Step By Step Design Of Psc Girder By Working Stress Method 68h4y
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DESIGN OF PSC GIRDER WORKING STRESS METHOD
1.0
SALIENT FEATURES AND DESIGN DATA c/c of pier to face of dirtwall angle of skew Span ( c/c of bearings) length of precast girder Span ( c/c of temporary s ) for precast girder No of girders clc distance of the girders clear carriage way width of footpath + ACB width of median Overall width of the deck width of deck slab beyond centre line of outer girder thickness of deck slab thickness of end diaphragm Grade of concrete
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
= = = = = = = = = = = = = = for PSC girder for RCC deck slab
M M
TYPICAL CROSS SECTION
2.0 2.1 a)
CALCULATION OF SECTIONAL PROPERTIES SECTION AT MIDSPAN (3,4,5,6) PROPERTIES OF PRECAST SECTION A = 0.621 m2 Yt = 0.889 m Yb = 0.861 m Effective width of the slab Minimum of the following
Icg Zt Zb
= = =
0.250
1 1/4th the effective span of the girder = 2 The distance between centres of the ribs of the girder 1 x( 1.50 + 3 The breadth of the rib plus 1/5 times the span 0.290 + 0.2 x . . . Effective width of the slab for M40 grade
24.400 4
=
6.100
1.500
)'=
3.000
24.400
= =
5.17 3.000
= b)
PROPERTIES OF COMPOSITE SECTION A Yt Yb
2.2
3.000
= = =
1.371 m2 0.585 m 1.415 m
Icg Zt Zb
= = =
SECTION AT (1,2) same as above for different sections
3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7
4.0
CALCULATION OF BENDING MOMENTS AND SHEAR FORCES AT VARIOUS SECTIONS BM & SF DUE TO SELF WEIGHT OF GIRDER BM & SF DUE TO DIAPHRAGMS BM & SF DUE TO INSITU DECK SLAB BM & SF DUE TO SUPERIMPOSED DEAD LOAD BM & SF DUE TO VEHICULAR LIVE LOAD BM & SF DUE TO FOOTPATH LIVE LOAD SUMMARY OF BENDING MOMENTS AND SHEAR FORCES AT VARIOUS SECTIONS CABLE PROFILE OF OUTER GIRDER (G1,G5) 4.1 ) CABLE POSITIONS AT MIDSPAN AND ANCHORAGES cable no Type of cable = Area of cable mm2. 98.74 = 2 UTS kg/mm . = days of prestress Total length of girder = Distance of Anchorage from Mid span = DISTANCES OF VARIOUS SECTIONS FROM AND MIDSPAN
Cable force Cables are stressed from both the end. Calculation of forces in the cables before and after slip (slip =
1 8 T 13 789.92 189.720478 21 24.600 12.200
6
Section
length of section l in (m)
k = 0.002
Angle theta in rad
k*l
mu = 0.17
x=kl+
e-x calculated for each
Force Diagram Calculation of slip SUMMARY OF CABLE FORCE AFTER SLIP: HORIZONTAL CABLE FORCE COMPONENTS (F = PCOS(Q)) VERTICAL CABLE FORCE COMPONENTS (F = PSIN(Q)) )CABLE ELONGATION Elongation =
7.0
fxL AxE
where, f L A
= = =
Average cable force at reference section (in kN) Length of cable (in mm) Area of cable (in mm2)
E
=
Youngs modulus (in N/mm2)
EFFECT OF FIRST STAGE PRESTRESS STRESSES IMMEDIATELY AFTER Ist STAGE PRESTRESS CALCULATION OF LOSSES DUE TO Ist STAGE PRESTRESS
7.1 7.2
1)
Losses due to creep in concrete ( cl.11.2 of IRC:18 - 2000 ) Creep strain in period between 9.22E-04 -
5.40E-04
... Creep loss
2)
Losses due to shrinkage of concrete ( cl.11.3 of IRC:18 - 2000 ) Shrinkage of concrete in the period of 4
=
3 days 42% 10 days 77% 3.82E-04 per 100 kg/cm2 stress in concrete at the centroid of prestressing steel. = 3.82E-004 x = = = =
3 days and
2.08E-04 creep strain x modulus of elasticity of H.T ste 2.08E-04 x 405.33 kg/cm2.
10
=
0.00043 -
0.0003
= = =
3)
Loss due to Elastic shortening
1.30E-04
1.30E-04
x
253.50 kg/cm2.
( cl.11.1 of IRC:18 - 2000 )
Modulus of Elasticity of Steel, Es
=
1.95E+06 kg/cm2.
Modulus of Elasticity of Concrete, Ec
= = = = =
5000 Fc 5000 20 22360.6798 223606.798 kg/cm2. 8.72
=
54.41 x 2 237.26 kg/cm2.
Modular ratio,
m
=
1.95E+06
223606.798 Loss Due to Elastic Shortening
= 4)
Loss due to relaxation of H.T steel ( cl.11.4 of IRC:18 - 2000 ) Ultimate tensile strength of wires Ultimate tensile strength of Area of each strand No. of cables = Equivalent No. 19 T 13
Referring cl. Average force in cables = 299.33 = = =
19 T 13
2.00 cables
( = = of Design
+ 6
306.32 t. 306.32 355.93 x 0.430 UTS
Average stress in cables
...
Loss due to relaxation of H.
tendon
2.00 2
= = = = of x
18.733 19 355.93 0.9874 19 T 13 18.7606 18.7606
2.00
301.79
+
305.37
+
306.32 2.00
x x
1.00E+03
=
8163.9355
x
3
=
-213.34
UTS 2
=
kg/cm2.
18.76
...
Total loss
= =
...
% age loss =
405.33 + 682.75 kg/cm2.
% age loss due to elastic shortening
682.75 8163.9355 =
i.e Instantaneous loss ... Balance loss
= =
x 237.26 8163.9355 2.91 % 8.36
253.5
+
100
=
x
100
-
2.91
5.46 % 20% higher loss
8.0
=
6.55
%
EFFECT OF SECOND STAGE PRESTRESS 8.1
STRESSES IMMEDIATELY AFTER IInd STAGE PRESTRESS
8.2
CALCULATION OF LOSSES DUE TO IInd STAGE PRESTRESS same as in 1st stage ADDITIONAL LOSS IN Ist STAGE DUE TO IInd STAGE PRESTRESS Additional stress @ c.g of Cables = Err:512 = Err:512 kg/cm2. Loss due to Creep in concrete Creep strain in concrete = 5.40E-04 x 100 = Err:512 Loss due to Creep in concrete = Err:512 x = Err:512 kg/cm2.
8.3 1) 2)
...
3) .. .
4)
Loss due to Shrinkage in concrete Shrinkage strain at 2nd stage Loss due to shrinkage in concrete Loss Due to Elastic Shortening
... Total Loss % Loss
20% higher loss
= = = = = = = =
=
3.00E-04 3.00E-04 x 585.00 kg/cm2. Err:512 x 2 Err:512 kg/cm2. Err:512 + Err:512 kg/cm2. Err:512 x 8163.9355 Err:512 % Err:512 %
54.41
Err:512 100 1.95E+06
1.95E+06
6.63
Err:512 100
9.0
STRESS DUE TO DIFFERENTIAL SHRINKAGE For Age of Precast Unit upto Differential shrinkage strain = reduction factor for creep effect modulus of elasticity of concrete
90 2.00E-04
days M
= =
45 5000.00 x\ 5000.00 x\
t . ... Differential s = 8.60E-05 Area of effective deck slab = 300.000 Tensile force in the slab due to differential shrinkage
Fcj 45 x x
3.35E+05
25.0
Moment in the girder due to differential shrinkage
10.0 10.1
RECAPITULATION OF STRESSES UPTO SERVICE CHECK FOR STRESSES AT VARIOUS STAGES OF LOADING I)
CHECK FOR MAXIMUM COMPRESSIVE STRESSES As per cl.7.1 of IRC:18 - 2000 The Compressive stress in the extreme fibre of concrete immediately after prestressing or after the transfer of prestress & before allowing for further losses due to shrinkage & creep shall not exceed: i) 0.45 x cube strength at the time of transfer As per cl.7.2 of IRC:18 - 2000 The compressive stress in the extreme fibre of concrete after allowing for all losses either due to full D.L or full D.L & L.L shall be 0.33 fck:= 0.33 x = 148.50 kg/cm2.
1)
STRESS CHECK IMMEDIATELY AFTER 1st STAGE PRESTRESSING Referring cl. Max. Compressive Stress =
of Design
The 1st Stage Prestressing is done after the concrete has attained a cube strength of ... The max. permissible comp. stress: i) 0.5 x 200 ...
70.48 kg/cm2. 3 200
days of casting of girder or after kg/cm2., whichever is later.
=
The max. permissible comp. stress
100 kg/cm2. =
> 2)
( At Section
STRESS CHECK IMMEDIATELY AFTER 2nd STAGE PRESTRESSING
100.00 70.48 kg/cm2.
The 2nd Stage Prestressing is done after the concrete has attained a cube strength of ... The max. permissible comp. stress: i) 0.5 x 346.5 . .. The max. permissible comp. stress Referring cl. of Design Max. Compressive Stress =
II )
10 346.5 = =
days of casting of girder or after kg/cm2., whichever is later. 173.25 kg/cm2. 173.25 kg/cm2.
kg/cm2. 173.25 kg/cm2.
( At Section ...
