652

0.5733

0.5815

0.5897

0.4624

0.4691

0.4759

0.4826

0.4894

0.4204

0.4265

0.4326

0.4388

0.4450

0.90

0.92

0.94

0.96

0.98

0.4473

0.4581

0.4690

0.4800

0.4909

0.2695

0.2760

0.2825

0.2891

0.2958

0.2237

0.2291

0.2345

0.2400

0.2455

0.2033

0.2082

0.2132

0.2182

0.2232

1.80

1.82

1.84

1.86

1.88

1.9926

1.0064

1.0204

1.0344

1.0485

0.5980

0.6063

0.6147

0.6231

0.6316

0.4963

0.5032

0.5102

0.5172

0.5243

0.4512

0.4575

0.4638

0.4702

0.4766

1.00

1.02

1.04

1.06

1.08

0.5020

0.5131

0.5242

0.5354

0.5466

0.3024

0.3091

0.3158

0.3225

0.3293

0.2510

0.2565

0.2621

0.2677

0.2773

0.2282

0.2332

0.2383

0.2433

0.2485

1.90

1.92

1.94

1.96

1.98

1.0627

1.0772

1.0915

1.1061

1.1207

0.6402

0.6488

0.6575

0.6663

0.6751

0.5314

0.5285

0.5458

0.5530

0.5604

0.4831

0.4896

0.4961

1.10

1.12

1.14

1.16

1.18

0.5579

0.5692

0.5806

0.5920

0.6035

0.3361

0.3429

0.3498

0.3537

0.3636

0.2789

0.2846

0.2903

0.2960

0.3018

0.2536

0.2587

0.2699

0.2691

0.2743

2.00

2.02

2.04

2.06

2.08

1.1355

1.1504

1.1654

1.1806

1.1959

0.6840

0.6930

0.7021

0.7112

1.20

1.22

1.24

1.26

1.28

0.6151

0.6267

0.6384

0.6501

0.6619

0.3705

0.3775

0.3846

0.3916

0.3967

0.3075

0.3134

0.3192

0.3251

0.3309

0.2796

0.2849

0.2903

0.2955

0.3009

2.10

2.12

2.14

2.16

2.18

1.2113

1.2268

1.2425

1.2583

1.2743

1.40

1.42

1.44

1.46

1.48

0.6737

0.6856

0.6976

0.7096

0.7217

0.4059

0.4130

0.4202

0.4275

0.4348

0.3369

0.3428

0.3488

0.3548

0.3609

0.36062

0.3117

0.3171

0.3226

2.20

2.22

2.24

1.2904

1.3067

0.7339

0.7461

0.7584

0.7708

0.7832

0.4421

0.4495

0.4569

0.4643

0.4718


79



2Mu/bd2N/mm

250 415 500 550* 2Mu/b d

2N/mm250 415 500 550

0.30

0.35

0.40

0.45

0.50

0.1404

0.0990

0.1884

0.2126

0.2369

0.0846

0.0990

0.1135

0.1281

0.1427

0.0702

0.0822

0.0942

0.1063

0.1185

0.0638

0.0747

0.0856

0.0966

0.1077

2.22

2.24

2.26

2.28

2.30

1.2023

1.2155

1.2288

1.2421

1.2555

0.7243

0.7322

0.7402

0.7482

0.7563

0.6011

0.6077

0.6144

0.6210

0.6277

0.5465

0.5525

0.5585

0.5646

0.5707


0.55

0.60

0.65

0.70

0.75

0.2615

0.2861

0.3110

0.3360

0.3612

0.1575

0.1724

0.1874

0.2024

0.2176

0.1307

0.1431

0.1555

0.1680

1.1806

0.1188

0.1301

0.1414

0.1527

0.1642

2.32

2.34

2.36

2.38

2.40

1.2690

1.2825

1.2961

1.3098

1.3235

0.7644

0.7726

0.7808

0.7890

0.7973

0.6345

0.6345

0.6412

0.6549

0.6617

0.5768

0.5829

0.5891

0.5953

0.6016

0.80

0.85

0.90

0.95

1.00

0.3866

0.4121

0.4379

0.4638

0.4899

0.2329

0.2483

0.2638

0.2794

0.2951

0.1933

0.2061

0.2189

0.2319

0.2450

0.1757

0.1873

0.1990

0.2108

0.2227

2.42

2.44

2.46

2.48

2.50

1.3373

1.3512

1.3652

1.3792

1.3933

0.8056

0.8140

0.8224

0.8308

0.8393

0.6687

0.6756

0.6826

0.6896

0.6966

0.6079

0.6142

0.6205

0.6269

0.6333

1.05

1.10

1.15

1.20

1.25

0.5162

0.5428

0.5695

0.5964

0.6236

0.3110

0.3270

0.3431

0.3593

0.3756

0.2581

0.2714

0.2847

0.2982

0.3118

0.2347

0.2467

0.2589

0.2711

0.2834

2.52

2.54

2.56

2.58

2.60

1.4075

1.4218

1.4361

1.4505

1.4650

0.8479

0.8565

0.8651

0.8738

0.8826

0.7037

0.7109

0.7180

0.7253

1.7325

0.6398

0.6463

0.6528

0.6593

0.6659

1.30

1.35

1.40

1.45

1.50

0.6509

0.6785

0.7064

0.7344

0.7627

0.3921

0.4088

0.4255

0.4424

0.4595

0.3255

0.3393

0.3532

0.3672

0.3814

0.2954

0.3084

0.3211

0.3338

0.3467

2.62

2.64

2.66

2.68

2.70

104796

1.4943

1.5091

1.5239

1.5389

0.8913

0.9002

0.9091

0.9180

0.9270

0.7398

0.7472

0.7545

1.55

1.60

1.65

1.70

1.75

0.7913

0.8201

0.8492

0.8786

0.9082

0.4767

0.4941

0.5116

0.5293

0.5471

0.3975

0.4101

0.4245

0.4393

0.4541

0.3593

0.3728

0.3860

0.3994

0.4128

2.72

2.74

2.76

2.78

2.80

1.5539

1.5690

1.5843

1.5996

1.6150

0.9361

0.9452

0.9544

1.80

1.85

1.90

1.95

2.00

0.9382

0.9684

0.9989

0.0298

1.0609

0.5652

0.5834

0.6018

0.6203

0.6391

0.4691

0.4842

0.4995

0.5149

0.5305

0.4264

0.4402

0.4541

0.4681

0.4822

2.82

2.84

2.86

2.88

2.90

1.6306

1.6462

1.6619

1.6778

1.6637

2.02

2.04

2.06

2.08

2.10

1.0735

1.0861

1.0988

1.1115

1.1243

0.6467

0.6543

0.6619

0.6696

0.6773

0.5368

0.5431

0.5494

0.5558

0.5622

0.4880

0.4937

0.4995

0.5052

0.5111

2.92

2.94

2.96

2.98

1.7098

1.7259

1.7422

1.1372

1.1501

1.1630

1.1760

1.1891

0.6850

0.6928

0.7006

0.7085

0.7163

2.12

2.14

2.16

2.18

2.20

0.5686

0.5750

0.5815

0.5880

0.5946

0.5169

0.5228

0.5286

0.5346

0.5405


80



2Mu/bd2N/mm

250 415 500* 2Mu/b d

2N/mm250 415 500 550

0.30

0.35

0.40

0.45

0.50

0.1399

0.1636

0.1874

0.2114

0.2355

0.0843

0.0986

0.1129

0.1273

0.1418

0.0699

0.0818

0.0937

0.1057

0.117

1.3577

1.3894

1.4215

1.4538

1.4864

0.8179

0.8370

0.8563

0.8758

0.8954

0.6788

0.6947

0.7107

0.7269

0.7432

0.6171

0.6316

0.6461

0.6608

0.6756


0.55

0.60

0.65

0.70

0.75

0.3596

0.2840

0.3084

0.3330

0.3577

0.1564

0.1711

0.1858

0.2006

0.2155

0.1298

0.1420

0.1542

0.1665

1.1788

1.5194

1.5526

1.5862

1.6201

1.6544

0.9153

0.9353

0.9555

0.9760

0.9966

0.7597

0.7763

0.7931

0.8101

0.8272

0.6906

0.7057

0.7210

0.7264

0.7520

0.80

0.85

0.90

0.95

1.00

0.3825

0.4075

0.4326

0.4578

0.4832

0.2304

0.2455

0.2606

0.2758

0.2911

0.1913

0.2037

0.2163

0.2289

0.2416

1.6890

1.7240

1.7594

1.7951

1.8313

1.0175

1.0385

1.0599

1.0814

1.1032

0.8445

0.8620

0.8797

0.8976

0.9156

1.05

1.10

1.15

1.20

1.25

0.5088

0.5345

0.5603

0.5863

0.6124

0.3065

0.3220

0.3375

0.3532

0.3689

0.2544

0.2672

0.2801

0.2931

0.3062

1.8676

1.8826

1.8975

1.9124

1.9273

0.9339

0.9413

1.30

1.35

1.40

1.45

1.50

0.6387

0.6652

0.6918

0.7186

0.7455

0.3848

0.4007

0.4167

1.4329

0.4491

0.3193

0.3326

0.3459

0.3593

0.3728

1.9424

1.9575

1.9727

1.9880

2.0033

1.55

1.60

1.65

1.70

1.75

0.7726

0.7999

0.8274

0.8551

0.8829

0.4554

0.4819

0.4984

0.5151

0.5319

0.3863

0.4000

0.4137

0.4275

0.4415

1.80

1.85

1.90

1.95

2.00

0.9110

0.9392

0.9677

0.9963

1.0252

0.5488

0.5658

0.5829

0.6002

0.6176

0.4555

0.4693

0.4838

0.4982

0.5126

2.0972

2.1131

2.1292

2.1453

2.1615

2.05

2.10

2.15

2.20

2.25

1.0542

1.0835

1.1130

1.1427

1.1727

0.6351

0.6527

0.6705

0.6884

0.7064

0.5271

0.5418

0.5565

0.5714

0.5863

2.1778

2.1942

1.2029

1.2333

1.2640

1.2950

1.3262

0.7246

0.7430

0.7615

0.7801

0.7989

2.30

2.35

2.40

2.45

2.50

0.6014

0.6167

0.6323

0.6475

0.6631

* 2Mu/b d2N/mm

2.55

2.60

2.65

2.70

2.75

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

2.80

2.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

3.25

3.05

3.10

3.15

3.20

3.25

3.30

3.32

3.34

3.36

3.38

3.30

3.32

3.34

3.36

3.38

1.1252

1.1341

1.1431

1.1520

1.1611

3.40

3.42

3.44

3.46

3.48

3.40

3.42

3.44

3.46

3.48

1.1701

1.1792

1.1884

3.50

3.52

3.54

3.56

3.58

3.50

3.52

3.54

3.56

3.58

2.0188

2.0343

2.0499

2.0656

2.0813

3.60

3.62

3.64

3.66

3.68

3.60

3.62

3.64

3.66

3.68

3.70

3.72

3.74

3.70

3.72

3.74


81



2Mu/bd2N/mm

250 415 500 550* 2Mu/b d

2N/mm250 415 500 550

0.30

0.35

0.40

0.45

0.50

0.1396

0.1631

0.1868

0.2106

0.2345

0.0841

0.0983

0.1125

0.1269

0.1413

0.0698

0.0816

0.0934

0.1053

0.1172

0.0634

0.0742

0.0849

0.0957

0.1066

2.55

2.60

2.65

2.70

2.75

1.3179

1.3475

1.3772

1.4072

1.4374

0.7939

0.8117

0.8297

0.8477

0.8659

0.6589

0.6737

0.6886

0.7036

0.7187

0.5990

0.6125

0.6260

0.6396

0.6524


0.55

0.60

0.65

0.70

0.75

0.2585

0.2825

0.3067

0.3310

0.3554

0.1557

0.1702

0.1848

0.1994

0.2141

0.1292

0.1423

0.4534

0.1655

0.1777

0.1175

0.1284

0.1394

0.1505

0.1615

2.80

2.85

2.90

2.95

3.00

1.4678

1.4984

1.5292

1.5602

1.5914

0.8842

0.9026

0.9212

0.9399

0.9587

0.7339

0.7492

0.7646

0.7801

0.7957

0.6672

0.6811

0.6951

0.7092

0.7234

0.80

0.85

0.90

0.95

1.00

0.3799

0.4045

0.4229

0.4540

0.4790

0.2287

0.2437

0.2586

0.2735

0.2885

0.1900

0.2023

0.2146

0.2270

0.2395

0.1727

0.1839

0.1951

0.2064

0.2177

3.05

3.10

3.15

3.20

3.25

1.6229

1.6546

1.6856

1.7186

1.7510

0.9776

0.9967

1.0160

1.0353

1.0548

0.8114

0.8273

0.8432

0.8593

0.8755

0.7377

0.7521

0.7666

0.7812

0.7959

1.05

1.10

1.15

1.20

1.25

0.5040

0.5292

0.5545

0.5799

0.6054

0.3036

0.3188

0.3340

0.3493

0.3647

0.2520

0.2646

0.2772

0.2899

0.3027

0.2291

0.2405

0.2520

0.2636

0.2752

3.30

3.35

3.40

3.45

3.50

1.7837

1.8166

1.8498

1.8832

1.9170

1.0745

1.0943

1.1143

1.1345

1.1548

0.8918

0.9083

0.9249

0.9416

0.9585

0.8108

0.8257

0.8408

0.8560

0.8713

1.30

1.35

1.40

1.45

1.50

0.6311

0.6568

0.6827

0.7087

0.7249

0.3802

0.3957

0.4113

0.4269

0.4227

0.3155

0.3284

0.3414

0.3544

0.3674

0.2868

0.2986

0.3103

0.3222

0.3340

3.55

3.60

3.65

3.70

3.75

1.9510

1.9652

2.0198

2.0547

2.0899

1.1753

1.1959

1.2168

1.2378

1.2590

0.9755

0.9926

1.0099

0.0274

0.0450

0.8868

0.9024

0.9181

0.9340

0.9500

1.55

1.60

1.65

1.70

1.75

0.7612

0.7876

0.8141

0.8408

0.8676

0.4585

0.4744

0.4904

0.5065

0.5227

0.3806

0.3938

0.4071

0.4204

0.4338

0.3460

0.3580

0.3822

0.3944

0.3944

3.80

3.85

3.90

3.95

4.00

2.1255

2.1613

2.1976

2.2341

2.2710

1.2804

1.3020

1.3238

1.3458

1.3681

1.80

1.85

1.90

