Detailed Calculation for Box Girder Design

REFERENCES 1. BS 5400 Part 2: 1978, Steel, Concrete and Composite Bridges- Specification for loads. 2. BS 5400 Part 4: 1990 Steel, Concrete and Composite Bridges- Code of Practice for Design of Concrete Bridges. 3. Jayasinghe M.T.R., Lecture Notes given forM. Eng. Degree Course in Structural Engineering Design. 4. Clark L.A., 1981 ,Concrete Bridge design to BS 5400, Construction Press London and New York. 5. Hurst M.K., Nanyang, Pre-Stresses Concrete Design, Technological Institute Singapore 6. User Manual, SAP 2000 V14 Integrated Solution for Structural Analysis and Design. 7. :; \'

',(.

8.

1ng1tj~i

!5orgicdc rJ~ti
!•

9.

II U.

10. Gee, A.F., "Bridge winners and losers", The Structural Engineer, Vol: 65 A, No 4, pp 141-145, 1987. 11. Burgoyne, C.J ., Jayasinghe, M. T.R., Rationalization of section design philosophy for prismatic pre-stressed concrete beams. 12. Swann, R.A ( 1972), "A future survey of concrete box spine-beam bridges", Technical Report 469, Cement and Concrete Association, London, 1972. 13. Podonly, W. & Muller, J.M., Construction and design ofpre-stressed concrete segmental

bridges, John Wiley & Sons, New York, 1982.

36

APPENDIXES APPENDIX 1- Manual calculation for box girder APPENDIX 2- Computer output of the box girder APPENDIX 3- Computer output of the doubleT beam APPENDIX 4- Comparison of the forces bending moment and stresses

37

CONTENTS OF MANUAL CALCULATION A. Notations and their descriptions

B. Load calculations C. Design of pre-stressed concrete Box Girder 1. Magnal Diagram 2. Calculation of number of ducts 3. Profile of individual ducts 4. Analysis of the Box Girder

5. Losses 6. Check for ultimate limit state 7. Design of End Blok and transverse reinforcement.

~efere nee

Description

Output

Data Density of Concrete,

Pc

Density of Screed Concrete,

P.vc

Density of Asphalt Concrete,

Pac

Pre stress Loss ratio,

R

= 24 = 24 = 23.6 = 0.8

Span of the bridge,

I

30

= 29 Carriageway width, = 7.4 Number of lanes =2 Width of the foot walk = 1500 Characteristic Concrete cube strength of the beam, feu = 50 Concrete strength at (initial) transfer( at the age of 7
s 540 0-4 199(

I able 20

::) 540 1-4

/e

kN/m 3 kN/m 3 kN/m 3

m m m

mm N/mm 2 N/mm 2 N/mm 2 N/mm 2 N/mm 2

Permissible stresses for class 2 member

199( 324

a (2' Allowable tensile stress at service,

larrin = 0.36xvfcu

= 50 = o.36xv5o = 2.55

Characteristic Concrete cube strength of the beam, feu

farrin

N/mm 3 N/mm2

farrin N/mm2

2.55 N/mm2

; 5401.) 4

Allowable tensile stress at transfer,

farrint

=1

N/mm2

199l

1

3.2.4 (1) Allowable compressive stress at service, 3.2

<

farmx

= Design load in Bending = 0.4xfcu = 0.4x50 N/mm2 = 20 N/mm2

!,

_ Triangular or near Triangular

fatmX

(a)

)ble,

5400 4

Allowable compressive stress at transfer,

DIIBX

t -

1990 3.2.2 :b)

1ble 2

fanint

farmxt

N/mm2

fatmX 20 N/mm2

rfic::trin11tinn nf c:tr<=>c::c::

= 0.5xfci = 0.5x36 = 18 s 0.4x50 s 20

buts 0.4xfcu

farm.xt N/mm2

18 N/mm2

Reference I

Description

I

Details of Precast section

Thckness of bottom flange

tb

Thckness of top flange

II

Thckness of one web

I,.

Width of the cantilever overhang

we

Width of bottom flange

wb

Width of top flange

WI

Overall depth of beam (Pre cast section)

hp

= 200 = 250 = 350 = 1000 = 3200 = 4400 = 1667

Number of web

N

=2

E5 ~ r~

mm mm mm mm mm mm mm

Cross section of the brigde .

_L

o.2sor0

''"~

I

M

0.350M

r=}-

~ 1.500M --1 __r_!l.225M

,.,~ 'l~r

I

f

o.200M

Output

2.500M - - - - - - j

~-200M 0.200..;-r-

0.200M

1

3.200M

Figure 1

Details of the Precast Section after grouting

I

4.400M

r

-r[

r

0.250r~

I ::Jf290M

0.350r1=

-J

0.3 50 M

~

~

Q.200M

+----il------

2.5001'1

~ Q.200M

0.200!'1

I

1

1-

Q.200M J 3.2001'1 Figure 2

.. _ _ _.___t_:__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___:__ _ _ _ _ _ _ _ _ _..J__ _____.

---- Reference 1

Description

I

Cross sectional Area,

AP

= 2.740E+06

mm 2

Total Depth,

hp

= 1.667E+03

mm

= 4.400E+03

mm

Total width of the top flange

wt

Total width of the bottom flange

wb

zpb

= 3.200E+03 = 7.150E+02 = 9.520E+02 = 1.016E+12 = 1.421E+09 = 1.067E+09

w pgl

--

wpgl

= 65.76

Height to the top fiber from the neutral axis.

Ypt

Height to the bottom fiber from the neutral axis,

Ypb

Second Moment of Inertia along x axis,

Jxp

Sectional Modulus of the top fiber,

zpt

Sectional Modulus of the bottom fiber

Weight of the beam per unit length,

Ac

Output

mm mm mm mm4 mm 3 mm 3

xpc xi

wpgl

I

kN/m

65.76 kN/m

Details of the Composite Sections

1.Edge beam I

1

~.350M t

-

5.200M

. O.OF. :)UM

L_Q.132M

~

I

_(r

0.200M

Q.J50M

2.500M

f.- 1.000M

__r__9.200M

I

I

f250M

c---

---------.......

0.200M

~

~

~1.667M

1-

0.200;-r-

I

3.200M

l

Figure 3

= 3.45E+06 = 1764 = 5200

mm

wclb

= 3200

mm

Yc1t

= 665

mm

Yclb

= 1099

mm

Moment of Inertia,

/xcl

= 1.31E+12

mm4

Seactional Modulus of the top fiber,

zeit

= 1.97E+09

mm 3

Sectional Modulus of the bottom fiber,

zclb

= 1.19E+09

mm3

Weight of the beam per unit length,

welgl

=A P x p c x 1 kN/m

Weigl

= 82.80


Ac

Total Depth,

hcl

Total width of the top flange,

welt

Total width of the bottom flange Height to the top fiber from the neutral axis, Height to the bottom fiber from the neutral axis,

mm

2

mm

kN/m

I I

Weigl

82.80 kN/m

Refer, :mce

Description

Output

Load CaJcuJations

Dead Loads Dead Loads due to grecast beam Weight of the beam per unit length,

wpgl

= 65.76

wpgl

kN/m

65.76 kN/m

Dead Loads due to comgosite beams 1.Edge beam Weight of the beam per unit length,

Weigl Weigl

= 82.80

kN/m

82.80 kN/m

Cross sectional Area of the Screed concrete,

Asci

Weight of the screed concrete per unit length of bea w sci wscl

= 7.15E+05 = AscxPscx1 = 17.16

mm

2

wscl

kN/m

17.16 kN/m

Super imposed dead loads Super imposed dead loads on edge beam

Cross sectional Area of the Asphalt concrete, Weight of the Asphalt concrete,

Aocl woe! woe!

= 1.85E+05 mm2 = Aocl X Poe X 1 = 4.37 kN/m

woe)

4.37 kN/m

Weight of the hand railings per unit length of beam,

whr

= 0.585

kN/m

whr

0.585 Cross sectonal area of the footwalk,

Afw

Weight of the footwalk,

wfw

= 3.38E+05 = AfwxPscx1 = 8.10

mm

2

kN/m wfw

kN/m

8.10 kN/m

Weight of the kerb per unit length of beam,

W.v

= 0.85

kN/m

Akr

0.85 kN/m HA Loading HA Uniformly Distributed Load (UDL) Carriage way width Number of notional lanes

) 5400 -4 1990

I 6.2

For loaded length up to 30 m HA UDL HA UDL per unit width of the beam

= 7.4 =2

m

= 30 = 30x2x29

kN/mllane

7.4x29

= 8.11

kN/m 2

--

Description

~efer' ence

Output

= 3700 = 8.11x3.7 = 30.00

Effective width for edge beam HA UDL on the edge beam

mm HAUDL kN/m

30.00 kN/m

's 54 00-4 19'

'()

d 6 {2

HA Knife Edge Load (KEL)

= 120 = 120x2

KEL Load for per notional lane KEL for a meter width of road

kN/Iane

7.4

Effective width for edge beam HA KEL on the edge beam

= 32.43

kN/m

= 3700 = 120.00

mm

KEL

kN

120.00 kN

S54 )0-4

199 D

71

1

(a)

Pedestrian Load

=5 Pedestrian load per beam per unit length of bear = 5x1.5 = 7.5

kN/m 2

Pedestrian load per beam

I

kN/m

7.5 kN/m

s 54 10-4

HB Loading

199 I.;

d6.

1

Case I

300

300

~

tR1

300

~

0

:1.8:

6.0

... 1.8 ...

300

i

R2

Figure 4 Where, 0 - Bridge Centre 300 a

...

b

v

...

~ - .~ l

...

_

Figure 5 From the theory ; q1

---

-------

-

= = = -

Pab I (a+b) 300*13.2*~30-13.2}

2217.6

30

2218

kNm

kNm

Description

~eference

Output

=

(q1 * Ll2)1b

=

1980

qo1

From Figure 5;

1980

kNm

kNm

300

Q02=CI29 L

......

Figure 6 From Figure 6;

q2

=qo2 = =

(P * L/2 * L/2) I L

2250

2250

kNm

kNm

~

a

~~

?

b

•

"

>

:

L Figure 7 From the theory;

q3

= =

Pab I (a+b)

300*21*(30-21! 30

=

1890

1890

kNm

kNm

qo3 =

From Figure 7 ;

=

(q3 * U2)1b

1350

1350

kNm

kNm

300 ~

a

b

.,

~ .....

L Figure 8

From the theory;

q4

= =

=

Pab I (a+b)

300*22.8*(30-22.8)

1641.6

30

1642

kNm

kNm

-----

-

Description

teference From Figure 8;

Moment @ mid span 0 ;

Output

qo4

=

(q4 * U2)/b 1080

mq1

= =

1080

kNm

kNm

qo1 + qo2 + qo3 + qo4

=

6660

kNm

6660 kNm

Similarlly; Case II

300

300

i

~

1R1

300

0

.1.8 .. 3.0 ~~ 3.0

300

u ~

i

1.8 ...

R2

Figure 9


mq2 = qo'1 + qo'2 + qo'3 + qo'4 qo4

=

6660

kNm

6660 kNm

Case Ill

300

300

300

u

LAo 1R1

... 1.8~ 1.5~~ 4.5

300

j

.. 1.8 ...

R2

Figure 10


mq3

= qo"1 + qo"2 -t qo"3 ; qo"4 =

6660

kNm

6660 kNm

Similarfly; Moment @ mid span A ;

mq4

= qo"11 +qo"22· qo"33 .+qo"44 =

6750

kNm

6750 kNm

Section Check 1.Edge beam Moment at mid span due to self weight of the beam, M gi

=

Wc 1g 1 x

2

1

8

M gl

= 65. 76x292 8

= 6913.02

kNm Mg2

Moment at mid span due to screed concrete,

Mg2

=

wscl

xP

8

6913.02 kNm

_ _ _ _ _.....__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.....J...-----1

··-·

Description

Reference

-

Mcz

Output

= 17.16x292 8

= 1803.95

Mcz kNm

1803.95 kNm

Moment at mid span due to Asphalt concrete

Macl

=

Wacl

X /2

8

= 4.37x292 8

= 458.98

Macl kNm

458.98 kNm

M

Moment at mid span due to hand railings

hr

= whr x/2 8

= 0.585x292 8

= 61.50

Mhr kNm

61.50 kNm

Moment at mid span due to footwalk

Mfw

= wfw x/2 8

= 8.10x292 8

= 851.51

Mfw

kNm

851.51 kNm

Moment at mid span due to kerbs

M~cr

= wkr x/2

8 = 0.85x292 8

= 89.36

Mkr kNm

89.36 kNm

Moments due to HA Moment at mid span due to HA UDL,

MHAUDLCI M HAUDLCI

= 3153.75

kNm

3153.75 kNm

Moment at mid span due to HA KEL,

M HAKELCI

= 870.00

kNm

MHAKELCI

870.00 Moment at mid span due to pedestrian load,

M PL =

788.44

kNm

kNm MPL

788.44

.

kNm

-·---·-

Description

Reference

Load

Output

Amount (KN/m)

Moment at mid span (KNm)

Unit weight of pre cast section, wpg1

65.76

6913.02

Unit weight of screed concrete, W5 c

17.16

1803.95

Unit weight of Asphalt concrete, Wac

4.37

458.98

a.."' E ro

Unit weight of handrails, Whr

0.585

61.50

L.

Unit weight of kerbs, Wkr

0.85

89.36

Unit weight of foot walk, Wrw

8.10

851.51

Uniformly distributed pedestrian live load

7.50

788.44

HA UDL on the beam

30.00

3153.75

HA KEL on the beam

120.00

870.00

"01/)

ro-o ro

G>

o.3 "0 Q)

If)

0

If)

-

0 ...J

Q)"'

-

a..ro

:::s

Q)

U)Q

If)

u

ro

0 ...J Q)

> ::::;

HB Loading - Case I

6660.00

HB Loading- Case II

6660.00

HB Loading- Case Ill(@ mid span)

6660.00

HB Loading -Case Ill(@ point "A")

6750.00

Table 1

Table 1

= =

Total moment due to HA loading Maximum moment due to HB loading

4023.75

kNm

6750.00

kNm

'

If compare the moments due to HA and HB, moment due to HB is the higher value than the moment due to HA loading. But for the design purpose should use moment due to HA loading.

By using Table 1

M gl

= 6913.02

Mgl

kNm

6913.02

Mg2

= 1803.95

kNm

kNm

M,,J x120

( M.., +M" +M1• + Mq = MHA UDL + MHAKEL +MPL xl.OO

= 7370.55

kNm

Mg2 1803.95 kNm

Mq 7370.55 kNm

--

-

L_ _____

.

----------

-

.

Description

~eference

Output

Design of prestressed concrete beam Design criterian:Stress in concrete should not exceed the allowable values during the life time of structure.

Sign convention: Axial compressive force positive Distances measured upwards from the neutral axis positive Compresive stress positive

Transfer condition stresses Top fiber (fur tensi on)

(Ap) + (-PxeJ (Mgz J 1

Z pi

+

2:: -fa mini

pi

(:) -(~:: J+ ( ~:,' J~-/..,., .......... ·········· ..............

(!)

Bottom fiber (fur compressio n)

(Ap) + (PxeJ + (-Mg J (:)+ (~:e J-( ~~I J 1

Z ph

< fa maxi

Z ph

< fomnr········ ·········· ..............(2)

Service condition stresses Top fiber (for compressio n)

(R:P)+( -R;:xe ]+( M,,;#M, J+(::) < ( R: p) -( R X:,x eJ+( M •';#M,, ]+( ::) < / ••~·········· .......... ·········· .... 2

fomn

(J)

Bottom fiber (fur temi on)

. (RxP)+(RxPxeJ+(-(Mg A Z z +Mg )J+(-MqJ>z famm 1

ph

2

ph

ph

(R~ p)+( R~:xe J-( M,,2+"M,, J-( ~ J> _ / ••,•..................................( 4) .

<

____

Description

teference

M R

gl

+M

X famin t

g2 -

R

X

+ famax

M gl Mq

z

-

Output

= 1.87E+08

cit

= 1.87E+08

< zp,

1.42E+09

1.07E+09

Section is ok at the top fiber

M R

gl

+M

X famaxt

g2 -

+

R

X

M gl Mq

famin-

z

= 2.96E+08

clh

= 2.96E+08 Section is ok at the bottom fiber

--~-

·---- -

Description

!terence

Output

Magnel digram at the mid span of the bridge

(1) =>

e~ ( z~l ]+ zpl X:anint

+;I·········· ••••·· · · . . . . . . .

(S)

(2) =>

e~ -( z~h

J+zph x;armx I+ M;l .................... ·········· . .

(3) =>

(6)

l l

Mq x(____e_)

e~(Z~~ J- ZP~x:;rrm +((Mg~:~g2)J+ [ Rx:ct z ..................................(?) (4)=>

M

X(

______e_)

e~-(z~h J- ZP~x:;ni• +((Mg~:~g2)J+ [ qRx!ch z ..................................(8) 1.Edge Beam farrin

=

2.55

N/mm2

fanint

=

1

N/mm2

hrmx = hrraxt =

20

N/mm2

18

N/mm2

R AP zpl zph zeit zclb Mgi Mg2 Mq

'

-665

0

1099

2500

1/P1

-1.12E-07

-4.92E-08

5.51E-08

1.88E-07

1/P2

-1.05E-08

1.49E-08

5.70E-08

1.11E-07

11P3

6.58E-08

2.88E-08

-3.23E-08 -1.10E-07

11P4

-1.75E-08

2.47E-08

9.45E-08

e/(mm)

.

1.83E-07

= 0.80 = 2.74E+06 mm2 = 1.42E+09 mm 3 = 1.07E+09 mm3 = 1.97E+09 mm3 = 1.19E+09 mm3 = 6913.02 kNm = 1803.95 kNm = 7370.55 kNm

Description

~terence

Iemax

Output

-665

-665

1/P

-1.5E-07

1.6E-07

Chosen1/P

4.00E-08

4E-08

lemin

1099

1099

e

0

1000

1/P

-1.5E-07

1.6E-07

3.E-07

1

z

::::::: a.

....

2.E-071 ~:-.:

2.E-07

-+-1/Pl ~

--a--1/P2 __._1/P3

l.E-07

·""""*'·- 1/P4 Eccentricity,e/(m"!), --~-

------,-- · - r - - - --- ,

2000

-1000

2500

3000 ·!!!-

-

i(~

I

•

-2.E-07

E max

.