CHECK FOR MAXIMUM TENSILE STRESSES No tensile stress shall be allowed except under partial D.L in the extreme fibre limited to 1/10 of the permissible compressive stress which will disappear completely, when full D.L is allowed to act. Referring cl. 8.00 of Design The permissible temporary tensile compr= 100.00 = 10.00 after 1st stage prestress 10 Tensile stress in the bottom fibre = kg/cm2. before second stage of prestress > kg/cm2. SAFE
III )
CHECK FOR MAX. COMPRESSIVE STRESS BEFORE SERVICE Max. permissible comp stress before ser
=
kg/cm2.
Max. compressive stress before service
= <
kg/cm2. kg/cm2. ...
IV ) CHECK FOR MAX. COMPRESSIVE STRESS AT SERVICE
V)
Max. permissible comp. stress at service
=
kg/cm2.
Max. compressive stress at service
=
kg/cm2. kg/cm2. ...
CHECK FOR MINIMUM STRESS AT SERVICE Stress at service
under full live
= >
kg/cm2. 5.00 kg/cm2. 0.00 kg/cm2.
SAFE
11.0
ULTIMATE STRENGTH CHECK
( Vide cl.12 of IRC:18 - 2000 ) #REF!
) Failure by Yield of Steel
Mult where
= As fp db
#REF!
= = =
0.176 bdb2fck + 2/3 0.8(Bf-b)(db-t/2) x t fck
= b Bf t
12.2
Area of high tensile steel the ultimate tensile strength of steel the depth of the beam from the maximum compression edge to the cg of steel tendons
) Failure by crushing of concrete in compression zone
Mult where
12.0 12.1
0.9 x db x As x fp
= = =
width of web the width of flange thickness of flange
SHEAR FORCE CALCULATION CALCULATION OF SHEAR REINFORCEMENT AT VARIOUS SECTIONS MAX SHEAR AND CORRESPONDING BENDING MOMENT Vu = 1.25 ( S.F1 +
S.F2) + 2 ( SF3)
+ 2.5(S.F4)
Mu = 1.25 ( M1 +
M2) + 2 (M3) +
2.5(M4 )
a) Ultimate shear resistance of section uncracked in flexure V co.
Vco = 0.67 bDft2+0.8 f x ft
+
p sin
b) Ultimate shear resistance of section cracked in flexure V cr. Vcr = ( 0.037 x bd Fc )/1000
.+ ( Mt x Vu ) / Mu ( t )
Mt=(0.37 Fc + 0.8fpt) INA /y
(t-m)
.= ( Vu - Vc )100 c) shear reinforcement
Aw ( cm2 / m )
12.3
.= ( Vu - Vc )100 0.87 fy dt
CHECK FOR MAXIMUM SHEAR
Maximum shear
force =
bd
x
0.05
(t)
12.4
12.5
PROVISION FOR HORIZONTAL SHEAR h Horizontal shear stress
V AsYts bif Ic
=
DESIGN OF TRANSVERSE REINFORCEMENT
(refer cl 611.5 IRC:22-1986) The longitudinal shear force VL per unit length shall not exceed (i) 0.4Ls fck Ls = length of shear plane 0.7As y + 0.08 Ls fck (ii) As = Sum of c/s area of steel per unit len As > VL 0.08Ls fck 0.7 y 13.0
DEFLECTION CALCULATIONS
Max. deflection under a UDL causing a max. moment of ' M ' : = x M L2. 5 EI 48 Where , L = Effective span of Girder. E = Modulus of Elasticity. I = Moment of inertia. i ) Deflection under self wt. ( 1 ) ii ) Deflection under dead wt.of deck slab. ( 2 ) iii ) Deflection under Foot path, Kerbs & Hand Rail & Wearing Coat ( 3 ) iv ) Deflection under Vehicular Live load ( 4 ) vi ) Upward deflection due to prestress First stage prestress Second stage prestress = Total downward deflection - Total upward deflection. Net deflection 14.0
CABLE DETAILS OF INNER GIRDER (G2,G4)
15.0
PRECAST END BLOCK DESIGN
( Vide cl.17.2 of Irc:18 - 2000 ) 2 Ypo 2 Yo For
= = = = Ypo Yo
Ypo Yo
Fbst Pk
0.3 0.353
0.23 x
width of Bearing plate 265 mm. width of End Block 750.0 mm. = 132.5 = 375.0 x
= =
0.3533
0.2300 0.2140
+
-0.0300 0.1000
0.4
0.2
Fbst Pk
=
Pk
= =
Fbst
=
0.214
= =
0.214
0.2140
Max. prestressing force at anchorage end t.
0 Fbst
...
...
x
0
0.00 t.
Permissible stress for Fe - 415 st
= =
Area of steel required
=
0.87 x 3610.5 kg/cm2.
4150
=
0.00
0.00
3610.5 Provided SPIRAL
Area of ste
20
= = >
16.0
,
3.142
8
rounds
x
8
1 no
x
25.13 cm . 0.00 cm2.
1
2
...
SAFE
Temperature gradient:
The temperature gradient effect shall be evaluated as per IRC: 6 for rise and fall in tempe The effect of temperature difference within the PSC girder and deck slab shall be derived positive and reverse temperature differences as shown in fig below.
h1=0.3h<0.15m
h1
h2=0.3h<0.10m
h2
17.8
10.6
4
0.7
0.8 h3=0.3h<0.15m
h3 2.1
6.6
positive temperature diff
reverse temperature
The procedure adopted for longitudinal analysis for temperature gradient is as generally d in the text "Bridge Deck Behaviour" by C. Hambly.
Assume that the deck experiences temperature change which induces stresses while the d rigidly restrained throughout and then the effects of releasing the theoretical restraints ar superimposed. Section properties:
The thermal stresses shall be evaluated for each of the longitudinal of the grid separately for different depth and for solid slab in the cantilever portion and shall be as sh #REF! #REF! average depth #REF!
#REF! #REF!
#REF! #REF! EQUIVALENT SECTION OF PSC GIRDER FOR PURPOSE OF EVALUATING THERMAL STRESSES
Material properties:
For the purpose of calculating thermal effects, the material properties shall be a) Coefficient of thermal expans= / OC 0.0000117 for concrete and steel b) Modulus of elasticity = 0.5 times the short term modulus = 0.5 x 3.35E+05 = 167500.0 kg/cm2
section of the girder in span h1 h2 h3
stress diagram kg/cm2 #REF!
150 mm 250 mm 175 mm
#REF!
#REF!
#REF!
#REF!
#REF!
#REF! properties of section area = cg from bottom = force F1 = F2 = F3 = F = F1+F2+F3
#REF! cm2 #REF! cm #REF! #REF! #REF! #REF! kg
#REF! t
#REF! x
#REF!
-
=
#REF! kg/cm2
0.150 #REF!
+
34.88 7.84 #REF! 0.00
acting at #REF! #REF! #REF! #REF!
= =
#REF! #REF!
#REF!
#REF! +
#REF! #REF! #REF! -
= -
0.175
+
4.12
stress in restrained deck
average stress due to compression
#REF! stess due to restraint moment
Calculation of stresses due to release of restraint moment stress at to = #REF! = #REF! kg/cm2 #REF! stress at b
=
#REF! #REF!
=
#REF! kg/cm2
#REF! +
#REF!
-
#REF! #REF! #REF! #REF! #REF! m + #REF! m
#REF! #REF!
#REF!
stess due to restraint moment
stress due to release of rotation
It can be seen form the above calculations that the resultant stresses due to rise in tempe gives compressive stress I deck slab and soffit slab of the girder and tensile stress in the w #REF! #REF! #REF! + #REF! #REF! #REF! -
#VALUE!
#REF!
+ #REF! Final stresses in kg/cm2
#REF! Resultant under service under 50% LL (section 6-6)
section of the girder in span
stress diagram kg/cm2 #REF!
h1 h2 h3 h4
= = = =
250 mm 200 mm 200 mm 250 mm #REF!
#REF!
#REF! #REF! #REF!
#REF! properties of section area = cg from bottom = F1 = F2 = F3 = F4 = F = F1+F2+F3+F4 = moment at cg =
#REF! cm2 #REF! cm #REF! #REF! #REF! #REF! #REF! kg #REF! x
acting at #REF! #REF! #REF! #REF! #REF! #REF!
#REF! t #REF! =
The average tensile stress is given by = #REF! t/m2
0.250 0.200
-20.77 -1.37 0.00
+
#REF!
#REF! -
#REF! #REF! -
= +
0.2 0.25
-1.57 -12.93
+
stress in restrained deck
#REF! #REF! average stress due to compression
stess due to restraint moment
Calculation of stresses due to release of restraint moment stress at top = #REF! = #REF! t/m2 #REF! stress at bottom
=
#REF! #REF!
=
#REF! t/m2
#REF! +
#REF!
#REF!
#REF! #REF! m
#REF!
#REF! + #REF! m #REF!
#REF!
#REF! #REF!
#REF!
stess due to restraint moment
stress due to release of rotation
It can be seen form the above calculations that the resultant stresses due to rise in tempe gives compressive stress I deck slab and soffit slab of the girder and tensile stress in the w #REF!
#REF!
#REF!
#REF! #REF!
#REF!
#REF!
+ #REF!