1.95

2.00

0.8946

0.9217

0.9490

0.9764

1.0040

0.5389

0.5553

0.5717

0.5882

0.6048

0.4473

0.4609

0.4745

0.4882

0.5020

0.4066

0.4190

0.4314

0.4438

0.4563

4.05

4.10

4.15

4.20

4.25

2.3083

2.3460

2.3841

2.4225

2.4514

2.05

2.10

2.15

2.20

2.25

1.0317

1.0595

1.0876

1.1158

1.1441

0.6215

0.6383

0.6552

0.6721

0.6892

0.5158

0.5298

0.5438

0.5579

0.5721

0.4689

0.4816

0.4943

1.5072

0.5201

4.30

4.35

4.40

4.45

4.50

2.5008

2.5406

2.5406

2.5808

2.6216

1.1726

1.2013

1.2302

1.2592

1.2885

0.7064

0.7237

0.7411

1.7586

0.7762

1.0627

1.0807

1.0988

0.0988

1.1171

0.9661

0.9824

0.9989

1.3906

1.4132

2.30

2.35

2.40

2.45

2.50

0.5863

0.6007

0.6151

0.6296

0.6442

0.5330

0.5461

0.5592

1.5724

0.5857


82

Table 5 Flexure - Reinforcement Percentage For Doubly Reinforced Sections

d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

2.08

2.10

2.20

2.30

2.40

0.7190

0.7249

0.7540

0.7832

0.8123

0.0025

0.0085

0.0382

0.0679

0.0976

0.7192

0.7253

0.7561

0.7869

0.8177

0.0027

0.0089

0.0403

0.0716

0.1030

0.7193

0.7258

0.7584

0.7910

0.8236

0.0028

0.0095

0.0427

0.0759

0.1091

0.7195

0.7254

0.7610

0.7957

0.8303

0.0030

0.0100

0.0453

0.0806

0.1159

2.50

2.60

2.70

2.80

2.90

0.8415

0.8706

0.8998

0.9290

0.9581

0.1273

0.1570

1.1867

0.2164

0.2461

0.8484

0.8792

0.9100

0.9408

0.9715

0.1343

0.1657

0.1971

0.2284

0.2598

0.8562

0.8888

0.9214

0.9539

0.9865

0.1423

0.1755

0.2087

0.2419

0.2751

0.8649

0.8995

0.9342

0.9688

1.0034

0.1511

0.1864

0.2217

0.2570

0.2922

3.00

3.10

3.20

3.30

3.40

0.9873

0.0164

1.0456

1.0747

1.1039

0.2758

0.3055

0.3352

0.3649

0.3946

1.0023

1.0331

1.0639

1.0946

1.1254

0.2911

0.3225

0.3538

0.3852

0.4165

1.0191

1.0517

1.0843

1.1169

1.1494

0.3082

0.3414

0.3746

0.4078

0.4410

1.0380

1.0726

1.1073

1.1419

1.1765

0.3275

0.3628

0.3981

0.4333

0.4686

3.50

3.60

3.70

3.80

3.90

1.1330

1.1622

1.1913

1.2205

1.2497

0.4243

0.4540

0.4837

0.5134

0.5431

1.1562

1.1869

1.2177

1.2485

1.2793

0.4479

0.4793

0.5106

0.5420

0.5733

1.1820

1.2146

1.2472

1.2798

1.3124

0.4742

0.5074

0.5406

0.5738

0.6070

1.2111

1.2457

1.2804

1.3150

1.3496

0.5039

0.5392

0.5744

0.6097

0.6450

4.00

4.10

4.20

4.30

4.40

1.2788

1.3080

1.3371

1.3663

1.3954

0.5729

0.6026

0.6323

0.6620

0.6917

1.3100

1.348

1.3716

1.4024

1.4331

0.6047

0.6360

0.6674

0.6987

0.7301

1.3450

1.3775

1.4101

1.4427

1.4753

0.6402

0.6734

0.7066

0.7398

0.7730

1.3842

1.4189

1.4535

1.4881

1.5227

0.6803

0.7155

0.7508

0.7861

0.8214

4.50

4.60

4.70

4.80

4.90

1.4246

1.4537

1.4829

1.5120

1.5412

0.7214

0.7511

0.7808

0.8105

0.8402

1.4639

1.4947

1.5255

1.5562

1.5870

0.7615

0.7928

0.8242

0.8555

0.8869

1.5079

1.5405

1.5730

1.6056

1.6382

0.8062

0.8394

0.8726

0.9058

0.9390

1.5573

1.5920

1.6266

1.6612

1.6958

0.6803

0.7155

0.7508

0.7861

0.8214

5.00

5.10

5.20

5.30

5.40

1.5704

1.5995

1.6287

1.6578

1.6870

0.8699

0.8966

0.9293

0.9590

0.9887

1.6178

1.6848

1.6793

1.7101

1.7409

0.9182

0.9496

0.9809

1.0123

1.0437

1.6708

1.7034

1.7360

1.7686

1.8011

0.9722

0.0054

1.0386

1.0718

1.1050

1.7304

1.7651

1.7997

1.8343

1.8689

0.8566

0.8919

0.9272

0.9625

0.9977

5.50

5.60

5.70

5.80

5.90

1.7161

1.7453

1.7744

1.8036

1.8328

1.0184

1.0481

1.0778

1.1075

1.1373

1.7717

1.8024

1.8332

1.8640

1.8948

1.0750

1.1064

1.1377

1.1691

1.2004

1.8337

1.8663

1.8989

1.9315

1.9641

1.1382

1.1714

1.2046

1.2378

1.2710

1.9035

1.9882

1.9728

2.0074

2.0420

1.2094

1.2447

1.2799

1.3152

1.3505

6.00

6.10

6.20

6.30

6.40

1.8619

1.8911

1.9202

1.9494

1.9785

1.1670

1.1967

1.2264

1.2561

1.2858

1.9255

1.9563

1.9871

2.0179

2.0486

1.2318

1.2631

1.2945

1.3259

1.3572

1.9967

2.0292

2.0618

2.0944

2.1270

1.3042

1.3374

1.3706

1.4038

1.4370

2.0767

2.1113

2.1459

2.1805

2.2151

1.3858

1.4210

1.4563

1.4916

1.5269


83


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

2.77

2.80

2.90

3.00

3.10

0.9577

0.9665

0.9956

1.0248

1.0540

0.0024

0.0113

0.0412

0.0711

0.1010

0.9579

0.9671

0.9979

1.0287

1.0594

0.0025

0.0120

0.0435

0.0751

0.1066

0.9580

0.9678

1.0004

1.0330

1.0656

0.0027

0.0127

0.0461

0.0795

0.1129

0.9582

0.9686

1.0032

1.0378

1.0724

0.0028

0.0135

0.0490

0.0845

0.1200

3.20

3.30

3.40

3.50

3.60

1.0831

1.1123

1.1414

1.1706

1.1997

0.1309

0.1608

0.1907

0.2206

0.2505

1.0902

1.1210

1.1518

1.1825

1.2133

0.1382

0.1697

0.2013

0.2329

0.2644

1.0981

1.1307

1.1633

1.1959

1.2285

0.1463

0.1797

0.2131

0.2466

0.2800

1.1071

1.1417

1.1763

1.2109

1.2455

0.1555

0.1910

0.2265

0.2620

0.2975

3.70

3.80

3.90

4.00

4.10

1.2289

1.2580

1.2872

1.3164

1.3455

0.2804

0.3103

0.3402

0.3701

0.4000

1.2441

1.2749

1.3056

1.3364

1.3672

0.2960

0.3275

0.3591

0.3906

0.4222

1.2611

1.2936

1.3262

1.3588

1.3914

0.3134

0.3468

0.3802

0.4136

0.4470

1.2802

1.3148

1.3493

1.3840

1.4186

0.3330

0.3685

0.4040

0.4395

0.4750

4.20

4.30

4.40

4.50

4.60

1.3747

1.4038

1.4330

1.4621

1.4913

0.4299

0.4597

0.4896

0.5195

0.5494

1.3980

1.4287

1.4595

1.4903

1.5210

0.4537

0.4853

0.5168

0.5484

0.5799

1.4240

1.4566

1.4892

1.5217

1.5543

0.4804

0.5138

0.5472

0.5807

0.6141

1.4533

1.4879

1.5225

1.5571

1.5918

0.5104

0.5459

0.5814

0.6169

0.6524

4.70

4.80

4.90

5.00

5.10

1.5204

1.5496

1.5787

1.6079

1.6371

0.5793

0.6092

0.6391

0.6690

0.6989

1.5518

1.5826

1.6134

1.6441

1.6749

0.6115

0.6431

0.6746

0.7062

0.7377

1.5869

1.6195

1.6521

1.6847

1.7172

0.6475

0.6809

0.7143

0.7477

0.7811

1.6264

1.6610

1.6956

1.7302

1.7649

0.6879

0.7234

0.7589

0.7944

0.8299

5.20

5.30

5.40

5.50

5.60

1.6662

1.6954

1.7245

1.7537

1.7828

0.7288

0.7587

0.7886

0.8185

0.8484

1.7057

1.7365

1.7672

1.7980

1.8288

0.7693

0.8008

0.8324

0.8639

0.8955

1.7498

1.7824

1.8150

1.8476

1.8802

0.8145

0.8479

0.8813

0.9148

0.9482

1.7995

1.8341

1.8687

1.9033

1.9380

0.8654

0.9009

0.9364

0.9719

1.0074

5.70

5.80

5.90

6.00

6.10

1.8120

1.8411

1.8703

1.8994

1.9286

0.8783

0.9081

0.9380

0.9679

0.9978

1.8596

1.8903

1.9211

1.9219

1.9827

0.9270

0.9586

0.9902

1.0217

1.0533

1.9128

1.9453

1.9779

2.0105

2.0431

0.9816

0.0150

1.0484

0.0818

0.1152

1.9726

2.0072

2.0418

2.0764

2.1111

1.0129

1.0784

1.1139

1.1494

1.1849

6.20

6.30

6.40

6.50

6.60

1.9578

1.9869

2.0161

2.0452

2.0744

1.0277

1.0576

1.0875

1.1174

1.1473

2.0134

2.0442

2.0750

2.1058

2.1365

1.0848

1.1164

1.1479

1.1795

1.2110

2.0757

2.1083

2.1408

2.1734

2.2060

1.1486

1.1820

1.2154

1.2489

1.2823

2.1457

2.1803

2.2149

2.2496

2.2842

1.2204

1.2559

1.2914

1.3269

1.3624

6.70

6.80

6.90

7.00

7.10

2.1035

2.1327

2.1618

2.1910

2.2201

1.1772

1.2071

1.2370

1.2669

1.2968

2.1673

2.1981

2.2289

2.2596

2.2904

1.2426

1.2741

1.3057

1.3372

1.3688

2.2368

2.2712

2.3038

2.3364

2.3689

1.3157

1.3491

1.3825

1.4159

1.4493

2.3188

2.3534

2.3880

2.4227

2.4573

1.3979

1.4334

1.46898

1.5044

1.5269


84


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

3.46

3.50

3.60

3.70

3.80

1.1965

1.2081

1.2373

1.2664

1.2956

0.0022

0.0141

0.0438

0.0735

0.1032

1.1966

1.2089

1.2397

1.2704

1.3012

0.0023

0.0149

0.0462

0.0776

0.14089

1.1967

1.2097

1.2423

1.2749

1.3075

0.0025

0.0158

0.0490

0.0822

0.1154

1.1969

1.2107

1.2453

1.2800

1.3146

0.0026

0.0167

0.0520

0.0873

0.1226

3.90

4.00

4.10

4.20

4.30

1.3247

1.3539

1.3830

1.4122

1.4414

0.1329

0.1626

0.1923

0.2220

0.2517

1.3320

1.3628

1.3935

1.4243

1.4551

0.1403

0.1717

0.2030

0.2344

0.2657

1.3401

1.3727

1.4053

1.4378

1.4704

0.1486

0.1818

0.2150

0.2482

0.2814

1.3492

1.3838

1.4184

1.4531

1.4877

0.1578

0.1931

0.2284

0.2637

0.2989

4.40

4.50

4.60

4.70

4.80

1.4705

1.4997

1.5288

1.5580

1.5871

0.2814

0.3111

0.3409

0.3706

0.4003

1.4859

1.5166

1.5474

1.5782

1.6090

0.2971

0.3284

0.3598

0.3911

0.4225

1.5030

1.5356

1.5682

1.6008

1.6333

0.3146

0.3478

0.3810

0.4142

0.4474

1.5223

1.5569

1.5915

1.6262

1. 660

0.3342

0.3695

0.4048

0.4400

0.4753

4.90

5.00

5.10

5.20

5.30

1.6163

1.6454

1.6746

1.7037

1.7329

0.4300

0.4597

0.4894

0.5191

0.5488

1.6397

1.6705

1.7013

1.7321

1.7628

0.4539

0.4852

0.5166

0.5479

0.5793

1.6659

1.6985

1.7311

1.7637

1.7963

0.4805

0.5137

0.5469

0.5801

0.6133

1.6954

1.6300

1.7647

1.7993

1.8339

0.1506

0.5459

0.5811

0.6164

0.6617

5.40

5.50

5.60

5.70

5.80

1.7621

1.7912

1.8204

1.8495

1.8787

0.5785

0.6082

0.6379

0.6676

0.6973

1.7936

1.8244

1.8551

1.8859

1.9167

0.6106

0.6420

0.6733

0.7047

0.7361

1.8289

1.8614

1.8940

1.9266

1.9592

0.6465

0.6797

0.7129

0.7461

0.7793

1.8685

1.9031

1.9378

1.9724

2.0070

0.6870

0.7222

0.7575

0.7928

0.8281

5.90

6.00

6.10

6.20

6.30

1.9078

1.9370

1.9661

1.9953

2.0242

0.7270

0.7567

0.7864

0.8161

0.8458

1.9475

1.9782

2.0090

2.0398

2.0706

0.7674

0.7988

0.8301

0.8615

0.8928

1.9918

2.0244

2.0569

2.0895

2.1221

0.8125

0.8457

0.8789

09121

0.9453

2.0416

2.0762

2.1109

2.1455

2.1801

0.8633

0.8986

0.9339

0.9692

1.0044

6.40

6.50

6.60

6.70

6.80