Emrn

-6 - Chosenl/P

Chosen e

-2.E-07

Prestressing force for the section,P

Eccentricity,e

= 2s,ooo,ooo N

=

500 mm

p 25000000

N Feasible Tendon Profile Zone

Bendingmomentat a point x from one support in a simply supportedbeamof length~ due to a uniformly distributerlload w, M•..u wxlxx wxx 2 IMxudl = - - - - 2 2 ! Bendingmomentat a point x from one supportin a simply supportedbeamof length I due to a point load load P, Mxpr Pxx(l-x) Mrpl=

[

j1.Edge Beam

= 29 = 65.76 = 17.16 = 4.37 = 0.585 = 8.10 = 0.85

kN/m

HA UDL on the edge beam = 30.00

kN/m

l, Weigl

wscl wac! whr wfo' WAr

= 120.00 udl due to pedestrian load = 7.5

HA KEL on the edge beam

m kN/m kN/m kN/m kN/m kN/m

kN kN/m

--Description

Ference

Output

Length along the Beam /(m),X

0

3.625

7.25

10.875

14.5

Moment due to self wt of the beam,Mg1 /(Nmm)

0

3.0E+09

5.2E+09

6.5E+09

6.9E+09

Moment due to Screed Concrete,Mg2/(Nmm)

0

7.9E+08

1.4E+09

1.7E+09

1.8E+09

Total Moment due to dead load/(Nmm)

0

3.8E+09

6.5E+09

8.2E+09

8.7E+09

Moment due to Asphalt Concrete, /(Nmm)

0

2.0E+08

3.4E+08

4.3E+08

4.6E+08

Moment due to hand raii/(Nmm)

0

2.7E+07

4.6E+07

5.8E+07

6.1E+07

Moment due to footwalki(Nmm)

0

3.7E+08

6.4E+08

8.0E+08

8.5E+08

Moment due to pedestrian load/I(Nmm)

0

3.4E+08

5.9E+08

7.4E+08

7.9E+08

Moment due to kerb/(Nmm)

0

3.9E+07

6.7E+07. 8.4E+07

8.9E+07

Total Moment due to super imposed load/(Nmm)

0

9.5E+08

1.6E+09

2.0E+09

2.2E+09

Moment due to live loads,HAUDL/(Nmm)

0

1.4E+09

2.4E+09

3.0E+09

3.2E+09

Moment due to live loads,HA KEL/(Nmm)

0

3.8E+08

6.5E+08

8.2E+08

8.7E+08

Total Moment due to live loads

0

1.8E+09

3.0E+09

3.8E+09

4.0E+09

Eccentricity,e1/(mm)

575

696

783

835

852


379

500

586

638

655


-902

-613

-406

-281

-240


-525

-212

12

147

192

Emin/(mm)

-902

-613

-406

-281

-240

Emax/(mm)

575

696

783

835

852

i

----

l Cable Zone

--+- Emin/(mm)

-1000~ E E

-500

2

::::::::: cu

~ ·;::; ·.: ....

4

-Emax/(mm)

~6 8 lU

16 ChianagiaT'ong the beam/(m)

0

c

cu

u u

500

LLI

1000-

.

·---

i

-"

L

-

--

--

Description

~eference

Output

Calculation of number of ducts

1.Edge beam

Prestressing force,P

= 25,000,000 N

Type of strand

= BS 5896-3 super strand-1770-15. 7-relax 1

-able 6

Nominal tensile strength

= 1770

N/mm 2

.cl. 20

Nominal steel area

= 150

mm

Specified characteristic breaking load

= 265,500

N

Maximum prestress force allowed for tendons

= 70%xCharacteristic strength

:s 5896 1980

s

2

5400

199l'

= 185,850

16.i '

Number of tendons needed

N

= Prestressing force Maximum prestress force allowed for tendons = 25.000.000 185850 = 135

Nos.

External diametre of duct

=60

mm

Internal diametre of duct

=50

mm

Number of strands per duct Number of ducts

=7 = 135 7

Nos.

= 20

Nos.

Number of, ducts

Nos.

I

t

:n

h

he

BJ i

y

X 0

'--

20

I le

ho

/A

Description

ference

Output

Assumed equation for parabolic portion

I

At A;

At 8;

X

=

X

= 0

X

=

b

So;

c i At 8;

= =

l

dy 'dx

= 0 =

_!__ n

ho

=

2ax

dy dx

=

_!__ n

1

+hX+c

0

dy dx

- =

2

ho

O,Y = dy 'dx

Y=aX

2ax

n

a

=

1 2nl

Y=mX+c

Assumed equation for straight portion;

dy 1 X=l-=m='dx n X= lc,Y =he

At 8;

Straight

y = (X - le) + he n

Curve

Y=--+ho 2nl X= l,and,Y

xz

At 8;

n= .

.

Equation of Parabolic curve Y = Equation of Straight line

= h

(2le -!) 2(he-ho) (he- ho) ( ) X l 2/e - I

2

+ ho

y = 2(he-hoXX-le) +he 2/e-1

>40(

90 !

e

36

Minimum cover to the ducts at the end of parabolic section

=50

Minimum spacing between the centrelines of ducts at the = 140 371 end of the parabolic section

mm

mm

------.-------------------------------------,.-----, Description

1ference

Output

Profiles of individual ducts

:; 5400 I Cover to ducts

Cover

I Minimum cover to ducts

tart 4

=50

mm

50

3.8.2 3

mm

Clear distance between ducts Maximum size of coarse aggregate,

= 19

mm

+5mm = 24

mm

=50

mm

=50

mm

50

=50

mm

mm

hagg hagg

. 5400 Ivertical internal dimension of the duct

IHorizontal internal dimension of the duct

art 4

i.8

3 3 IClear distance between ducts

Height to centorid of a duct from bottom fibre at level n

= Yn

Cross sectional area of a duct at level n

= AJn

Height to the bottom fiber from the neutral axis (Composite

=Y =(Adl

Centroid of all ducts from the bottom fibre,

y

i :· :..

x Yt + Ad2 x Y2 + ····· + Adn x Y

=

y

ph

-

y

At mid span Chainage

=0

m

Eccentricity obtained from the Magnel Diagram

=500

mm

External diametre of the duct

=50

Number of ducts

= 20

Strands/duct

=7

Height to the bottom fiber from the neutral axis,

--t

Ypb

t.'

pb -

(Adl + Ad2 + ···· + Adn)

Eccentricity of all ducts in the section considered,e

Clear spacing

=952

mm

=25,000,000

N

I)

Description

tference

Duct position

Duds

No. of duds No of Strands

Output

Cross sectional area of a ducU(mm 2)

y1

100

12

84

1963

y2

300

2

14

1963

y3

500

2

14

1963

y4

700

2

14

1963

y5

900

2

14

1963

Total

20

-

Centrad of all ducts from bottom fiber

= 300

mm

Resultant Eccentricity of all tendons,e

= 652

mm

Profile5 ~

Projile4~

~--------~

Profile 3

Profile 2

-------

Profile~

r--!---

Is

lp

lo Zone I

Zone3

Zone2

Eccentricity at Length of Length of start of zone 1 Zone 1/(m) Zone 2/(m) /(mm)

Eccentricity at end Length of Zone Lenth up to mid of zone 2 (mid 3/(m) span /(m) span) /(mm)

Number of ducts

Number of strands

Profile 1

1

852

8

852

5.5

14.5

12

84

Profile 2

1

542

8

652

5.5

14.5

2

14

Profile 3

1

232

8

452

5.5

14.5

2

14

Profile 4

1

-78

8

252

5.5

14.5

2

14

Profile 5

1

-388

8

52

5.5

14.5

2

14

Total

20

140

Description

tferen ce

Output

Eccentricity/(mm)

Chainage I (m)

Profile 1

Profile 2

Profile 3

0

852

542

232

1

852

564

2

852

3

Profile 5

Resultant

-78

-388

542

276

-12

-300

564

585

317

50

-218

585

852

603

353

104

-146

603

4

852

618

383

149

-86

618

5

852

630

408

186

-36

630

6

852

640

427

215

3

640

7

852

647

441

236

30

647

8

852

651

449

248

47

651

9

852

652

452

252

52

652

!

10

852

652

452

252

52

652

I

11

852

652

452

252

52

652

12

852

652

452

252

52

652

13

852

652

452

252

52

652

14

852

652

452

252

52

652

14.5

852

652

452

252

52

652

100

410

720

1030

1340

I

Profile 4

I '

-1000 ~

-800 --600 E E-400

-

Cl)-200

~ (.)

0

~

.. ......

... .. .

... ...

1000

-

•

• Emin

-

• - Emax

.....

-)'(

Cha~a9~in~~ • • "1£ • "14•

·Profile 2

--------Profile 3 - - 1 - Profile 4

~~ 400

800

6

•

---ts- Profile 1

~

JJ 600)1·- ·;

i

.. .. .

~

:sc:: 200 G) (.)

Eccentricity of cables along the beam

- ':

-ProfileS

-

~

.....

"'

....

-

.....

.:.-:'-."':-:"*·-----#-~-- "'' . +- --~~ -~ ...---*·--~ - • • -.A. • • - • • • - _Il -

- - - - - - - - - - -

-

-~

------

~-Resultant

Description

terence

Analysis of the beam

--

-------·-

-----~---------

~~-

-- -----

Output

--·-

------

-----·----- ··------------- ----------

~--~--

Post tensioning sequence feu

5400-4

Stage 1

Stage 2

Age

14 days

1 month

Strength

36

50

=50 Stage 3

N/mm 2

Stage4

Stage 5

990

Jle 20 When cables are prestressed,all cables are not stresses at once.Differents cable sets are chosen for stressing procedure.A post tensioning seaquence is introduced and cables are stressed taking each set of cables at once.At each stage after tensioning stresses are checked at top and bottom fiber.

Number of cables in each set of cables Cable profile

Stage 4

Stage 3

Stage 5

Total no of cables

Stage 1

Stage 2

Profile 1

8

4

Profile 2

2

2

Profile 3

2

2

12

2

Profile 4 Profile 5

Stage 6

2

2

2 Total

20

Cables are stressed according to the the sequence chosen in the above table

The sectional properties at diifferent sections of the beam changes according to the tendon profiles at each section of the beam. Therefore the section properties has to be found at each section of the beam before grouting of the beam.when tendons are stressed at stage one(cable set 1) at transfer the section will have all the ducts without grout. But when the stressing is done at stage two in cable set two,the the ducts which consists of the cables that are stresses at stage one wil be grouted,thus section properties will be changed. Therefore section properties at each stage of stressing has to be calculated as well.

Calculation of sectional l!rol!erties

L

J

0

-

Cl

-

C2

0

0

Y5 Y4 Y3 G--

0

Y2 -------------

!fl

1----------

tference I

I

Description

= A - Ad! - Ad2 -

AP'

Cross sectional Area of the pre cast section . before groutmg

P

Height to the centriod of precast section after grouting

yp

Height to the centriod of precast section before grouting

Y' -

Centroidof the precast section before grouting

cl

Centroidof the precast section after grouting

c2

Y' = (Ap

Y' =

X Yp-

Adl

X

,

X Yn)

AP

L

y p -

X

- Adn

Y1- Ad2 X Y2····.Adn

(A p

••••

Output

A di

X

y i)

Ap

= Adl xyl +Ad2 xy2 + ..... +An xyn

LAd; xy;

I xp

- Moment of inertia of precat section after grouting

, fxp

- Moment of inertia of precat section before grouting

From parallel axis theorem

Ixp'= Ixp + (Y'- Y)2 x Ap -{(Idl + Adl x (i''-

~)2 + /~2 + Ad2 x (i''- y2)2·····}

····· + 1dn + Ad2 x (Y'- Yn)

= Jdl +fd2 + ... +fdn LAd; X (Y'- y;)2 = Adl X (Y'- YI}2 + A2 X (Y'- Y2)2 + .. + Adn X (Y'- Yn)2

Lfdi

fxp

,

= fxp

-

-

+(Y' -Y)

2

X

Ap- Lfdi- 'LAd;

moment of inertia of a duct of diametre d with respect to x axis Area of a duct of diametre d

Id

= -mf4 64

Ad

=

mf2 -~

4

L----------------------------------------------~----~

Description

eference

Output

1.Edge beam At mid span (Chainage 14.5 m)

Ducts

Duct position

I No.ofducts INoofStrands Externaldiametre, at one level,n of duct/(mm)

Cross sectional areaofa ITotaiAreaofthel ducts /(mm2) 2 ductl(mm)

Ad;XY;

Ad y1

100

12

84

60

I

2827

I

33929

I

3,392,920

y2

300

2

14

60

I

2"827

I

5655

I

1,696,460

y3

500

2

14

60

I

2827

I

5655

I

2,827,433

y4

700

2

14

60

I

2827

I

5655

I

3,958,407

y5

900

2

14

60

I

2827

I

5655

I

5,089,380

I

56549

I

16964600

Total

I

20

I

I

140

IAd;XY; I

Ixp

= I xp + ( y

I -

y) 2

X

Ap

L I di - L Adi

-

yl = (A p X y p

-

I

Adi

X

X

(Y I

-

y i) 2

y i)

I

AP yp

=

Ypb

= 952

Cross sectional Area of the pre cast section after grouting

AP

Adl + Ad2 + ···· + Adn

A~

mm

=2.74E+06 mm2

= 56549

= AP

-

Ad! - Ad2 - ···· - Adn

= 2.68E+06

mm2

Y' IAd;XY;

=16,964,600

mm

3

966 mm

Height to the centriod of precast section before grouting

Y' y~_y

Second moment of area of a circle with diametre d around its centre

External diametre of a duct Second moment of area of a duct around its centre

= 966

mm

=14

mm

=

7ld4 64

=60 =636,173

mm

4

·---Description

eference

Ducts

Duct position

No. of ducts at one level,n

External diametre of ducU(mm)

Output

Id /(mm

4

nxld

(Y'- y;)z

Adi X (Y'- y;)

)

y1

100

12

60

636,173

7634070

749505

25430111423

y2

300

2

60

636,173

1272345

443209

2506289580

y3

500

2

60

636,173

1272345

216913

1226616598

1272345

70618

399332958

1272345

4322

24438660

y4

700

2

60

636,173

y5

900

2

60

636,173

Total

20

12723450

29586789218

IIdi

=12,723,450 =3.0.E+10 =1.0E+12

_LJdi L(Ad; x(Y'- Y;)2)

Jxp , Jxp

= Ixp + (Y'- .YY X

Ap-

L(Adi x(Y'- Y;)2)

mm

4

mm

4

mm

4

L Idi- L Adi

X

(Y'- Y;)2 ,,

,

9.87E+11

=9.87E+11

Jxp

mm

4

4

mm

, Ypb Total depth of the precast section

Ypb

I

= 1667 = Y' =966

mm

966 mm

mm

Ypt Ypt

=701

1

mm

,

I zp, =~ Ypt

zp,~

mm

3

,

1.41E+09 mm

' Jxp zpb =--, Ypb

=1.02E+09

701 mm

,

= 1.41E+09

I

3

zpb 3

mm

I

1.02E+09 mm

3

Description

ference

Output

Similarly,

At qarter span

At edge of beam

14.5

7.25

0

2.68E+06

2.68E+06

2.68E+06

9.87E+11

9.87E+11

9.96E+11

701

701

704

966

966

963

1.41E+09

1.41E+09

1.42E+09

1.02E+09

1.02E+09

1.03E+09

6770

5078

0

At qarter span

·At edge of beam

14.5

7.25

0

2.72E+06

2.72E+06

2.72E+06

1.01E+12

1.01E+12

1.01E+12

711

711

712

956

956

955

Sectional modulus at the top fiber of the section before 3 zpll grouting/(mm )

1.42E+09

1.42E+09

1.42E+09

Sectional modulus at the bottom fiber of the section before I 3 zpb grouting/(mm )

1.05E+09

1.05E+09

1.05E+09

5153

0

when stressing is done at stage 1

Mid Span

A~

Cross sectonal area of the precast section before grouting/(mm

2

)

, Second moment of area before grouting/(mm

4

Jxp

)

I

Heght to the top fiber from the neutral axis/(mm)

Ypt

Heght to the bottom fiber from the neutral axis/(mm)

I

Ypb

Sectional modulus at the top fiber of the section before grouting/(mm

3

)

-

zptl

Sectional modulus at the bottom fiber of the section before grouting/(mm

3

I

)

zpb

Moment due to self weight before grouting/(kNm)

Mgl

when stressing is done at stage 2

Mid Span


2

A~

)

Second moment of area before grouting/(mm

4

, )

]xp

Heght to the top fiber from the neutral axis/(mm)

1

Ypt

Heght to the bottom fiber from the neutral axis/(mm) y

1

pb

,

Moment due to self weight before grouting/(kNm)

' i

l

I

Mel

6870

-------.-------------------------------------------------------------------------------.-------, Description eference Output Prestressing force along a cable changes from point to pont because of friction present Therefore the prestressing force along the cable is calculated as follows Friction in the duct due to unintentional variation from the specified profile 5400-4

I

1990

~ = Poe -Kx

Prestressing force at distance x from the jack

Equation 31

where Kx ~ 0.2,e-Kx = 1-Kx

67 3 3j

P.