-
+
Final stresses in kg/cm2
35.0 36.0 37.0
DESIGN OF DECK SLAB DESIGN OF DIAPHRAGM CABLE ELONGATION CALCULATION STAAD ANALYSIS OUTPUT
Resultant under service under 50% LL (section 6-6)
REF
1 m deg m m m nos m m m m m m m m 40 40
2-6 2 0.1990 m4 0.2237 m3 0.2312 m3
m
m m x
m
0.553 m4 0.945 m3 0.390 m3
4
7-17 7 9 11 12 13 15 16
18
m m
mm at jack end)
ence section (in kN) = = =
0 T 13
x
98.74
mm . 1.95E+04 N/mm2. 2
29 30 31
maturity and maturity 2 stress in concrete at the stressing steel. 54.41 100
modulus of elasticity of H.T steel 1.95E+06
days
1.95E+06
( cl.10.1.1 of IRC:18 - 1985 ) ( cl.10.2 of IRC:18 - 1985 ) stress in concrete at the time of stressing
8.72
tonnes x tonnes cm2. + +
308.39
18.733
0 0
of x
19 T 13 18.7606
+
310.49
+
=
8163.9355 kg/cm2.
x
-0.87 %
312.56
-213.34
+
237.26
8.36 %
33 34 37 38
+
585.00
39
=
0.430
=
335410.2 kg/cm2.
=
28.85 kg/cm2. 7500 cm2. 216339.577 kg 216.34 t
= = =
40 43
sing or after
either due to 450
5-5 of girder or after
kg/cm2. ...
SAFE
)
of girder or after
( At Section
6-6
)
kg/cm2.
.. .
(Section
6-6
)
( At Section
4-4
)
( At Section
6-6
)
( At Section
6-6
)
45
ompression edge to the
47 48 51
54
55
56
rea of steel per unit length
57
upward deflection. 59 141
x
0.0533
cm2.
or rise and fall in temperature k slab shall be derived from the
0.25
h1=0.2h < 0.25m
0.25
h2=0.2h < 0.25m
0.2 0.2
h3=0.25h < 0.2m h4=0.25h < 0.2m
reverse temperature diff
radient is as generally discussed
uces stresses while the deck is theoretical restraints are
al of the grid ortion and shall be as shown below.
ties shall be
m modulus
am kg/cm2 34.88 7.84
4.12
cm cm cm cm
from from from from
cg cg cg cg
kgcm tm
#REF! #REF!
=
+
tress due to elease of rotation
#VALUE! + #REF! Final stresses in t/m2
ses due to rise in temperature nd tensile stress in the web. #REF! #REF!
#VALUE! #REF! Resultant stress in kg/cm2 with temperature
tress diagram kg/cm2 20.77 1.37
1.57
12.93
cm from cm from cm from cm from cm from kgcm
cg cg cg cg cg
#REF! + #REF!
=
#REF!
tress due to elease of rotation
+ #REF! Final stresses in t/m2
ses due to rise in temperature nd tensile stress in the web. #REF! #REF!
#REF!
#REF! Resultant stress in kg/cm2 with temperature
142 150 159
#REF! ) CALCULATION OF BENDING MOMENT AND SHEAR FORCES AT VARIOUS SECTIONS Following sections are considered for the design of PSC girder
Section Section Section Section Section Section Section
0-0 @ 1-1 @ end of thickning of web 2-2 @ mid of thickning of web 3-3 @ start of thickning of web 4-4 @ 0.3L 5-5 @ 0.4L 6-6 @ 0.5L mid span
#REF! I BENDING MOMENT DUE TO SELF WEIGHT OF GIRDER (M1) Weight of midspan section = #REF! Weight of section = #REF! Weight of end thickning = B.M & S.F. at various sections due to SELF WEIGHT M S.F. #REF!
1 1
SECTION 1-1
2-2
0.00 0.00
37.00 0.66
BENDING MOMENT DUE TO INSITU DIAPHRAGM + DECK SLAB (M2) Calculation of weight of deck slab width of deck slab on girder thickness of deck slab weight of deck slab Diaphragm = #REF! B.M & S.F. at various SECTION sections due to 1-1 diaphragm M 2 0.00 S.F. 2 0.00
3.3
x x
= = = x
#REF!
x
2-2 26.00 0.47
BENDING MOMENT DUE SUPERIMPOSED DEAD LOAD (M3) Bending moment due to superimposed dead load is taken from output of Grid analysis Superimposed dead load UDL on outer member
Reaction due to crashbarrier on girder G1 and G3 (a) crash barrier (b) wearing coat floor load (c) railing
B.M & S.F. at various sections due to SIDL M S.F.
3 3
= = =
0.3335 0.065 0.2
1-1
2-2
-64.00 0.00
-59.20 74.35
x x x
3.4 BENDING MOMENT AND SF DUE TO VEHICULAR LIVE LOAD (M4) Class 70R wheeled critical IMPACT FACTOR
=
B.M & S.F. at various sections due to LL class 70R
1
1-1
2-2
M S.F.
4 4
-101.00 0.00
-81.16 45.96
M S.F.
4 4
0.00 0.00
0.00 0.00
+
LL incl impact
Class A 2 lanes IMPACT FACTOR
=
1
(Refer computer output pages including reduction factor of 0.9) B.M & S.F. at various sections due to 1-1 2-2 LL Class a 2lanes M 4 0.00 0.00 S.F. 4 0.00 0.00 sections incl impact M 4 0.00 0.00 S.F. 4 0.00 0.00
+
Class A 1 lanes for max moment
#REF!
#REF!
IMPACT FACTOR
#REF!
=
1
+
(Refer computer output pages including reduction factor of 0.9) B.M & S.F. at various sections due to 1-1 2-2 LL Class a 2lanes M 4 S.F. 4 sections incl impact M 4 0.00 0.00 S.F. 4 0.00 0.00 Footpath Live Load effective span L Basic intensity P' Intensity of load P
= = = = = = =
width of footpath load on kerb
B.M & S.F. at various sections due to FOOTPATH LL M S.F.
4 4
#REF! m c/c bearings 500 kg/m2. P' -( 500
#REF! kg/m2. 1.5 365.0 x
1-1
2-2
0.00 0.00
0.00 0.00
3.5 BENDING MOMENT AND SF DUE TO LAUNCHING (M5) B.M & S.F. at various sections due to LL class 70R M S.F.
5 5
-(
1-1
2-2
0.00 0.00
0.00 0.00
3.5 SUMMARY OF BENDING MOMENTS AND SHEAR FORCES AT VARIOUS SECTIONS B.M. DUE TO SECTION central SELF WEIGHT 0.00 M1 0.00 SF1 DECK SLAB 0.00 M2 0.00 SF2 SUPERIMPOSED -64.00 M3 LOAD 0.00 SF3 VEHICULAR 0.00 M4 0.00 SF4 -64.00 TOTAL M SF 0.00
2-2 37.00 0.66 26.00 0.47 -59.20 74.35 0.00 0.00 3.80 75.47
= = = = = = =
2.6 2.6
= = =
Distance of section from 0.000 m 0.000 m 2.000 m 2.675 m 5.850 m 9.025 m #REF! m
Mid span #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
Length of each section m m m m m m m
0.000 2.000 0.675 3.175 3.175 #REF!
#REF! t/m t/m #VALUE! t/m
3-3
4-4
5-5
6-6
54.00 14.79
94.00 9.86
116.05 4.93
122.52 0.01
#REF! m #REF! m #REF! t/m 2.500
x
#REF!
=
#REF! t
3-3
4-4
5-5
6-6
61.50 22.84
107.75 16.88
133.10 7.61
141.69 1.66
t of Grid analysis
m m m m m m
1 1 1
x x x
2.4 2.3 2.4
= = =
0.800 t/m 0.150 t/m2 0.480 t/m
SECTION 3-3
4-4
5-5
6-6
-41.59 25.39
2.08 24.03
11.98 12.57
20.84 4.93
4.5 6
= +
#REF!
#REF! SECTION
3-3
4-4
5-5
6-6
-41.23 37.07
72.73 34.02
131.61 20.09
160.95 28.45
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
4.5 6
= +
#REF!
#REF! SECTION
3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.4
1.8
#REF!
#REF!
#REF!
4.5
=
6
+
#REF!
#REF! SECTION
3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
c/c bearings 40L-300 9 40
) x
#REF! 9
-
300 say
1.5 2
=
)
365.0 kg/m2.