2.0236

2.0828

2.1119

2.1411

2.1702

0.8755

0.9052

0.9350

0.9647

0.9944

2.1013

2.1321

2.1629

2.1937

2.2244

0.92420

0.9555

0.9868

1.0183

1.0496

2.1247

2.1873

2.2199

2.2525

2.2850

0.9785

1.0117

1.0449

1.0781

1.1113

2.2147

2.2493

2.2840

2.3186

2.3532

1.0397

1.0750

1.1103

1.1455

1.1808

6.90

7.00

7.10

7.20

7.30

2.1994

2.2285

2.2577

2.2868

2.3160

1.0241

1.0535

1.0835

1.1123

1.1429

2.2552

2.2860

2.3138

2.3475

2.3783

1.0810

1.1123

1.1437

1.1750

1.2064

2.3176

2.3502

2.3828

2.4154

2.4480

1.1445

1.1777

1.2107

1.2441

1.2773

2.3878

2.4225

2.4571

2.4917

2.5163

1.2161

1.2514

1.2866

1.3219

1.3572

7.40

7.50

7.60

7.70

7.80

2.3452

2.3743

2.4035

2.4326

2.4618

1.1726

1.2023

1.2320

1.2617

1.2914

2.4091

2.4399

2.4706

2.5014

2.5322

1.2377

1.2691

1.3004

1.3318

1.3632

2.4805

2.5131

2.5457

2.5783

2.6109

1.3105

1.3437

1.3769

1.4101

1.4433

2.5609

2.5956

2.6302

2.6648

2.6994

1.3925

1.4277

1.4630

1.4983

1.5336


85


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

4.15

4.20

4.30

4.40

4.50

1.4352

1.4495

1.4789

1.5081

1.5372

0.0021

0.0169

0.0466

0.0763

0.1060

1.1453

1.4507

1.4814

1.5122

1.5430

0.0022

0.0179

0.0492

0.0806

0.119

1.4354

1.4517

1.4843

1.5169

1.5494

0.0023

0.0189

0.0521

0.0853

0.1185

1.4355

1.4529

1.4875

1.5221

1.5567

0.0024

0.0201

0.0554

0.0906

0.1259

4.60

4.70

4.80

4.90

5.00

1.5664

1.5995

1.6247

1.6538

1.6380

0.1357

0.1654

1.1951

0.2248

0.2546

1.5738

1.6045

1.6353

1.6661

1.6969

0.1433

0.1746

0.2060

0.2373

0.2687

1.5820

1.6146

1.6472

1.6798

1.7124

0.1517

0.1849

0.2181

0.2513

0.2845

1.5913

1.6260

1.6606

1.6952

1.7298

0.1612

0.1965

0.2317

0.2670

0.3023

5.10

5.20

5.30

5.40

5.50

1.7121

1.7413

1.7704

1.1996

1.8288

0.2843

0.3140

0.3437

0.3734

0.4031

1.7276

1.7584

1.7892

1.8200

1.8507

0.3001

0.3314

0.3628

0.3941

0.4255

1.7450

1.7775

1.8101

1.8427

1.8753

0.3177

0.3509

0.3841

0.4173

0.4505

1.7644

1.7991

1.8337

1.8683

1. 9029

0.3376

0.3728

0.4081

0.4434

0.4787

5.60

5.70

5.80

5.90

6.00

1.8579

1.8871

1.9162

1.9454

1.9745

0.4328

0.4625

0.4922

0.5219

0.5516

1.8815

1.9123

1.9431

1.9738

2.0046

0.4568

0.4882

0.1595

0.5509

0.5822

1.9079

1.9405

1.9730

2.0056

2.0382

0.4837

0.5169

0.5501

0.5833

0.6165

1.9376

1.9722

2.0068

2.0414

2.0760

0.5139

0.5492

0.5845

0.6198

0.6550

6.10

6.20

6.30

6.40

6.50

2.0037

2.0328

2.0620

2.0911

2.1203

0.5813

0.6110

0.6407

0.6704

0.7001

2.0354

2.0662

2.0969

2.1277

2.1585

0.6136

0.6450

0.6763

0.7077

0.7390

2.0708

2.1034

2.1360

2.1686

2.2011

0.6497

0.6829

0.7161

0.7493

0.7825

2.1107

2.1453

2.1799

2.2145

2.2491

0.6903

0.7256

0.7609

1.7961

0.8314

6.60

6.70

6.80

6.90

7. 00

2.1495

2.1786

2.2078

2.2369

2.2661

0.7298

0.7595

0.7892

0.8190

0.8487

2.1893

2.2200

2.2508

2.2816

2.3123

0.7704

0.8017

0.8331

0.8644

0.8958

2.2337

2.2663

2.2989

2.3315

2.3641

0.8157

0.8489

0.8821

0.9153

0.9458

2.2838

2.3184

2.3530

2.3876

2.4222

0.8667

0.9020

0.9372

0.9725

1.0078

7.10

7.20

7.30

7.40

7.50

2.2952

2.3244

2.3535

2.3827

2.4118

0.8784

0.9801

0.9378

0.9675

0.9972

2.3431

2.3739

2.4047

2.4354

2.4662

0.9272

0.9585

0.9899

1.0212

1.0526

2.3967

2.4292

2.4618

2.4944

2.5270

0.9817

1.0149

1.0481

1.0813

1.1145

2.4569

2.4915

2.5261

2.5607

2.5954

1.0431

1.0783

1.1136

1.1489

1.1842

7.60

7.70

7.80

7.90

8.00

2.4410

2.4702

2.4993

2.5285

2.5576

1.0269

1.0566

1.0863

1.1160

1.1457

2.4970

2.5278

2.5585

2.5893

2.6210

1.0839

1.1153

1.1466

1.1780

1.2094

2.5596

2.5922

2.6247

2.6573

2.6899

1.1477

1.1809

1.2141

1.2473

1.2805

2.6300

2.6646

2.6992

2.7338

2.7685

1.2194

1.2547

1.2900

1.3253

1.3605

8.10

8.20

8.30

8.40

8.50

2.5686

2.6195

2.6748

2.6742

2.7034

1.1754

1.2051

1.2348

1.2645

1.2942

2.6509

2.6816

2.7124

2.7432

2.7740

1.2407

1.2721

1.3034

1.3348

1.3661

2.7225

2.7551

2.7877

2.8203

2.8528

1.3137

1.3469

1.3801

1.4133

1.4465

2.8031

2.8377

2.8723

2.9069

2.9416

1.3958

1.44311

1.4664

1.5016

1.5369


86


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

2.00

2.10

2.20

2.30

2.40

0.5672

0.5914

0.6156

0.6398

0.6640

0.0011

0.0257

0.0503

0.0749

0.0994

0.5673

0.5928

0.6184

0.6439

0.6695

0.0012

0.0271

0.0531

0.0790

0.1050

0.5674

0.5944

0.6214

0.6485

0.6755

0.0013

0.0287

0.0562

0.0837

0.1111

0.5674

0.5962

0.6249

0.6536

0.6824

0.0013

0.0305

0.0597

0.0889

0.1181

2.50

2.60

2.70

2.80

2.90

0.6882

0.7124

0.7366

0.7608

0.7850

0.1240

0.1486

1.1732

0.1977

0.2223

0.6950

0.7205

0.7461

0.7972

0.8227

0.1306

0.1568

0.1828

0.2087

0.2347

0.7026

0.7296

0.7567

0.7837

0.8108

0.1386

0.1661

0.1935

0.2210

0.2485

0.7111

0.7398

0.7686

0.7973

0.8260

0.1473

0.1765

0.2056

0.2348

0.2640

3.00

3.10

3.20

3.30

3.40

0.8092

0.8834

0.8576

0.8818

0.9060

0.2469

0.2715

0.2961

0.3206

0.3452

0.8483

0.8738

0.8993

0.9249

0.9504

0.2606

0.2866

0.3125

0.3384

0.3644

0.8378

0.8648

0.8919

0.8919

0.9460

0.2759

0.3034

0.3309

0.3583

0.3858

0.8548

0.8835

0.9123

0.9410

0.9697

0.2932

0.3224

0.3516

0.3807

0.4099

3.50

3.60

3.70

3.80

3.90

0.9302

0.9544

0.9786

1.0028

1.0270

0.3698

0.3944

0.4189

0.4435

0.4681

0.9760

1.0015

1.0271

1.0526

1.0781

0.3903

0.4163

0.4422

0.4682

0.4941

0.9730

1.0001

1.0271

1.0542

1.0812

0.4133

0.4408

0.4682

0.4957

0.5232

0.9985

1.0272

1.0559

1.0847

1.1134

0.4391

0.4683

0.4975

0.5267

0.5559

4.00

4.10

4.20

4.30

4.40

1.0512

1.0754

1.0996

1.1238

1.1480

0.4927

0.5172

0.5418

0.5664

0.5910

1.1037

1.1292

1.1548

1.1803

1.2059

0.5200

0.5460

0.5719

0.5979

0.6238

1.1083

1.1353

1.1623

1.1894

1.2164

0.5506

0.5781

0.6056

0.6330

0.6605

1.1421

1.1709

1.1996

1.2283

1.2571

0.5850

0.6142

0.6434

0.6726

0.7018

4.50

4.60

4.70

4.80

4.90

1.1722

1.1964

1.2206

1.2448

1.2690

0.6155

0.6401

0.6647

0.6893

0.7139

1.2314

1.2569

1.2825

1.3080

1.3336

0.6497

0.6757

0.7016

0.7276

0.7535

1.2435

1.2705

1.2976

1.3246

1.3517

0.6880

0.7154

0.7429

0.7704

0.7978

1.2858

1.3146

1.3433

1.3720

1.4008

0.7310

0.7601

0.7893

0.8185

0.8477

5.00

5.10

5.20

5.30

5.40

1.2932

1.3174

1.3416

1.3658

1.3900

0.7384

0.7630

0.7876

0.8122

0.8367

1.3591

1.3847

1.4102

1.4357

1.4613

0.7795

0.8054

0.8313

0.8573

0.8832

1.3787

1.4058

1.4328

1.4598

1.4869

0.8253

0.8528

0.8802

0.9077

0.9352

1.4295

1.4582

1.4870

1.5157

1.5444

0.8769

0.9061

0.9353

0.9644

0.9936

5.50

5.60

5.70

5.80

5.90

1.4142

1.4384

1.4626

1.4868

1.5110

0.8613

0.8859

0.9105

0.9350

0.9596

1.4868

1.5124

1.5379

1.5634

1.5890

0.9092

0.9351

0.9610

0.9870

1.0129

1.5139

1.5410

1.5680

1.5951

1.6221

0.9626

0.9901

1.0176

1.0450

1.0725

1.5732

1.6019

1.6306

1.6594

1.6881

1.0228

1.0520

1.0812

1.1104

1.1395

6.00

6.10

6.20

6.30

6.40

1.5352

1.5594

1.5836

1.6078

1.6320

0.9842

1.0088

1.0333

1.0579

1.0825

1.6145

1.6401

1.6656

1.6912

1.0389

1.0648

1.0908

1.1167

1.1426

1.6492

1.6762

1.7033

1.7303

1.7573

1.1000

1.1274

1.1549

1.1824

1.2098

1.7169

1.7456

1.7743

1.8031

1.8318

1.1687

1.1979

1.2271

1.2563

1.2855


87


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

2.67

2.70

2.20

2.90

3.00

0.7571

0.7644

0.7886

0.8128

0.8370

0.0023

0.0098

0.0345

0.0592

0.0839

0.7572

0.7649

0.7904

0.8160

0.8415

0.0025

0.0103

0.0364

0.0625

0.0885

0.7574

0.7655

0.7925

0.8196

0.8466

0.0026

0.0109

0.0385

0.0661

0.0937

0.7575

0.7662

0.7949

0.8236

0.8524

0.0028

0.0116

0.0409

0.0703

0.0996

3.10

3.20

3.30

3.40

3.50

0.8612

0.8854

0.9095

0.9337

0.9579

0.1086

0.1333

1.1580

0.1827

0.2074

0.8671

0.8926

0.9181

0.9437

0.9692

0.1146

0.1407

0.1668

0.1928

0.2189

0.8737

0.9007

0.9278

0.9548

0.9818

0.1214

0.1490

0.1766

0.2042

0.2318

0.8811

0.9098

0.9386

0.9673

0.9960

0.1289

0.1586

0.1876

0.2169

0.2463

3.60

3.70

3.80

3.90

4.00

0.9821

1.0063

1.0305

1.0547

1.0789

0.2321

0.2568

0.2815

0.3062

0.3309

0.9948

1.0203

1.0459

1.0714

1.0969

0.2450

0.2711

0.2972

0.3232

0.3493

1.0089

1.0359

1.0630

1.0900

1.1171

0.2594

0.2870

0.3146

0.3422

0.3699

1.0248

1.0535

1.0822

1.1110

1.1397

0.2756

0.3050

0.3343

0.3636

0.3930

4.10

4.20

4.30

4.40

4.50

1.1031

1.1273

1.1515

1.1757

1.1999

0.3556

0.3803

0.4050

0.4297

0.4544

1.1225

1.1480

1.1736

1.1991

1.2247

0.3754

0.4015

0.4275

0.4536

0.4797

1.1441

1.1712

1.1982

1.2253

1.2523

0.3975

0.4251

0.4527

0.4803

0.5079

1.1684

1.1972

1.2259

1.2547

1.2834

0.4223

0.4516

0.4810

0.5103

0.5397

4.60

4.70

4.80

4.90

5.00

1.2241

1.2483

1.2725

1.2967

1.3209

0.4792

0.5039

0.5286

0.5533

0.5780

1.2502

1.2757

1.3013

1.3268

1.3524

0.5058

0.5318

0.5579

0.5840

0.6101

1.2793

1.3064

1.3334

1.3605

1.3875

0.5355

0.5631

0.5907

0.6184

0.6460

1.3121

1.3409

1.3696

1.3983

1.4271

0.5690

0.5983

0.6277

0.6570

0.6863

5.10

5.20

5.30

5.40

5.50

1.3451

1.3693

1.3935

1.4177

1.4419

0.6027

0.6274

0.6521

0.6768

0.7015

1.3779

1.4035

1.4290

1.4545

1.4801

0.6362

0.6622

0.6883

0.7144

0.7405

1.4146

1.4416

1.4687

1.