0

-

Pre stressing force in the tendon at the jacking end

K - constant depending on the type of duct

Friction in the duct due to curvature of the tendon 5400-4

990

-px

I

Equation 32

px = Poe rP,

Prestressing force at distance x from the jack

where

3.7.3.4

-px

J.LX ~ 0.2, e

rps

=I- J.LX

rps

rps

(Kx + px) ~ 0.2, rps -(Kx+JLX)

e

rps

= 1- (Kx

+ JlX) rps

J.l - Coefficient of friction rps

Prestressing force alonQ the profile 1 I I Zone Start Chainage length

End Chanage

Zone 1

0

1

1

Zone2

1

8

9

~ne3

9

5.5

14.5

-

Radius of curvature,R

Description

eferem.e

Output

Zone 1 is a staright section

px = Poe-Kx

Equation 31 ,

where

Kx :S: 0.2,e-Kx = 1- Kx

Po

= 1300950

N

X

:0

m

Start Chainage

-

K = 0.0033

Kx = 0.000

< 0.2

i

540u--

4j

..,

1-kx

t

199t " J,l

Therefore, = 1.000

pX =

I

px = 1300950

Prestressing force at the beam edge

N

1,300,950 N

End Chanage

X

= 1

m

Kx = 0.0033 eKx

< 0.2

ok

=1-Kx pX =

= 0.9967

px

= 1296657

N

1,296,657 N

Zone 2 has a curvature -( J.IX +Kx)

~=Poe

Equation 31 and 32,

where

i400 390

(Kx+ ~) :s:; 0.2, e

I

734

I

-(Kx+JIX)

Start Chainage

for steel moving on steel

=1

m

Po

= 1296657

N

J.L

= 0.3

rps

=R

Radius of curvature at the end of zone 2 =

I -

R

I

1 R = 2.70E-06

rp,

= 1-(Kx+ ,ux) rps

rps

733 &

rps

mm

Description

eferenc e

Output

Therefore,

=370.37

m

=9

m

=0.0065

< 0.2

R

At the end of zone 2,

Chainage

X

f..K

-+Kx rps

ok

-(Kx + JiX) rps

e

( Kx+-) J.iX -1-

pX

rps

=

1,288,255

px

= 1,288,255

px

= Poe-Kx

N

N i

Zone 3 is a straight section

I

where Kx ~ 0.2,e-Kr

= 1,288,255 Chianage = 14.5 X =5.50 =0.01815 Kx Po

I At the end of zone 3,

1 i

P= X

0 Chianage/(_mj_ t-'restressmg rorce or 1,300,950 the orofile 2HN}

t

m m < 0.2

N

1

9

14.5

1,296,657

1,288,255

1,264,873

Quarter span

0.0

2.0

7.25

12.0

14.5

Profile 1

1300950

1292364

1269825

1249432

1238700

Profile 2

1300950

1295607

1290093

1275501

1264873

-~ li=

Profile 3

1300950

1295560

1289803

1275134

1264509

Q)O. Q) en..c Q) ._ ......

-=

Profile 4

1300950

1295045

1286584

1271054

1260463

a_

Profile 5

1300950

1294524

1283324

1266923

1256366

Chianage/(m)

0

Q) ...--.

oZ ._ ........

o-..-OlQ)

en ._ o en

_j_

1264873

N

Beam edg_e

t·

!

= 1- Kx

Midspan

ok

,Reference

I

Description

I

At mid span Chosen cables for tension in 1 Number of cables Duct Profile position tensioned from each name y/(mm) profile in stage 1

I

Profile 1

I

100

Prestressing . force 1n one cable

T t t o a1 orce t 1 Force X y 1a one 1eve1

I

8

1,238,700

I 9909596.341 990959634

1,264,873

I 2529745.4 I 758923620

Profile 2

I

300

I

2

Profile 3

I

500

I

2

1,264,509

12529017.4511264508723

Profile 4

I

700

I

0

1,260,463

J

Profile 5

I

900

I

2

1,256,366

12512732.6712261459407

Total

I 17481092 15275851385

0

I

0

0

Total prestressing force at stage one= 17,481,092 N Centroid of forces from the bottom of the beam =

L Force x Y Totalforce

= 5275851385 17481091.9 yf = 302

Eccentricity

Y'

mm

Y'-Yf

=

=966

mm

Eccentricity of force = 664

mm

Calculation of stresses

Stage 1 Pre-cats section before grouting at transfer condition-Mid span

PIA

Neutral Axis Level

8 8

-Pxe/Zpt'

Mg l/Zpt'

~ ~ ~~ -Mgl/Zpb'

Pxe/Zpb'

6.514 Stress at top most fibre = _!_ _

,

Ap

O.OOOE+OO

P x ,e + M gl, zpt zpt

4.80

Output

·.Reference

Description

Output

P = 17,481,092 N

Eccentricity of force = 664

,

A ,xp

=

Mg,

p

A~ Pc [e

mm

c

X

J

( l,x - -x' 1X 2 2

= 2.68E+06

mm2

= 24

kN/m 3

= 29

m

At mid span x = 14.5

m

,

= 6770

kNm

zpr'

= 1.41E+09

mm3

zpb

' = 1.02E+09

Mg,

mm

N/mm 2

Stress at top most fibre = 3.08

N/mm 2

Allowable tensile stress at transfer, = -1

Stress at the bottom most fibre=

P P x e -M --+ - gl -1 1 I

z

AP

N/mm 2

Stress at tendon level --- - ,

+

AP

, pe

N/mm 2

N/mm2

Allowable compressive stress at transfer, = 18

P

3.08

Z pb

pb

Stress at the bottom most fibre = 11.26

Z

3

Pxe

Mgl

Zpe

Zpe

11.26

, - --,

N/mm2

, -

J xp

e = 1.49E+09

Stress at tendon level = 9. 77

mm 3

N/mm2

10 N/mm2

··~---------------------j_

_

_j

-·-·--

Description

~eference

Output

Similarly Midspan

Stage 1 Prestressing force,P/(N)

17481091.9 17,885,037

, Mal

Moment due to self weight before grouting/(kNm} Eccentricity of the force,e/(mm)

Sectional modulus at the top fiber of the section before grouting/(mm

3

grouting/(mm

)


5078

0

664

660

553

1.41E+09

1.41E+09

1.42E+09

-

1.02E+09

1.02E+09

1.03E+09

9.87E+11

9.87E+11

9.96E+11

1.49E+09

1.50E+09

1.80E+09

2.68E+06

2.68E+06

2.68E+06

)


6770

/xp

)

Sectional modulus at the centroid of force before grouting/(mm

18,213,300

zpb ' 4

3

Beam Edge

zpt,

)

Sectional modulus at the bottom fiber of the section before 3

Quarter Span

2

A~

)

Stress at the top most fibre/(N/mm

2 )

3.08

1.88

-0.33

Stress at bottom most fiber/(N/mm

2 )

11.25

13.25

16.53

9.77

11.16

12.39

Midspan

Quarter Span

Beam Edge

7475724.28

7,652;467

7,805,700

6870

5153

0

654

650

545

1.42E+09

1.42E+09

1.42E+09

1.05E+09

1.05E+09

1.05E+09

9.87E+11

9.87E+11

9.96E+11

1.51E+09

1.52E+09

1.83E+09

2.72E+06

2.72E+06

2.72E+06

-0.70

-0.70

-0.14

7.38

7.53

6.90

5.98

6.09

5.20

654

650

545

5.99

6.09

5.20

Stress at tendon leveV(N/mm

2

)

Stage 2 Prestressing force,P/(N) Moment due to self weight before grouting!(kNm}

M _,'

Eccentricity of the force of stage 2,e/(mm) Sectional modulus at the top fiber of the section before grouting/(mm

3

zpt,

)

Sectional modulus at the bottom fiber of the section before 3 grouting/(mm ) zpb I


4

)

/xp

Sectional modulus at the centroid of force before grouting/(mm 3 ) Cross sectonal area of the precast section before grouting/(mm 2 ) Stress at the top most fibre/(N/mm

2

Stress at bottom most fiber/(N/mm

2

A~

)

)

Stress at tendon level of the cables in stage 2/(N/mm

2

Eccentricity of the force of stage 1,e/(mm) Stress at tendon level of the cables in stage1/(N/mm

2

)

)

r------.--------------------------------------------------------------~----~

Description

.,Reference

Output

Short term prestress losses A. loss of Prestress due to elastc defonnaion of concrete

BS 5400 Strain in concrete, = 8 c

Part 4

(J"c

1990

&c=E

ci.6J.2. &

_c

O" c - Stress of concrete

cl.6. 7.2.3

&c

-

Strain in concrete

Ec - Modulus of Elasticity of concrete Strain in concrete = &s & s

/l(J" s E

=--s

&s

-

Strain in concrete

llO" s

-

Loss of prestress in steel

Es

- Modulus of Elasticity of steel

Strain in steel = Strain in concrete

At the tendon level

&s =Ec

/l(J"s Es

Loss of force in the steel,

llP

= (J"c Ec

= !lO" s x As

Cross sectional area of steel = As

= (J"c x-As XEs

.......... ()

Ec Since the tensioning of the steel is done gradually during post tensioning, the stress in tendons are taken as the half of the stress in the steel for calculation of prestress loss

Loss of prestressing force= O.S x O"c x As xEs

Ec

r--------,------------------------------------------------------------------------------~------~

Description

.~eference

Output

Stage 1 Stress in concete at tendon level

Chainage/(m)

/(N/mm 2 )

14.5 (mid span)

9.77

7.25 (quarter span)

11.16

0 (beam edge)

12.39

Average stress along the cable/Nmm, u

11

c

Cross sectional area of steel

=Cross sectional area of one tendon X

As

number of tendons stresses

mm2

Cross sectional area of one tendon = 150 Number of tendons needed = 98

mm 2

As = 14700 Characteristic Concrete cube strength at transfer Modulus of Elasticity of concrete

Ec

3S 5400-4

=36 =29.8

kN/mm 2

= 29,800

N/mm

=200

KN/mm

= 200,000

N/mm2

N/mm2

after 7 days

2

1990 ~.6.7.2.3.

Table3

Modulus of Elasticity of steel

Es

I

Loss of prestressing force

;r.4.3.2.2.

2

= 0.5 x Uc x As xEs Ec

Figure2

=547,823

N

AP Loss of pre stress

547,823 Loss of stress due to direct force loss

=

AP A' p

N

=547,823 2.68E+06

= 0.20 loss of stress due to loss of moment at the top fiber

= AP x e zp,'

N/mm2

'-

Description

.•Reference

Output

AP

= 547,823 e = 664

zpl,

N mm

= 1.41E+09

mm

zpb ' = 1.02E+09

mm

loss of stress due to loss of moment at the top fiber= -0.26

3 3

2

-0.05

N/mm2

0.56

N/mm

0

Loss of stress due to loss of moment at the bottom fiber

=

M xe zpb '

=0.36 Stresses after stage 1 stressing -Mid span,

=3.08 Stress at bottom most fiber/(N/mm2) = 11.25 Stress at tendon leveii(N/mm2) =9. 77

Stress at the top most fibre/(N/mm2)

Stresses after the losses,

=2.62 Resultant stresses at botttom fiber = 10.69 Resultant stresses at top fiber

N/mm2 N/mm2

Similarly, Mid Span Cables considered

Stage 1

Average stress along the

A.

M

Loss of stress due to direct force loss

Loss of stress Loss of stress due due to loss of to loss of moment moment at the at the bottom fiber top fiber

cable/N/mm2

mm 2

N

St1 cbls

11.11

14700

547823

0.20

-0.26

0.36

St2 cbls

5.76

6300

121668

0.04

-0.06

0.08

St1 cbls

5.76

14700

283968

0.10

-0.13

0.18

Stage 2

Total prestress loss

953458

Quarter Span Cables considered

Average stress along the cable/N/mm

Stage 1

2

As

M

2

N

mm



St1 cbls

11.11

14700

547823

0.20

-0.26

0.35

St2 cbls

5.76

6300

121668

0.04

-0.06

0.08

St1 cbls

5.76

14700

283968

0.10

-0.13

0.18

Stage 2

--


953458

.--.Reference I

Description

I

I

I

Beam Edse Average stress along the cable/N/mm 2 ,

mm 2

N

St1 cbls

11.11

14700

547823

0.20

-0.21

St2 cbls

5.76

6300

121668

0.04

-0.05

I

0.06

St1 cbls

5.76

14700

283968

-0.11

I

0.15

Cables considered

Stage 1

A.

Stage 2 Total prestress loss

Loss of stress due to loss of Loss of stress due to loss of moment moment at the t th b 11 fibe topfiber a e o om r


I1P

I

I

0.10

Output

I

0.29

953458

B. loss of prestress due to slip during anchorage

BS

if,Anchorage slip = 8

5400-4 1990

loss of prestressing force = ~ x

Cl6 7.2.6

I

E

x s

A s

Stage 1

E.

Modulus of Elasticity of steel

A. I Assume

mm

= 30

m

Slip of the cable = 6

8 loss of prestressing force

At mid span

=200,000 = 14700

loss of direct stress

N/mm2 2

mm per 15m

= 12

mm

= 1, 176,000

N

=M A' p

1,176,000

A'p =2.68E+06 loss of direct stress

loss of stress at the top most fiber

e

zpt' Mxe

zpt, loss of stress at the bottom most fiber

=0.44 =

M

mm

2

N/mm2

xe

zpt,

=664

mm

= 1.41E+09

mm 3

=-0.55

N/mm2

Mxe =--Zph'

N

Description

..Reference

z

pb '

Mxe

zph,

Output

=1.02E+09 =0.76

mm

3

N/mm

2

Stresses after the elastic deformation,

=2.62 Stress at bottom most fibre = 10.69 Stress at top most fibre

N/mm N/mm

2

2

. Stresses after the losses,

=1.62 Resultant stresses at botttom fiber =9.48 Resultant stresses at top fiber

N/mm N/mm

2

2

Mid Span Cables considered

Stage 1

A

mms:z

llP N


Loss or stress Loss of stress due due to loss of to loss of moment moment at the at the bottom fiber top fiber

St1 cbls

14700

1176000

0.44

-0.55

0.76

St2 cbls

6300

504000

0.19

-0.23

0.31

St1 cbls

14700

0

0.00

0.00

0.00

Stage 2


1680000

Quarter Span

N

St1 cbls

14700

1176000

0.44

-0.55

0.76

St2 cbls

6300

504000

0.19

-0.23

0.31

St1 cbls

14700

0

0.00

0.00

0.00

A

(Jr

Stage 1

LOSS 01 Suess


Cables considered

mmi

M

Loss of stress due due to loss of to loss of moment moment at the at the bottom fiber too fiber

Stage 2


1680000

Beam Ed e Cables considered

Stage 1 Stage2

As

a

mm2

N


St1 cbls

14700

1176000

0.44

-0.46

0.63

St2 cbls

6300

504000

0.19

-0.19

0.26

St1 cbls

14700

0

0.00

0.00

0.00


--

M


.

1680000

.

.-..Reference

Description

Output

C.Loss of prestress due to creep of concrete Stage 1 at mid span

BS 5400-4

= Creep coefficient X Modulus of elasticity

Loss of prestress of the tendon

of the tendon X stress at the tendon level

1990 cl.6.7.2.5

N/mm2


1

After 14 days of concreting,

Strength of concrete

=.36

N/mm 2

<40

BS 5400-4!1

N/mm2

1990 T.able 20

= 0.000036 X 40/fci = 0.00004

After 14 days of concreting, Creep coefficient

Es

perN/mm 2

N/mm2

= 200,000

=0.5X(Creep coefficient X Modulus of elasticity of the

After 14 days of concreting,Loss of prestress of the tendon

tendon X stress at the tendon level)

= 11.25

Maximum stress in the section

ok


Loss of prestress of the tendon = 39

A,

N/mm2

= 14700

Loss of prestressing force/(N) = 574343

N

Loss of stress Direct loss

=

M

574,343

A' p

N

=574.343 2.68E+06

=0.21 Loss of stress due to loss of moment at the top fiber =

N/mm 2

AP x e zp,~

= 574,343

AP

e=664

z pr = 1.41E+09 I

1

Z ph Loss of stress due to loss of moment at the top fiber

N mm mm

3

=1.02E+09

mm3

= -0.27

N/mm2

Description

Reference

Output

Loss of stress due to Joss of moment at the bottom fiber =

Mxe zpb '

= 0.37

N/mm2

Stresses after the elastic deformation and anchorage slip mid span after 14 days, Stress at top most fibre = 1.62

N/mm2

:= 9.48

N/mm 2

Resultant stresses at top fiber = 1.14

N/mm 2

Stress at bottom most fibre

Resultant stresses after 14 days creep of concrete

Resultant stresses at botttom fiber = 8.90

Nlmm

2

I Similarly, Mid Span Cables considered

Stage 1

Stress at cable levei/N/mm

A, 2

mm

N

M

2


Loss of stress due to loss of moment at the top fiber


St1 cbls

9.768

14700

574343

0.21

-0.27

0.37

St2 cbls

5.983

6300

135685

0.05

-0.06

0.08

St1 cbls

5.985

14700

316736

0.12

-0.15

0.20

Stage 2

Total prestress loss 1026763 Quarter Span Stress at cable

A,

leveVN/mm 2

mm 2

St1 cbls

11.164

St2 cbls St1 cbls

Cables considered

Stage 1


N


14700

656426

0.24

-0.31

0.42

6.086

6300

138036

0.05

-0.06

0.09

6.088

14700

322192

0.12

-0.15

0.20

Stage 2

Total prestress Joss 1116654 Beam Ed! e Stress at cable leveVN/mm 2

mm

St1 cbls

12.385

St2 cbls St1 cbls

Cables considered

Stage 1

N

14700

728247

0.27

-0.28

0.39

5.196

6300

117854

0.04

-0.05

0.06

5.196

14700

274993

0.10

-0.11

0.14

A, 2

Stage 2

Total prestress loss 1121095

-·~·~

Loss ot stress Loss of stress due due to loss of to loss of moment moment at the at the bottom fiber top fiber


r----------,-----------------------------------------------------------------------------------------~---------,

Description

·.Reference

Output

D.Loss of prestress due to shrinkage of the concrete Shrinkage per unit length, =

c_,h

BS 5400

Prestress loss due to shrinkage=

Part4

ci.6.7.2.4,After 14 days

Prestress loss due to shrinkage = 0.5 x Total area of steel

Table29

x E, x A.