0.274 t/m
SECTION 3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
SECTION 3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
3-3
4-4
5-5
6-6
54.00 14.79 61.50 22.84 -41.59 25.39 0.00 0.00 73.91 63.02
94.00 9.86 107.75 16.88 2.08 24.03 0.00 0.00 203.83 50.77
116.05 4.93 133.10 7.61 11.98 12.57 0.00 0.00 261.13 25.11
122.52 0.01 141.69 1.66 20.84 4.93 0.00 0.00 285.05 6.60
Beam
L/C 197 467 467 197 188 483 188 483 451 206 451 158 206 499 158 20 180 499 173 180 20 17 173 166 15 17 166 15
P57-P58 Girder G1-laterally deflected Max moment Node Axial ForceShear-Y kN Shear-Z kNTorsion kN Moment-Y 1 196 0 0.019 0 1.635 0 1 196 0 0.13 0 1.441 0 1 337 0 48.621 0 -1.441 0 1 345 0 48.73 0 -1.635 0 1 337 0 -48.945 0 5.363 0 1 345 0 -49.262 0 4.867 0 1 187 0 97.696 0 -5.363 0 1 205 0 98.013 0 -4.867 0 1 187 0 -70.139 0 7.579 0 1 205 0 -69.987 0 7.154 0 1 329 0 118.89 0 -7.579 0 1 329 0 -117.608 0 6.219 0 1 353 0 118.737 0 -7.154 0 1 353 0 -117.127 0 10.339 0 1 92 0 133.898 0 -6.219 0 1 92 0 -133.898 0 7.197 0 1 165 0 -133.422 0 6.71 0 1 165 0 133.422 0 -10.339 0 1 158 0 -161.917 0 4.732 0 1 158 0 161.917 0 -6.71 0 1 83 0 162.393 0 -7.197 0 1 83 0 -162.393 0 9.831 0 1 144 0 168.61 0 -4.732 0 1 144 0 -168.61 0 4.732 0 1 56 0 -169.087 0 6.214 0 1 56 0 169.087 0 -9.831 0 1 136 0 180.658 0 -4.732 0 1 38 0 181.135 0 -6.214 0
nt Moment-Z kN-m -1147.632 1147.572 -1072.924 1072.647 1072.62 -1072.352 -846.868 845.628 843.104 -841.739 -552.1 551.709 551.212 -550.732 -422.332 422.316 -421.878 421.805 -222.567 222.516 -222.314 222.213 181.251 -181.251 180.93 -180.769 102.666 -102.13
15
1
17
1
20
1
158
1
166
1
173
1
180
1
188
1
197
1
206
1
451
1
467
1
483
1
499
1
38 56 56 83 83 92 92 329 144 136 158 144 165 158 187 337 196 345 205 353 329 187 337 196 345 205 353 165
Max reactions 0 181.135 0 -169.087 0 169.087 0 -162.393 0 162.393 0 -133.898 0 133.898 0 -117.608 0 -168.61 0 180.658 0 -161.917 0 168.61 0 -133.422 0 161.917 0 97.696 0 -48.945 0 0.019 0 48.73 0 -69.987 0 118.737 0 118.89 0 -70.139 0 48.621 0 0.13 0 -49.262 0 98.013 0 -117.127 0 133.422
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-6.214 6.214 -9.831 9.831 -7.197 7.197 -6.219 6.219 4.732 -4.732 4.732 -4.732 6.71 -6.71 -5.363 5.363 1.635 -1.635 7.154 -7.154 -7.579 7.579 -1.441 1.441 4.867 -4.867 10.339 -10.339
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-102.13 180.93 -180.769 222.213 -222.314 422.316 -422.332 551.709 -181.251 102.666 -222.567 181.251 -421.878 222.516 -846.868 1072.62 -1147.632 1072.647 -841.739 551.212 -552.1 843.104 -1072.924 1147.572 -1072.352 845.628 -550.732 421.805
Beam
L/C 470 189 198 454 486 160 207 502 34 31 181 29 174 29 167 167 31 174 34 160 181 454 502 189 207 486 470 198
G2 max moments Node Axial ForceShear-Y kN Shear-Z 1 197 0 4.351 1 339 0 -44.485 1 347 0 44.521 1 188 0 -104.484 1 206 0 93.052 1 331 0 -154.748 1 355 0 153.096 1 166 0 171.397 1 93 0 -171.038 1 84 0 -199.53 1 159 0 199.891 1 57 0 -206.226 1 145 0 206.582 1 39 0 218.273 1 137 0 218.629 1 145 0 -206.582 1 57 0 206.226 1 159 0 -199.891 1 84 0 199.53 1 93 0 171.038 1 166 0 -171.397 1 331 0 153.241 1 355 0 -155.103 1 188 0 93.229 1 206 0 -104.345 1 347 0 -44.303 1 339 0 44.393 1 197 0 4.235
kNTorsion kN Moment-Y 0 1.744 0 0 3.397 0 0 -1.654 0 0 6.095 0 0 -3.441 0 0 5.751 0 0 -6.211 0 0 -5.678 0 0 5.751 0 0 5.756 0 0 -5.678 0 0 5.753 0 0 -5.683 0 0 -5.753 0 0 -5.68 0 0 5.68 0 0 -5.756 0 0 5.683 0 0 -5.751 0 0 -5.751 0 0 5.678 0 0 -6.095 0 0 5.678 0 0 -3.397 0 0 6.211 0 0 3.441 0 0 -1.744 0 0 1.654 0
Moment-Z kN-m 1199.81 1138.468 1137.769 928.869 926.601 533.499 532.659 366.119 365.914 115.799 115.499 65.06 64.709 30.452 -30.962 -64.71 -65.06 -115.498 -115.8 -365.914 -366.119 -532.062 -534.119 -926.492 -928.976 -1138.045 -1138.175 -1199.793
Beam
L/C 167 29 174 31 181 34 502 160 454 207 189 486 198 470 470 198 486 189 207 454 160 502 34 181 31 174 29 167
Reaction Node Axial ForceShear-Y kN Shear-Z 1 137 0 218.629 1 39 0 218.273 1 145 0 206.582 1 57 0 206.226 1 159 0 199.891 1 84 0 199.53 1 166 0 171.397 1 93 0 171.038 1 331 0 153.241 1 355 0 153.096 1 188 0 93.229 1 206 0 93.052 1 347 0 44.521 1 339 0 44.393 1 197 0 4.351 1 197 0 4.235 1 347 0 -44.303 1 339 0 -44.485 1 206 0 -104.345 1 188 0 -104.484 1 331 0 -154.748 1 355 0 -155.103 1 93 0 -171.038 1 166 0 -171.397 1 84 0 -199.53 1 159 0 -199.891 1 57 0 -206.226 1 145 0 -206.582
kN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Torsion kN Moment-Y Moment-Z kN-m -5.68 0 -30.962 -5.753 0 30.452 -5.683 0 64.709 -5.756 0 -65.06 -5.678 0 115.499 -5.751 0 -115.8 -5.678 0 366.119 -5.751 0 -365.914 -6.095 0 -532.062 -6.211 0 532.659 -3.397 0 -926.492 -3.441 0 926.601 -1.654 0 1137.769 -1.744 0 -1138.175 1.744 0 1199.81 1.654 0 -1199.793 3.441 0 -1138.045 3.397 0 1138.468 6.211 0 -928.976 6.095 0 928.869 5.751 0 533.499 5.678 0 -534.119 5.751 0 365.914 5.678 0 -366.119 5.756 0 115.799 5.683 0 -115.498 5.753 0 65.06 5.68 0 -64.71
Beam
L/C 474 200 490 191 200 474 209 458 490 191 506 209 162 458 506 183 162 62 62 59 183 176 57 59 176 169 169 57
Node 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
max moments - G4 Axial ForceShear-Y kN Shear-Z 199 0 -6.958 199 0 -6.896 349 0 -55.816 341 0 -55.882 349 0 55.646 341 0 55.709 208 0 -107.216 190 0 -107.144 208 0 104.566 190 0 104.633 357 0 -154.67 357 0 155.965 333 0 -154.589 333 0 155.894 168 0 170.963 168 0 -170.963 95 0 170.879 95 0 -170.879 86 0 199.373 86 0 -199.373 161 0 199.457 161 0 -199.457 59 0 -206.066 59 0 206.066 147 0 206.15 147 0 -206.15 139 0 218.197 41 0 218.113
kNTorsion kN Moment-Y 0 0.012 0 0 0.017 0 0 0.024 0 0 0.02 0 0 -0.017 0 0 -0.012 0 0 0.045 0 0 0.046 0 0 -0.024 0 0 -0.02 0 0 0.039 0 0 -0.045 0 0 0.045 0 0 -0.046 0 0 -0.039 0 0 0.039 0 0 -0.045 0 0 0.045 0 0 -0.045 0 0 0.045 0 0 -0.039 0 0 0.039 0 0 0.045 0 0 -0.045 0 0 -0.039 0 0 0.039 0 0 -0.039 0 0 -0.045 0
Moment-Z kN-m 1277.443 -1277.441 -1181.735 1181.543 1181.164 -1180.97 -935.824 935.42 934.835 -934.439 -530.875 530.684 530.678 -530.487 363.337 -363.337 -363.257 363.257 -113.337 113.337 113.303 -113.303 62.658 -62.658 62.602 -62.602 -32.876 32.783
Beam
L/C 169 57 176 59 183 62 506 162 209 458 191 490 474 200 200 474 490 191 458 209 162 506 62 183 59 176 57 169
Node 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Reactions Axial ForceShear-Y kN Shear-Z 139 0 218.197 41 0 218.113 147 0 206.15 59 0 206.066 161 0 199.457 86 0 199.373 168 0 170.963 95 0 170.879 357 0 155.965 333 0 155.894 190 0 104.633 208 0 104.566 341 0 55.709 349 0 55.646 199 0 -6.896 199 0 -6.958 349 0 -55.816 341 0 -55.882 190 0 -107.144 208 0 -107.216 333 0 -154.589 357 0 -154.67 95 0 -170.879 168 0 -170.963 86 0 -199.373 161 0 -199.457 59 0 -206.066 147 0 -206.15
kN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Torsion kN Moment-Y Moment-Z kN-m -0.039 0 -32.876 -0.045 0 32.783 -0.039 0 62.602 -0.045 0 -62.658 -0.039 0 113.303 -0.045 0 -113.337 -0.039 0 363.337 -0.045 0 -363.257 -0.045 0 530.684 -0.046 0 -530.487 -0.02 0 -934.439 -0.024 0 934.835 -0.012 0 -1180.97 -0.017 0 1181.164 0.017 0 -1277.441 0.012 0 1277.443 0.024 0 -1181.735 0.02 0 1181.543 0.046 0 935.42 0.045 0 -935.824 0.045 0 530.678 0.039 0 -530.875 0.045 0 363.257 0.039 0 -363.337 0.045 0 113.337 0.039 0 -113.303 0.045 0 62.658 0.039 0 -62.602