1.5228

4687

0.6736

0.7012

0.7288

0.7564

0.7840

1.4558

1.4845

1.5133

1.5420

1.5707

0.7157

0.7450

0.7744

0.8037

0.8330

5.60

5.70

5.80

5.90

6.00

1.4661

1.4903

1.5145

1.5387

1.5629

0.0262

0.7509

0.7756

0.8003

0.8250

1.5056

1.5312

1.5567

1.5823

1.6078

0.7665

0.7926

0.8187

0.8448

0.8709

1.5498

1.5768

1.6039

1.6309

1.6580

0.8116

0.8392

0.8669

0.8945

0.9221

1.5995

1.6282

1.6570

1.6857

1.7144

0.8624

0.8917

0.9210

0.9504

0.9797

6.10

6.20

6.30

6.40

6.50

1.5871

1.6133

1.6355

1.6597

1.6839

0.8497

0.8744

0.8911

0.9238

0.9485

1.6333

1.6589

1.6844

1.7100

1.7855

0.8969

0.9230

0.9491

0.9752

1.0012

1.6850

1.7121

1.7391

1.7662

1.7932

0.9497

0.9773

1.0049

1.0325

1.0601

1.7432

1.7719

1.8006

1.8294

1.8581

1.0091

1.0384

1.0677

1.0971

1.1264

6.60

6.70

6.80

6.90

7.00

1.7091

1.7323

1.7565

1.7807

1.8049

0.9733

0.9980

1.0227

1.0474

1.0721

1.7611

1.7866

1.8121

1.8377

1.8632

1.0273

1.0534

1.0795

1.1056

1.9284

1.8202

1.8473

1.8743

1.9014

1.9284

1.0878

1.1154

1.1430

1.1706

1.1982

1.8868

1.9156

1.9443

1.9730

2.0018

1.1557

1.1851

1.2144

1.2437

1.2731


88


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

3.33

3.40

3.50

3.60

3.70

0.9446

0.9615

0.9857

1.0099

1.0341

0.0011

0.0183

0.0429

0.0674

0.0920

0.9446

0.9625

0.9880

1.0136

1.0391

0.0011

0.0193

0.0452

0.0712

0.0971

0.9447

0.9636

0.9907

1.0177

1.0488

0.0012

0.0204

0.0479

0.0784

0.1028

0.9448

0.9649

0.9936

1.0223

1.0511

0.0013

0.0217

0.0509

0.0801

0.1093

3.80

3.90

4.00

4.10

4.20

1.0583

1.0825

1.1067

1.1309

1.1551

0.1166

0.1412

1.1657

0.1903

0.2149

1.0647

1.0902

1.1158

1.1413

1.1668

0.1231

0.1490

0.1749

0.2009

0.2268

1.0718

1.0988

1.1259

1.1529

1.1800

0.1303

0.1578

0.1852

0.2127

0.2402

1.0798

1.1086

1.1373

1.1660

1.1948

0.1384

0.1676

0.1968

0.2260

0.2552

4.30

4.40

4.50

4.60

4.70

1.1793

1.2035

1.2277

1.2519

1.2761

0.2395

0.2640

0.2886

0.3132

0.3378

1.1924

1.2179

1.2435

1.2690

1.2946

0.2558

0.2787

0.3047

0.3306

0.3565

1.2070

1.2341

1.2611

1.2882

1.3152

0.2676

0.2951

0.3226

0.3500

0.3775

1.2235

1.2522

1.2810

1.3097

1.3384

0.2844

0.3135

0.3427

0.3719

0.4011

4.80

4.90

5.00

5.10

5.20

1.3003

1.3245

1.3487

1.3729

1.3971

0.3623

0.3869

0.4115

0.4361

0.4607

1.3201

1.3456

1.3712

1.3967

1.4223

0.3825

0.4084

0.4344

0.4603

0.4862

1.3422

1.3693

1.3963

1.4234

1.4504

0.4050

0.4324

0.4599

0.4874

0.1548

1.3672

1.3859

1.4246

1.4534

1.4821

0.4303

0.4595

0.4887

0.5178

0.5470

5.30

5.40

5.50

5.60

5.70

1.4213

1.4455

1.4697

1.4939

1.5181

0.4852

0.5098

0.5344

0.5590

0.5835

1.4478

1.4734

1.4989

1.5244

1.550

0.5122

0.5381

0.5641

0.5900

0.6160

1.4775

1.5045

1.5316

1.5586

1.5857

0.5423

0.5698

0.5972

0.6247

0.6522

1.5108

1.5396

1.5683

1.5971

1.6258

0.5762

0.6054

0.6346

0.6638

0.6929

5.80

5.90

6.00

6.10

6.20

1.5423

1.5665

1.5907

1.6149

1.6391

0.6081

0.6327

0.6573

0.6818

0.7064

1.5755

1.6011

1.6266

1.6522

1.6777

0.6419

0.6678

0.6938

0.7197

0.7457

1.6127

1.6397

1.6668

1.

1.7209

6938

0.6797

0.7071

0.7346

0.7621

0.7895

1.6545

1.6833

1.7120

1.7407

1.7695

0.7221

0.7513

0.7805

0.8097

0.8389

6.30

6.40

6.50

6.60

6.70

1.6633

1.6875

1.7116

1.7358

1.7600

0.7310

0.7556

0.7801

0.8047

0.8293

1.7032

1.7288

1.7543

1.7799

1.8054

0.7716

0.7975

0.8235

0.8494

0.8754

1.7479

1.7750

1.8020

1.8291

1.8561

0.8170

0.8445

0.8719

0.8994

0.9269

1.7982

1.8269

1.8557

1.8844

1.9131

0.8681

0.8972

0.9264

0.9556

0.9848

6.80

6.90

7.00

7.10

7.20

1.7842

1.8084

1.8326

1.5538

1.8810

0.8539

0.8785

0.9030

0.9276

0.9522

1.8310

1.8565

1.8820

1.9076

1.9331

0.9013

0.9273

0.9532

0.9791

1.0051

1.8832

1.9102

1.9372

1.9643

1.9913

0.9543

0.9818

1.0093

1.0367

1.0642

1.9419

1.9706

1.9994

2.0281

2.0568

1.0140

1.0432

1.0723

1.1015

1.1307

7.30

7.40

7.50

7.60

7.70

1.9052

1.9294

1.9536

1.9778

2.0020

0.9768

1.0013

1.0259

1.0505

1.0751

1.9587

1.9842

2.0098

2.0353

2.0608

1.0310

1.0570

1.0829

1.1088

1.1348

2.0184

2.0454

2.0725

2.0995

2.1266

1.0917

1.1191

1.1466

1.1741

1.2015

2.0856

2.1143

2.1430

2.1718

2.2005

1.1599

1.1891

1.2183

1.2475

1.2766


89


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

4.00

4.10

4.20

4.30

4.40

1.1344

1.1586

1.1828

1.2070

1.2312

0.0023

0.0268

0.0514

0.0760

0.1006

1.1346

1.1601

1.1856

1.2112

1.2367

0.0024

0.0283

0.0543

0.0802

0.1062

1.1347

1.1617

1.1888

1.2158

1.2429

0.0025

0.0300

0.0575

0.0849

0.1124

1.1349

1.1636

1.1923

1.2211

1.2498

0.0027

0.0319

0.0611

0.0903

0.1194

4.50

4.60

4.70

4.80

4.90

1.2554

1.2796

1.3038

1.3280

1.3522

0.1252

0.1497

1.1743

0.1989

0.2235

1.2623

1.2878

1.3134

1.3389

1.3644

0.1321

0.1580

0.1840

0.2099

0.5359

1.2699

1.2970

1.3240

1.3511

1.3781

0.1399

0.1673

0.1948

0.2223

0.2497

1.2785

1.3073

1.3360

1.3647

1.3935

0.1486

0.1778

0.2070

0.2362

0.2654

5.00

5.10

5.20

5.30

5.40

1.3764

1.4006

1.4248

1.4490

1.4732

0.2480

0.2726

0.2972

0.3218

0.3463

1.3900

1.4155

1.4411

1.4666

1.4927

0.2618

0.2878

0.3137

0.3396

0.3656

1.4052

1.4322

1.4592

1.4863

1.5133

0.2772

0.3047

0.3322

0.3596

0.3871

1.4222

1.4509

1.4797

1.5084

1.5372

0.2945

0.3237

0.3529

0.3821

0.4113

5.50

5.60

5.70

5.80

5.90

1.4974

1.5216

1.5458

1.5700

1.5942

0.3709

0.3955

0.4201

0.4446

0.4692

1.1577

1.5432

1.5688

1.5943

1.6199

0.3915

0.4175

0.4434

0.4693

0.4953

1.5404

1.5674

1.5945

1.6215

1.6486

0.4146

0.4420

0.4695

0.4970

0.5244

1.5659

1.5946

1.6234

1.6521

1.6808

0.4405

0.4696

0.4988

0.5280

0.5572

6.00

6.10

6.20

6.30

6.40

1.6184

1.6426

1.6668

1.6910

1.7152

0.4938

0.5184

0.5430

0.5675

0.5921

1.6454

1.6710

1.6965

1.7220

1.7476

0.5212

0.5472

0.5731

0.5991

0.6250

1.6756

1.7027

1.7297

1.7567

1.7838

0.5519

0.5794

0.6068

0.6343

0.6618

1.7096

1.7383

1.7670

1.7958

1.8245

0.5864

0.6156

0.6448

0.6739

0.7031

6.50

6.60

6.70

6.80

6.90

1.7394

1.7636

1.7878

1.8120

1.8362

0.6167

0.6413

0.6658

0.6904

0.7150

1.7731

1.7987

1.8242

1.8498

1.8753

0.6509

0.6769

0.7028

0.7288

0.7547

1.8108

1.8379

1.8649

1.

1.9190

8920

0.06892

0.7167

0.7442

0.7716

0.7991

1.8532

1.8820

1.9107

1.9395

1.9682

0.7323

0.7615

0.7907

0.8199

0.8490

7.00

7.10

7.20

7.30

7.40

1.8604

1.8846

1.9088

1.9330

1.9572

0.7396

0.7641

0.7887

0.8133

0.8379

1.9008

1.9264

1.9519

1.9775

2.0030

0.7806

0.8066

0.8325

0.8585

0.8844

1.9461

1.9731

2.0002

2.0272

2.0542

0.8266

0.8540

0.8815

0.9090

0.9364

1.9969

2.0257

2.0544

2.0631

2.1119

0.8782

0.9074

0.9366

0.9658

0.9950

7.50

7.60

7.70

7.80

7.90

1.0814

2.0056

2.0298

2.0540

2.0782

0.8624

0.8870

0.9116

0.9362

0.9608

2.0286

2.0541

2.0796

2.1052

2.1307

0.9104

0.9363

0.9622

0.9882

1.0141

2.0813

2.1083

2.1354

2.1624

2.1895

0.9639

0.9914

0.0188

1.0463

1.0738

2.1406

2.1693

2.1981

2.2268

2.2555

1.0242

1.0533

1.0825

1.1117

1.1409

8.00

8.10

8.20

8.30

8.40

2.1024

2.1266

2.1508

2.1780

2.1992

0.9853

1.0099

1.0345

1.0591

1.0836

2.1563

2.1818

2.2074

2.2329

2.2584

1.0401

1.0660

1.0920

1.1179

1.1438

2.2165

2.2436

2.2706

2.2976

2.3247

1.1012

1.1287

1.1562

1.1837

1.2111

2.2843

2.3130

2.3418

2.3705

2.3992

1.1701

1.1993

1.2284

1.2576

1.2868


90


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

1.96

2.00

2.10

2.20

2.30

0.5020

0.5108

0.5328

0.5548

0.5768

0.0013

0.0105

0.0328

0.0551

0.0774

0.5021

0.5114

0.5346

0.5578

0.5811

0.0017

0.0111

0.0346

0.0582

0.0817

0.5022

0.5120

0.5366

0.5612

0.5858

0.0018

0.0117

0.0367

0.0616

0.0865

0.5023

0.5128

0.5389

0.5650

0.5911

0.0019

0.0215

0.0390

0.0655

0.0920

2.40

2.50

2.60

2.70

2.80

0.5988

0.6208

0.6428

0.6648

0.6868

0.0997

0.1221

0.1444

0.1667

0.1890

0.6043

0.6275

0.6507

0.6739

0.6972

0.1053

0.1288

0.1524

0.1759

0.1995

0.6104

0.6350

0.6596

0.6841

0.7087

0.1115

0.1364

0.1614

0.1863

0.2112

0.6172

0.6434

0.6695

0.6956

0.7217

0.1185

0.1449

0.1714

0.1979

0.2244

2.90

3.00

3.10

3.20

3.30

0.7088

0.7308

0.7528

0.7748

0.7968

0.2113

0.2336

0.2559

0.2782

0.3005

0.7204

0.7436

0.7668

0.7900

0.8133

0.2230

0.2466

0.2701

0.2937

0.3172

0.7333

0.7579

1.7825

1.8071

0.8317

0.2362

0.2611

0.2860

0.3110

0.3359

0.7479

0.7740

0.8001

0.8262

0.8524

0.2509

0.2774

0.3039

0.3304

0.3569

3.40

3.50

3.60

3.70

3.80

0.8188

0.8408

0.8628

0.8848

0.9068

0.3229

0.3452

0.3675

0.3898

0.4121

0.8365

0.8597

0.8829

0.9061

0.9294

0.3408

0.3643

0.3879

0.4114

0.4350

0.8562

0.8808

0.9054

0.9300

0.9546

0.3608

0.3858

0.4107

0.4356

0.4606

0.8785

0.9046

0.9307

0.9569

0.9830

0.3834

0.4099

0.4364

0.4629

0.4894

3.90

4.00

4.10

4.20

4.30

0.9288

0.9508

0.9728

0.9948

1.0168

0.4344

0.4567

0.4790

0.5013

1.5236

0.9526

0.9758

0.9990

1.0222

1.0455

0.4585

0.4821

0.5056

0.5292

0.5527

0.9792

1.0038

1.0284

1.0529

1.0775

0.4855

0.5104

0.5354

0.5603

0.5853

1.0091

1.0352

1.0613

1.0875

1.1136

0.5159

0.5424

0.5688

0.5953

0.6218

4.40

4.50

4.60

4.70

4.80

1.0388

1.0608

1.0828

1.1048

1.1268

0.5460

0.5683

0.5906

0.6129

0.6352

1.0687

1.0919

1.1151

1.1383

1.1616

0.5763

0.5998

0.6234

0.6469

0.6705

1.1021

1.1267

0.1513

1.

1.2005

1759

0.6102

0.6351

0.6601

0.6850

0.7099

1.1397

1.1658

1.1920

1.2181

1.2442

0.6483

0.6748

0.7013

0.7278

0.7543

4.90

5.00

5.10

5.20

5.30

1.1488

1.1708

1.1928

1.2148

1.2364

0.6575

0.6798

0.7021

0.7244

0.7464

1.1848

1.2080

1.2312

1.2545

1.2777

0.6940

0.7176

0.7411

0.7647

0.7882

1.2250

1.2496

1.2742

1.2988

1.3234

0.7349

0.7598

0.7847

0.8097

0.8346

1.2703

1.2965

1.3226

1.3487

1.3748

0.7808

0.8073

0.8338

0.8603

0.8868

5.40

5.50

5.60

5.70

5.80

1.2588

1.2808

1.3028

1.3248

1.3463

0.7691

0.7914

0.8137

0.8360

0.8583

1.3009

1.3241

1.3473

1.3706

1.3918

0.8118

0.8353

0.8589

0.8824

0.9060

1.3480

1.3726

1.3972

1.4217

1.4463

0.8595

0.8845

0.9094

0.9343

0.9593

1.4009

1.4271

1.4532

1.4793

1.5054

0.9133

0.9398

0.9662

0.9927

1.0192

5.90

5.00

6.10

6.20

6.30

1.3688

1.3908

1.4128

1.4348

1.4568

0.8806

0.9029

0.9252

0.9475

0.9690

1.4170

1.4402

1.4634

1.4867

1.5099

0.9295

0.9531

0.9766

1.0002

1.0237

1.4709

1.4955

1.5201

1.5447

1.5693

0.9842

1.0092

1.0341

1.0590

1.0840

1.5316

1.5577

1.5838

1.6099

1.6361

1.0457

1.0722

1.0987

1.1252

1.1517


91


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

2.62

2.70

2.80

2.90

3.00

0.6708

0.6884

0.7104

0.7324

0.7544

0.0036

0.0215

0.0440

0.0664

0.0888

0.6710

0.6896

0.7128

0.7360

0.7593

0.0038

0.0227

0.0464

0.0701

0.0937

0.6712

0.6909

0.7155

0.7401

0.7647

0.0040

0.0241

0.0491

0.0742

0.0992

0.6715

0.6924

0.7185

0.7446

0.7708

0.0043

0.0256

0.0522

0.0788

0.1054

3.10

3.20

3.30

3.40

3.50

0.7764

0.7984

0.8204

0.8424

0.8644

0.1112

0.1336

0.1560

0.1785

0.2009

0.7825

0.8057

0.8289

0.8521

0.8754

0.1174

0.1411

0.1647

0.1884

0.2120

0.7893

0.8138

0.8384

0.8630

0.8876

0.1243

0.1493

0.1744

0.1995

0.2245

0.7696

0.8230

0.8491

0.8752

0.9014

0.1321

0.1587

0.1853

0.2119

0.2385

3.60

3.70

3.80

3.90

4.00

0.8864

0.9084

0.9304

0.9524

0.9744

0.2233

0.2457

0.2681

0.2905

0.3130

0.8986

0.9218

0.9450

0.9682

0.9915

0.2375

0.2594

0.2830

0.3067

0.3303

0.9122

0.9368

0.9614

0.9859

1.0105

0.2496

0.2746

0.2997

0.3247

0.3498

0.9275

0.9536

0.9797

0.10059

1.0320

0.2652

0.2918

0.3184

0.3450

0.3716

4.10

4.20

4.30

4.40

4.50

0.9964

0.0184

1.0404

1.0624

1.0844

0.3354

0.3578

0.3802

0.4026

0.4250

1.0147

1.0379

1.0611

1.0843

1.1076

0.3540

0.3777

0.4013

0.4250

0.4487

1.0351

1.0597

1.0843

1.1089

1.1335

0.3748

0.3999

0.4249

0.4500

0.4750

1.0581

1.0842

1.1104

1.1365

1.1626

0.3983

0.4249

0.4515

0.4781

0.5047

4.60

4.70

4.80

4.90

5.00

1.1064

1.1284

1.1504

1.1724

1.1944

0.4

0.