&sh

For normal exposure,

& sh

x

A. E.

= 21000

mm2

= 200000

kN/mm 2

Esh

= 0.0002

Prestress loss due to shrinkage = 420000

Loss of stress

E s x As

Direct force =

~

A

N

p p

420000

= 420000

N

2.74E+06 N/mm2

= 0.15

P x e

Loss of stress due to loss of moment at the top fiber = .6.

zpl e = 652

zp,

mm mm3

= 1.42E+09

N/mm2

Loss of stress due to loss of moment at the top fiber = -0.19 Loss of stress due to loss of moment at the bottom fiber =

Ll P

X

z

ph

Z ph = 1.07E+09 Loss of stress due to loss of moment at the bottom fiber = 0.26

e mm3 N/mm2

Resultant stresses after 14 days of creep of concrete


N/mm2

Resultant stresses at bottom fiber = 8.90

N/mm2

Resultant stresses after 14 days of the cable set one before stressing cable set 2 Resultant stresses at top fiber = 0. 79

N/mm2

Resultant stresses at bottom fiber = 8.49

N/mm2

·Reference

I

Description

Age

I

A.,

Output

Prestress . loss due to shnnkage/(N)

I

/(mm 2)

·

~~:st~~~::~;

Loss of stress due to d"1rect ~ orce 1oss

Loss of stress due t t th to loss of moment fibe momen a e t the bott top fiber a om r

Mid Span

1 month

21000

420,000

I

0.15

I

-0.19

I

0.26

Quarter Span

1month

21000

420,000

I

0.15

I

-0.19

I

0.25

Beam Edge

1 month

21000

420,000

I

0.15

I

-0.16

I

0.21

•After stressing cable set 2 at stage 2 after one month At mid span

Stress at top fiber due to stresses in cable set 2

=-0.70

N/mm2

Stress at bottom fiber due to stresses in cable set 2

= 7.38

N/mm2

=0.10

N/mm2

= -0.131

N/mm2

= 0.176

N/mm2

= 0.04 = -0.06

N/mm2

= 0.08

N/mm

=0.00 =0.00

N/mm2 N/mm2

=0.00

N/mm2

Loss due to elastic deformation Cable set 1 Loss of direct stress in cable set 1 Loss of stress in cable set 1 due to moment loss at the top fibre Loss of stress in cable set 1 due to moment loss at the bottom fibre

Cable set 2 loss due to elastic deformation

Loss of direct stress in cable set 2 Loss of stress in cable set 2 due to moment loss at the top fibre Loss of stress in cable set 2 due to moment loss at the bottom fibre

N/mm2 2

Anchorage loss

Cable set 1 anchorage loss

Loss of direct loss in cable set 1 Loss of stress in cable set 1 due to moment loss at the top fibre Loss of stress in cable set 1 due to moment loss at the bottom fibre

-----~------------------------------------------------------------------------------~------~

Description

Reference

Output



=0.19 =-0.23

N/mm2

=0.31

N/mm

N/mm

2

2

0

Total losses Loss of direct stress

=0.33

N/mm2

Loss of stress at top most fibre

= -0.420

N/mm 2

Loss of stres at bottom most fibre

=0.565

N/mm2

Resultant stresses at top fiber

= -0.67

N/mm2

Resultant stresses at botttom fiber

= 14.97

N/mm 2

I

Loss of prestress due to creep of concrete after 30 days

"

Cable set 1 N/mm 2

= 0.12 = -0.15

N/mm 2

= 0.20

N/mm2


= -0.40

N/mm


=14.66

N/mm2

= 0.05

N/mm2


2

Cable set 2 loss due to elastic deformation

I_


= -0.06

N/mm2

=0.08

N/mm2


= -0.29

N/mm2


= 14.52

N/mm2

i!.

Reference

Description

Output

E. loss of prestress due to relaxation of steel

BS 5400-41 For relaxation class 1, Maximum relaxation after 1000 h for an initial load of 70% of the breaking load, is 8 % of prestressing force 1990 Type of strand = BS 5896-3 super strand-1770-15.7-relax 1

cl.6.7.2.2

Relaxation class = class 1

BS 5896 1980 a In all cables

Prestresing force at the jacking end

At mid span

,~_h•-

=26,019,000

N

Percentage prestress loss

=8

%

Loss of Prestressing force

=2081520

N

= 21000

mm 2

=99.12

N/mm2

As Loss of stress in cable

Loss of stress

Direct force =

~ A

p

= 2081520 2.74E+06

=0.76

N/mm2

Loss of stress due to Joss of moment at the top fiber = !l.P x

z

e

pt

=652

mm

= 1.42E+09

mm3

Loss of stress due to Joss of moment at the top fiber

=-0.96

N/mm2

Loss of stress due to Joss of moment at the bottom fiber

_ !l.P x e

e Z P1

zph

= 1.07E+09

mm3

= 1.27

N/mm 2


=-0.29

N/mm2


= 14.52

N/mm2

Z ph Loss of stress due to Joss of moment at the bottom fiber

Resultant stresses after 30 days

After 2 months

---· Description

Reference

Output

Resultant stresses after 1 month 2


= 1.42

N/mm


= 12.49

N/mm 2

Similarly, "


Loss of stress due to toss of moment at the top fiber


0.76

-0.96

1.27

0.76

-0.95

1.26

0.76

-0.79

1.08

4411399

N

Total prestressing force = 24956816

N

'

M /(N)

Mid Span

2081520

Quarter Span

2081520

Beam Edge

2081520

Total prestress force loss =

Percentage prestress loss =

17.68

%

Smilarly,After stressing cable set 2 at stage 2 after one month streesses at quarter and mid span can be summarised as follows, MidSpan

Stresses after stage 1 stressing

Quarter span

Beam edge

3.08

1.88

-0.33

11.25

13.25

16.53

Loss due to elastic defonnation after stage 1 stressing Top fibre

-0.26

-0.26

-0.21

Bottom fibre

0.36

0.35

0.29

Direct

0.20

0.20

0.20

Top

2.62

1.42

0.09

Bottom

10.69

12.69

16.04

Top

-0.55

-0.55

-0.46

Bottom

0.76

0.76

0.63

0.44

0.44

0.44

Resultant

Loss of slip stage 1

--

Direct

---

I

--·-· ··Reference

Description

Output

Resultant Top

1.62

0.43

-0.81

I

Bottom

9.48

11.49

14.97

I

Creep loss after stage 1stressing Top

-0.27

-0.31

-0.28

Bottom

0.37

0.42

0.39

Direct

0.21

0.24

0.27

Top

1.14

-0.12

-0.25

Bottom

8.90

10.82

14.31

I I I

I I

!

Resultant

Loss of prestress due to shrinkage of the concrete

Top

-0.19

-0.19

-0.16

Bottom

0.26

0.25

0.21

Direct

0.15

0.15

0.15

0.79

0.23

0.06

Resultant Top Bottom

I

I

8.49

10.41

I

13.94

After stressing cable set 2 at stage 2 after one month Top Bottom

-0.70

-0.70

-0.14

7.38

7.53

6.90

Resultant stresses after stressing cable set 2

0.09

Top Bottom

15.87 --

--

---

-·

-0.47

-0.08

17.95

20.84

-~-------·-·

I

Description

nee

Output

Loss due to elastic deformation

Cable set 1 Top

-0.13

-0.13

-0.11

Bottom

0.18

0.18

0.15

Direct

0.10

0.10

0.15

Top

-0.15

-0.24

0.18

Bottom

15.59

17.67

20.55

Top

-0.06

-0.06

-0.05

Bottom

0.08

0.08

0.06

Direct

0.04

0.04

0.04

Top

-0.05

-0.14

0.09

Bottom

15.47

17.55

20.44

Top

0.00.

0.00

0.00

Bottom

0.00

0.00

0.00

Direct

0.00

0.00

0.00

Top

-0.05

-0.14

0.09

Bottom

15.47

17.55

20.44

Top

-0.23

-0.23

-0.19

Bottom

0.31

0.31

0.26

Direct

0.19

0.19

0.19

Resultant

Cable set2

Resultant

Anchorage loss


Resultant Cable set 2 anchorage loss

r-·

Description

.. Reference

Output

Resultant Top

0.37

0.28

-0.29

Bottom

14.97

17.05

20.00

Loss of prestress due to creep of concrete after 30 days cable set 1 Top

-0.15

-0.15

-0.11

Bottom

0.20

0.20

0.14

Direct

0.12

0.12

0.10

Top

0.11

0.01

-0.09

Bottom

14.66

16.73

19.75

Top

-0.06

-0.06

-0.05

Bottom

0.08

0.09

0.06

Direct

0.05

0.05

0.04

Top

0.00

-0.10

0.00

Bottom

14.53

16.60

19.65

Resultant

cable set 2

Resultant

Loss of prestress due to relaxation of steel

Top

-0.96

-0.95

-0.79

Bottom

1.27

1.26

1.08

Direct

0.76

0.76

0.76

Top

1.71

1.61

-1.55

Bottom

12.49

14.57

17.81

Resultant

r-------,-------------------------------------------------------------------------.-------, Description Output ·Reference Immediately after placing the concrete Mid span

P = 20,545,417 N

Prestressing force after initial losses, Moment at mid span due to self weight of the beam, Moment at mid span due to screed concrete,

Sectional Modulus of the bottom fiber, Cross sectional Area, Resultant Eccenticity of cables,

c±>

kNm

Mg2 = 1804

kNm

= 1.42E+09

mm 3

zpb

= 1.07E+09

mm 3

AP

=2. 74E+06

mm 2

=652

mm

Z pi

Sectional Modulus of the top fiber,

PIA

=6913

Mgt

e

Pxe/Zpt

Mgl/Zpt

8

Mg2/Zpt

[r

(±)

Neutral Axis

c±> PIA

CB

~

8

Pxe/Zpb

P

Stress at top most fibre

Mg2/Zpb

Mgl!Zpb

Pxe

Mg,

Mg2

=-A - - - + - - + - z

z

pi

=2.98

z

pi

pi

N/mm2

2.98 N/mm

stress at bottom most fibre

=

z- z

p Pxe Mg, A +2 ph ph

= 10.80

2

N/mm2

Mg2 ph

10.80 N/mm

2

---------L---------------------------------------------------------------------------------------------------L--------~

,.----··-

Description

Reference

Output

Similarly,

Initial prestressing force

!

Quarter Span

Beam Edge

25,537,504

26,019,000

4419206

4351826

21,118,298

21,667,174

5184.77

0

1352.96

0

1.42E+09

1.42E+09

Total pre stress losses Prestressing force after initiallosses,P/N Moment due to self weight of the

Mg, .

beam/(N/mm)

Mgz

Moment due to screed concrete/(N/mm)

zp, zpb

Sectional Modulus of the top fiber, Sectional Modulus of the bottom fiber, Cross sectional Area, Resultant Eccentricity of all tendons,

mm

3

3

1.07E+09

1.07E+09

AP mm2

2.74E+06

2.74E+06

mm

e

mm

648

542

2

-0.67

1.54

2

12.16

16.77

N/mm

Stress at top most fibre Allowable stress at bottom most fibre

N/mm

I

loss of prestress due to differential shrinkage After placing screed on the beam,

5.200M

__[_ t.Q6QM Prestress Designers Handbook P.W.Ables

p.290M

l

.J

rm

~w,

A

-

0.400rv

0

cr.1isr1

a

-

eP

__[_Q.132M

-r250M

..........

7

1.667M Q 952M

To find the neutral axis of added concrete, Taking moments along the axis through point A

X

=

(60x5200x30+0.5x72x5200x842x400x250x125-2x0.5x400x40x263) (60x5200+0.5x72x5200+2x400x250+2x0. 5x400x40)

=-5.77 mm ea +ep = 1670-5.77-ypb mm =712 ea eP

Ia Ixp

--= m - -

.

......... (1)

.......... (2)

ence

'•

I ar' -_ 9.40E+09

mm4

IxJ

mm 4

= 1.02E+12

nil -

Modular ratio=1

I

I) _ Moment of Inertia of added concrete I x~

Moment of inertia of precast concrete

_

e / e ; P: i

~=

m I__a I xp

j

i = 0.01

(1) And (2)

eP = 706

mm

ea = 7

mm

AP = 2.74E+06

mm

2

lxp = 1.02E+12

mm

4

Au = 7.15E+05

mm

2

Ia = 9.40E+09

mm

4

Ea,Ep = 34000

N/mm

2

F - Force exerted by differential Shrinkage

' 11& =

F APxEP

+

F AaxEa

++

. F xeP 2 Fxe

2

a

lxpxEP /axEa

11& = 0.43x200x1 0-6 F=

90

11&

- -1- +

t3.4

l

I

I

400-4

.

l

Description

AP xEP = 1.30E+06

1

++

Aa xEa

Loss of direct stress = 0.47 Bending stress at the top fibre = 0.65 Bending stress at the bottom fibre= -0.86

N

N/mm2 N/mm

2

N/mm2

jstresses at mid span after placing screed Stress at the top fiber = 2.98 .

Stress at the bottom fiber= 10.80

2 p

e

2

_ _a_

lxp xEP Ia xE,

Bending moment due to this force= 917586487 Nmm

At mid span

e

N/mm2 2

N/mm

Output

r.·fu

renee

Description

Output

- M

zq

Stress at the top fibre of the composite section due to Mq -

ct

2

= 3.14

N/mm

Stress at the top level of the pre cast section

= 2.70

N/mm2

Stress at the bottom fibre of the composite section due to Mq

=

Mq

zch 2

= -5.19

N/mm

Stress at the top most fiber of composite section

= 1.86

N/mm2

Resultant stress on the precast section top fibre

= 4.56

N/mm

Stress at the bottom most fiber of pre cast section

= 9.47 = 4.28

N/mm

2

N/mm

2

Resultant stress on the precast section bottom fibre

2

Similarly Quarter span Beam Edge Moment due to live loads

4.64E+09

O.OOE+OO

2.36

0.00

2.02

0.00

-3.89

0.00

Resultant stress on the precast section top fibre

1.35

1.54

Resultant stress on the precast section bottom fibre

8.27

Stress at the top fibre of the composite section due to Mq

Mq

zct Stress at the top level of the pre cast section Stress at the bottom fibre of the composite section due to Mq Mq

zcb ----·--

-

16.77 -

--

-

r·

Description

Reference

Output

Claculation of the balance losses after 2nd monthLoss of prestress due to shrinkage of the concrete

Loss of prestress due to shrinkage of the concrete = Rest 50% of the shrinkage loss

BS 5400 ILoss of stress

I!J>

Direct force =

Ac

Part4

="420000

cl6.7.2.4

3.45E+06

Table29

N/mm

= 0.12

2

tiP x e Loss of stress due to loss of moment at the top fiber = zclt

e = 799

zc!,

mm

= 1.97E+09

mm 3 N/mm 2

Loss of stress due to loss of moment at the top fiber = ..0.17

N/mm

Stress at top of precast section = ..0.15

2

tiP x e

Loss of stress due to loss of moment at the bottom fiber = - - - -

Z Zc!b

clb

= 1.19E+09

Loss of stress due to loss of moment at the bottom fiber = 0.28

mm3 N/mm2

Resultant stresses after live loading

Resultant stresses at top fiber= 9.47 Resultant stresses at botttom fiber = 4.28

N/mm2 N/mm

2


N/mm2


N/mm2

Loss due to creep In cabe set one at mid span Loss of pre stress = Rest 50% of the initial loss Loss of prestress = 1026763

--··

N

Loss of direct stress at the top fibre = 0.30

N/mm2

Loss of strees at the top fiber due to moment = -0.42

N/mm2

Loss of strees at the bottom fiber due to moment = 0.69

N/mm

2

r---

Description

Reference

Output

Resultant stresses


N/mm2


N/mm2

Resultant stresses after creep loss Resultant stresses at top fiber after all the losses = 8.49

N/mm2

-

Resultant stresses at botttom fiber after all the losses = 4.26

N/mm2

Mid Span

Stress resultants after rest of the losses for the quarter span and beam edge

Resultant streses after placing the screed Quarter span

Beam edge


1.35

1.54


8.27

16.77

Quarter span

Beam edge

1300240

1300240'

Loss of direct stress at the top fibre

0.47

0.47

N/mm2

Loss of strees at the top fiber de to moment

0.65

0.65

N/mm2

Loss of strees at the bottom fiber de to moment

-0.86

-0.86

N/mm


0.23

0.42

N/mm 2


6.93

15.44

N/mm2

Losses due to diferential shrinkage Loss of prestress

Quarter span

I

N

2

Beam edge

Losses due to shrinkage Loss of prestress

-

420000

420000


0.12

0.12

N/mm 2

Loss of strees at the top fiber due to moment

-0.17

-0.17

N/mm2

Loss of strees at the top fiber of the pre cast section due to moment

-0.15

-0.15

N/mm2

Loss of strees at the bottom fiber due to moment

0.28

0.28

N/mm2

Resultant stresses at top fiber after final shrinka_g_e losses Resultant stresses at botttom fiber after final shrinkage losses

-0.04

0.15

N/mm2

6.53

15.03.

N/mm2

N

~-

,----· Description

Reference

Output

Losses due to creep

1116654

1121095


0.32

0.32

N/mm

2

Loss of strees at the top fiber due to moment

-0.45

-0.46

N/mm

2

Loss of strees at the top fiber of the pre cast section due to moment

-0.39

-0.39

0.75

0.75

N/mm2


-0.04

0.15

N/mm


6.53

15.03

N/mm2

Resultant stresses at top fiber after all the losses

0.74

-0.63

N/mm

Resultant stresses at botttom fiber after all the losses

5.46

13.96

N/mm

Loss of p_!estress

Loss of strees at the bottom fiber due to moment

~

N

2

2

2 I

;

Allowable tensile stress at service,

famn

Allowable compressive stress at service,

farrax

=-2.55 =20

N/mm2 N/mm 2

Resultant prestress force after all the losses

--

Initial prestressing force/(N)

Prestress Loss/(N)

Final prestressing force/(N)

Percentage prestress Loss/(%)

Mid Span

24,956,816

8,908,745

16,048,072

36

Quarter span

25,537,504

9,088,525

16,448,979

36

Beam edge

26,019,000

9,097,408

16,921,592

35

--

Description

·.Reference

Output

Check for ultimate limit state

BS 5400-4 Cl.6.3.3.

-

"'E ~ ~ -... rJ)

.

rJ)

~

1pu

Ym 0.8fpu

Ym

"

___ /! I I

I I

I

I

I

I

I

I

200kNif

0.005

2

...... &I

&2

Strain

fpu Characteristic strength of pre-stressing tendons

rm Partial safety factor for strength fpu

Ym

:16.3.3.3.1e

fpu

=1770 =1.15 =1539

N/mm

=1231

N/mm

=200,000 =1231

N/mm2

N/mm

2

2

Ym 0.8/pu

Ym

E, &I

2

200000

&2

-----

=0.0062 0.005 = =0.0127

+

1539 200000

Reference

Description

Output

Mid Span

RxP

Prestressing force after all the losses

= 16,048,072

Area of steel = 21000 Stress in steel = 764

N mm

2

N/mm2

Corresponding strain in steel = 0.0038

Check the ultimate capacity immediately after laying the screed

Y pi = 715

mm

Height to the bottom fiber from the neutral axis, = 952

mm

Height to the top fiber from the neutral axis,

Second Moment of Inertia along x axis, = 1.016E+12

mm4

=2.74E+06

mm2

Eccentricity of cables, e

= 652

mm

Stressatthetendonlevel

= RxP +RxPxe2


Ap

Ec

(Mxl +Mg2)xt

IX

I

=6.98

Nlmm2

= 34000

Nlmm

X

2

Strain in concrete at tendon level = 6.98

34000

= 0.0002 Strian in prestressing steel due to strain in concrete = 0.0002 x - Depth to the neutral axis from the top fibre d - Effective depth of tendons

d

= Eccentricity + = 1367

Assume

X

= 0.6

d Depth to the neutral axis,x

=820

Y pi mm

·. -·-·

Description

•• Reference

Output

0.0035

v

820.2

/o

547 .