1.0
SALIENT FEATURES AND DESIGN DATA c/c of pier to face of dirtwall angle of skew Span ( c/c of bearings) length of precast girder Span ( c/c of temporary s ) for precast girder No of girders clc distance of the girders clear carriage way width of footpath + ACB width of median Overall width of the deck width of deck slab beyond centre line of outer girder thickness of deck slab thickness of end diaphragm Grade of concrete
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
= = = = = = = = = = = = = = for PSC girder for RCC deck slab
M M
TYPICAL CROSS SECTION
2.0 2.1 a)
CALCULATION OF SECTIONAL PROPERTIES SECTION AT MIDSPAN (3,4,5,6) PROPERTIES OF PRECAST SECTION A = 0.621 m2 Yt = 0.889 m Yb = 0.861 m Effective width of the slab Minimum of the following
Icg Zt Zb
= = =
0.250
1 1/4th the effective span of the girder = 2 The distance between centres of the ribs of the girder 1 x( 1.50 + 3 The breadth of the rib plus 1/5 times the span 0.290 + 0.2 x . . . Effective width of the slab for M40 grade
24.400 4
=
6.100
1.500
)'=
3.000
24.400
= =
5.17 3.000
= b)
PROPERTIES OF COMPOSITE SECTION A Yt Yb
2.2
3.000
= = =
1.371 m2 0.585 m 1.415 m
Icg Zt Zb
= = =
SECTION AT (1,2) same as above for different sections
3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7
4.0
CALCULATION OF BENDING MOMENTS AND SHEAR FORCES AT VARIOUS SECTIONS BM & SF DUE TO SELF WEIGHT OF GIRDER BM & SF DUE TO DIAPHRAGMS BM & SF DUE TO INSITU DECK SLAB BM & SF DUE TO SUPERIMPOSED DEAD LOAD BM & SF DUE TO VEHICULAR LIVE LOAD BM & SF DUE TO FOOTPATH LIVE LOAD SUMMARY OF BENDING MOMENTS AND SHEAR FORCES AT VARIOUS SECTIONS CABLE PROFILE OF OUTER GIRDER (G1,G5) 4.1 ) CABLE POSITIONS AT MIDSPAN AND ANCHORAGES cable no Type of cable = Area of cable mm2. 98.74 = 2 UTS kg/mm . = days of prestress Total length of girder = Distance of Anchorage from Mid span = DISTANCES OF VARIOUS SECTIONS FROM AND MIDSPAN
Cable force Cables are stressed from both the end. Calculation of forces in the cables before and after slip (slip =
1 8 T 13 789.92 189.720478 21 24.600 12.200
6
Section
length of section l in (m)
k = 0.002
Angle theta in rad
k*l
mu = 0.17
x=kl+
e-x calculated for each
Force Diagram Calculation of slip SUMMARY OF CABLE FORCE AFTER SLIP: HORIZONTAL CABLE FORCE COMPONENTS (F = PCOS(Q)) VERTICAL CABLE FORCE COMPONENTS (F = PSIN(Q)) )CABLE ELONGATION Elongation =
7.0
fxL AxE
where, f L A
= = =
Average cable force at reference section (in kN) Length of cable (in mm) Area of cable (in mm2)
E
=
Youngs modulus (in N/mm2)
EFFECT OF FIRST STAGE PRESTRESS STRESSES IMMEDIATELY AFTER Ist STAGE PRESTRESS CALCULATION OF LOSSES DUE TO Ist STAGE PRESTRESS
7.1 7.2
1)
Losses due to creep in concrete ( cl.11.2 of IRC:18 - 2000 ) Creep strain in period between 9.22E-04 -
5.40E-04
... Creep loss
2)
Losses due to shrinkage of concrete ( cl.11.3 of IRC:18 - 2000 ) Shrinkage of concrete in the period of 4
=
3 days 42% 10 days 77% 3.82E-04 per 100 kg/cm2 stress in concrete at the centroid of prestressing steel. = 3.82E-004 x = = = =
3 days and
2.08E-04 creep strain x modulus of elasticity of H.T ste 2.08E-04 x 405.33 kg/cm2.
10
=
0.00043 -
0.0003
= = =
3)
Loss due to Elastic shortening
1.30E-04
1.30E-04
x
253.50 kg/cm2.
( cl.11.1 of IRC:18 - 2000 )
Modulus of Elasticity of Steel, Es
=
1.95E+06 kg/cm2.
Modulus of Elasticity of Concrete, Ec
= = = = =
5000 Fc 5000 20 22360.6798 223606.798 kg/cm2. 8.72
=
54.41 x 2 237.26 kg/cm2.
Modular ratio,
m
=
1.95E+06
223606.798 Loss Due to Elastic Shortening
= 4)
Loss due to relaxation of H.T steel ( cl.11.4 of IRC:18 - 2000 ) Ultimate tensile strength of wires Ultimate tensile strength of Area of each strand No. of cables = Equivalent No. 19 T 13
Referring cl. Average force in cables = 299.33 = = =
19 T 13
2.00 cables
( = = of Design
+ 6
306.32 t. 306.32 355.93 x 0.430 UTS
Average stress in cables
...
Loss due to relaxation of H.
tendon
2.00 2
= = = = of x
18.733 19 355.93 0.9874 19 T 13 18.7606 18.7606
2.00
301.79
+
305.37
+
306.32 2.00
x x
1.00E+03
=
8163.9355
x
3
=
-213.34
UTS 2
=
kg/cm2.
18.76
...
Total loss
= =
...
% age loss =
405.33 + 682.75 kg/cm2.
% age loss due to elastic shortening
682.75 8163.9355 =
i.e Instantaneous loss ... Balance loss
= =
x 237.26 8163.9355 2.91 % 8.36
253.5
+
100
=
x
100
-
2.91
5.46 % 20% higher loss
8.0
=
6.55
%
EFFECT OF SECOND STAGE PRESTRESS 8.1
STRESSES IMMEDIATELY AFTER IInd STAGE PRESTRESS
8.2
CALCULATION OF LOSSES DUE TO IInd STAGE PRESTRESS same as in 1st stage ADDITIONAL LOSS IN Ist STAGE DUE TO IInd STAGE PRESTRESS Additional stress @ c.g of Cables = Err:512 = Err:512 kg/cm2. Loss due to Creep in concrete Creep strain in concrete = 5.40E-04 x 100 = Err:512 Loss due to Creep in concrete = Err:512 x = Err:512 kg/cm2.
8.3 1) 2)
...
3) .. .
4)
Loss due to Shrinkage in concrete Shrinkage strain at 2nd stage Loss due to shrinkage in concrete Loss Due to Elastic Shortening
... Total Loss % Loss
20% higher loss
= = = = = = = =
=
3.00E-04 3.00E-04 x 585.00 kg/cm2. Err:512 x 2 Err:512 kg/cm2. Err:512 + Err:512 kg/cm2. Err:512 x 8163.9355 Err:512 % Err:512 %
54.41
Err:512 100 1.95E+06
1.95E+06
6.63
Err:512 100
9.0
STRESS DUE TO DIFFERENTIAL SHRINKAGE For Age of Precast Unit upto Differential shrinkage strain = reduction factor for creep effect modulus of elasticity of concrete
90 2.00E-04
days M
= =
45 5000.00 x\ 5000.00 x\
t . ... Differential s = 8.60E-05 Area of effective deck slab = 300.000 Tensile force in the slab due to differential shrinkage
Fcj 45 x x
3.35E+05
25.0
Moment in the girder due to differential shrinkage
10.0 10.1
RECAPITULATION OF STRESSES UPTO SERVICE CHECK FOR STRESSES AT VARIOUS STAGES OF LOADING I)
CHECK FOR MAXIMUM COMPRESSIVE STRESSES As per cl.7.1 of IRC:18 - 2000 The Compressive stress in the extreme fibre of concrete immediately after prestressing or after the transfer of prestress & before allowing for further losses due to shrinkage & creep shall not exceed: i) 0.45 x cube strength at the time of transfer As per cl.7.2 of IRC:18 - 2000 The compressive stress in the extreme fibre of concrete after allowing for all losses either due to full D.L or full D.L & L.L shall be 0.33 fck:= 0.33 x = 148.50 kg/cm2.
1)
STRESS CHECK IMMEDIATELY AFTER 1st STAGE PRESTRESSING Referring cl. Max. Compressive Stress =
of Design
The 1st Stage Prestressing is done after the concrete has attained a cube strength of ... The max. permissible comp. stress: i) 0.5 x 200 ...
70.48 kg/cm2. 3 200
days of casting of girder or after kg/cm2., whichever is later.
=
The max. permissible comp. stress
100 kg/cm2. =
> 2)
( At Section
STRESS CHECK IMMEDIATELY AFTER 2nd STAGE PRESTRESSING
100.00 70.48 kg/cm2.
The 2nd Stage Prestressing is done after the concrete has attained a cube strength of ... The max. permissible comp. stress: i) 0.5 x 346.5 . .. The max. permissible comp. stress Referring cl. of Design Max. Compressive Stress =
II )
10 346.5 = =
days of casting of girder or after kg/cm2., whichever is later. 173.25 kg/cm2. 173.25 kg/cm2.
kg/cm2. 173.25 kg/cm2.
( At Section ...
