Detailed Calculation for Box Girder Design
February 22, 2017 | Author: leodegarioporral | Category: N/A
Short Description
Download Detailed Calculation for Box Girder Design...
Description
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~tiz 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
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
Eccentricity,e2/(mm)
379
500
586
638
655
Eccentricity,e3/(mm)
-902
-613
-406
-281
-240
Eccentricity,e4/(mm)
-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
Cross sectonal area of the precast section before grouting/(mm
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
)
, Second moment of area before 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
)
Cross sectonal area of the precast section before grouting/(mm
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
, Second moment of area before grouting/(mm
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
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
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
--
Total prestress loss
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
Loss of stress due to direct force loss
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 of stress due to direct force loss
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
Total prestress loss
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
Loss of stress due to direct force loss
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
Total prestress loss
1680000
Beam Ed e Cables considered
Stage 1 Stage2
As
a
mm2
N
Loss of 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
-0.46
0.63
St2 cbls
6300
504000
0.19
-0.19
0.26
St1 cbls
14700
0
0.00
0.00
0.00
Total prestress loss
--
M
Loss of stress due to direct force loss
.
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
Stress at tendon level = 9. 77
1
After 14 days of concreting,
Strength of concrete
=.36
N/mm 2
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
No. of bar required No. of bar provided Spacing of bar
= = =
2.93 4 250
mm
Area of reinforcement provided
=
314
mm /m
Therefore, provide T 10@
2
250 mm
T
@ Ultimate bending moment,
Mu
=
38.11
Assume,Serviceble bending moment
Ms
= =
Mu/1.5 25.4 KNm/m
Assume
12
KNm/m
mm diameter Tor steel can be used
h= d=
Effective depth for cover of 50mm,
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
Which is greater than the minimum of 0.15% of bd Therefore
No. of bar required No. of bar provided Spacing of bar
As =
517
= = =
4.6 8
mm
1000 8 .
~?t::
........
2
> 0.95d
10 250
.....
~
Output
Calculation
Reference
=
Area of reinforcement provided
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
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
=
For grade of 460, reinforcement
= =
Use
10
0.12
% ofbd
0 .12x1 000x192 100 2 mm /m 230
mm diameter Tor steel
No. of bar required No. of bar provided Spacing of bar
= = =
2.93 4 250
mm
Area of reinforcement provided
=
314
mm /m
Therefore, provide T 10@
2
250 mm
:;ign of bottom reinforcement of bottom flange ugto 1.70m from edge Ultimate bending moment, Mu 38.34 KNm/m
=
Assume,Serviceble bending moment
Assume
12
Ms
= =
Mu/1.5 25.6
KNm/m
mm diameter Tor steel can be used
Effective depth for cover of 50mm,
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
Single reinforcement is enough
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
No. of bar required No. of bar provided Spacing of bar
Area of reinforcement provided
mm2
=
520
= = = =
4.6 8 1000 8 125
mm
=
905
mm 2
Checking of crack width for top flange Assume reinforcement provided
T
12
@
&m
125 mm =&, -&2
=
0.0008
>0
Therefore section is cracked
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
Crack width is calculated using above precedure in top of top flange
BS 5400-4 1990 cl 5.8.4.2
Seconda!Y reinforcement Minimum area of secondary reinforcement
= =
For grade of 460, reinforcement
= Use
0.12
% ofbd
0.12x1000x194 100 mm2/m 233
mm diameter Tor steel
10
No. of bar required No. of bar provided Spacing of bar
= = =
2.96 4 250
mm
Area of reinforcement provided
=
314
mm2/m
Therefore, provide T 10@
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)
fcubd from equations (1) and (2)
z2 -dZ+
l.IMu =0 0.87 fcub
Z 2 -144Z +65 = o
=
142
mm
= 0.95d Z = 137
mm
Z
> 0.95d
If Z > 0.95d, therefore Z
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
No. of bar required No. of bar provided Spacing of bar
mm2
=
8
=
1000
=
125
mm
=
905
mm2
8
Area of reinforcement provided
Checking of crack width for top flanae Assume reinforcement provided
T
12
125 mm
@
Em =El -Ez
=
-0.0029
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
Which is greater than the minimum of 0.15% of bd Therefore
As =
1089
mm
= = =
=
5.4 8 1000 8 125
mm
=
1609
mm
No. of bar required No. of bar provided Spacing of bar
Area of reinforcement provided
2
2
Checking of crack width for web Assume reinforcement provided
T
16
@
125 mm
8 m =&1-&2
=
0.0010
>0
Therefore section is cracked
=
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 @
Crack width is calculated using above precedure in top of top flange
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
mm diameter Tor steel
No. of bar required No. of bar provided Spacing of bar
= = =
4.46 200
mm
Area of reinforcement provided
=
393
mm2/m
5
Therefore, provide T 10@
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
Ultimate Bending Moment 4
.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
Effective depth for cover of 50mm,
b = feu= fy =
=
294 1000 50 460
=
0.002
M 2
bd fcu
Single reinforcement is enough
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
If Z > 0.95d, therefore Z
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
No. of bar required No. of bar provided Spacing of bar
Area of reinforcement provided
=
441
= = =
3.9 6.67 1000 6.67
=
150
mm
=
755
mm
mm
2
2
Checking of crack width for top flange Assume reinforcement provided
T
12
150 mm
@
8 m =&I -&2
=
-0.0030
0.95d
Reference
Calculation
Output
No. of bar provided Spacing of bar
= =
200
mm
Area of reinforcement provided
=
393
mm /m
5
Therefore, provide T 10 @
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
Combination Combination
-1092.564 -1042.997
-8.027E-14
Combination
-993.43
-8.027E-14
2.498 COMBl 2.997 COMB1
Combination Combination
-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
Combination Combination
Max Max
Combination
Max
Combination
Max
Combination Combination
Max Max
1.5 COMB2 1.999 COMB2
Combination
Max
-959.943
197.4942
2.498 COMB2 2.997 COMB2
Combination Combination
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
Combination Combination
Min
Combination Combination
Min Min
Combination Combination
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
Combination Combination
0 COMB3 0.003 COMB3 0.003 COMB3
Combination Combination
Min Max Max
Combination
Max
0.502 COMB3 1.001 COMB3 1.5 COMB3
Combination Combination Combination
Max Max Max
-1090.092 -1030.544
1.999 COMB3 2.498 COMB3
Combination Combination
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
Combination Combination
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!
Combination Combination Combination
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
Combination Combination
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
Combination Combination
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
Combination Combination
Min Max
Combination Combination
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 -
View more...
Comments