0.00233333

. Total strain in steel This strain value is within

i

=0.0064

c 1andc2

Therefore linear ineterpolating witin this region in the above graphthe corresponding stress can be obtained 0.2xfu Corresponding stress

Force in steel

=

(E-E 1 )x(

(c 2

P)

Ym

(

-&1 )

=1241

N/mm

=26,058,076

N

0.8xfpu

Ym

)

2

I

:L6 3.3.3.1b

= 0.4x feu Sectional area under compression =Section above the neutral axis =1,670,000 mm 2 Stress in concrete

Force in concrete = 33,400,000

N

Ultimate Moment carrying capacity = Force in concrete x ( d- ~)

2 d = 1367

mm

X= 820.2

mm

=31960

kNm

Ultimate Moment carrying capacity

.

___

_,

Description

.. Rete renee

Output

3S 540 0-2

rf3

= (M gl + M g2) x r fJ x r Ft. = 1.1

:15.

YFL

= 1.15

Maximum moment when screed is laid

1

:1 5.1

<

Mgl +Mg2

1

= 8716965000 Nmm

Maximum moment when screed is laid = 11 027

kNm

.

Check the ultimate capacity with full live load present

Cross sectional Area, = 3450000

mm

Total Depth, = 1764

mm

Total width of the top flange, = 5200

mm

Height to the top fiber from the neutral axis, = 665 Height to the bottom fiber from the neutral axis,

= 1099

Moment of Inertia, = 1.31E+12

Ultimate moment= 21997

Assume

X

-

mm mm 4

mm

kNm

= 0.25

d d

=1464

Depth to the neutral axis,x = 366

mm

mm

0.0035

7 /o 366

1398

0.0134

Total strain in steel = 0.0174 This strain value is within

e 1ande2

2

mm

ok

Description

Reference

Output

Therefore linear ineterpolating witin this region in the above graph the corresponding stress can be obtained

(&-&J)x(

0.2xf u P )

Ym

Corresponding stress stress =

(

(&2-&1)

0.8xfpu

Ym

)

0

= 1760

Force in steel = 36,967,391

N

N

0.4xfcu

Stress in concrete =

Sectional area under compression = Section above the neutral axis

= 1,716,000

Force in concrete = 34,320,000

mm

N I

Ultimate Moment carrying capaCity = Force in concrete x ( d-!.)

2

"

d = 1464

mm

x=366

mm

UHimate Moment carrying capacity = 43964

kNm

ok

Oeasign for shear at ultimate limit state

Calculation of shear forces For a beam of udl w/m and length I, the shear force at a distance x fro the support can be derived as follows

f

t

Rl

-

Rz

J

--

--

--

X

tsF ---

-·

--

---····------

-

r-----"

Description

. Reference

Output

R1 -wxx-SF = 0

SF=R1 -wxx R-R-wxl I- 2---

2

i

I.

= 29 Weigl = 65.76 wscl = 17.16 wacl = 4.37 whr = 0.585 WJW = 8.10 W.v = 0.85 HA UDL on the edge beam = 30.00 HA KEL on the edge beam = 120.00 udl due to pedestrian load = 7.5

i I

c

m kN/m kN/m kN/m kN/m kN/m kN/m

!

kN/m KN kN/m

0

7.25

14.5

25

29

953520

476760

0

-690480

-953520

Shear force due to Screed Concrete,SF2/(N)

248820

124410

0

-180180

-248820

Total shear force due to dead load/(N)

1202340

601170

0

-870660

-1202340

63307

31654

0

-45843

-63307

Shear force due to hand raii/(N)

8483

4241

0

-6143

-8483

Shear force due to footwalki(N)

117450

58725

0

-85050

-117450

12325

6163

0

-8925

-12325

Total sher force due to super imposed loas/(N)

189240

94620

0

-137036

-189240

Shear force due to Live loads,HAUDL /(N)

435000

217500

0

-315000

-435000

Shear force due to Live loads,HA KEL /(N)

60000

60000

-60000

-60000

-60000

Shear force due to pedestrian load/I(N)

108750

54375

0

-78750

-108750

Total shear force due to live loads/(N)

603750

331875

-60000

-453750

-603750

Length along the Beam /(m),X Shear Force due to self wt of the beam,SF1 /(N)

Shear force due to Asphalt Concrete, /(N)

Shear force due to kerb/(N)

Description

·.Reference

Output

Check for Maximum shear stress

BS 5400-4 Section uncracked in flexture cl.6.3.4.2

The ultimate shear resistance

vco

vco = 0.67b~(f/ +fcpJ;) J;

Eq(28)

=0.24x fJ: = 1.70

N/mm

2

f.cp = YFLX(-+--) RP RPey Act

I

RP = 16,048,072 N i

Ac = 3.45E+06

mm

YFL = 1.15

cl.4.2.3

at centroid

y

=0

/cp

= 5.35

h

BS 5400-4

h

Cl.6.3.4.5

vco

N/mm

2

mm =1764 =(350-2/3X60)X2 mm =620 =2,533,945 N/mm2

vco 2,533,945 2

N/mm

BS 5400-4 Section cracked in flexture cl.6.3.4.3

The ultimate shear resistance

Vcr = 0.037bd.fl: +Me, V M

. :1.4.2.3

.

-·

Mer

=(0.37fl: + /P,)x I I y

fP,

RPey = YFL x RP (-+--)

YFL

=1.15

RP

=16,048,072 =3.45E+06 =1.31E+12

Ac /xcl

Acl

I

N mm2 mm4

Eq(29)

-··

Description

·.Reference

Output

y =

Ycth

= 1099

mm

e = 652

At mid span

mm

fpt = 15.45

Nmm

feu =50

N/mm

2

Me: =(0.37.Jf: + fp 1 )x//y = 2.15E+10

I I

Mid Span

Quarter Span

Beam Edge

YFL

1.15

1.15

1.15

RP

16,048,072

16,448,979

16,921,592

A

3.45E+06

3.45E+06

3.45E+06

Jxcl

1.31E+12

1.31E+12

1.31E+12

y

1099

1099

1099

e

652

648

542

15.45

15.77

14.50

2.15E+10

2.19E+10

2.04E+10

fpt Mer

Nmm

BS 5400-2 Table 1

Load Fcators-Uitimate limit state

3S 5400-4 d 4.2.3.

Nominal shear force/(N)

Type of load

YFL

YJ3

Mid Span

Ultimate load/(N)

Quarter Span

Beam Edge

Mid Span

Quarter Span

Beam Edge

Dead Load

1.15

1.1

0

601170

1202340

0

760480

1520960

Super lmpos-

1.75

1.1

0

94620

189240

0

182143

364286

Live Loads(H

1.5

1.1

-60000

331875

603750

-99000

547594

996188

-99,000

1,490,217

2,881,434

Total Ultimate shear force

:s

feu =50

5400-4

16 3.4.5

-·

v

Allowable shear force for grade 50 concrete

v

N/mm

b = 620

mm

d = 749

mm

IIIIX

= 23,219,000

N

2

--Description

·-Reference

Output

At mid quarter and beam edge the shear force is less than allowable shear force force for grade 50 concrete. Nominal Moment/(Nmm)

Type of load

rFI.

rf3

Ultimate Momeni/(Nmm)

Beam Edge

Mid Span

M

Mid Span

Quarter Span

0.00

1.10E+10

8.27E+09

O.OOE+OO

Quarter Span

Beam Edge I

Dead Load

1.15

1.1

8.72E+09

6.54E+09 .

Super ImposE

1.75

1.1

2.16E+09

1.62E+09

0.00

4.16E+09

3.12E+09

O.OOE+OO

Live Loads(H

1.5

1.1

4.02E+09

3.02E+09

0.00

6.64E+09

4.98E+09

O.OOE+OO

2.18E+10

1.64E+10

O.OOE+OO

Total Ultimate Moments

At mid span

Mer= 2.15E+10 v =-99000

At mid span

M

At mid span

d

.

.

b

=2.18E+10 = 749 =620

Vc,

= 0.037bdfJ: +Mer V

Nmm mm mm

M-

= 2.19E+05 Midspan

Quarter Span

Beam Edge

14.5

7.25

0

/(mm)

620

620

620

/(mm)

749

745

639

2.15E+10

2.19E+10

2.04E+10

2.18E+10

1.64E+10

O.OOE+OO

-99000

1490217

2881434

0

0.005

0.022

25,537,504

26,019,000

0

131,676

572,280

-99,000

1,358,541

2,309,154

/(N)

219,115

2,114,664

0

/(N)

2,533,945

2,533,945

2,533,945

/(N)

219,115

2,114,664

0

Chianage/(m)

b d

Mcri(Nmm)

M

v

/(Nmm) /(N)

Sin(e)

Prestressing force/(N) 24,956,816 Vertical component of prestressing force Resultant ultimate shear force

V,,

-

-

N

vco vc

If Vis greater than Vc shear reinforcement are needed. ---·

------·

vc

is lesser of

vcr and v"

Description

·• R'eference

Shear reinforcement

Output

Mid span

Quarter Span

Beam Edge

not needed

not needed

needed

v + 0.4bdt- vc

Asv = sv-

BS 400-4 cl.6 1.4.4

0.87 fyvdt

f yv - Characteristic strength of reinforcement A.v - Total cross sectional area of the leg of the links

s.

- link spacing along the length of the beam

1l

2 Asv =-¢ xn 4

¢

- diametre of the links

n - number of legs Assumed diametre of the links = 16

mm

I

n =4 b = 620

mm.

Asv = 804

mm

/yv

N/mm2

= 460

d, = 749 At beam span

mm

v

= 2881434

vc

=0

s

=

v

Asv

2

X

(0.87 fyvdt)

v + 0.4bdt - vc

= 79

mm

s. 79 mm

Maximim spacing = 0.75d1 or 4b 0.75d, = 562

mm

4b = 2480

-·-

----

--

-----

-~

-----

----

---·-

mm

--

-

-

...---Description

. Reference

BS 5400-4

Output

'At mid span provide minimum reinforcement

cl.6.3.4.4

A~ (

0.8:/,.) ~ 0.4

Sv

sv

=

N I mm'

Asv(0.87Jyv) 0.4b mm

= 1298

>maximum spacing provide spacing of 400 mm

BS 5400-4

'Check for Deflection

1990 ci.A21

The deflection of a beam is given by, 2

a= K I I e 1

rb

a

- Deflection

Ie

-

effective span of the member

K, - coefficient depending on the shape of the bending moment diagram 1

- curvature at mid span

rb 1 d2 -=____1:'_

rb

dx2

From simple bending formula

1 M -=--r6 EJ

Ec - Youngs modulus of concete I

- Second moment of area of the section

Therefore

a=K/2 M 1 e E

J

1298 mm

Description

·.Reference

Output

BS 5400-4 Deflection of the beam due to dead load 1990

KI

Table 34

I,

= 0.104 = 29

m

M=Mg 1

At mid span

=6913020000 Ec = 34000 I = lxp = 1.02E+12

Nmm Nmm mm mm

2

4

4

zM

downward

a=Kl, - -

EJ

a

= 17.50

a mm

downward

17.50 mm

Deflection due to prestress

= 16,048,072 N Eccentricity = 652 mm Bending Moment = 1.0463E+1 0 Nmm K 1 = 0.125 4 I = 1.02E+12 mm 2 perN/mm Creep coefficient = 0.000036 t/J =creep coefficient X elastic modulus = 1.224

Prestressing force afetr all the losses

"

E 1+¢

=

E elf

= 15,288

N/mm2

Deflection due to prestress

=70.82

mm

upward

Resultant deflection

=53.31

mm

upward

BS8110-3 1997

Allowable deflection for flange or rectangular beams

=

CL3 4.6.3

Span 250

= 116

-·--


--

--

ok

------

mm ---·-

·. Reference

Description

Output

Deflection of the beam during service condition

Deflection due to screed Bending moment due to screed concrete -

= Mgz =1803945000

Nmm

=0.104 4 I = 1.02E+12 mm Creep coefficient =0.000036 per N/mm2 (; =creep coefficient X elastic modulus =1.224 Kl

E

=

efT

E 1+ ¢

=15,288

N/mm2

2M a=Kle - -

,,

EJ


=10.16

mm

downwards

=43.16

mm

upwards

Deflection due to footwalk,hand rails, wearing surface,kerb and pedestrian load(Super imposed loads)

=851512500 Bending moment due to hand rails =61498125 Bending moment due to wearing surface =458975750 Bending moment due to pedestrian load =788437500 Bending moment due to kerb =89356250 Bending moment due to footwalk

Bending moment due to footwalk,hand rails, wearing surface and pedestrian load

=2249780125

Nmm Nmm Nmm

Nmm

Nmm

..---Description

Reference

Output

= 0.104 I = Ixcl = 1.31E+12 Creep coefficient = 0.000036 K1

I

mm

4

mm

4

perN/mm

2

=creep coefficient X elastic modulus -=1.224

¢

Eeff

=

E

1+¢

=15,288

N/mm2

2M e £I c

a=KlI


= 9.83

mm

downwards

=33.32

mm

upwards

Deflection due to HA UDL(SLS)

BS 5400-2 Table 1

'·

=3153750000 Nmm Load factor (HA alone) = 1.2 K, =0.104 4 I = Ixcl mm =1.31E+12 mm4 perN/mm 2 Creep coefficient =0.000036 ¢ =creep coefficient X elastic modulus =1.224

Bending moment due to HA udl

Eeff

=

E

1+¢

=15288

2

N/mm

2M

1 -a=K,.

EJ

=13.78 ~

mm

downwards

~-

Reference

Description

Output


=-19.54

mm

downwards

Deflection due to HA KEL(SLS) BS 5400-2 Table 1

j

=870000000 Nmm Load factor (HA alone) = 1.2 K~· =0.083 4 I = Jxcl mm =1.31E+12 mm4 Creep coefficient =0.000036 perN/mm 2 rjJ =creep coefficient X elastic modulus =1.224

Bending moment due to HA KEL

E eff =

E 1+¢

=15288

N/mm2

2M a=K1/e - -

EJ

'·

=3.66

mm

downwards

a Resultant deflection

=-15.88

mm

downwards

-15.88 mm

B.S8110-3 1997 cl.34.6.3

Allowable deflection for flange or rectangular beams

=

Span 250

=116 Resultant deflection =ok

-·

mm

r-·

.~eference

I

n-u-·

I

-

I

Output

BS 5400-4,Design of End Block

1990

Tensile stress

cl.6.7.5

J;m

1------

I I

0

0.2yo

2y0

0.5y0

Distance from loaded face

Fig: Transverse stress distribution along block centreline

---1 0.125M t-

J;m -

Olt@]

Maximum transverse tensile stress

2yp0f]

f

2yo

L_t_

Design of Spiral

Size of the end block= 175 x 175 mm

Yo - Half the side of end block Y po - Half the side of loaded area

J>* - Loadinthetendon Fhst -

Bursting tensile force

2y0 = 175

mm

2ypo = 125

mm

3S 5400-4 1990

·able 30

2 Ypo = 0.71 2yo

F;,SI : pk

0.11

pk = 1m X Jacking end fOrce Jacking end force = 1300950

N

Ym = 1.15

Pk ~

= 1496092.5

J>k 1496093

N

N

Description

.~eference

Output Fbst

= 164570

Fhst

N

164570 N

Design strength of reinforcement = 0.87 JY Characteristic strength of mild steel

fY = 250

N/mm2

Allowable strength of mild steel bars

0.87JY = 218

Nlmm 2

F;,s,

Area of steel required =

0.87xfY

= 757

mm2

Using 10 mm diameter bar, number of required= 4.817 turns in the spiral Say,= 5

(2Yo- 0.2yo)

Pitch of a spiral =

number of turns of the spirals

= 31.5 Concrete Reinforcement to resist spalling force Bridge Design Spalling force = 0.04Pk LA.Ciark p 146 = 59844

mm

N

Area of reinforcement required= 0.04P* 0.87Ivy Characteristic strength of Tor steel

f yv

= 460

Area of reinforcement required = 149.5

mm

2

Diameter of the bar = 10 Number of bars required = 1.90 Say,= 2

h5

h4

END BLOCK

Considering the blocks in the bottom flange ·

.-Description

.•Reference

Output

Number of plates = 12 Width of the equivalent area of all the plates = 125

mm mm2

Area of one plate = 15625 Length of the equivalent plate = 1500

= 100 Centroid of the equivalent plate from the bottom = 100 h1

BS 5400-4

In horizontal direction

- 1990

mm mm mm

2 Y po = 1500 2y0 3200

=0.47

Te.ble 30 Fbst

pk In vertical direction

= 0.18

2 Y po = 125 2y0 200 = 0.625 Fbst

=0.23

pk Selecting maximum from above two cases Fbst

= 0.23

pk

Total prestressing force

pk = Y m X Jacking end fOrce

Jacking end force= 15611400

Ym

N

= 1.15

Pk = 17953110

N

=4129215 Design strength of reinforcement = 0.87 JY Characteristic strength of Tor steel /y =460 Allowable strength of Tor steel bars 0.87/y =400 Fbst Area of steel required = 0.87 x fY

N

Total force on the plate

Fbst

= 10318 Diameter of the bar = 20 Reuired number of bars with two legs = 16.42

N/mm2 N/mm2

mm2

Say,= 17

= 1700 Spacing = 106

Legth of the beam reinforcement are provided

·say,

100

mm. mm

Description

·Reference

'•

Output

Considering the blocks in the web

Number of plates = 5 mm

Width of the equivalent area of all the plates = 125

mm

Area of one plate = 15625

2

Total area of the equvalent plate = 78125

BS

5400-4

Length of the equivalent plate = 625

mm

Centroid of the equivalent plate from the bottom = 625

mm

In horizontal direction

1990

2Ypo = 125 350 2yo

Table 30

= 0.36 Fbsr

= 0.213

pk

In vertical direction

2yp0 = 625 1670 2yo = 0.37

~

Fbsr

= 0.208

pk Selecting maximum from above two cases Fbst

= 0.213

pk Total prestressing force

pk

= ym

X

Jacking end furce

Jacking end force= 6504750

N

Ym = 1.15 Total force on the plate

pk = 7480463

N

= 1592270

N

Fbst

Design strength of reinforcement = 0.87 [y Characteristic strength of Tor steel

[y = 460

N/mm

Allowable strength of Tor steel bars 0.87 fY = 400 Area of steel required =

N/mm2 Fbst

0.87xfy = 3979

mm2

Diameter f the bars = 16 Required number of bars with two legs

= 9.89

Say,= 10

2

.