CHECK FOR MAXIMUM TENSILE STRESSES No tensile stress shall be allowed except under partial D.L in the extreme fibre limited to 1/10 of the permissible compressive stress which will disappear completely, when full D.L is allowed to act. Referring cl. 8.00 of Design The permissible temporary tensile compr= 100.00 = 10.00 after 1st stage prestress 10 Tensile stress in the bottom fibre = kg/cm2. before second stage of prestress > kg/cm2. SAFE
III )
CHECK FOR MAX. COMPRESSIVE STRESS BEFORE SERVICE Max. permissible comp stress before ser
=
kg/cm2.
Max. compressive stress before service
= <
kg/cm2. kg/cm2. ...
IV ) CHECK FOR MAX. COMPRESSIVE STRESS AT SERVICE
V)
Max. permissible comp. stress at service
=
kg/cm2.
Max. compressive stress at service
=
kg/cm2. kg/cm2. ...
CHECK FOR MINIMUM STRESS AT SERVICE Stress at service
under full live
= >
kg/cm2. 5.00 kg/cm2. 0.00 kg/cm2.
SAFE
11.0
ULTIMATE STRENGTH CHECK
( Vide cl.12 of IRC:18 - 2000 ) #REF!
) Failure by Yield of Steel
Mult where
= As fp db
#REF!
= = =
0.176 bdb2fck + 2/3 0.8(Bf-b)(db-t/2) x t fck
= b Bf t
12.2
Area of high tensile steel the ultimate tensile strength of steel the depth of the beam from the maximum compression edge to the cg of steel tendons
) Failure by crushing of concrete in compression zone
Mult where
12.0 12.1
0.9 x db x As x fp
= = =
width of web the width of flange thickness of flange
SHEAR FORCE CALCULATION CALCULATION OF SHEAR REINFORCEMENT AT VARIOUS SECTIONS MAX SHEAR AND CORRESPONDING BENDING MOMENT Vu = 1.25 ( S.F1 +
S.F2) + 2 ( SF3)
+ 2.5(S.F4)
Mu = 1.25 ( M1 +
M2) + 2 (M3) +
2.5(M4 )
a) Ultimate shear resistance of section uncracked in flexure V co.
Vco = 0.67 bDft2+0.8 f x ft
+
p sin
b) Ultimate shear resistance of section cracked in flexure V cr. Vcr = ( 0.037 x bd Fc )/1000
.+ ( Mt x Vu ) / Mu ( t )
Mt=(0.37 Fc + 0.8fpt) INA /y
(t-m)
.= ( Vu - Vc )100 c) shear reinforcement
Aw ( cm2 / m )
12.3
.= ( Vu - Vc )100 0.87 fy dt
CHECK FOR MAXIMUM SHEAR
Maximum shear
force =
bd
x
0.05
(t)
12.4
12.5
PROVISION FOR HORIZONTAL SHEAR h Horizontal shear stress
V AsYts bif Ic
=
DESIGN OF TRANSVERSE REINFORCEMENT
(refer cl 611.5 IRC:22-1986) The longitudinal shear force VL per unit length shall not exceed (i) 0.4Ls fck Ls = length of shear plane 0.7As y + 0.08 Ls fck (ii) As = Sum of c/s area of steel per unit len As > VL 0.08Ls fck 0.7 y 13.0
DEFLECTION CALCULATIONS
Max. deflection under a UDL causing a max. moment of ' M ' : = x M L2. 5 EI 48 Where , L = Effective span of Girder. E = Modulus of Elasticity. I = Moment of inertia. i ) Deflection under self wt. ( 1 ) ii ) Deflection under dead wt.of deck slab. ( 2 ) iii ) Deflection under Foot path, Kerbs & Hand Rail & Wearing Coat ( 3 ) iv ) Deflection under Vehicular Live load ( 4 ) vi ) Upward deflection due to prestress First stage prestress Second stage prestress = Total downward deflection - Total upward deflection. Net deflection 14.0
CABLE DETAILS OF INNER GIRDER (G2,G4)
15.0
PRECAST END BLOCK DESIGN
( Vide cl.17.2 of Irc:18 - 2000 ) 2 Ypo 2 Yo For
= = = = Ypo Yo
Ypo Yo
Fbst Pk
0.3 0.353
0.23 x
width of Bearing plate 265 mm. width of End Block 750.0 mm. = 132.5 = 375.0 x
= =
0.3533
0.2300 0.2140
+
-0.0300 0.1000
0.4
0.2
Fbst Pk
=
Pk
= =
Fbst
=
0.214
= =
0.214
0.2140
Max. prestressing force at anchorage end t.
0 Fbst
...
...
x
0
0.00 t.
Permissible stress for Fe - 415 st
= =
Area of steel required
=
0.87 x 3610.5 kg/cm2.
4150
=
0.00
0.00
3610.5 Provided SPIRAL
Area of ste
20
= = >
16.0
,
3.142
8
rounds
x
8
1 no
x
25.13 cm . 0.00 cm2.
1
2
...
SAFE
Temperature gradient:
The temperature gradient effect shall be evaluated as per IRC: 6 for rise and fall in tempe The effect of temperature difference within the PSC girder and deck slab shall be derived positive and reverse temperature differences as shown in fig below.
h1=0.3h<0.15m
h1
h2=0.3h<0.10m
h2
17.8
10.6
4
0.7
0.8 h3=0.3h<0.15m
h3 2.1
6.6
positive temperature diff
reverse temperature
The procedure adopted for longitudinal analysis for temperature gradient is as generally d in the text "Bridge Deck Behaviour" by C. Hambly.
Assume that the deck experiences temperature change which induces stresses while the d rigidly restrained throughout and then the effects of releasing the theoretical restraints ar superimposed. Section properties:
The thermal stresses shall be evaluated for each of the longitudinal of the grid separately for different depth and for solid slab in the cantilever portion and shall be as sh #REF! #REF! average depth #REF!
#REF! #REF!
#REF! #REF! EQUIVALENT SECTION OF PSC GIRDER FOR PURPOSE OF EVALUATING THERMAL STRESSES
Material properties:
For the purpose of calculating thermal effects, the material properties shall be a) Coefficient of thermal expans= / OC 0.0000117 for concrete and steel b) Modulus of elasticity = 0.5 times the short term modulus = 0.5 x 3.35E+05 = 167500.0 kg/cm2
section of the girder in span h1 h2 h3
stress diagram kg/cm2 #REF!
150 mm 250 mm 175 mm
#REF!
#REF!
#REF!
#REF!
#REF!
#REF! properties of section area = cg from bottom = force F1 = F2 = F3 = F = F1+F2+F3
#REF! cm2 #REF! cm #REF! #REF! #REF! #REF! kg
#REF! t
#REF! x
#REF!
-
=
#REF! kg/cm2
0.150 #REF!
+
34.88 7.84 #REF! 0.00
acting at #REF! #REF! #REF! #REF!
= =
#REF! #REF!
#REF!
#REF! +
#REF! #REF! #REF! -
= -
0.175
+
4.12
stress in restrained deck
average stress due to compression
#REF! stess due to restraint moment
Calculation of stresses due to release of restraint moment stress at to = #REF! = #REF! kg/cm2 #REF! stress at b
=
#REF! #REF!
=
#REF! kg/cm2
#REF! +
#REF!
-
#REF! #REF! #REF! #REF! #REF! m + #REF! m
#REF! #REF!
#REF!
stess due to restraint moment
stress due to release of rotation
It can be seen form the above calculations that the resultant stresses due to rise in tempe gives compressive stress I deck slab and soffit slab of the girder and tensile stress in the w #REF! #REF! #REF! + #REF! #REF! #REF! -
#VALUE!
#REF!
+ #REF! Final stresses in kg/cm2
#REF! Resultant under service under 50% LL (section 6-6)
section of the girder in span
stress diagram kg/cm2 #REF!
h1 h2 h3 h4
= = = =
250 mm 200 mm 200 mm 250 mm #REF!
#REF!
#REF! #REF! #REF!
#REF! properties of section area = cg from bottom = F1 = F2 = F3 = F4 = F = F1+F2+F3+F4 = moment at cg =
#REF! cm2 #REF! cm #REF! #REF! #REF! #REF! #REF! kg #REF! x
acting at #REF! #REF! #REF! #REF! #REF! #REF!
#REF! t #REF! =
The average tensile stress is given by = #REF! t/m2
0.250 0.200
-20.77 -1.37 0.00
+
#REF!
#REF! -
#REF! #REF! -
= +
0.2 0.25
-1.57 -12.93
+
stress in restrained deck
#REF! #REF! average stress due to compression
stess due to restraint moment
Calculation of stresses due to release of restraint moment stress at top = #REF! = #REF! t/m2 #REF! stress at bottom
=
#REF! #REF!
=
#REF! t/m2
#REF! +
#REF!
#REF!
#REF! #REF! m
#REF!
#REF! + #REF! m #REF!
#REF!
#REF! #REF!
#REF!
stess due to restraint moment
stress due to release of rotation
It can be seen form the above calculations that the resultant stresses due to rise in tempe gives compressive stress I deck slab and soffit slab of the girder and tensile stress in the w #REF!
#REF!
#REF!
#REF! #REF!
#REF!
#REF!
+ #REF!