0.4923

0.5147

0.5371

475

4699

1.1308

1.1540

1.1772

1.2004

1.2237

0.4723

0.4960

0.5196

0.5433

0.5670

1.1581

1.1826

1.2070

1.2318

1.2564

0.5001

0.55252

0.5502

0.5753

0.6003

1.1887

1.2148

1.2410

1.2671

1.2932

0.5314

0.5580

0.5846

0.6112

0.6378

5.10

5.20

5.30

5.40

5.50

1.2164

1.2384

1.2604

1.2824

1.3044

0.5595

0.5820

0.6044

0.6268

0.6492

1.2469

1.2701

1.2933

1.3166

1.3398

0.5906

0.6143

0.6380

0.6616

0.6853

1.2810

1.3056

0.3302

1.

1.3793

3547

0.6254

0.6504

0.6755

0.7005

0.7256

1.3193

1.3455

1.3716

1.3977

1.4238

0.6645

0.6911

0.7177

0.7443

0.7709

5.60

5.70

5.80

5.90

6.00

1.3264

1.3484

1.3704

1.3924

1.4144

0.6716

0.6940

0.7165

0.7389

0.7613

1.3630

1.3862

1.4094

1.4327

1.4559

0.7089

0.7326

0.7563

0.7799

0.8036

1.4039

1.4285

1.4531

1.4777

1.5023

0.7506

0.7757

0.8007

0.8258

0.8509

1.4500

1.4761

1.5022

1.5283

1.5545

0.7976

0.8242

0.8508

0.8774

0.9040

6.10

6.20

6.30

6.40

6.50

1.4364

1.4584

1.4804

1.5024

1.5244

0.7837

0.8061

0.8285

0.8510

0.8734

1.4791

1.5023

1.5255

1.5488

1.5720

0.8272

0.8509

0.8746

0.8982

0.9219

1.5269

1.5514

1.5760

1.6006

1.6252

0.8759

0.9010

0.9260

0.9511

0.9761

1.5806

1.6067

1.6328

1.6289

1.6851

0.9307

0.9573

0.9839

1.0105

1.0371

6.60

6.70

6.80

6.90

7.00

1.5464

1.5684

1.5904

1.6124

1.6344

0.8958

0.9182

0.9406

0.9630

0.9855

1.5952

1.6184

1.6416

1.6649

1.6881

0.9456

0.9622

0.9929

0.0165

1.0402

1.6498

1.6744

1.6990

1.7235

1.7481

1.0012

1.0262

1.0513

1.0769

1.1014

1.7112

1.7373

1.7634

1.7896

1.8157

1.0637

1.0904

1.1170

1.1436

1.1702


92


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

3.30

3.40

3.50

3.60

3.70

0.8440

0.8660

0.8880

0.9100

0.9320

0.0101

0.0324

0.0547

0.0770

0.0993

0.8446

0.8678

0.8910

0.9142

0.9375

0.8446

0.8678

0.8910

0.9142

0.9375

0.5452

0.8698

0.8944

0.9190

0.6435

0.0113

0.0362

0.0611

0.0861

0.1110

0.8459

0.8420

0.8981

0.9243

0.9504

0.0120

0.0385

0.0649

0.0914

0.1179

3.80

3.90

4.00

4.10

4.20

0.9540

0.9760

0.9980

1.0200

1.0420

0.1216

0.1439

0.1662

0.1886

0.2109

0.9607

0.9839

1.0071

1.0303

1.0536

0.9607

0.9839

1.0071

1.0303

1.0536

0.9681

0.9927

0.01736

1.0419

1.0665

0.1359

0.1609

0.1858

0.2107

0.2357

0.9765

1.0026

1.0287

1.0549

1.0810

0.1444

0.1709

0.1974

0.2239

0.2504

4.30

4.40

4.50

4.60

4.70

1.0640

1.0860

1.1080

1.1300

1.1520

0.2332

0.2555

0.2778

0.3001

0.3224

1.0768

1.1000

1.1232

1.1464

1.1697

1.0768

1.1000

1.1232

1.1464

1.1697

1.0911

1.1156

1.1402

1.1648

1.1894

0.2606

0.2855

0.3105

0.3354

0.3604

1.1071

1.1332

1.1594

1.1855

1.2116

0.2769

0.3034

0.3299

0.6564

0.4094

4.80

4.90

5.00

5.10

5.20

1.1740

1.1960

1.2180

1.2400

1.2620

0.3447

0.3670

0.3894

0.4117

0.4340

1.1929

1.2161

1.2393

1.2625

1.2858

1.1929

1.2161

1.2393

1.2625

1.2858

1.2140

1.2386

1.2632

1.2878

1.3123

0.3853

0.4102

0.4350

0.4601

0.4850

1.2377

1.2639

1.2900

1.3161

1.3422

0.4359

0.4624

0.4888

0.5153

0.5418

5.30

5.40

5.50

5.60

5.70

1.2840

1.3060

1.3280

1.3500

1.3720

0.4

0.

0.5009

0.5232

0.5455

563

4786

1.3090

1.3322

1.3554

1.3787

1.4019

1.3090

1.3322

1.3554

1.3787

1.4019

1.3369

1.3615

1.3861

1.4107

1.4353

0.5100

0.5349

0.5598

0.5848

0.6097

1.3684

1.3945

1.4206

1.4467

1.4728

0.5683

0.5948

0.6213

0.6478

0.6743

5.80

5.90

6.00

6.10

6.20

1.3940

1.4160

1.4380

1.4600

1.4820

0.5678

0.5901

0.6125

0.6348

0.6571

1.4251

1.4483

1.4715

1.4948

1.5180

1.4251

1.4483

1.4715

1.4948

1.5180

1.4599

1.4844

1.5090

1.

1.5582

5336

0.6346

0.6596

0.6845

0.7094

0.7344

1.4990

1.5251

1.5512

1.5773

1.6035

0.7008

0.7273

0.7538

0.7803

0.8068

6.30

6.40

6.50

6.60

6.70

1.5040

1.5260

1.5480

1.5700

1.5920

0.6794

0.7017

0.7240

0.7463

0.7686

1.5412

1.5644

1.5876

1.6109

1.6341

1.5412

1.5644

1.5876

1.6109

1.6341

1.5828

1.6074

1.6320

1.6566

1.6811

0.7593

0.7843

0.8092

0.8341

0.8591

1.6296

1.6557

1.6818

1.7080

1.7341

0.8333

0.8598

0.8863

0.9127

0.9392

6.80

6.90

7.00

7.10

7.20

1.6140

1.6360

1.6580

1.6800

1.7020

0.7909

0.8133

0.8356

0.8579

0.8802

1.6573

1.6805

1.7037

1.7270

1.7502

1.6573

1.6805

1.7037

1.7270

1.7502

1.7057

1.7303

1.7549

1.7795

1.8041

0.8840

0.9089

0.9339

0.9588

0.9837

1.7602

1.7863

1.8124

1.8386

1.8647

0.9657

0.9922

0.0187

1.0452

1.0717

7.30

7.40

7.50

7.60

7.70

1.7240

1.7460

1.7680

1.7900

1.8120

0.9025

0.9248

0.9471

0.9694

0.9917

1.7734

1.7966

1.8198

1.8431

1.8663

1.7734

1.7966

1.8198

1.8431

1.8663

1.8287

1.8582

1.8778

1.9024

1.9270

1.0087

1.0336

1.0585

1.0835

1.1084

1.8908

1.9169

1.9431

1.9692

1.9953

1.0982

1.1247

1.1512

1.1777


93


d’/d = 0.052Mu/bd

2)(N/mm Pt Pc

d’/d = 0.1

Pt Pc

d’/d = 0.15

Pt Pc

d’/d = 0.2

Pt Pc

3.95

4.00

4.10

4.20

4.30

1.0106

1.0216

1.0436

1.0656

1.0876

0.0099

0.0210

0.0433

0.0656

0.0879

1.0112

1.0228

1.0460

1.0692

1.0924

0.0104

0.0222

0.0457

0.0693

0.0928

1.0118

1.0241

1.0487

1.0732

1.0378

0.0110

0.0235

0.0484

0.0734

0.0983

1.0125

1.0255

1.0516

1.0778

1.1039

0.0117

0.0250

0.0514

0.0779

0.1044

4.40

4.50

4.60

4.70

4.80

1.1096

1.1316

1.1536

1.1756

1.1976

0.1103

0.1326

0.1549

0.1772

0.1995

1.1157

1.1389

1.1621

1.1853

1.2085

0.1164

0.1399

0.1635

0.1870

0.2106

1.1224

1.1470

1.1716

1.1962

1.2208

0.1232

0.1482

0.1731

0.1980

0.2230

1.1300

1.1561

1.1823

1.2084

1.2345

0.1309

0.1574

0.1839

0.2104

0.2369

4.90

4.00

5.10

5.20

5.30

1.2196

1.2416

1.2636

1.2856

1.3076

0.2218

0.2441

0.2664

0.2887

0.3110

1.2318

1.2550

1.2782

1.3014

1.3246

0.2341

0.2577

0.2812

0.3048

0.3283

1.2453

1.2699

1.2945

1.3191

1.3737

0.2479

0.2728

0.2978

0.3227

0.3476

1.2606

1.2867

1.3129

1.3390

1.3651

0.2634

0.2899

0.3164

0.3429

0.3694

5.40

5.50

5.60

5.70

5.80

1.3296

1.3516

1.3736

1.3956

1.4176

0.3334

0.3557

0.3780

0.4003

0.4226

1.3479

1.3711

1.3943

1.5175

1.4408

0.3519

0.3754

0.3990

0.4225

0.4461

1.3683

1.3929

1.4175

1.4420

1.4666

0.3726

0.3975

0.4224

0.4474

0.4723

1.3912

1.4174

1.4435

1.4696

1.4957

0.3959

0.4224

0.4489

0.4753

0.5018

5.90

6.00

6.10

6.20

6.30

1.4396

1.4616

1.4836

1.5056

1.5276

0.4

0.

0.4865

0.5118

0.5342

449

4672

1.4640

1.4872

1.5104

1.5336

1.5569

0.4696

0.4932

0.5167

0.5403

0.5638

1.4912

1.5158

1.5404

1.5650

1.5896

0.4973

0.5222

0.5471

0.5721

0.5970

1.5219

1.5480

1.5741

1.6002

1.6263

0.5283

0.5548

0.5813

0.6078

0.6343

6.40

6.50

6.60

6.70

6.80

1.5496

1.5716

1.5936

1.6156

1.6376

0.5565

0.5788

0.6011

0.6234

0.6457

1.5801

1.6039

1.6265

1.6497

1.6730

0.5874

0.6109

0.6345

0.6580

0.6816

1.6141

1.6387

1.6633

1.

1.7125

6879

0.6219

0.6469

0.6718

0.6967

0.7217

1.6525

1.6786

1.7047

1.7308

1.7570

0.6608

0.6873

0.7138

0.7403

0.7668

6.90

7.00

7.10

7.20

7.30

1.6596

1.6816

1.7036

1.7256

1.7476

0.6680

0.6903

0.7126

0.7349

0.7573

1.6962

1.7194

1.7426

1.7658

1.7891

0.7051

0.7287

0.7522

0.7758

0.7993

1.7371

1.7617

1.7863

1.8108

1.8354

0.7466

0.7715

0.7965

0.8214

0.8463

1.7831

1.8092

1.8353

1.5615

1.8876

0.7933

0.8198

0.8463

0.8728

0.8992

7.40

7.50

7.60

7.70

7.80

1.7696

1.7916

1.8136

1.8356

1.8576

0.7796

0.8019

0.8242

0.8465

0.8688

1.8123

1.8355

1.8587

1.8819

1.9052

0.8229

0.8464

0.8700

0.8935

0.9171

1.8600

1.8846

1.9092

1.9338

1.9584

0.8713

0.8962

0.9212

0.9461

0.9710

1.9137

1.9398

1.9660

1.9921

2.0182

0.9257

0.9522

0.9787

1.0052

1.0317

7.90

8.00

8.10

8.20

8.30

1.8796

1.9016

1.9236

1.9456

1.9676

0.8911

0.9134

0.9357

0.9581

0.9804

1.9284

1.9516

1.9748

1.9980

2.0213

0.9406

0.9642

0.9877

1.0113

1.0348

1.9829

2.0075

2.0321

2.0567

2.0813

0.9960

1.0209

1.0458

1.0708

1.0957

2.0443

2.0704

2.0966

2.1227

2.1488

1.0582

1.0847

1.1112

1.1377

1.1642


95

CHAPTER - 4

Compression

Members


96

4.1 Axially Loaded Compression Members

4.1.1 All compression members shall be designed for a minimum eccentricity of load in two principal directions. As per clause 24.4 of IS-456 2000, the

efollowing minimum eccentricity, in shall be calculated for the deign of columns:

emin = (L/500)+(D/30)subject to a minimum of 20 mm.

Where,L is the unsupported length of the column (refer 24.13 of 15-456:200) for the definition of the unsupported length) and D is the lateral dimension of the column in the direction under consideration.

4.1.2 The section shall be designed for the calculated eccentricity for combined axial load and bending. The value of the minimum eccentricity shall be calculated as per above eq. and if emin/D is less than or equal to 0.05 then as per clause 38.3 of 1 s-456:2000,the column may be designed as a short exially loaded compression member by the following equation:

P = 0.4 f A + 0.67 f Ac scu yckWhere

P is the axial loaduA is the net area of concrete, andcA is the are of reinforcement.scThe above equation may be rewritten as:P /A = 0.4f + p/100 (0.67fy - 0.4f )u cg k ck

WhereA is the gross area of cross section andgP is the percentage of reinforcement.

4.1.3 For grade of steel TMT 415 to TMT 550 equation is modified because in the above mentioned equation, the stress in reinforcement corresponding to 0.002 strain (max. strain in concrete at failure for axial loads) is 0.85f ybased on the stress strain curve of cold twisted steel. But Applying a material safety factor 1.15 and 1.1 for min eccentricity, the factor (0.67xf ) term in the yabove equation is modified as 4001 Equation is modified as follows:

P /A = 0.4f + p/100 (316.2 - 0.4f )u g ck ck


97

4.1.4 The charts 1 to 4 havebeen prepared for values of P /A on x-axis and 100 guA /A on the lower most portion for different grades of Concrete. Also P /A s g guhas been plotted against P for different values of A in the bottom most u gportion. The top and bottom graphs may be combined together and this can be used for designing the columns subjected to axial loads only. These graphs will be particularly useful in deciding the size of the column for preliminary design.