..Reference

Description

Output

Spacing

= 189

mm

Say,

100

mm

'··

Concrete , Bridge Checking of Interface shear stresses Design to 5400by L.A. Clerk

I

V,S

vh = - -

Jbe

pp 108 109

v1o Horizontal interface shear stress

be width of the interface

v_

Vertical shear stres at the point considered

"

S- First moment of area about the neujral axis of the one side interface

~

I - Second moment of area the transformed composite section

__J.e6el'l

I

-~"x

5.2001'1 4.4t01'1

o~rl'l

0.250JLJ·

.4001'1

-

NA of composite secti.m

Neutral axis of the Screed

X

(60x5200x30+0.5x72x5200x84-2x250x400x125-

X

=

2x0.5x40x400x265) (60x5200+0.5x72x5200+2x250x400+2x0.5x40x400)

= -5.81

mm

= 4400 Distance between the neutral axes of slab and = 563

mm

Contact width of the beam

be

composite beam

mm

.

Description

••Reference

Area of the slab = 715200

·.

S

First moment of area

Second Moment of area of the composite sectiO!J

vu

Ultimate shear force

mm2

=402793600 = 1.31 E+12

mm

3

mm

4

= 99,000

N

=

vh

Horizontal interface shear stress

Output

VIF

vus Ib.

0.007

2

N/mm

Similarly, Quarter Span Beam Edge Contact width of the bearn/(mm)

b.

4,400

4,400

563

563

715,200

715,200

402793600

402793600

1.31E+12

1.31E+12

1,490,217

2,881,434

0.104

0.202

Distance between the neutral axes of slab and composite beam/(mm) Area of the slab/(mm First moment of area/(mm

3

)

2

)

S

Second Moment of area of the composite section/(rd Ultimate shear force[{Nl

Vu

vh

Longitudinal Shear Longitudinal shear should not exceed the lesser of following

(a)

k,fcuLs

(b)

v, Ls + 0. 7 A.fy Where,

v1 _ Ultimate longitudinal shear stress (Table 31)

s 5400-4 ·1990 .7.423

k, _ Constant depending on the concrete bond A - Area of fully anchored reinorcement crossing shear plane

e

Ls

f

_

Y_

Length of the shear plane Characteristic strenght of reinforcement

feu _ Characteristic cube strength of concrete

v; _ Longitudinal shear force = 0.202 Applied shear force = 887

Maximum longitudinal shear stress applied

2

N/mm N/mm

Description

~eference

Eqn (a)

BS 5400-4

~=

Output

krf,-uL,. N/mm 2

fcu= 50

1990

k1=

Surface type 2

Table 31

0.09

Ls= 4400

mm

klfcuLf= 19800

N/mm

BS 5400-4 1990

Eqn (b)

Table 31

for Surface type 2

~ = v 1Ls VI

+ 0.7 Aefy

=0.5

N/mm

2

Ls = 4400 Assume there are no other reinforcement

Ae = 0

v 1Ls + 0.7 Aefy = 2200

N//mm

Therefore, ultimate shear force 2200N/mm is greater than the applied shear force 893 N/mm. Therefore interface shear reinforcement is not necessary.

~S 5400-41According to the BS 5400 provide 0.15% of contact area of reinforcement acorss the surface.

1990

:;t."7 .4.2.3

mm2/m

0.15 % of surface area = 660 Diameter of the bar = 12

mm

No. bars needed = 6

/m

Check for shear at support

Ultimate shear at support occurs due to HB Load???????? Ultimate shear force at the support = 2 1881,434 Prestressing force at the support (force along the cable)= 16 921 592 1

ngle of the cable at the beam edge to the vertical

1

= 1.05727 = 61

N N rad degrees

Vertical component of the Prestressing force at= 8 312 790 the support

N

Resultant vertical force at the beam edge = -5,431,356

N

I

I

3 5400-4 Shrinkage Reinforcement and Temperature reinforcement 1990 To prevent cracking due to shrinkage and thermal movement,reinforcement should be provided in the direction of any restraint to such movements. 5 ,8.9

As> k,(Ac -0.5Aco,)

Calculation

Reference

Output

Design of transverce reinforcement Consider load combinations Combination1 Dead loads + Superimposed dead loads Combination1 + HB load on mid of lanes Combination2 Combination3 = Combination1 + HA UDL + HA KEL mid Combination1 + HA UDL + HA KEL edge Combination4 Combination1 + HB load on lane CombinationS

= =

= =

Maximum transverce ultimate bending moment of top flange at mid of the beam using grillage analysis

Combination

Distance(m) 1.2 2.6 16 22.4 -48.3 38.11 -17.4 9.25 -48.3 38.11

0 -5.14 -5.44 -0.08 -5.44

Combination3 Combination4 CombinationS Max bending moment

4 18.5 -82.9 -15.68 -82.9

5.2 -5.18 -2.98

-0.77 -s.18 I

Ultimate Bending Moment 60

.E

40

E

z

20

::.::: c

0

~

CD

E 0

~~J~

:IE m c :ac

-60

m

-80

Gl

1

/

3

2

\.

y

4

Distance(m)

-100

Design of top reinforcement of top flange Ultimate bending moment,

Mu

=

Assume,Serviceble bending moment

Ms

= =

Assume

16

82.9

KNm/m

Mu/1.5 55.3 KNm/m

mm diameter Tor steel can be used

Effective depth for cover of 50mm,

250 mm h= d = 250-50-8 =

192 1000 50 460

b = feu= [y = M bd2fcu

=

mm mm N/mm2 N/mm2

0.045

< 0.15

Single reinforcement is enough :; 5400-4

990 5.3.2.3

Mu Z

= 0.87J;,AsZ =

(I

----(1)

1.1/,y As )d - - - -(2) . fcubd

6

Reference

Calculation

Output

'•

from equations (1) and (2)

z2 -dZ + z2 -

1.1Mu = 0 0.87 fcub 192 z + 2096 = 0

=

180

mm

=Z Z =

180

mm

Z If Z < 0.95d, therefore

Z

M

A=--~

0.87Zfy

s

BS 5400-4

l OOAS bd

1\990 cl 5.8.4

=

1151

=

0.599

mm

2

Which is greater than the minimum of 0.15% of bd Therefore

=

1151

mm2

= = = =

5.7 10 1000 10 100

mm

=

2011

mm2

As

No. of bar required No. of bar provided Spacing of bar

Area of reinforcement provided

Checking of crack width for top flange Assume reinforcement provided BS 5400-4

1990

T

16

Modulus of elasticity of steel, Modulus of elasticity of concrete,

Es

Ec

~

4.3.2.2 fable 3

100 mm

@

=

200 KN/mm 2 28 KN/mm 2

=

Stress and strain distribution of section 3S ~00-4

E

1~90

:15.8.8.2 N/A

h

_,JJ~--

II 0

0 I

I

f. Step- 1

; = where,

a

af/J[~l + :l/J E

=-s = Ec A

A. 'I'

=-s bd =

14.29 0 .0105

28 2

E =-KN/mm c

x

-

= 80.17 mm •

X

-1]

2

< 0.95d

---Reference

..

Calculation Step- 2

Output

Z=d-x 3

=

165.3 mm

hb=~~

Step- 3

2

< 0.45fcu

2

< 0.87fy

= 8.342 N/mm Satisfied

Ms

Step- 4

fs=AZ s

=

166.2 Nfl!lm Satisfied Step- 5

&I=

.fs

Es

= Step- 6

[~] d-x

0.001262

&=Is

Es

s

= &2

=

M= g M= q

Moment due to pennanent load, Moment due to live load,

£2

Therefore,

0.000831

=

Mq) 1- xlO _ [3.8b,h(a'-dc)][( &sAs(h- de) Mg 9]

48

KNm KNm

35 0.0002

>0

&m =&! -&2

=

0.0011

>0

Therefore section is cracked Step -7

c5

A _U

coo.

Step- 8 Design crack width

_ ac,-

68.6

mm

3ac,£m

= =

l+2(acr -Cco%-dJ 0.22

mm

< 0.25mm

Crack width satisfied Therefore, provide T 16@

100 mm

T @

) 6400-4

Secondary reinforcement Minimum area of secondary reinforcement

=

0.12

%ofbd

990 5.8.4.2

For grad~ of 460, reinforcement

=

0.12x1000x192 100 • 2

16 100

..

I

Use

10

mm diameter Tor steel


= = =

2.93 4 250

mm


=

314

mm /m

Therefore, provide T 10@

2

250 mm

T

@ Ultimate bending moment,

Mu

=

38.11


Ms

= =

Mu/1.5 25.4 KNm/m

Assume

12

KNm/m


h= d=


250 250-50-6 194 1000 50 460

=

b = feu=

!y = M hd fcu

-2 - -

mm mm mm 2 N/mm 2 N/mm

0.020

< 0.15

Single reinforcement is enough

Mu

3S 5400-4

1r.9o :15.3.2 3

Z

= 0.87 /yA.Z

----(1)

= {1- 1.1 Jy+As)d

----(2)

fcubd from equations (1) and (2)

zz -dZ +

1.1Mu =0 0.87 fcub

Z 2 -I94Z + 964 = o

=

Z If Z > 0.95d, therefore Z

189

mm

= 0.95d = 184

mm

Z

M 0.87Zfy

A=--

•

s 5400-4

IOOAS bd

1990 5.8 4

=

517

=

0.266

mm

2



As =

517

= = =

4.6 8

mm

1000 8 .

~?t::

........

2

> 0.95d

10 250

.....

~

Output

Calculation

Reference

=


mm2

905

Checking of crack width for top flange Assume reinforcement provided

T

12

@

125 mm

&m =&1-&2

=

0.0008

>0

Therefore section is cracked •

3acr&m

=

Design crack width

l+2(acr -cco%-dJ

=

0.17

mm

<0.25mm

Crack width satisfied

Therefore, provide T 12 @

125 mm

T 12 @ 125

Crack width is calculated using above precedure in the top of top flange

Seconda~

as· 5400-4

reinforcement Minimum area of secondary reinforcement

=

1990 cl ~.8.4.2

For grade of 460, reinforcement

= =

Use

10

0.12

%ofbd

0.12x1000x194 100 2 mm /m 233



= = =

2.96 4 250

mm


=

314

mm2/m 250 mm


Maximum transverce ultimate bending moment of bottom flange upto 1.?Om from edge of the beam using grillage analvsis Combination Combination3 Combination4 CombinationS Max bending moment

0 -112.87 -116.4 -108.99 -116.4

Distance(m) 1.6 3.2 -112.45 36.48 -119.31 38.34 36.23 -106.67 -119.31 38.34

,.. ,... "·~ ~"" ~ ...... '-.

l)

T 10 @ 250

--

r

Reference

Calculation

Output

Ultimate Bending Moment

I

60 40 20

'E

"E

z

~ c:

0 -20

E

-40 -60 -80 -100 -120

Gl

0

::E Cl

c:

'i5 c: Gl

Ol

...

/ 0.5

1

~

1.5

2

2.5

3

3.5

Distance(m)

-

j

-140

Design of toQ reinforcement of bottom flange Ultimate bending moment, Mu Assume,Serviceble bending moment

Assume

16

Ms

=

119.31

KNm/m

= =

Mu/1.5 79.5

KNm/m


h= d=


250 250-50-8 192 1000 50 460

=

b = feu= fy =

M 2 bd fcu

=

mm mm mm N/mm2 N/mm2

0.065

< 0.15


) 5400-4 }90 5.3.2.3

Mu

=

0.87 f;,A.Z

z

=

(1- I. I};yA, )d ----(2)

----(1)


Z 2 -dz +

z

2

-

192

I.IMu =0 0.87fcub

z + 3017

=0

z If Z < 0.95d, therefore

=

Z=Z =

z

A=

lOOA. bd

~0

.8_4

·-

·~-

.

mm

175

mm

M 0.87Z/"y

s

5400-4

175

=

1704

=

0.887

Wbich is greater than the minimum of 0.15% of bd A

mm 2

<0.95d

'·

Therefore

A,=

1704

= = = =

8.5 13.33 1000 13.33 75

mm

=

2681

mm



Assume reinforcement provided

T

@

16

75

2

mm

&m =&1-&2 =

>0

0.0013

Therefore section is cracked

3acr&m

Design crack width

= 1+2(acr-Cco%-dJ =

0.24

mm

< 0.25mm

Crack width satisfied Therefore, provide T 16 @

75

mm

16 75

Crack width is calculated using above precedure in top of top flange

BS 5400-4 1990 cl5.8.4.2

Minimum area of secondary reinforcement

=


= =

Use

10

0.12

% ofbd

0 .12x1 000x192 100 2 mm /m 230



= = =

2.93 4 250

mm


=

314

mm /m


2

250 mm

:;ign of bottom reinforcement of bottom flange ugto 1.70m from edge Ultimate bending moment, Mu 38.34 KNm/m

=


Assume

12

Ms

= =

Mu/1.5 25.6

KNm/m



h d

= =

250 mm 250-50-6

IT 10 @ 250

I

Reference

Calculation b = 1000 50 fc..u 460 fy =

Output

mm N/mm 2 N/mm 2

=

M bd2fc.u

---

0.020

< 0.15


BS 5400-4 1990 cl 5.3.2.3

= 0.87 f;,A.Z

Mu

1.1/,Y A. )d - - - - ( 2) fcubd

= (I -

Z

--- -(1)

from equations (1} and {2)

z2 -dZ +

z

2

-

l.lMu =0 0.87/cub

194 z + 970 Z

If Z > 0.95d, therefore Z

=0 =

189

mm

= 0.95d = 184

mm

Z

> 0.95d

M

A=-s 0.87Zf;,

BS 5400-4 1990 cl5.8.4

1OOA.

=

520

=

0.268

mm

2

bd Which is greater than the minimum of 0.15% of bd Therefore

As



mm2

=

520

= = = =

4.6 8 1000 8 125

mm

=

905

mm 2


T

12

@

&m

125 mm =&, -&2

=

0.0008

>0


3acr&m

Design crack width

=

1+2(acr -Cco%-dJ

=

0.17

mm

< 0.25mm

Crack width satisfied •

,.

.

Reference I

l

Calculation Therefore, provide T 12 @

125 mm

Output

T 12 @ 125


BS 5400-4 1990 cl 5.8.4.2

Seconda!Y reinforcement Minimum area of secondary reinforcement

= =


= Use

0.12

% ofbd

0.12x1000x194 100 mm2/m 233


10


= = =

2.96 4 250

mm


=

314

mm2/m


T

250 mm

10 @ 250

Maximum transverce ultimate bending moment of bottom flange of interior slab of the beam using grillage analysis I

Combination Combination3 Combination4 CombinationS Max bending moment

0 1.33 1.23 2.57 2.57

Distance(m) 1.6 -2.01 -2.11 -2.02 -2.11

3.2 0.25 2.12 0.61 2.12

I

Ultimate Bending Moment

.€

E

z

X:: ;::: c Cl)

E

0

:::E CJ c :sc Cl)

a:a

3 -1

-2 -3

Design of top and bottom reinforcement of bottom flange Ultimate bending moment, Mu 2.57 Assume,Serviceble bending moment

Ms

=

KNrnlm

=

Mu/1.5 1.7 KNm/m

= Assume

12

mm

d~ameter

Tor steel can be used

h . d

=

200

= .200-50-6

mm

3.5

I

Reterence

Ca\cu\at\on = 144 b = 1000 50 f..u = 460 ~=

M

-2

Output

mm mm N/mm 2 N/mm 2

0.002

< 0.15

bd fcu

Single reinforcement is enough BS 5400-4 1990 cl5.3.2.3

Z =(1-

1.11, A

~s)d

----(1)

----(2)


z2 -dZ+

l.IMu =0 0.87 fcub

Z 2 -144Z +65 = o

=

142

mm

= 0.95d Z = 137

mm

Z

> 0.95d


M As = 0.87ZJ;,

IS 5400-4 1990 15.84

S00-4

= 0.87~AsZ

Mu

IOOAS bd

=

47

=

0.033

mm2

Which is not greater than the minimum of 0.15% of bd Therefore

As =

216

=

1.9


mm2

=

8

=

1000

=

125

mm

=

905

mm2

8


Checking of crack width for top flanae Assume reinforcement provided

T

12

125 mm

@

Em =El -Ez

=

-0.0029

<0

Therefore section is uncracked Therefore, provide T 12 @

125 mm


Secondary reinforcement Minimum area of secondarv reinforcement

I

0 1?