-
+
Final stresses in kg/cm2
35.0 36.0 37.0
DESIGN OF DECK SLAB DESIGN OF DIAPHRAGM CABLE ELONGATION CALCULATION STAAD ANALYSIS OUTPUT
Resultant under service under 50% LL (section 6-6)
REF
1 m deg m m m nos m m m m m m m m 40 40
2-6 2 0.1990 m4 0.2237 m3 0.2312 m3
m
m m x
m
0.553 m4 0.945 m3 0.390 m3
4
7-17 7 9 11 12 13 15 16
18
m m
mm at jack end)
ence section (in kN) = = =
0 T 13
x
98.74
mm . 1.95E+04 N/mm2. 2
29 30 31
maturity and maturity 2 stress in concrete at the stressing steel. 54.41 100
modulus of elasticity of H.T steel 1.95E+06
days
1.95E+06
( cl.10.1.1 of IRC:18 - 1985 ) ( cl.10.2 of IRC:18 - 1985 ) stress in concrete at the time of stressing
8.72
tonnes x tonnes cm2. + +
308.39
18.733
0 0
of x
19 T 13 18.7606
+
310.49
+
=
8163.9355 kg/cm2.
x
-0.87 %
312.56
-213.34
+
237.26
8.36 %
33 34 37 38
+
585.00
39
=
0.430
=
335410.2 kg/cm2.
=
28.85 kg/cm2. 7500 cm2. 216339.577 kg 216.34 t
= = =
40 43
sing or after
either due to 450
5-5 of girder or after
kg/cm2. ...
SAFE
)
of girder or after
( At Section
6-6
)
kg/cm2.
.. .
(Section
6-6
)
( At Section
4-4
)
( At Section
6-6
)
( At Section
6-6
)
45
ompression edge to the
47 48 51
54
55
56
rea of steel per unit length
57
upward deflection. 59 141
x
0.0533
cm2.
or rise and fall in temperature k slab shall be derived from the
0.25
h1=0.2h < 0.25m
0.25
h2=0.2h < 0.25m
0.2 0.2
h3=0.25h < 0.2m h4=0.25h < 0.2m
reverse temperature diff
radient is as generally discussed
uces stresses while the deck is theoretical restraints are
al of the grid ortion and shall be as shown below.
ties shall be
m modulus
am kg/cm2 34.88 7.84
4.12
cm cm cm cm
from from from from
cg cg cg cg
kgcm tm
#REF! #REF!
=
+
tress due to elease of rotation
#VALUE! + #REF! Final stresses in t/m2
ses due to rise in temperature nd tensile stress in the web. #REF! #REF!
#VALUE! #REF! Resultant stress in kg/cm2 with temperature
tress diagram kg/cm2 20.77 1.37
1.57
12.93
cm from cm from cm from cm from cm from kgcm
cg cg cg cg cg
#REF! + #REF!
=
#REF!
tress due to elease of rotation
+ #REF! Final stresses in t/m2
ses due to rise in temperature nd tensile stress in the web. #REF! #REF!
#REF!
#REF! Resultant stress in kg/cm2 with temperature
142 150 159
#REF! ) CALCULATION OF BENDING MOMENT AND SHEAR FORCES AT VARIOUS SECTIONS Following sections are considered for the design of PSC girder
Section Section Section Section Section Section Section
0-0 @ 1-1 @ end of thickning of web 2-2 @ mid of thickning of web 3-3 @ start of thickning of web 4-4 @ 0.3L 5-5 @ 0.4L 6-6 @ 0.5L mid span
#REF! I BENDING MOMENT DUE TO SELF WEIGHT OF GIRDER (M1) Weight of midspan section = #REF! Weight of section = #REF! Weight of end thickning = B.M & S.F. at various sections due to SELF WEIGHT M S.F. #REF!
1 1
SECTION 1-1
2-2
0.00 0.00
37.00 0.66
BENDING MOMENT DUE TO INSITU DIAPHRAGM + DECK SLAB (M2) Calculation of weight of deck slab width of deck slab on girder thickness of deck slab weight of deck slab Diaphragm = #REF! B.M & S.F. at various SECTION sections due to 1-1 diaphragm M 2 0.00 S.F. 2 0.00
3.3
x x
= = = x
#REF!
x
2-2 26.00 0.47
BENDING MOMENT DUE SUPERIMPOSED DEAD LOAD (M3) Bending moment due to superimposed dead load is taken from output of Grid analysis Superimposed dead load UDL on outer member
Reaction due to crashbarrier on girder G1 and G3 (a) crash barrier (b) wearing coat floor load (c) railing
B.M & S.F. at various sections due to SIDL M S.F.
3 3
= = =
0.3335 0.065 0.2
1-1
2-2
-64.00 0.00
-59.20 74.35
x x x
3.4 BENDING MOMENT AND SF DUE TO VEHICULAR LIVE LOAD (M4) Class 70R wheeled critical IMPACT FACTOR
=
B.M & S.F. at various sections due to LL class 70R
1
1-1
2-2
M S.F.
4 4
-101.00 0.00
-81.16 45.96
M S.F.
4 4
0.00 0.00
0.00 0.00
+
LL incl impact
Class A 2 lanes IMPACT FACTOR
=
1
(Refer computer output pages including reduction factor of 0.9) B.M & S.F. at various sections due to 1-1 2-2 LL Class a 2lanes M 4 0.00 0.00 S.F. 4 0.00 0.00 sections incl impact M 4 0.00 0.00 S.F. 4 0.00 0.00
+
Class A 1 lanes for max moment
#REF!
#REF!
IMPACT FACTOR
#REF!
=
1
+
(Refer computer output pages including reduction factor of 0.9) B.M & S.F. at various sections due to 1-1 2-2 LL Class a 2lanes M 4 S.F. 4 sections incl impact M 4 0.00 0.00 S.F. 4 0.00 0.00 Footpath Live Load effective span L Basic intensity P' Intensity of load P
= = = = = = =
width of footpath load on kerb
B.M & S.F. at various sections due to FOOTPATH LL M S.F.
4 4
#REF! m c/c bearings 500 kg/m2. P' -( 500
#REF! kg/m2. 1.5 365.0 x
1-1
2-2
0.00 0.00
0.00 0.00
3.5 BENDING MOMENT AND SF DUE TO LAUNCHING (M5) B.M & S.F. at various sections due to LL class 70R M S.F.
5 5
-(
1-1
2-2
0.00 0.00
0.00 0.00
3.5 SUMMARY OF BENDING MOMENTS AND SHEAR FORCES AT VARIOUS SECTIONS B.M. DUE TO SECTION central SELF WEIGHT 0.00 M1 0.00 SF1 DECK SLAB 0.00 M2 0.00 SF2 SUPERIMPOSED -64.00 M3 LOAD 0.00 SF3 VEHICULAR 0.00 M4 0.00 SF4 -64.00 TOTAL M SF 0.00
2-2 37.00 0.66 26.00 0.47 -59.20 74.35 0.00 0.00 3.80 75.47
= = = = = = =
2.6 2.6
= = =
Distance of section from 0.000 m 0.000 m 2.000 m 2.675 m 5.850 m 9.025 m #REF! m
Mid span #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
Length of each section m m m m m m m
0.000 2.000 0.675 3.175 3.175 #REF!
#REF! t/m t/m #VALUE! t/m
3-3
4-4
5-5
6-6
54.00 14.79
94.00 9.86
116.05 4.93
122.52 0.01
#REF! m #REF! m #REF! t/m 2.500
x
#REF!
=
#REF! t
3-3
4-4
5-5
6-6
61.50 22.84
107.75 16.88
133.10 7.61
141.69 1.66
t of Grid analysis
m m m m m m
1 1 1
x x x
2.4 2.3 2.4
= = =
0.800 t/m 0.150 t/m2 0.480 t/m
SECTION 3-3
4-4
5-5
6-6
-41.59 25.39
2.08 24.03
11.98 12.57
20.84 4.93
4.5 6
= +
#REF!
#REF! SECTION
3-3
4-4
5-5
6-6
-41.23 37.07
72.73 34.02
131.61 20.09
160.95 28.45
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
4.5 6
= +
#REF!
#REF! SECTION
3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
0.4
1.8
#REF!
#REF!
#REF!
4.5
=
6
+
#REF!
#REF! SECTION
3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
c/c bearings 40L-300 9 40
) x
#REF! 9
-
300 say
1.5 2
=
)
365.0 kg/m2.