4.2 Combined Axial Load And Uniaxial Bending

As mentioned above, the columns are always subjected to bending either in one direction or in both the directions. Here, the columns subjected to uniaxial bending is described.

4.2.1 Assumptions

The assumptions made for flexure are also applicable to columns subjected to axial load and uniaxial bending (a),(c),(d) and (e) except (b) and (f).The assumption (b) is modified as follows:

The maximum strain in the outer most fiber in the concrete is assumed as 0.0035 as in the case of flexure, but this is applicable only if the neutral axis lies within the section and this is also applicable when the neutral axis lies along one edge of the section. In the limiting case, where the neutral axis lies exactly along one edge of the section then the strain varies from 0.0035 at the highly compressed edge to zero at the opposite edge. For sections subjected to pure axial compression, the strain is assumed to be uniformly equal to 0.002 across the section. It may be seen that, the strain distribution for the above two cases intersect each other at a distance of 3D/7 from the highly compressed edge. This point is assumed to act as fulcrum for the strain distribution line when the neutral axis lies outside the section. This leads to the assumption that the strain at the highly compressed edge is 0.0035 minus 0.75 times the strain at the least compressed edge. This is also stated in clause 38.1 (b) of J5-456:2000.

4.2.2 Construction Of Interaction DiagramDesign charts for combined axial compression and bending are given in the

2form of interaction diagrams in which curves for P /bd f versus M /f bd uu ck ckare plotted for different values p/f , where p is the reinforcement ckpercentage. The design charts are prepared for columns with reinforcement distributed equally on two sides only.


98

For the case of purely axial load i.e. M = O.the points plotted on the y-axis are uobtained as follows:

P /f bd = 0.446 + (f -0.446 f ) x(p/100 f )c ckk sc ckuWhere f is the compressive stress in steelsccorresponding to a strain of 0.002.

As discussed in SP - 16.fck is taken as 20 for simplification.

When the neutral axis lies outside the section, the expression for the interaction diagram may be written as:

P /f bd = C1 +{(f -f )+ (t -f )}xu ck st ct sc cc{p/(200f )}ck

2M /f bd =C1(0.5-C2)+u ck[{(f -f )+(f -f )} {p/200f )}xst ct sc cc ck(D/2 - d')

Similarly when the neutral axis lies inside the section the expression for the interaction diagram may be written as:

P /f bd = 0.36K+u ck[{(f -f ) + (f -f )}{p/200f )} xst ct sc cc ck

2M /f bd = 0.36k(0.5 - 0.416k) +cku[{(f -f ) + (f -f )}{p/(200f )) xctst s cc cc k(d/2-d')]

WhereK depth of neutral axis/DC-1 coefficient for the area of stress blockC2 the distance of the centroid of the stress block

measured from the highly compressed edge.P total percentage of reinforcement required.fsc stress in reinforcement nearest to the maximum

stressed edge of the section.fst stress in reinforcement farthest to the maximum

stressed edge of the section.fcc stress in.concrete nearest to the maximum

stressed edge of the section.fct stress in concrete farthest to the maximum

stressed edge of the section.

For this, a program was written in AutoLISP for reading the value of P / f bd u ck2and M /f bd for different values of p/f Charts have been prepared for four u ck ck

grades of steel and four values of d'/d.


99

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

4.0

3.0

2.0

1.0

00 3 10 12 14 16 18 20 22 24 26

fy

415

500

550

fck

15

20

25

30

2

g8

0c

k=

00m

7000

6000

5000

4000

3000

0250

0002

0150

1 000

050

2

fc

Nm

k=15

/m20

25

30

Re

info

rce

me

nt

Pe

rce

nta

ge

, 1

00

As/

Ag

L

oa

d P

,KN

2Pu/Ag,N/mm

CHART 1- AXIAL COMPRESSION


100

D

b

dd

2fy=415 N/mm d'/D=0.05

TMT415

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.55

Pu

/ fck

bD

CHART 2 - COMPRESSION WITH BENDING( Rectangular Section - Reinforcement Distrusted equally in two sides)

0.28

260.

0.24

.2

02

0.200.180.160.410

2.1

100.

0.8

.06

0.4

.20

0

Axis of bending

As=pbD/100

Mu / fck bD2


101

D

b

dd

2fy=415 N/mm d'/D=0.15

TMT415

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.55

Pu

/ fck

bD


0.28

20.

60.240.220.020.180.160

4.1

20.1

100.

0.8

0.6

0.4

.20

0

Axis of bending

As=pbD/100

Mu / fck bD2


102

D

b

dd

2fy=415 N/mm d'/D=0.15

TMT415

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.55

Mu / fck bD2

Pu

/ fck

bD


0.28

20.

60.240.220.020.180.160

4.1

20.1

100.

0.8

0.6

0.4

.20

0

Axis of bending

As=pbD/100


103

TMT415

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.55

Pu

/ fck

bD


0.28

260.

0.24

.2

02

0.200.180.160.410

2.1

100.

0.8

.06

0.4

.20

0

D

b

dd

2fy=415 N/mm d'/D=0.05

Axis of bending

As=pbD/100

Mu / fck bD2


104

TMT500

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6

Pu

/ fck

bD


0.28

260.

0.240.22

.0 200.180.16

40.10.12

100.

0.8

.06

0.40.2

0

D

b

dd

2fy=500 N/mm d'/D=0.05

Axis of bending

As=pbD/100

2Mu / fck bD


105

TMT500

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.55

Pu

/ fck

bD


/k0.

8

pf c

2.260

0.240.22

.0 200.180.16

40.10.12

100.

0.8

.06

0.40.2

0

2Mu / fck bD

D

b

dd

2fy=500 N/mm d'/D=0.05

Axis of bending

As=pbD/100


106

TMT500

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5

Pu

/ fck

bD


/k0.

8

pf c

2.260

0.240.22

.0 200.180.16

40.10.12

100.

0.8

.06

0.40.2

0

2Mu / fck bD

D

b

dd

2fy=500 N/mm d'/D=0.05

Axis of bending

As=pbD/100


107

TMT500

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5

Pu

/ fck

bD


k.

8

p/fc02

.260

0.240.22

.0 200.180.16

40.10.12

100.

0.8

.06

0.40.2

0

2Mu / fck bD

D

b

dd

2fy=500 N/mm d'/D=0.05

Axis of bending

As=pbD/100


108

TMT550

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Pu

/ fck

bD


p/ ck0.2

f

8

0.260.240.22

00.20

1. 8016.

40.10.120.100.8

0.60.4

20.

0

2Mu / fck bD

D

b

dd

2fy=500N/mm d'/D=0.05

Axis of bending

As=pbD/100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


109

TMT550

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Pu

/ fck

bD


p/ ck0.2

f

8

0.260.240.22

00.20

1. 8016.

40.10.120.100.8

0.60.4

20.

0

2Mu / fck bD

D

b

dd

2fy=500N/mm d'/D=0.05

Axis of bending

As=pbD/100

0 0.1 0.2 0.3 0.4 0.5 0.6


110

TMT550

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Pu

/ fck

bD


p/ ck0.2

f

8

0.260.240.22

00.20

1. 8016.

40.10.120.100.8

0.60.4

20.

0

2Mu / fck bD

D

b

dd

2fy=550N/mm d'/D=0.15

Axis of bending

As=pbD/100

0 0.1 0.2 0.3 0.4 0.5 0.55


111

TMT550

1.5

1.4

1.3

1.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Pu

/ fck

bD


p

0.

/fck28

0.620

4.2

.220

.0

020

1. 80.164

0.10.120.100.8

0.60.4

20.

0

2Mu / fck bD

D

b

dd

2fy=550N/mm d'/D=0.20

Axis of bending

As=pbD/100

0 0.1 0.2 0.3 0.4 0.5


112

CHAPTER - 5

Shear and Torsion


113

5.1 Since, there is no change in the design shear stresses of TMT rebars form that of CTD/TOR bars, the tables are prepared as per SP-16 and there is no change in tables form those in SP-16. Since 6mm bars (both CTD/TOR bars and TMT rebars) are not being manufactured in Nepal. They have not been included in the design tables.


114

2Table 17 Shear - Design Shear Strength of Concrete, Tc' N/mm fck (N/sqmm)

pt 15 20 25 30 35 40

0.200.250.300.35

0.39170.35120.37870.4031

0.32620.35920.38810.4139

0.33080.36480.39460.4214

0.33680.37220.40340.4316

0.33410.36890.39960.4271

0.33890.37480.40660.4352

0.400.450. 00.55

5

0.42510.44520.46370.4809

0.43730.45870.47850.4969

0.44580.46820.48890.5082

0.45730.48090.50290.5235

0.45220.47530.49670.5167

0.46140.48550.50800.5290

0.600.650.700.75

0.49680.51180.52590.5391

0.51410.53030.54550.5600

0.52630.54340.55950.5748

0.54280.56110.57840.5949

0.53550.55330.57010.5860

0.54880.56750.58530.6022

0.800.850.900.95

1.001.051.101.15

1.201.251.301.35

1.401.451.501.55

1.601.651.701.75

1.801.851.901.95

2.002.252.302.35

0.55170.56360.57500.5858

0.59620.60610.61560.6247

0.63350.64190.65010.6579

0.66550.67280.67990.6868

0.69350.70000.70620.7113

0.71130.71130.71130.7113

0.71130.71130.77130.7713

0.57370.58680.59920.6111

0.62250.63350.64400.6542

0.66390.67340.68250.6913

0.69980.70810.71610.7239

0.73150.73880.74600.7529

0.75970.76630.77270.7790

0.78510.79110.79700.8027

0.58930.60320.61650.6292

0.64140.65310.66440.6753

0.68590.69600.70590.7154

0.72460.73360.74230.7508

0.75900.76700.77480.7824

0.78990.79710.80420.8111

0.81780.82440.83080.8371

0.61060.62570.64010.6539

0.66730.68010.69250.7044

0.71600.72720.73810.7487

0.75890.76890.77860.7881

0.79730.80620.81500.8236

0.83190.84010.84810.8559

0.86350.87100.87830.8855

0.60120.61570.62960.6430

0.65580.66810.68000.6915

0.70260.71340.72380.7339

0.74370.75320.76250.7715

0.78020.78880.79710.8052

0.81320.82090.82850.8359

0.84310.85020.85710.8639

0.61840.63380.64870.6629

0.67670.68990.70270.7151

0.72700.73870.74990.7609

0.77150.78150.79190.8017

0.81130.78150.82980.8387

0.84740.85590.86430.8724

0.88040.88820.89590.9034

2.002.252.302.35

2.602.652.702.75

2.802.852.902.95

3.003.053.103.15

0.71130.77130.77130.7713

0.71130.71130.71131.1173

0.71130.71130.71131.1173

0.71130.71130.71131.1173

0.80820.81370.81900.8214

0.80820.81370.81900.8214

0.80820.81370.81900.8214

0.80820.81370.81900.8214

0.84330.84940.85530.8611

0.88840.89360.89870.9036

0.90850.91330.91810.9183

0.90850.91330.91810.9183

0.89250.89950.90620.9129

0.94430.95030.95620.9620

0.96760.97320.97870.9841

0.98950.99470.99990.0050

0.87060.87710.88350.8897

0.91930.92490.93040.9358

0.94120.94640.95150.9566

0.96160.96650.97130.9761

0.91080.91800.92510.9321

0.96520.97150.97770.9837

0.98970.99581.00141.0071

1.01281.01831.02381.0291


115

Table 22 Shear - Vertical Sirrups Values of Vus/D For Two Legged Stirrups, Kn/Cm

Stirrupspacing

cmDiameter, Mm

6

Fy = 250 N/Sqmm

8 10 12 8 10 12 14

Diameter, Mm

Fy = 415 N/Sqmm (CTD &TMT)

56789

10

2.45992.04991.75701.53741.36661.2299

1.37313.04993.12362.73322.42952.1865

6.83305.69414.88074.27063.79613.4165

9.83958.19967.02826.14975.46644.9197

7.25936.04955.18524.53714.03303.6297

11.34279.45238.10197.08926.30155.6714

16.333513.611311.666810.20849.07428.1668

22.231718.526415.879813.894812.351011.1159

56789

10

1112131415

1.11811.02490.94610.87850.8200

1.98781.82211.68201.56181.4577

3.10592.84712.62812.44032.2777

4.47254.09983.78443.51413.2798

3.29973.02472.79212.59262.4198

5.15584.72614.36264.05103.7809

7.42436.80566.28215.83345.4445

10.10539.26328.55077.93997.4106

1617181920

0.76870.72350.68330.64730.6150

1.36661.28621.21471.15081.0933

2.13532.00971.89801.79811.7082

3.07482.89402.73322.58932.4599

2.26852.13512.01651.91041.8148

3.54463.33613.15082.98492.8357

5.10424.80404.52714.29834.0834

6.94746.53876.17555.85055.5579

2122232425

0.58570.55910.53480.51250.4920

1.04120.99390.95070.91110.8446

1.62691.55291.48541.42351.3666

2.34272.23622.13902.04991.9679

1.72841.64991.57811.51241.4519

2.70062.57792.46582.36312.2685

3.88893.71223.55083.40283.2667

5.29335.05274.83304.63164.4463

2627282930

0.47310.45550.43930.42410.4100

0.84100.80980.78090.75400.7288

1.31401.26541.22021.17811.1388

1.89221.82211.75701.69651.6399

1.39601.34431.29631.25161.2099

2.18132.10052.02552.95561.8905

3.14113.02472.91672.81612.7223

4.27534.11703.97003.83313.7053

3132333435

0.39680.38440.37270.36170.3514

0.70530.68330.66260.64310.6247

1.10211.06771.03531.00480.9761

1.58701.53741.49081.44701.4056

1.17091.13431.09991.06761.0370

1.82951.77231.71861.66801.6204

2.63442.55212.47482.40202.3334

3.58583.47373.36843.26943.1760

3637383940

0.34160.33240.32370.31540.3075

0.60740.59100.57540.65070.5466

0.94900.92340.89910.87600.8541

1.36661.32971.29471.26151.2299

1.00820.98100.95520.93070.9074

1.57541.53281.49251.45421.4178

2.26852.20722.14912.09402.0417

3.08773.00432.92522.85022.7790

4142434445

0.30000.29230.28600.27950.2733

0.53330.52060.50850.49690.4859

0.83330.81340.79450.77650.7592

1.19991.17141.14411.11811.0933

0.88530.86420.84410.82490.8066

1.38331.35031.31891.28891.2603

1.99191.94451.89921.85611.8148

2.71122.64662.58512.52632.4702

4647484950

0.26740.26170.25620.25100.2460

0.47530.46520.45550.44620.4373

0.74270.72690.71180.69720.6833

1.06951.04681.02491.00400.9839

0.78910.77230.75620.74070.7259

1.23291.20671.18151.15741.1343

1.77541.73761.70141.66671.6334

2.41652.36512.31582.26852.2232


116

Table 23 Shear -Bent - up Bars

Bar Diameter mm Bending Angle

Fy = 250 Mpa

ALPHA = 45 ALPHA = 60

Bending Angle

Fy = 415 Mpa

ALPHA = 45 ALPHA = 60

10

12

16

20

22

25

28

32

12.0791

17.3939

30.9225

48.3164

58.4618

75.4943

94.7000

123.6899

14.7938

21.3031

37.8721

59.1752

71.6020

92.4613

115.9834

151.4885

20.0513

51.3313

80.2051

97.0482

125.3205

205.3252

259.8647

320.8206

24.5577

35.3631

62.8677

98.2308

118.8593

153.4857

192.5324

251.4709


117

CHAPTER - 6

Development

Length & Anchorage


118

6.1 Since the surface characteristics of TMT rebars and CTD/TOR bars are similar, the bond characteristics will be similar as well. Hence, the tables for development length and anchorage will be same as given in SP-16. However, one table has been presented in this handbook for TMT 550. (Table 23).