OL. nf brl

T @

12 125

.-Reference

I

I

Calculation

1990 cl 5.8.4.2


Use

10

= 0.12x1000x192 100 2 = 173 mm /m



= = =

2.20 4 250

mm


=

314

mm /m


2

250 mm

T

10 @ 250

Maximum transverce ultimate bending moment of web upto 3.00m from edge of the beam using grillage analysis

Combination Combination3 Combination4 CombinationS Max bending moment

0 23.57 11.2 26.86 26.86

Distance(m) 0.68 1.32 -103.36 -117.61 -112 -120.89 -98.12 -113.1 -112 -120.89


:§ E

z

~ ~

20~ -2~

c CD E 0 ::E IJ) c :cc

-100

m

-120

CD

-40 -60

I

"b.Z

0.4

0.8

0.6

""'-

1

Distance(m)

-80

-140

Design of reinforcement of web Ultimate bending moment, Assume,Serviceble bending moment

Assume

16

Output

Mu

=

120.9

KNrn/m

Ms

= =

Mu/1.5 80.6

KNrn/m

mm diameter Tor steel can be used mm 350 h= d = 350-50-8


b = feu= fy =

=

292 1000 50 460

=

0.028

M 2

bd fcu

SinniA rAinfnrr<>mi:>nt ic: onnoonh

.

mm mm N/mm2 2 N/mm

< 0.15

1.2

1.4

I

.---Reference

Calculation

= 0.87 fyAsZ

Mu

BS 5400-4 1990 cl 5.3.2.3

Output

=

Z

(1-

I.l~"A Jy s

----(1) )d ----(2)

fcubd from equations (1) and (2}

z2 -dZ +

1.1Mu 0.87 f:-ub 2 Z -292Z +3057 Z

=0 =o

=

281

mm

277

mm

> 0.95d

= 0.95d

If Z > 0.95d, therefore Z Z

=

M As= 0.87Zfy

IOOAS bd

BS 5400-4 1990 cl 5.8.4

=

1089

=

0.373

mm

2


As =

1089

mm

= = =

=

5.4 8 1000 8 125

mm

=

1609

mm



2

2

Checking of crack width for web Assume reinforcement provided

T

16

@

125 mm

8 m =&1-&2

=

0.0010

>0


=

Design crack width

=

3ac,em 1+ 2(acr -ccom)/ /(h-dc) 0.22

mm

< 0.25mm

Crack width satisfied Therefore, provide T 16@

125 mm

T @


s 5400-4

Secondary reinforcement Minimum area of secondary reinforcement

=

0.12

% ofbd

990 5.8.4.2

For grade of 460. reinforcement

= n 1?Y1nnnv?Q?

16 125

I

Calculation

Reference

= Use

10

Output

100 350

2

mm /m



= = =

4.46 200

mm


=

393

mm2/m

5


T

200 mm

@

Maximum transverce ultimate bending moment of interior web of the beam using grillage analysis

--

Combination

Distance(m) 0.68 1.32 -1.65 2.12 2.14 -0.1 2.2 3.1

0 -9

Combination3 Combination4 CombinationS Max bending moment

-4.1 2.8 -9

2.2

3.1


.E

2

z

0

~

~

E

-

~ r::: Gl E 0 ::!!: Cl r::: '6 r::: Gl

Ill

0.2

-2

0.6

0

0.8

1.2

1.4

Distance(m)

-4 -6 -8

-10

Design of reinforcement of web Ultimate bending moment, Assume,Serviceble bending moment

Assume

12

Mu

=

Ms

= =

9

KNm/m

Mu/1.5 6.0 KNm/m

mm diameter Tor steel can be used mm 350 h= d= 350-50-6


b = feu= fy =

=

294 1000 50 460

=

0.002

M 2

bd fcu


mm mm N/mm2 N/mm2 < 0.15

.

10 200

Reference

Calculation

= 0.87 fYA.,Z

Mu

BS 5400-4

11990 cl 5 3.2.3

Output

----(1)

I. If. A

Z = (I

y

·'

)d ----(2)

f:.ubd from equations (1) and (2)

z2-dZ+ I.lMu =0 0.87 f."Ub

Z

2

-

294Z + 228 = o Z

=

293

mm

Z

= =

0.95d 279

mm


M

= 0.87 Zf;,

As

100As bd

3S 5400-4

1990 :15.84

=

81

=

0.027

mm

2

Which is not greater than the minimum of 0.15% of bd Therefore,

As



=

441

= = =

3.9 6.67 1000 6.67

=

150

mm

=

755

mm

mm

2

2


T

12

150 mm

@

8 m =&I -&2

=

-0.0030

<0

Therefore section is uncracked Therefore, provide T 12 @

150 mm


) 5400-4 ~30

5.8.4.2

Seconda!Y reinforcement Minimum area of secondary reinforcement

I I


Use

--

10

=

0.12

%ofbd

=

0.12x1 000x294 100 2 mm /m 353 =


No. of bar required

=

4.49

.

> 0.95d

Reference

Calculation

Output

No. of bar provided Spacing of bar

= =

200

mm


=

393

mm /m

5


2

T 10

200 mm

@ 200

. I

,,

-----

l~Jll!D

xog ~lp JO lfld lflO ~dWO:J

ZXIGN3ddV

,frlent I forces -frames Outputcase caseType Text Text

.,.._,

'Station m

0.003 COMBl

Combination

-1191.699

Combination Combination

-1191.699 -1142.132

-8.027E-14 -8.027E-14

1.001 COMBl 1.5 COMBl 1.999 COMBl


-1092.564 -1042.997

-8.027E-14

Combination

-993.43

-8.027E-14

2.498 COMBl 2.997 COMB1


-943.863 -894.296

-8.027E-14 -8.027E-14

2.224E-07 2.224E-07

4026.564 4026.564

2.054E-07

4608.8551 5166.412.

1.885E-07 1.716E-07

5699.H

1.547E-07 1.378E-07

6207.3231

1.209E-07

7149.298:

1.209E-07 1.208E-07

7149.298: 7151.981:

6690.678:

Combination

-894.296

-8.027E-14

Combination

-893.998 -1175.509

-8.027E-14 220.606

2.225E-07

5561.953:

-1175.178 -1175.178

220.5727 220.5727

2.224E-07 2.224E-07

5566.932~

-1121.369 -1067.56 -1013.752

214.803

2.054E-07

6348.324~

209.0334 203.2638

1.885E-07 1.716E-07

7836.905~

1.547E-07 1.378E-07


Max Max

Combination

Max

Combination

Max


Max Max

1.5 COMB2 1.999 COMB2

Combination

Max

-959.943

197.4942

2.498 COMB2 2.997 COMB2


Max Max

-906.134

191.7246 185.9549

Combination

Max Max

0.003 COMB2 0.003 COMB2 0.502 COMB2 1.001 COMB2

-·--

M3 KN-m

3 COMB! 0 COMB2

0 COMB2

r··-

-8.027E-14

M2 KN-m

2.997 COMB!

2.997 COMB2 3 COMB2

t-·

T

0.003 COMBl 0.502 COMBl

0.502 COMB2 1.001 COMB2

-

V2 KN

KN-m -8.027E-14

0.003 COMB2 0.003 COMB2

-

'~

StepType Text


Min


Min Min


Min Min Min Min

-852.326 -852.326 -852.01 -1664.485 -1664.106 -1664.106 -1599.818 -1535.53 -1471.243

1.5 COMB2

Combination

1.999 COMB2 2.498 COMB2 2.997 COMB2

Combination Combination Combination

2.997 COMB2 3 COMB2


0 COMB3 0.003 COMB3 0.003 COMB3


Min Max Max

Combination

Max

0.502 COMB3 1.001 COMB3 1.5 COMB3


Max Max Max

-1090.092 -1030.544

1.999 COMB3 2.498 COMB3


2.997 COMB3 2-:997 COMB3 3 COMB3 0 COMB3 0.003 COMB3 0.003 COMB3 0.502 COMB3 1.001 COMB3 1.5 COMB3 1.999 COMB3 2.498 COMB3 2.997 COMB3 2.997 COMB3 3 COMB3 0 COMB1 0.003 COMB1

Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination Combination

Max Max Max Max

-911.45 -851.903 -792.356 -792.356 -792.058 -2079.877

Min Min Min

Max Min Min Min Min Min Min Min Min Min Min Min

-1406.955 -1342.667 -1278.38 -1278.38 -1277.986 -1150.057 -1149.639 -1149.639

-970.997

-2079.579 -2079.579 -2010.052 -1940.524 -1870.997 -1801.47 -1731.943 -1662.416 -1662.416 -1661.878 -893.998 -893.7

5566.932~

7104.982:1 8544.095~

9226.551 9884.2725

1.209E-07 1.209E-07

9884.2725

-220.606

1.208E-07 2.225E-07

9887.909 4022.9894

-220.5727 -220.5727

2.224E-07 2.224E-07

4026.5649 4026.5649

-214.803 -209.0334 -203.2638

2.054E-07 1.885E-07

4608.8556 5166.4123

185.9549 185.9188

1.716E-07

5699.235

-191.7246 -185.9549

1.547E-07 1.378E-07 1.209E-07

-185.9549 -185.9188

1.209E-07 1.208E-07

6207.3236 6690.6781 7149.2987 7149.2987,

599.316

2.225E-07 2.224E-07

-197.4942

599.316 599.316 585.8432 572.3703 558.8974 545.4246 531.9517 518.4788 518.4788 518.3168 -599.316 -599.316 -599.316 -585.8432 -572.3703 -558.8974 -545.4246 -531.9517 -518.4788 -518.4788 -518.3168 -8.027E-14 -8.027E-14

2.224E-07 2.054E-07 1.885E-07 1.716E-07

7151.9811 6686.6294 6692.8686 6692.8686 7598.5113 8479.42

9335.5946 1.547E-07 10167.0352 1.378E-07 10973.7418 1.209E-07 11755.7143 1.209E-07 11755.7143 1.208E-07 11759.8011 2.225E-07 4022.9894 2.224E-07 4026.5649 2.224E-07 4026.5649 2.054E-07 4608.8556 1.88SE-07 5166.4123 1.716E-07 5699.235 1.547E-07 6207.3236 1.378E-07 6690.6781 1.209E-07 7149.2987 1.209E-07 7149.2987 1.208E-07 7151.9811 1.208E-07 7151.9811 1.207E-07 7154.6627

'"'"··)

ent Forces •:frames caseType Text Text m Combination 2.498 COMB1 Combination 2.997 COMB1 Combination 2.997 COMB1 Combination 3 COMB1 Combination 0 COMB2 Combination 0.003 COMB2 Combination 0.003 COMB2 Combination 0.502 COMB2 Combination 1.001 COMB2 Combination 1.5 COMB2 Combination 1.999 COMB2 Combination 2.498 COMB2 Combination 2.997 COMB2 Combination 2.997 COMB2 Combination 3 COMB2 Combination 0 COMB2 r--· Combination 0.003 COMB2 Combination 0.003 COMB2 Combination 0.502 COMB2 Combination 1.001 COMB2 Combination 1.5 COMB2 Combination 1.999 COMB2 Combination 2.498 COMB2 Combination 2.997 COMB2 Combination 2.997 COMB2 Combination 3 COMB2 Combination 0 COMB3 Combination 0.003 COMB3 Combination 0.003 COMB3 Combination 0.502 COMB3 Combination 1.001 COMB3 I-· Combination 1.5 COMB3 Combination 1.999 COMB3 Combination 2.498 COMB3 Combination 2.997 COMB3 2,997 COMB3 Combination Combination 3 COMB3 Combination 0 COMB3 -·· Combination 0.003 COMB3 Combination 0.003 COMB3 Combination COMB3 0.502 Combination 1.001 COMB3 Combination 1.5 COMB3 Combination 1.999 COMB3 Combination 2.498 COMB3 Combination 2.997 COMB3 Combination 2.997 COMB3 Combination 3 COMB3 Combination 0 COMB1 Combination 0.003 COMB1 Combination 0.003 COMB1 Combination 0.502 COMBl Combination 1.001 COMBl Combination 1.5 COMBl Combination 1.999 COMBl Combination 2.498 COMBl I

Station

-

OutputCase

StepType Text

Max

V2 KN

T KN-m

M2 KN-m

M3

844.132

-8.027E-14

-4.721E-07

7588.251

893.7 893.7

-8.027E-14 -8.027E-14

-0.000000489 -0.000000489

7154.662 7154.662

893.998

-8.027E-14

900.486

159.5566

-4.891E-07 -3.875E-07

7151.981 12977.867

KN-m

Max

900.871

159.5844

-3.876E-07

12975.5021

Max Max

900.871

159.5844 163.9693

-3.876E-07

12975.5021

-4.045E-07

12523.368~

-4.214E-07 -4.383E-07

11544.898:

Max Max Max Max

963.662 1026.453 1089.244 1152.034 1214.825

Max

1277.616

Max

1277.616 1277.986

Max Min Min Min Min Min

519.51 519.835 519.835 575.141

168.3542 172.7391 177.1241

-4.552E-07

181.509 185.8939

-4.721E-07

185.8939

-0.000000489 -0.000000489

185.9188 -159.5566

-4.891E-07 -3.875E-07

-159.5844 -159.5844

-3.876E-07 -3.876E-07

-163.9693

-4.045E-07 -4.214E-07

Min

630.447 685.753

-168.3542 -172.7391

Min Min

741.058 796.364

-177.1241

Min

851.67

Min Min Max

851.67 852.01 1243.878

Max Max

1244.416 1244.416

Max Max

1313.944

Max Max Max Max Max Max Min Min Min Min Min Min Min Min Min Min Min

-181.509 -185.8939 -185.8939 -185.9188 437.3176 437.4796 437.4796 450.9525

-4.383E-07 -4.552E-07 -4.721E-07 -0.000000489 -0.000000489

12046.500~

11018.562: 10467.4921 9891.688~ 9891.688~ 9887.90~ 9386.975~ 9385.186~

9385.186S 9075.2679 8740.6149 8381.2279 7997.1069 7588.2518 7154.6627

7154.6627 -4.891E-07 7151.9811 -3.875E-07 15326.7952 -3.876E..()7 15324.1064 -3.876E-07 15324.1064

464.4254 477.8982 491.3711

-4.045E-07 -4.214E..()7

14792.6315 14236.4225

-4.383E-07 -4.552E-07

13655.4795

1661.58 1661.58

504.844 518.3168

-4.721E-07 -0.000000489

518.3168

1661.878 422.088

518.3168 -437.3176

-0.000000489 -4.891E..()7

422.386 422.386

-437.4796 -437.4796

483.929 545.471 607.Q13 668.555 730.097 791.64 791.64 792.058 893.998 894.296 894.296 943.863 993.43 1042.997 1092.564 1142.132

-450.9525 -464.4254 -477.8982

1383.471 1452.998 1522.525 1592.052

-491.3711 -504.844 -518.3168 -518.3168 -518.3168 -8.027E-14 -8.027E-14 -8.027E-14 -8.027E-14 -8.027E-14 -8.027E-14 -8.027E-14 -8.027E-14

-3.875E-07 -3.876E-07 -3.876E-07 -4.045E-07 -4.214E-07 -4.383E-07 -4.552E-07 -4.721E-07 -0.000000489 ..().000000489 -4.891E..()7 -4.891E..()7 -4.892E..()7 -4.892E..()7 -5.061E..()7 -5.231E..()7 -0.00000054 -5.569E..()7 -5.738E-OJ

13049.8025 12419.3914 11764.2463 11764.2463 11759.8011 9386.9752 9385.1868 9385.1868 9075.2679 8740.6149 8381.2279 7997.1069 7588.2518 7154.6627 7154.6627 7151.9811 7151.9811 7149.2987 7149.2987 6690.6781 6207.3236 5699.235 5166.4123 4608.8556

-~

r ~·· , -

'

-

-

me ___1t Forces - ----- -,F1_ -,-----,--

...,

Station

OutputCase

CaseType

StepType

V2

m

Text

Text

Text

KN

T KN-m

M2

M3

KN-m

KN-m

2.99 7 COMB!

Combination

1191.699

-8.027E-14

-5.907E-07

2.997 COMB!

Combination

1191.699

-8.027E-14

-5.907E-07

4026.5649

3 COMB!

Combination

1191.997

-8.027E-14

-5.908E-07

4022.9894

0 COMB2

Combination

Max

1277.986

185.9188

-4.891E-07

9887.909

0.003 COMB2

Combination

Max

1278.38

185.9549

-4.892E-07

9884.2725 9884.2725

4026.5649

0.003 COMB2

Combination

Max

1278.38

185.9549

-4.892E-07

0.502 COMB2

Combination

Max

1342.667

191.7246

-5.061E-07

9226.551

1.001 COMB2

Combination

1406.955 1471.243

197.4942 203.2638

-5.231E-07 -0.00000054

8544.0954 7836.9058

1.5 COMB2

Combination

Max Max

1.999 COMB2

Combination

Max

1535.53

209.0334

-5.569E-07

7104.9821

2.498 COMB2

Combination

Max

1599.818

214.803

-5.738E-Q7

6348.3245

2.997 COMB2

Combination

Max

1664.106

220.5727

-5.907E-Q7

5566.9328

2.997 COMB2

Combination

Max

1664.106

220.5727

-5.907E-D7

5566.9328

3 COMB2

Combination

Max

1664.485

220.606

-5.908E-Q7

5561.9533

0 COMB2

Combination

Min

852.01

-185.9188

-4.891E-07

7151.9811

0.003 COMB2

Combination

Min

852.326

-185.9549

-4.892E-07

7149.2987

0.003 COMB2

Combination

Min

852.326

-185.9549

-4.892E-07

7149.2987

0.502 COMB2

Combination

Min

906.134

-191.7246

-5.061E-07

6690.6781

1.001 COMB2

Combination

Min

959.943

-197.4942

-5.231E-07

6207.3236

1.5 COMB2

Combination

Min

1013.752

-203.2638

-0.00000054

5699.235

1.999 COMB2

Combination

Min

1067.56

-209.0334

-5.569E-07

5166.4123

2.498 COMB2

Combination

Min

1121.369

-214.803

-5.738E-07

4608.8556

2.997 COMB2

Combination

Min

1175.178

-220.5727

-5.907E-D7

4026.5649

2.997 COMB2

Combination

Min

1175.178

-220.5727

-5.907E-07

4026.5649

3 COMB2

Combination

Min

1175.509

-220.606

4022.9894

0 COMB3

Combination

Max

1661.878

518.3168

-5.908E-07 --4.891E-07

11759.8011

0.003 COMB3

Combination

Max

1662.416

518.4788

-4.892E-07

11755.7143

0.003 COMB3

Combination

Max

1662.416

518.4788

-4.892E-07

11755.7143

0.502 COMB3

Combination

Max

1731.943

531.9517

-5.061E-07

10973.7418

1.001 COMB3

Combination

Max

1801.47

545.4246

-5.231E-07

10167.0352

1.5 COMB3

Combination

Max

1870.997

558.8974

-0.00000054

9335.5946

1.999 COMB3

Combination

Max

1940.524

572.3703

-5.569E-07

8479.42

2.498 COMB3

Combination

Max

2010.052

585.8432

-5.738E-Q7

7598.5113

2.997 COMB3

Combination

Max

2079.579

599.316

-5.907E-Q7

6692.8686

2.997 COMB3

Combination

Max

2079.579

599.316

-5.907E-07

6692.8686

3 COMB3

Combination

Max

2079.877

599.316

-5.908E-07

6686.6294

0 COMB3 0.003 COMB3

Combination

Min

792.058

-518.3168

-4.891E-07

7151.9811

Combination

Min

792.356

-518.4788

-4.892E-07

7149.2987

0.003 COMB3

Combination

Min

792.356

-518.4788

-4.892E-07

7149.2987

0.502 COMB3 1.001 COMB3

Combination

Min

851.903

-531.9517

-5.061E-07

6690.6781 6207.3236

1.5 COMB3 1.999 COMB3

Combination

Min

911.45

-545.4246

-5.231E-07

Combination

Min

970.997

-558.8974

-0.00000054

5699.235

Combination

Min

1030.544

-572.3703

-5.569E-D7

5166.4123 4608.8556 4026.5649

2.498 COMB3

Combination

Min

-5.738E-D7

Combination

Min

1090.092 1149.639

-585.8432

2.997 COMB3 2.997 COMB3

-599.316

-5.907E-D7

Combination

Min

1149.639

-599.316

-5.907E-07

4026.5649

3 COMB3 0 COMB1 0.003 COMB1


Min

1150.057

-599.316 -8.027E-14

-5.908E-D7

4022.9894

-5.908E-07

4022.9894

Combination

1192.295

0.003 COMB1 0.502 COMB1 1.001 COMB1 1.5 COMB!


1192.295 1241.862 1291.429

-8.027E-14 -8.027E-14

-5.909E-07 -5.909E-07

4019.4129 4019.4129

-8.027E-14 -8.027E-14


1340.996 1390.564

-8.027E-14 -8.027E-14

-6.078E-07 -6.247E-D7 -6.416E-07

3412.0908 2780.0346 2123.2444

Combination

1440.131

Combination

·1489.698

-8-027E-14 -8.027E-14

1.999 COMB1 2.498 COMB1 2.997 ~OMB1

-----

1191.997

-6.585E-07

1441.7201

-6.754E-07

735.4619

-6.923E-07

4.4695

~a ~ ;)Jqnoa ;}tp JO Jlld Jno J;)Jndwo;)