0.274 t/m
SECTION 3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
SECTION 3-3
4-4
5-5
6-6
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
3-3
4-4
5-5
6-6
54.00 14.79 61.50 22.84 -41.59 25.39 0.00 0.00 73.91 63.02
94.00 9.86 107.75 16.88 2.08 24.03 0.00 0.00 203.83 50.77
116.05 4.93 133.10 7.61 11.98 12.57 0.00 0.00 261.13 25.11
122.52 0.01 141.69 1.66 20.84 4.93 0.00 0.00 285.05 6.60
Beam
L/C 197 467 467 197 188 483 188 483 451 206 451 158 206 499 158 20 180 499 173 180 20 17 173 166 15 17 166 15
P57-P58 Girder G1-laterally deflected Max moment Node Axial ForceShear-Y kN Shear-Z kNTorsion kN Moment-Y 1 196 0 0.019 0 1.635 0 1 196 0 0.13 0 1.441 0 1 337 0 48.621 0 -1.441 0 1 345 0 48.73 0 -1.635 0 1 337 0 -48.945 0 5.363 0 1 345 0 -49.262 0 4.867 0 1 187 0 97.696 0 -5.363 0 1 205 0 98.013 0 -4.867 0 1 187 0 -70.139 0 7.579 0 1 205 0 -69.987 0 7.154 0 1 329 0 118.89 0 -7.579 0 1 329 0 -117.608 0 6.219 0 1 353 0 118.737 0 -7.154 0 1 353 0 -117.127 0 10.339 0 1 92 0 133.898 0 -6.219 0 1 92 0 -133.898 0 7.197 0 1 165 0 -133.422 0 6.71 0 1 165 0 133.422 0 -10.339 0 1 158 0 -161.917 0 4.732 0 1 158 0 161.917 0 -6.71 0 1 83 0 162.393 0 -7.197 0 1 83 0 -162.393 0 9.831 0 1 144 0 168.61 0 -4.732 0 1 144 0 -168.61 0 4.732 0 1 56 0 -169.087 0 6.214 0 1 56 0 169.087 0 -9.831 0 1 136 0 180.658 0 -4.732 0 1 38 0 181.135 0 -6.214 0
nt Moment-Z kN-m -1147.632 1147.572 -1072.924 1072.647 1072.62 -1072.352 -846.868 845.628 843.104 -841.739 -552.1 551.709 551.212 -550.732 -422.332 422.316 -421.878 421.805 -222.567 222.516 -222.314 222.213 181.251 -181.251 180.93 -180.769 102.666 -102.13
15
1
17
1
20
1
158
1
166
1
173
1
180
1
188
1
197
1
206
1
451
1
467
1
483
1
499
1
38 56 56 83 83 92 92 329 144 136 158 144 165 158 187 337 196 345 205 353 329 187 337 196 345 205 353 165
Max reactions 0 181.135 0 -169.087 0 169.087 0 -162.393 0 162.393 0 -133.898 0 133.898 0 -117.608 0 -168.61 0 180.658 0 -161.917 0 168.61 0 -133.422 0 161.917 0 97.696 0 -48.945 0 0.019 0 48.73 0 -69.987 0 118.737 0 118.89 0 -70.139 0 48.621 0 0.13 0 -49.262 0 98.013 0 -117.127 0 133.422
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-6.214 6.214 -9.831 9.831 -7.197 7.197 -6.219 6.219 4.732 -4.732 4.732 -4.732 6.71 -6.71 -5.363 5.363 1.635 -1.635 7.154 -7.154 -7.579 7.579 -1.441 1.441 4.867 -4.867 10.339 -10.339
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-102.13 180.93 -180.769 222.213 -222.314 422.316 -422.332 551.709 -181.251 102.666 -222.567 181.251 -421.878 222.516 -846.868 1072.62 -1147.632 1072.647 -841.739 551.212 -552.1 843.104 -1072.924 1147.572 -1072.352 845.628 -550.732 421.805
Beam
L/C 470 189 198 454 486 160 207 502 34 31 181 29 174 29 167 167 31 174 34 160 181 454 502 189 207 486 470 198
G2 max moments Node Axial ForceShear-Y kN Shear-Z 1 197 0 4.351 1 339 0 -44.485 1 347 0 44.521 1 188 0 -104.484 1 206 0 93.052 1 331 0 -154.748 1 355 0 153.096 1 166 0 171.397 1 93 0 -171.038 1 84 0 -199.53 1 159 0 199.891 1 57 0 -206.226 1 145 0 206.582 1 39 0 218.273 1 137 0 218.629 1 145 0 -206.582 1 57 0 206.226 1 159 0 -199.891 1 84 0 199.53 1 93 0 171.038 1 166 0 -171.397 1 331 0 153.241 1 355 0 -155.103 1 188 0 93.229 1 206 0 -104.345 1 347 0 -44.303 1 339 0 44.393 1 197 0 4.235
kNTorsion kN Moment-Y 0 1.744 0 0 3.397 0 0 -1.654 0 0 6.095 0 0 -3.441 0 0 5.751 0 0 -6.211 0 0 -5.678 0 0 5.751 0 0 5.756 0 0 -5.678 0 0 5.753 0 0 -5.683 0 0 -5.753 0 0 -5.68 0 0 5.68 0 0 -5.756 0 0 5.683 0 0 -5.751 0 0 -5.751 0 0 5.678 0 0 -6.095 0 0 5.678 0 0 -3.397 0 0 6.211 0 0 3.441 0 0 -1.744 0 0 1.654 0
Moment-Z kN-m 1199.81 1138.468 1137.769 928.869 926.601 533.499 532.659 366.119 365.914 115.799 115.499 65.06 64.709 30.452 -30.962 -64.71 -65.06 -115.498 -115.8 -365.914 -366.119 -532.062 -534.119 -926.492 -928.976 -1138.045 -1138.175 -1199.793
Beam
L/C 167 29 174 31 181 34 502 160 454 207 189 486 198 470 470 198 486 189 207 454 160 502 34 181 31 174 29 167
Reaction Node Axial ForceShear-Y kN Shear-Z 1 137 0 218.629 1 39 0 218.273 1 145 0 206.582 1 57 0 206.226 1 159 0 199.891 1 84 0 199.53 1 166 0 171.397 1 93 0 171.038 1 331 0 153.241 1 355 0 153.096 1 188 0 93.229 1 206 0 93.052 1 347 0 44.521 1 339 0 44.393 1 197 0 4.351 1 197 0 4.235 1 347 0 -44.303 1 339 0 -44.485 1 206 0 -104.345 1 188 0 -104.484 1 331 0 -154.748 1 355 0 -155.103 1 93 0 -171.038 1 166 0 -171.397 1 84 0 -199.53 1 159 0 -199.891 1 57 0 -206.226 1 145 0 -206.582
kN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Torsion kN Moment-Y Moment-Z kN-m -5.68 0 -30.962 -5.753 0 30.452 -5.683 0 64.709 -5.756 0 -65.06 -5.678 0 115.499 -5.751 0 -115.8 -5.678 0 366.119 -5.751 0 -365.914 -6.095 0 -532.062 -6.211 0 532.659 -3.397 0 -926.492 -3.441 0 926.601 -1.654 0 1137.769 -1.744 0 -1138.175 1.744 0 1199.81 1.654 0 -1199.793 3.441 0 -1138.045 3.397 0 1138.468 6.211 0 -928.976 6.095 0 928.869 5.751 0 533.499 5.678 0 -534.119 5.751 0 365.914 5.678 0 -366.119 5.756 0 115.799 5.683 0 -115.498 5.753 0 65.06 5.68 0 -64.71
Beam
L/C 474 200 490 191 200 474 209 458 490 191 506 209 162 458 506 183 162 62 62 59 183 176 57 59 176 169 169 57
Node 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
max moments - G4 Axial ForceShear-Y kN Shear-Z 199 0 -6.958 199 0 -6.896 349 0 -55.816 341 0 -55.882 349 0 55.646 341 0 55.709 208 0 -107.216 190 0 -107.144 208 0 104.566 190 0 104.633 357 0 -154.67 357 0 155.965 333 0 -154.589 333 0 155.894 168 0 170.963 168 0 -170.963 95 0 170.879 95 0 -170.879 86 0 199.373 86 0 -199.373 161 0 199.457 161 0 -199.457 59 0 -206.066 59 0 206.066 147 0 206.15 147 0 -206.15 139 0 218.197 41 0 218.113
kNTorsion kN Moment-Y 0 0.012 0 0 0.017 0 0 0.024 0 0 0.02 0 0 -0.017 0 0 -0.012 0 0 0.045 0 0 0.046 0 0 -0.024 0 0 -0.02 0 0 0.039 0 0 -0.045 0 0 0.045 0 0 -0.046 0 0 -0.039 0 0 0.039 0 0 -0.045 0 0 0.045 0 0 -0.045 0 0 0.045 0 0 -0.039 0 0 0.039 0 0 0.045 0 0 -0.045 0 0 -0.039 0 0 0.039 0 0 -0.039 0 0 -0.045 0
Moment-Z kN-m 1277.443 -1277.441 -1181.735 1181.543 1181.164 -1180.97 -935.824 935.42 934.835 -934.439 -530.875 530.684 530.678 -530.487 363.337 -363.337 -363.257 363.257 -113.337 113.337 113.303 -113.303 62.658 -62.658 62.602 -62.602 -32.876 32.783
Beam
L/C 169 57 176 59 183 62 506 162 209 458 191 490 474 200 200 474 490 191 458 209 162 506 62 183 59 176 57 169
Node 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Reactions Axial ForceShear-Y kN Shear-Z 139 0 218.197 41 0 218.113 147 0 206.15 59 0 206.066 161 0 199.457 86 0 199.373 168 0 170.963 95 0 170.879 357 0 155.965 333 0 155.894 190 0 104.633 208 0 104.566 341 0 55.709 349 0 55.646 199 0 -6.896 199 0 -6.958 349 0 -55.816 341 0 -55.882 190 0 -107.144 208 0 -107.216 333 0 -154.589 357 0 -154.67 95 0 -170.879 168 0 -170.963 86 0 -199.373 161 0 -199.457 59 0 -206.066 147 0 -206.15
kN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Torsion kN Moment-Y Moment-Z kN-m -0.039 0 -32.876 -0.045 0 32.783 -0.039 0 62.602 -0.045 0 -62.658 -0.039 0 113.303 -0.045 0 -113.337 -0.039 0 363.337 -0.045 0 -363.257 -0.045 0 530.684 -0.046 0 -530.487 -0.02 0 -934.439 -0.024 0 934.835 -0.012 0 -1180.97 -0.017 0 1181.164 0.017 0 -1277.441 0.012 0 1277.443 0.024 0 -1181.735 0.02 0 1181.543 0.046 0 935.42 0.045 0 -935.824 0.045 0 530.678 0.039 0 -530.875 0.045 0 363.257 0.039 0 -363.337 0.045 0 113.337 0.039 0 -113.303 0.045 0 62.658 0.039 0 -62.602
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