Table 20- Development of Length fo fully stressed plain Bars

2f = 250 N/mm for bars up to 20mm diametery 2 = 240 N/mm for bars up over 20mm diameterTabulated values are in cm.

Bar Diameter

mm

Grade of Concrete

Tension Bars

M 15 M 20 M 25 M 30

Grade of Concrete

Compression Bars

M 15 M 20 M 25 M 30

Bar Diameter

mm

Grade of Concrete

Tension Bars

M 15 M 20 M 25 M 30

Grade of Concrete

Compression Bars

M 15 M 20 M 25 M 30

68

10121618202225283236

Note: The Development Length Given Above For A Stress Of 0.87 Fy in the bar


32.643.554.465.387.097.9

108.8114.8130.5146.2167.0187.9

27.236.345.354.472.581.690.695.7

1.808121.8139.2156.6

23.331.138.846.662.169.977.782.093.2

104.4119.3134.2

21.829.036.343.558.065.372.576.682.097.4111.4125.3

26.134.843.552.269.678.387.091.9

104.4116.9133.6150.3

21.829.036.343.558.065.372.576.697.4111.4125.3

17.423.229.034.846.452.258.061.269.678.089.1

100.2

810121618202225283236

45.156.467.790.3

101.5112.8124.1141.0158.0180.5203.1

37.647.056.475.284.694.0

103.4117.5131.5150.4169.2

32.240.348.464.572.580.688.7

100.7112.3128.9145.1

30.137.645.160.267.775.282.794.0

105.3120.4135.4

36.145.154.272.281.290.399.3112.8126.4144.4162.5

25.832.238.751.658.064.570.980.690.3

103.2116.1

24.130.136.148.154.260.266.275.284.296.3

108.3

18.624.931.137.349.755.962.165.274.683.595.5

107.4

30.137.645.160.267.775.282.794.0

105.3120.4135.4

Table 21 - Development Lengths For Fully Stressed Deformed / TMT Bars


118

Bar Diameter

mm

Grade of Concrete

Tension Bars

M 15 M 20 M 25 M 30

Grade of Concrete

Compression Bars

M 15 M 20 M 25 M 30

81012


Table 22 - Development Lengths For Fully Stressed Deformed / TMT Bars Fy = 500n/Sqmm

Tabulated Values Are in cm

54.468.081.6

45.366.668.0

38.848.558.3

36.345.354.4

43.554.465.3

36.345.354.4

31.138.846.6

29.036.343.5

16182022

25283236

108.8122.3135.9149.5

169.9190.3217.5244.7

90.6102.0113.3124.6

141.6158.6181.3203.9

77.787.497.1

106.8

121.4135.9155.4174.8

72.581.690.699.7

113.3126.9145.0163.1

87.097.9

108.8119.6

135.9152.3174.0195.8

72.581.690.699.7

113.3126.9145.0163.1

62.169.977.785.4

97.1108.8124.3139.8

58.065.372.579.0

90.6101.5116.0130.5

Bar Diameter

mm

Grade of Concrete

Tension Bars

M 15 M 20 M 25 M 30

Grade of Concrete

Compression Bars

M 15 M 20 M 25 M 30

81012


Table 23 - Development Lengths For Fully Stressed Deformed / TMT Bars Fy = 550n/Sqmm

Tabulated Values Are in cm

59.874.889.7

49.862.374.8

42.753.464.1

39.949.859.8

47.959.871.8

39.949.859.8

34.242.751.3

31.939.947.9

16182022

25283236

119.6134.6149.5164.5

186.9209.3239.3269.2

99.7112.1124.6137.1

155.8174.5199.4224.3

85.496.1

106.8117.5

133.5149.5170.9192.3

79.889.799.7

109.7

124.6139.6159.5179.4

95.7107.7119.6131.6

149.5167.5191.4215.3

79.889.799.7

109.7

124.6139.6159.5179.4

68.476.985.494.0

106.8119.6136.7153.8

63.871.879.887.7

99.7111.7127.6143.6


120

Conversion Table

Annexure I

UNIT EQUIVALENCE

Length

Area

Volume

Force

Force per unit length

Pressure/Stress

Force per unit Volume

Moment

1m

1sq.m.

1cu.m.

1kg

1kg.\M.

1kg./Sq.m.

1kg./cu.m.

1kg.m.

100 cm

10,000 sq. cm

1,000,000 cu. cm

9.807 N

9.807 N/m

9.807/sq.m

9.807 N/cu.m

9.807 N.m


121

Annexure II

Perimeter

Wt.Kg \ m.

No. of

Bars

18.85 25.13 31.42 37.7 43.98 50.27 62.83 69.12 78.54 87.965 100.53 113.1

0.222 0.395 0.617 0.888 1.208 1.578 2.466 2.984 3.853 4.8337 6.3133 7.9903

Bar Diameter, mm

6 8 10 12 14 16 20 22 25 28 32 36

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

2Areas Of Given Numbers Of Bars In cm

0.28

0.57

0.85

1.13

1.41

1.70

1.98

2.26

2.54

2.83

3.11

3.39

3.68

3.96

4.24

4.52

4.81

5.09

5.37

5.65

0.50

1.01

1.51

2.01

2.51

3.02

3.52

4.02

4.52

5.03

5.53

6.03

6.53

7.04

7.54

8.04

8.55

9.04

9.55

10.05

0.79

1.57

2.36

3.14

3.93

4.71

5.50

6.28

7.07

7.85

8.64

9.42

10.21

11.00

11.78

12.57

13.35

14.14

14.92

15.71

1.13

3.08

4.62

6.16

7.70

9.24

10.78

12.32

13.85

15.39

16.93

18.47

20.01

21.55

23.09

24.63

26.17

27.71

29.25

30.79

1.13

3.08

4.62

6.16

7.70

9.24

10.78

12.32

13.85

15.39

16.93

18.47

20.01

21.55

23.09

24.63

26.17

27.71

29.25

30.79

2.01

4.02

6.03

8.04

10.05

12.06

14.07

16.08

18.10

20.11

22.12

24.13

26.14

28.15

30.16

32.17

34.18

36.19

38.20

40.21

3.14

6.28

9.42

12.57

15.71

18.85

21.99

25.13

28.27

31.42

34.56

37.70

40.84

43.98

47.12

50.27

53.41

56.55

59.69

62.83

3.80

7.60

11.40

15.21

19.01

22.81

26.61

30.41

34.21

38.01

41.81

45.62

49.42

53.22

57.02

60.82

64.67

68.42

72.23

76.03

4.91

9.82

14.73

19.63

24.54

94.45

34.36

39.27

44.18

49.09

54.00

58.90

63.81

68.72

73.63

78.54

83.45

88.36

93.27

98.17

6.16

12.32

18.47

24.63

30.79

36.95

43.10

49.26

55.42

61.58

67.73

73.89

80.05

86.21

92.36

98.52

104.68

110.84

116.99

123.15

8.04

16.06

24.13

32.17

40.21

48.25

56.30

64.34

72.38

80.42

88.47

96.51

104.55

112.59

120.64

128.68

136.72

144.76

152.81

160.85

10.18

20.36

30.54

40.72

50.89

61.07

71.25

81.43

91.61

101.79

111.97

112.15

132.32

142.50

152.68

162.86

173.04

183.22

193.40

203.58


122

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

5.65

4.71

4.04

3.53

3.14

2.83

2.57

2.36

2.17

2.02

1.88

1.77

1.66

1.57

1.49

1.41

1.35

1.29

1.23

1.18

1.13

1.09

1.05

1.01

0.97

0.94

0.91

0.88

0.86

0.83

0.81

0.79

0.76

0.74

0.72

0.71

10.05

8.38

7.18

6.28

5.59

5.03

4.57

4.19

3.87

3.59

3.35

3.14

2.96

2.79

2.65

2.51

2.39

2.28

2.19

2.09

2.01

1.93

1.86

1.80

1.73

1.68

1.62

1.57

1.52

1.48

1.44

1.40

1.36

1.32

1.29

1.26

15.71

13.09

11.22

9.82

8.73

7.85

7.14

6.54

6.04

5.61

5.24

4.91

4.62

4.36

4.13

3.93

3.74

3.57

3.41

3.27

3.14

3.02

2.91

2.80

2.71

2.62

2.53

2.45

2.38

2.31

2.24

2.18

2.12

2.07

2.01

1.96

22.62

18.85

16.16

14.14

12.57

11.31

10.28

9.42

8.70

8.08

7.54

7.07

6.65

6.28

5.95

5.65

5.39

5.14

4.92

4.71

4.52

4.35

4.19

4.04

3.90

3.77

3.65

3.53

3.43

3.33

3.23

3.14

3.06

2.98

2.90

2.83

30.79

25.66

21.99

19.24

17.10

15.39

13.99

12.83

11.84

11.00

10.26

9.62

9.06

8.55

8.10

7.70

7.33

7.00

6.69

6.41

6.16

5.92

5.70

5.50

5.31

4.97

4.81

4.66

4.53

4.40

4.28

4.16

4.05

4.05

3.95

3.85

40.21

33.51

28.72

25.13

22.34

20.11

18.28

16.76

15.47

14.36

13.40

12.57

11.83

11.17

10.58

10.05

9.57

9.14

8.74

8.38

8.04

7.73

7.45

7.18

6.93

6.70

6.49

6.28

6.09

5.91

5.74

5.59

5.43

5.29

5.16

5.03

62.83

52.36

44.88

39.27

39.91

31.42

28.56

26.18

24.17

22.44

20.94

19.63

18.48

17.45

16.53

15.71

14.96

14.28

13.66

13.09

12.57

12.08

11.64

11.22

10.83

10.47

10.13

9.82

9.52

9.24

8.98

8.73

8.49

8.27

8.06

7.85

76.03

63.36

54.30

47.52

42.24

38.01

34.56

31.68

39.24

27.15

25.34

23.76

22.36

21.12

20.01

19.01

18.10

17.28

16.53

15.84

15.21

14.62

14.08

13.58

13.11

12.67

12.26

11.88

11.52

11.18

10.86

10.56

10.27

10.00

9.75

9.50

76.03

63.36

54.30

47.52

42.24

38.01

34.56

31.68

39.24

27.15

25.34

23.76

22.36

21.12

20.01

19.01

18.10

17.28

16.53

15.84

15.21

14.62

14.08

13.58

13.11

12.67

12.26

11.88

11.52

11.18

10.86

10.56

10.27

10.00

9.75

9.50

123.15

102.63

87.96

76.97

68.42

61.58

55.98

51.31

47.37

43.98

41.05

38.48

36.22

34.21

32.41

30.79

29.32

27.99

26.77

25.66

24.63

23.68

22.81

21.99

21.23

20.53

19.85

19.24

18.66

18.11

17.59

17.10

16.64

16.20

15.79

15.39

160.85

134.04

114.89

100.53

89.36

80.42

73.11

67.02

61.87

67.45

53.62

50.27

47.31

44.68

42.33

40.21

38.30

36.56

34.97

33.51

32.17

30.93

29.79

28.72

27.73

26.81

25.94

25.13

24.37

23.65

22.98

22.34

21.74

21.16

20.62

20.11

203.58

169.65

145.41

127.23

113.10

101.79

92.53

84.82

78.30

72.71

67.86

63.62

59.88

56.55

53.57

50.89

48.47

46.27

44.26

42.41

40.72

39.15

37.70

36.35

35.10

33.93

32.83

31.81

30.84

29.94

29.08

28.27

27.51

26.79

26.10

25.45

Areas Of Given Bars at Given Spacings.2Values in cm per meter width

6 8 10 12 14 16 20 22 25 28 32 36cm.