£XIGNHddV

8ridge0bj Text BOBJl BOBJl BOBJl BOBJl BOBJl BOBJl BOBJl BOBJl BOBJl BOBJl BOBJl 80811 80811 BOBJl BOBJl 808J1 BOBJ1 BOBJl BOBJl BOBJl BOBJ1 BOBJ1 IBOBJl IBOBJ1 BOBJl

Distance m

OutputCase

CaseType

StepType

T

V2

M3 KN-m

Text 12 COMB3

Text Combination

Text Min

KN -832.284

KN-m -356.3189

12 COMB3 12 COMB3 15 COMB3 15 COMB3

Combination Combination Combination Combination

Max Min

-832.284 -16.524

-356.3189 356.3189

Max Min

15 COMB3 15 COMB3 18 COMB3

Combination Combination Combination Combination

Max Min Max Min

407.88 -407.88 -407.88

299.7 -299.7 -299.7

407.88 832.284 16.524

17618.1721 10958.5321


Max

16.524

299.7 356.3189 -356.3189 -356.3189

Min

832.284

356.3189

17618.1721

Combination

Max

1256.687 437.3188

15528.5356

18 COMB3 18 COMB3 18 COMB3 21 COM83 21 COMB3 21 COMB3 21 COMB3 24 COMB3 24 COMB3 24 COMB3 24 COMB3 27 COMB3 27 COMB3 27 COMB3 27 COMB3 30 COMB3 30 COMB3


Min Max


Min Max Min

Combination Combination Combination Combination Combination Combination Combination Combination Combination

434.897 434.897 1256.687 1681.091 811.271 811.271 1681.091

-437.3188 -437.3188

10958.532: 10958.532J 17618.172J 18075.137f 11415.137€ 11415.137€ 18075.137«:

10958.5321

9588.7156

9588.7156 15528.5356 11913.5081

437.3188 518.3188 -518.3188 -518.3188

Max Min

2105.495 1175.675 1175.675 2105.495

518.3188 599.3187 -599.3187 -599.3187 599.3187

7305.6881 7305.6881 11913.5081 6773.0895 4109.4495 4109.4495 6773.0895

Max Min

2529.999 1522.018

680.3996 -680.3996

0 0

Max Min Max Min

~-

-

.....__

;-,;· _;;_-, ?f.-

•'-: '.I>' ~. ' ~-

·•;

~ }:)- '

OUT PUT DATA FOR DOUBLET BEAM

COMB!

Moment about Horizontal axis p Distance V2

m

KN

0 3 3 6 6 9 9 12 12 15 15 18 18 21 21 24 24 27 27 30

-2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07 -2.95E-07

KN

-1522.018 -1217.615 -1217.615 -913.211 -913.211 -608.807 -608.807 -304.404 -304.404 -3.02E-08 -3.01E-08 304.404 304.404 608.807 608.807 913.211 913.211 1217.615 1217.615 1522.018

V3

T

M2

KN

KN-m

KN-m

6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09 6.84E-09

1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E,14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14 1.75E-14

6.39E-08 4.34E-08 4.34E-08 2.29E-08 2.29E-08 2.37E-09 2.37E-09 -1.82E-08 -1.82E-08 -3.87E-08 -3.87E-08 -5.92E-08 -5.92E-08 -7.97E-08 -7.97E-08 -l.OOE-07 -l.OOE-07 -1.21E-07 -1.21E-07 -1.41E-07

M3 KN-m

-1.33E-06 4109.4495 4109.4495 7305.6881 7305.6881 9588.7156 9588.7156 10958.5321 10958.5321 11415.1376 11415.1376 10958.5321 10958.5321 9588.7156 9588.7156 7305.6881 7305.6881 4109.4495 4109.4495 -4.23E-07

COMB3 Distance

ItemType

m

--·

"--·-

p KN

0 Max 0 Min 3 Max 3 Min 3 Max 3 Min 6 Max 6 Min 6 Max 6 Min 9 Max 9 Min 9 Max 9 Min 12 Max 12 Min 12 Max 12 Min 15 Max 15 Min 15 Max 15 Min 18 Max 18 Min 18 Max 18 Min 21 Max 21 Min 21 Max 21 Min 24 Max 24 Min 24 Max 24 Min 27 Max 27 Min 27 Max 27 Min 30 Max 30 Min

-2.95£-07 -4.56£-07 -2.95E-07 -4.56£-07 -2.95E-07 -4.56E-07 -2.95E-Q7 -4.56£-07 -2.95£-07 -4.56£-07 -2.95E-07 -4.56E-07 -2.95E-07 -4.56E-07 -2.95E-07 -4.56E-07 -2.95E-07 -4.56E-Q7 -2.95E-07 -4.56E-07 -2.95E-07 -4.56E-07 -2.95£-07 -4.56£-07 -2.95£-07 -4.56E-07 -2.95E-07 -4.56E-07 -2.95£-07 -4.56£-07 -2.95£-07 -4.56E-07 -2.95E-07 -4.56£-07 -2.95£-07 -4.56£-07 -2.95E-07 -4.56E-07 -2.95E-07 -4.56E-07

V2 KN

-1522.018 -2530.018 -1175.675 -2105.495 -1175.675 -2105.495 -811.271 -1681.091 -811.271 -1681.091 -434.897 -1256.687 -434.897 -1256.687 -16.524 -832.284 -16.524 -832.284 407.88 -407.88 407.88 -407.88 832.284 16.524 832.284 16.524 1256.687 434.897 1256.687 434.897 1681.091 811.271 1681.091 811.271 2105.495 1175.675 2105.495 1175.675 2529.999 1522.018

V3 KN

1.54£-04 -1.54£-04 1.54£-04 -1.54£-04 1.54£-04 -1.54E-Q4 1.54£-04 -1.54£-04 1.54£-04 -1.54£-04 1.54£-04 -1.54£-04 1.54£-04 -1.54E-04 1.54E-Q4 -1.54E-Q4 1.54E-Q4 -1.54E-D4 1.54£-04 -1.54£-04 1.54£-04 -1.54£-04 1.54£-04 -1.54E-04 1.54£-04 -1.54E-Q4 1.54£-04 -1.54£-04 1.54£-04 -1.54E-04 1.54£-04 -1.54E-04 1.54E-04 -1.54E-04 1.54£-04 -1.54£-04 1.54£-04 -1.54E-04 1.54£-04 -1.54£-04

T

M2

KN-m

KN-m

680.3996 -680.3996 599.3187 -599.3187 599.3187 -599.3187 518.3188 -518.3188 518.3188 -518.3188 437.3188 -437.3188 437.3188 -437.3188 356.3189 -356.3189 356.3189 -356.3189 299.7 -299.7 299.7 -299.7 356.3189 -356.3189 356.3189 -356.3189 437.3188 -437.3188 437.3188 -437.3188 518.3188 -518.3188 518.3188 -518.3188 599.3187 -599.3187 599.3187 -599.3187 680.3996 -680.3996

-0.0046 0.0046 -0.0042 0.0042 -0.0042 0.0042 -0.0037 0.0037 -0.0037 0.0037 -0.0032 0.0032 -0.0032 0.0032 -0.0028 0.0028 -0.0028 0.0028 -0.0023 0.0023 -0.0023 0.0023 -0.0018 0.0018 -o.0018 0.0018 -0.0014 0.0014 -0.0014 0.0014 -9.24£-04 9.24£-04 -9.24E-Q4 9.24E-04 -4.62£-04 4.62£-04 -4.62£-04 4.62E-04 -2.18E-Q7 -1.41£-07

M3 KN-m

-1.33£-0( -2.06£-0( 6773.0895 4109.4495 6773.0895 4109.4495 11913.508 7305.6881 11913.508 7305.6881 15528.536 9588.7156 15528.536 9588.7156 17618.172 10958.532 17618.172 10958.532 18075.138 11415.138 18075.138 11415.138 17618.172 10958.532 17618.172 10958.532 15528.536 9588.7156 15528.536 9588.7156 11913.508 7305.6881 11913.508 7305.6881 6773.0895 4109.4495 6773.0895 4109.4495 -4.23£-07 -6.54£-07

1

COMB2 Distance

ItemType

p KN

m

0 Max 0 Min 3 Max 3 Min 3 Max 3 Min 6 Max 6 Min 6 Max 6 Min 9 Max 9 Min 9 Max 9 Min 12 Max 12 Min 12 Max 12 Min 15 Max 15 Min 15 Max 15 Min 18 Max 18 Min 18 Max 18 Min 21 Max 21 Min 21 Max 21 Min 24 Max 24 Min 24 Max 24 Min 27 Max 27 Min 27 Max 27 Min 30 Max 30 Min

-2.95E-07 -3.99E-07 -2.95E-07 -3.99E-07 -2.95E-07 -3.99£-07 -2.95£-07 -3.99E-07 -2.95£-07 -3.99£-07 -2.95£-07 -3.99£-07 -2.95£-07 -3.99£-07 -2.95E-Q7 -3.99E-Q7 -2.95£-07 -3.99£-07 -2.95£-07 -3.99£-07 -2.95£-07 -3.99£-07 -2.95£-07 -3.99E-Q7 -2.95E-07 -3.99E-07 -2.95E-07 -3.99E-07 -2.95E-Q7 -3.99£-07 -2.95E-07 -3.99E-07 -2.95E-07 -3.99E-07 -2.95E-07 -3.99E-07 -2.95E-07 -3.99E-07 -2.95E-07 -3.99E-07

V2 KN

-1522.018 -2092.018 -1201.127 -1690.103 -1201.127 -1690.103 -871.223 -1297.199 -871.223 -1297.199 -532.319 -913.295 -532.319 -913.295 -184.416 -538.392 -184.416 -538.392 172.488 -172.488 172.488 -172.488 538.392 184.416 538.392 184.416 913.295 532.319 913.295 532.319 1297.199 871.223 1297.199 871.223 1690.103 1201.127 1690.103 1201.127 2091.973 1522.018

V3 KN

5.41£-05 -5.41£-05 5.41£-05 -5.41£-05 5.41£-05 -5.41£-05 5.41£-05 -5.41£-05 5.41E-Q5 -5.41£-05 5.41£-05 -5.41£-05 5.41£-05 -5.41£-05 5.41E-Q5 -5.41£-05 5.41£-05 -5.41£-05 5.41E-Q5 -5.41£-05 5.41E-05 -5.41£-05 5.41£-05 -5.41E-05 5.41E-05 -5.41E-05 5.41£-05 -5.41E-05 5.41E-05 -5.41E-05 5.41E-05 -5.41E-Q5 5.41£-05 -5.41E-Q5 5.41E-05 -5.41E-05 5.41E-05 -5.41E-05 5.41E-05 -5.41E-05

T KN-m

263.6248 -263.6248 220.6068 -220.6068 220.6068 -220.6068 185.9194 -185.9194 185.9194 -185.9194 159.5569 -159.5569 159.5569 -159.5569 141.5194 -141.5194 141.5194 -141.5194 131.8069 -131.8069 131.8069 -131.8069 141.5194 -141.5194 141.5194 -141.5194 159.5569 -159.5569 159.5569 -159.5569 185.9194 -185.9194 185.9194 -185.9194 220.6068 -220.6068 220.6068 -220.6068 263.6248 -263.6248

M2 KN-m

-0.0016 0.0016 -0.0015 0.0015 -0.0015 0.0015 -0.0013 0.0013 -0.0013 0.0013 -0.0011 0.0011 -0.0011 0.0011 -9.74£-04 9.74£-04 -9.74£-04 9.74E-04 -8.12E-04 8.11£-04 -8.12£-04 8.11£-04 -6.49£-04 6:49E-04 -6.49E-04 6.49E-04 -4.87E-04 4.87E-04 -4.87E-04 4.87E-04 -3.25E-04 3.25E-04 -3.25E-04 3.25E-04 -1.62E-04 1.62E-Q4 -1.62E-04 1.62E-04 -1.91E-07 -1.41E-07

M3 KN-m

-1.33£-01 -1.80£-01 5648.413L 4109.449~

5648.413~ 4109.449~

10041.61€ 7305.6881 10041.616 7305.6881 13179.608 9588.7156 13179.608 9588.7156 15062.388 10958.532 15062.388 10958.532 15689.958 11415.138 15689.9581 11415.138 15062.388 10958.532 15062.388 10958.532 13179.608 9588.7156 13179.608 9588.7156 10041.616 7305.6881 10041.616 7305.6881 5648.4134 4109.4495 5648.4134 4109.4495 -4.23E-Q7 -5.71E-07

PXICINHddV

Shear Force ,Bending Moment Torsion

....

BOX

DOUBLET

COM2

Distance

ItemType

m

0 0 3 3 3 3 6 6 6 6 9 9 9 9 12 12 12 12 15 15 15 15 18 18 18 18 21 21 21 21 24 24 24 24 27 27 27 27 30 30

Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min

COM3

V2

T

M3

V2

KN

KN-m

KN-m

KN

-1490 -2060 -1176 -1664 -1176 -1664 -852 -1278 -852 -1278 -520 -900 -520 -900 -178 -532 -178 -532 172 -172 172 -172 532 178 532 178 900 520 900 520 1278 852 1278 852 1664 1176 1664 1176 2060 1490

264 -264 221 -221 221 -221 186 -186 186 -186 160 -160 160 -160 142 -142 142 -142 132 -132 132 -132 142 -142 142 -142 160 -160 160 -160 186 -186 186 -186 221 -221 221 -221 264 -264

0 0 5562 4023 5562 4023 9888 7152 9888 7152 12978 9387 12978 9387 14832 10728 14832 10728 15450 11175 15450 11175 14832 10728 14832 10728 12978 9387 12978 9387 9888 7152 9888 7152 5562 4023 5562 4023 0 0

-

--

--

:____

T

COM3

COM2 M3

KN-m KN-m

-1490 680 0 -2498 -680 0 -1150 599 6687 -2080 -599 4023 -1150 599 6687 -2080 -599 4023 -792 518 11760 -1662 -518 7152 -792 518 11760 -1662 -518 7152 -422 437 15327 -1244 -437 9387 -422 437 15327 -1244 -437 9387 -10 356 17388 -826 -356 10728 -10 356 17388 -826 -356 10728 408 300 17835 -408 -300 .11175 408 300 17835 -408 -300 11175 826 356 17388 10 -356 10728 826 356 17388 10 -356 10728 1244 437 15327 422 -437 9387 1244 437 15327 422 -437 9387 1662 518 11760 792 -518 7152 1662 518 11760 792 -518 7152 2080 599 6687 1150 -599 4023 2080 599 6687 1150 -599 4023 2498 680 0 0 1490 --680 _______ ·

V2

T

M3

V2

KN

KN-m

KN-m

KN

-1522 264 0 -1522 -2092 -264 0 -2530 -1201 221 5648 -1176 -1690 -221 4109 -2105 -1201 221 5648 -1176 -1690 -221 4109 -2105 -871 186 10042 -811 -1297 -186 7306 -1681 -871 186 10042 -811 -1297 -186 7306 -1681 -532 160 13180 -435 -913 -160 9589 -1257 -532 160 13180 -435 -913 -160 9589 -1257 -184 142 15062 -17 -538 -142 10959 -832 -184 142 15062 -17 -538 -142 10959 -832 172 132 15690 408 -172 -132 11415 -408 172 132 15690 408 -172 -132 11415 -408 538 142 15062 832 17 184 -142 10959 538 142 15062 832 17 184 -142 10959 913 160 13180 1257 532 -160 9589 435 913 160 13180 1257 532 -160 9589 435 1297 186 10042 1681 871 -186 7306 811 1297 186 10042 1681 871 -186 7306 811 1690 221 5648 2105 1201 -221 4109 1176 1690 221 5648 2105 1201 -221 4109 1176 2092 ·, 264 /I .·, IQ 2530 1522 ·-264 - .· _. 0./i522 .. __ ____:___

-------

--

-

T

M3

KN-m KN-m ( 680 ( -680 599 6773 -599 4109 599 6773 -599 4109 518 11914 -518 7306 518 11914 -518 7306 437 15529 -437 9589 437 15529 -437 9589 356 17618i -356 10959 356 17618 -356 10959 300 18075 -300 11415 300 18075 -300 11415 356 17618 -356 10959 356 17618 -356 10959 437 15529 -437 9589 437 15529 -437 9589 518 11914 -518 7306 518 11914 -518 7306 599 6773 -599 4109 599 6773 -599 4109 0 680 0 -680 -

Detailed Calculation for Box Girder Design

Recommend Documents