Spacing Bar Diameter, mm


123

Fixed End MomentsBuilt-in Beams of Constant Cross Section

Annexure I

Loadings Values of + M & MA B

Total U.D.L =W

Total U.D.L =W

W

A B

A B

A B

A B

A B

A B

A B

P

a b

W

a b

a b

P

a b

Frame 1


124

B

h

A

CL2

D

L1

L

Frame Data

Coefficients

kl2l1

=h

L

N1 = K+2 N =6k+12

B

h

A

C

L

Frame Data

W per Unit Length

A D

B

B C+

L/2 2Wll

HA

VA

MA

H0

M0

V0

2M = M = WLA 0

12N1

2M = M = WLB C

6N1

2M = Wlmax

8

2V = V = WlA 0

2

=29MA

H =H =3MA D A

h

B

h

C

L

A D

W p

er

Un

it L

en

gth

A DMA

VA

H0

M0

V0

HA

B c

h/2+

-2

Wh /8

-

+

2M = WhA

4 [-k+36N1

4k+1N2 [

2M = Wh0

4 [-k+36N1

4k+1N2 [

+

+

2M = WhB

4 [-2k

6N1

2kN2 [

2M = WhA

4 [ k6N1

2kN2 [

+

+

2 V = -V =A 0

2Wh LN2

H =0

2/2k+3bWh 8N1

H = -A Wh- HD[ [


125

MA

PLLM1

=

B

h

A

CL2

D

L1

L

L/2

P

MO

VA= VO

P

2

MA= MO 2MA

HA= HO

3MA

h=

- +

+- -

+ +A D

HA

MAVA

HO

MO

VO

4

PL

C

L/2h / 3

MA

Ph

2=

B

h

A

CL2

D

L1

L

P

+3k+1

N2

MC

Ph

2= +

3k+1

N2

MA

Ph

2= +

3k+1

N2

MC

Ph

2= +

3k

N2

MA= -HD +-P

2VA= -

2MD

LVD =

B C

L/2

+

-

-

- +A DMA

VA

HA HD

MD

VD

B

h

A

CL2

D

L1

L

P ba

Pab

L

B C

A D

- + -

+ +HA

MA

VA

HD

MD

VD

a - a/L b1=b/L1

M = +A

Pab

L [ 1

2N1

b -a1 1

2N1

[M = +D

Pab

L [ 1

2N1

b -a1 1

2N1

[

M = +C

Pab

L [ 1

2N1

b -a1 1

2N1

[ V = +A Pb1 [1+V a (b -a )D 1 1 1 [N2

M = +C

Pab

L [ 1

2N1

b -a1 1

2N1

[ V = P- V H = HD A A D

3Pab

2LhN1


126

Annexure IVSubstitution Tables For Using HAMA 500 Bars in Place of

CTD/TOR Bars in CompressionBar DIA. 12

1

2

3

4

5

6

7

8

9

10

No. Area of

CTDRqd. Area of

CTDReplacement Alternatives Actual Area

Bar DIA. 14

1

2

3

4

5

6

7

8

9

10

No.Area of

CTDRqd. Area of


Bar DIA. 16

1

2

3

4

5

6

7

8

9

10

No. Area of

CTDRqd. Area of


1.13

2.26

3.39

4.52

5.65

6.79

7.92

9.05

10.18

11.31

1.00

1.99

2.99

3.99

4.99

5.98

6.98

7.98

8.98

9.97

1 TMT-12

2 TMT-12

2 TMT-14

2 TMT-16

2 TMT-16 + 1 TMT-12

4 TMT-14

1 TMT-18 + 4 TMT-12

4 TMT-14 + 2TMT-12

8 TMT-12

9 TMT-12

1.13

2.26

3.08

4.02

5.15

6.16

7.07

8.42

9.05

10.18

1.54

3.08

4.62

6.16

7.70

9.42

10.78

12.32

13.85

15.39

1.36

2.72

4.07

5.43

6.79

8.15

9.50

10.86

12.22

13.58

1 TMT-14

2 TMT-14

2 TMT-14 + 1 TMT-12

2 TMT-16 + 1 TMT-14

3 TMT-14 + 2 TMT-12

4 TMT-14 + 2 TMT-12

4 TMT-14 + 3 TMT-12

4 TMT-16 + 2TMT-14

8 TMT-14

6 TMT-14 + 4TMT-12

1.54

3.08

4.21

5.56

6.88

8.42

9.55

11.12

12.32

13.76

1 TMT-16

1 TMT-16 + 1 TMT-12

2 TMT-16 + 1 TMT-14

3 TMT-16 + 1 TMT-12

2 TMT-18 + 1 TMT-16

3 TMT-18 + 1 TMT-14

4 TMT-18 + 1 TMT-12

4 TMT-16 + 1 TMT-14

8 TMT-16

5 TMT-16 + 5 TMT-14

2.01

4.02

6.03

8.04

10.05

12.06

14.07

16.08

18.10

20.11

1.77

3.55

5.32

7.09

8.87

10.64

12.41

14.18

15.96

17.73

2.01

3.55

5.56

7.16

9.11

10.71

12.44

14.20

16.08

17.75


127

Substitution Tables For Using HAMA 500 Bars in Place of CTD/TOR Bars in Compression

Bar DIA. 18

1

2

3

4

5

6

7

8

9

10

No. Area of

CTDRqd. Area of


2.54

5.09

7.63

10.18

12.72

15.27

17.81

20.36

22.90

25.45

2.24

4.49

6.98

8.98

11.22

13.46

15.71

17.95

20.20

22.44

1 TMT-18

1 TMT-18 + 1 TMT-16

2 TMT-18 + 1 TMT-16

2 TMT-18 + 2 TMT-16

4 TMT-20 + 1 TMT-12

3 TMT-20 + 2 TMT-16

5 TMT-20

4 TMT-20 + 3TMT-16

8 TMT-18

5 TMT-18 + 5 TMT-16

2.54

4.56

7.10

9.11

11.31

13.45

15.71

18.60

20.36

22.78

Bar DIA. 20

1

2

3

4

5

6

7

8

9

10

No. Area of

CTDRqd. Area of


3.14

6.28

9.42

12.57

15.71

18.85

21.99

25.13

28.27

31.42

2.77

5.54

8.31

11.08

13.85

16.62

19.39

22.16

24.93

27.70

1 TMT-20

1 TMT-20 + 1 TMT-18

2 TMT-20 + 1 TMT-16

3 TMT-16 + 2 TMT-18

2 TMT-18 + 3 TMT-18

3 TMT-18 + 2TMT-16

4 TMT-18 + 4 TMT-16

4 TMT-16 + 4TMT-18

8 TMT-16 +3 TMT-16

5 TMT-16 + 4 TMT-20

3.14

5.69

8.29

11.37

13.92

16.59

19.45

22.75

25.04

27.83

Bar DIA. 22

1

2

3

4

5

6

7

8

9

10

No. Area of

CTDRqd. Area of


3.80

7.60

11.40

15.21

19.01

22.81

26.61

30.41

34.21

38.01

3.35

6.70

10.06

13.41

16.76

20.11

23.47

26.82

30.17

33.52

1 TMT-22

1 TMT-22 + 1 TMT-20

2 TMT-22 + 1 TMT-18

3 TMT-22 + 1 TMT-16

4 TMT-22 + 1 TMT-14

3 TMT-22 + 1 TMT-20

3 TMT-22 + 1 TMT-20

4 TMT-25 + 1TMT-16

8 TMT-22

5 TMT-22 + 5 TMT-20

3.80

6.94

10.15

13.41

16.74

20.83

23.97

27.68

30.41

34.71


128

No. Area of

CTDRqd. Area of

CTDReplacement Alternatives

Actual Area

Substitution Tables For Using HAMA 500 Bars in Place of CTD/TOR Bars in Compression

Bar DIA. 25

1

2

3

4

5

6

7

8

9

10

4.91

9.82

14.73

19.63

24.54

29.45

34.36

39.27

44.18

49.09

4.33

8.66

12.99

17.32

21.64

25.97

30.30

34.63

38.96

43.29

1 TMT-25

1 TMT-25 + 1 TMT-22

2 TMT-25 + 1 TMT-20

2 TMT-25 + 2 TMT-22

4 TMT-25 + 1 TMT-16

4 TMT-25 + 2 TMT-20

4 TMT-25 + 3 TMT-22

4 TMT-25 + 4 TMT-22

6 TMT-25 + 3 TMT-20

5 TMT-25 + 5 TMT-22

4.91

8.71

12.96

17.42

21.65

25.92

31.04

34.84

38.88

43.55


129

No. of Bars Area Required Replacement

CTD 28 Grade: Fe 500

Substitution Tables For Reinforcing Bars( in Tens & Compression)

1

2

3

4

5

6

7

8

9

10

2 - TMT 20 OR 1 TMT 25 =TMT 14( 6.45 )( 6.28 )

4 - TMT 20 OR 2 TMT 22 +2 TMT 18( 19.8 )( 12.26 )

4 - TMT 25 OR 3 TMT 25 + 2TMT 18( 19.8 )(19.63 )

5 - TMT 25 + 4TMT 20 OR 2 TMT 25 + 4 TMT 22(25.01 )( 24.54 )

( )31.03( 30.82 )

( 37.10 )

9 - TMT 25 ( 44 ).17

10 - TMT 25 ( 49.08 )

10 - TMT 25 + 2 TMT 20 ( 55.36 )

13 - TMT 25 OR 12 TMT 25 +TMT 20( 62.04 )( 63.81 )

CTD 32

6.16

12.31

24.63

30.78

36.94

36.94

43.11

49.26

55.41

61.57

5 - TMT 25 + 4TMT 20 OR 4 TMT 25 + 3 TMT 22

5 - TMT 25 + 4TMT 20

No. of Bars Area Required Replacement

Grade: Fe 500

1

2

3

4

5

6

7

8

9

10

1 - TMT 25 + TMT 20 ( 8.05 )

2 TMT 25 + 2 - TMT 20 ( 16.10 )

5 - TMT 25 (24.54 )

5 - TMT 25 + 2- TMT 22 ( 32.14 )

( )404.6( 39.27 )

( 49.08 )

10 - TMT 25 +2 - TMT 22 ( 56.68 )

13 - TMT 25 OR 10 TMT 25 + 4 TMT 22 ( 63.81 )

15 - TMT 25 ( 73.63 )

14 - TMT 25 + 3 - TMT 22( 80.12 )

8.04

16.08

24.12

32.17

40.21

48.25

56.29

64.34

72.38

80.42

8 - TMT 25 OR 7 TMT 25 + 2 TMT 20

10 - TMT 25

( 64.28 )


SLNo

Type of Structure Remarks

Grade: Fe 500

Guidelines For Switching Over To HAMA 500 BarsFrom CTD/TOR Bars

130

Annexure V

1

2

3

4

5

6

7

8

9

10

11

12

13

1 Singly Reinforced Beams

Doubly Reinforced Beams

Axially Loades Columns

Columns subjected to uniaxial

Bending with compression

Columns subjected to Biaxial

Bending with compression

Tension Members

Shear

Anchor and Development length

Pedestals

Bunkers and Silos

Equipment Foundations

Walls

Stabs

No change

Compression reinforcement to be changed

Reinforcement to be redesigned

Columns to be redesigned

Columns to be redesigned

No change

No change

However, the bars may be welded with out any

preheating or loss of strength

Reinforcement to be changed

No change

No change

No change

No change


Ch

em

ica

l C

om

po

sit

ion

(3

.2)*

Ca

rbo

nS

ulp

hu

rP

ho

sp

ho

rus

Su

lph

ur

+P

ho

sp

ho

rus

HA

MA

Iro

n a

nd

Ste

el

NS

19

1 -

20

46

/ IS

17

86

- 1

98

5

Ph

ys

ica

l P

rop

ert

ies

(7

.1)*

Yie

ld S

tre

ss

(Min

)

At

0.2

%P

roo

f s

tre

ss

2 N

/mm

Elo

ng

ati

on

(Min

) %

Ma

nd

rel d

ia. (B

en

d T

es

t) (

Re

be

nd

te

st)

(8

.3\8

.4)*

Te

ns

il S

tre

ng

th(M

in)

D<

= 1

01

0<

d<

= 2

2

D=

dia

me

ter

of

ba

r2

N/m

mm

mm

m %

Ma

x

0.3

0

0.1

6-0

.25

0.3

0

0.1

6-0

.25

0.3

0

0.1

6-0

.25

0.0

60

0.0

50

0.0

55

0.0

50

0.0

55

0.0

50

(%M

ax

)

0.1

10

.06

0

0.0

50

0.0

55

0.0

50

0.0

55

0.0

50

0.1

00

0.1

05

0.1

00

0.1

00

0.1

00

0.0

20

.00

50

.00

5.0

.01

Gu

ara

nte

ed

We

lda

bilit

y -

0.0

25

% C

arb

on

Ma

x

(mm

)/ 2

Le

ng

th (

mm

) (4

.2)*

No

min

al D

ia (

mm

)Tra

ns

ve

rse

rib

(a

lon

e)

Min

. a

rea

of

rib

s

D =

Dia

me

ter

of

ba

r

Pu

ll-O

ut

(Bo

nd

Te

st)

Be

nd

Te

st

Re

Be

nd

Te

st

Ma

ss

Te

st

* R

efe

ren

ce

Cla

us

e N

o. O

f N

S 1

91

/ IS

17

86

- 9

5

10

<d

= 1

6

0.1

2d

0.1

5d

0.1

7d

Cla

us

e

4.7

*

8.3

*

8.4

*

6.2

*

8.2

*

Re

fere

nc

e

IS:

27

70

(P

art

)-1

96

7

Bo

nd

Le

ng

th

Bo

nd

Str

en

gth

IS:

15

99

-19

74

IS:

15

99

-19

74

IS:

16

08

-19

72

41

5.0

41

5.0

50

0.0

50

0.0

50

0.0

50

0.0

41

.5

22

.0

12

.0

20

.0

8.0

18

.0

10

% m

ore

>=

48

5.0

10

% m

ore

>=

54

5.0

50

0.0

10

% m

ore

>=

58

5.0

58

0.0

63

0.0

3/S

d

1/4

d (

clo

se

r b

en

d/r

e b

en

d)

4/S

d

5/7

d

3/7

d

3/7

d

1/4

d (

clo

se

r b

en

d/r

e b

en

d)

5/8

d

1/4

d (

clo

se

r b

en

d/r

e b

en

d)

To

lera

nc

e%

of

No

rmin

al M

as

s (

6.2

)*Te

st

Sa

mp

le Q

ty.

Ba

tch

Ind

iviu

al

He

at/

ca

st<

10

0 H

ea

t/c

as

t.1

00

tC

oll

(+)

(-)

7

(+)

(-)

5

(+)

(-)

3

(+)

8

(+)

6

(+)

4

(+)

(-)

8

(+)

(-)

6

(+)

(-)

4

1N

u .fo

r 2

5t 1

Nu

.fo

r 4

0t

1N

u .fo

r 3

5t 1

Nu

.fo

r 4

5t

1N

u .fo

r 4

5t 1

Nu

.fo

r 5

0t

= 5

x d

ia o

f b

ar

I) lo

ad

at

me

as

ure

slip

0.0

25

mm

> 4

0%

w.r

.t p

lain

ba

r

II)

loa

d a

t m

ea

su

re s

lip

0.0

25

mm

> 8

0%

w.r

.t p

lain

ba

r

Re

f. T

ab

le a

bo

ve

Re

f. T

ab

le a

bo

ve

Re

f. T

ab

le a

bo

ve

Te

ns

ile

str

en

gth

, 0

.2%

pro

of

str

es

s %

elo

ng

ati

on

131

P <

22

mm

Fe

41

5

TM

T 4

15

Fe

50

0

TM

T 5

00

Fe

55

0

TM

T 5

50

Va

ria

tio

n

D<

= 1

0

Te

sti

ng

Te

ns

ile

D<

d =

16

3/7

d

5/7

d

6/8

d


132

Reinforcement Characteristics

Nominal SizeCross-Sectional

AreaMass per meter Perimeter Length per ton

( meter )( cm )( Kg/meter )2( cm )( mm )

6

7

8

8.7

9

10

10.5

11

12

14

16

18

20

22

25

28

32

36

40

45

50

0.283

0.385

0.503

0.595

0.636

0.786

0.866

0.951

1.131

1.540

2.011

2.546

3.143

3.803

4.911

6.160

8.046

10.183

12.571

15.911

19.643

0.222

0.302

0.395

0.467

0.500

0.617

0.680

0.746

0.888

1.209

1.579

1.998

2.467

2.985

3.855

4.836

6.316

7.994

9.869

12.490

15.420

0.222

0.302

0.395

0.467

0.500

0.617

0.680

0.746

0.888

1.209

1.579

1.998

2.467

2.985

3.855

4.836

6.316

7.994

9.869

12.490

15.420

4504

3309

2533

2142

2002

1621

1471

1340

1126

827

633

500

504

335

259

207

158

125

101

80

65

Bend Test


133

D

Support

TMT 500

D

Support

TMT 5

00

90

Support

TM

T 5

00

180

D = Mandrel - Diammeter

The bend test shall be performed in accordance with the requirements of NS 333 - 2050 and the mandrel diameter shall be as specified in table.The specimen shall be considered to have passed the test if there is no transverse crack in the bent portion.

Mandrel Diameter for Bend Test

Nominal Size Mandrel Diameter for Different Gradesmm Fe 415 Fe 500 Fe 550(1) (2) (3) (4) Up to and including 22 3 O 4 O 5 OOver 22 4 O 5 O 6 O

Documents

Inspiration - Hamasteel › wp-content › themes › franco...Provide4 - DIA25 +4-DIA12 =24.15 cm2 at bottom Provide 2 - DIA12 = 2.26cm 2 at top Designing for shear Provide dia 8