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Live Load Serv

The document details the structural analysis for the TMbeam-26m of the Bridge Sungai Muda, including calculations for prestress, live load bending moments, and various stress conditions throughout the beam. It follows the BS 5400-4:1990 design code and includes information on initial prestress, relaxation losses, shrinkage, and creep losses. The analysis assumes ductile failure and provides specific stress values at different sections of the beam under various loading conditions.

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idah135
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13 views9 pages

Live Load Serv

The document details the structural analysis for the TMbeam-26m of the Bridge Sungai Muda, including calculations for prestress, live load bending moments, and various stress conditions throughout the beam. It follows the BS 5400-4:1990 design code and includes information on initial prestress, relaxation losses, shrinkage, and creep losses. The analysis assumes ductile failure and provides specific stress values at different sections of the beam under various loading conditions.

Uploaded by

idah135
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Job: Bridge Sungai Muda Job No.

: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

WARNING - This analysis assumes ductile failure of the beam, with calculation
of maximum allowable compressive stress in accordance with clause 7.4.3.2 of
BS 5400 Part 4.
Use the ULS results from SAM to check that this assumption is valid.

Section details:
Ref 1 "Section 1"
at 0.5 x span = 13 m from left end of beam
Analysis:
Live Load Bending
Live load BM 1
Serviceability Limit State
Prestress classification - clause 4.1.1.1:
Class 1

Load Combination 1

—————————————————————————————————————
ACTUAL STRESSES IN PRECAST BEAM
—————————————————————————————————————
No. of tendons fully bonded at this section: 33
No. of tendons fully debonded at this section: 0
No. of tendons deflected at this section: 0

INITIAL PRESTRESS
——————————————————————————————————————————————————————————————
height No of fpu area % of fpu initial force
mm tendons N/mm² mm² kN
——————————————————————————————————————————————————————————————
60.0 17 1860.0 150.0 75.0 3557.25
110.0 14 1860.0 150.0 75.0 2929.5
1040.0 2 1860.0 150.0 75.0 418.5
——————— —————————
TOTAL 33 6905.25

INITIAL RELAXATION
———————————————————————————————————————————————————————————————————
relaxation After relaxation
height No of total trans. loss force moment
mm tendons % % kN kN kN.m
———————————————————————————————————————————————————————————————————

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 1
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

60.0 17 2.5 50.0 44.465625 3512.7844 210.76706


110.0 14 2.5 50.0 36.61875 2892.8812 318.21694
1040.0 2 2.5 50.0 5.23125 413.26875 429.7995
——————— ————————— —————————
TOTAL 33 6818.9344 958.7835

Moment about the centroid of the precast beam:


Mr = 958.7835-(6818.9344*0.55819)
= -2847.51 kN.m
Corresponding stresses:
top stress = 6818.9344/480.412+-2847.51/1.5685E8
= 14.193915+-18.15409
= -3.9602 N/mm²
bottom stress = 6818.9344/480.412+-2847.51/-1.579E8
= 14.193915+18.037421
= 32.2313 N/mm²

Self weight moment:


c.s.a. = 4.804E5 mm²
density = 23.6 kN/m³
self weight = 4.804E5*23.6
= 11.3377 kN/m
beam length = 26.0 m
distance = 13.0 m
Msw = 0.5*11.3377*13.0*(26.0-13.0)
= 958.039 kN.m
Corresponding stresses:
top stress = 958.039/1.5685E8
= 6.10791 N/mm²
bottom stress = 958.039/-1.579E8
= -6.0687 N/mm²

ELASTIC DEFORMATION LOSSES


stress at top of precast beam = 2.14773 N/mm²
stress at bottom of precast beam = 26.1627 N/mm²
depth of precast beam = 1120.0 mm
——————————————————————————————————————————————————————————————
height No of conc conc tendon tendon
tendons stress strain force moment
mm N/mm² kN kN.m
——————————————————————————————————————————————————————————————
60.0 17 24.87617 6.91E-4 352.4124 21.144744
110.0 14 23.80407 6.612E-4 277.71418 30.54856
1040.0 2 3.863083 1.073E-4 6.4384725 6.6960114
——————— ————————— —————————
TOTAL 33 636.56505 58.389315

Moment about the centroid of the precast beam:


Med = 58.389315-(636.56505*0.55819)
= -296.9379 kN.m

hence top stress = 2.14773-636.56505/480.412--296.9379/1.5685E8


= 2.14773-1.3250385--1.893106
= 2.7158 N/mm²

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 2
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

bottom stress = 26.1627-636.56505/480.412--296.9379/-1.579E8


= 26.1627-1.3250385-1.8809399
= 22.9567 N/mm²

After a further 2 iterations of the above process, the top and bottom
stresses are as follows:
top stress = 2.65004 N/mm²
bottom stress = 23.2964 N/mm²

REMAINING RELAXATION
———————————————————————————————————————————————————————————————————
relaxation initial relaxation loss
height No of total rem. force force moment
mm tendons % % kN kN kN.m
———————————————————————————————————————————————————————————————————
60.0 17 2.5 50.0 3557.25 44.465625 2.6679375
110.0 14 2.5 50.0 2929.5 36.61875 4.0280625
1040.0 2 2.5 50.0 418.5 5.23125 5.4405
——————— ————————— —————————
TOTAL 33 86.315625 12.1365

Moment about the centroid of the precast beam:


Mr = 12.1365-(86.315625*0.55819)
= -36.04443 kN.m
Corresponding stresses:
top stress = 86.315625/480.412+-36.04443/1.5685E8
= 0.1796698+-0.229798
= -0.0501 N/mm²
bottom stress = 86.315625/480.412+-36.04443/-1.579E8
= 0.1796698+0.2283217
= 0.40799 N/mm²

SHRINKAGE LOSS - before in situ cast


Total design shrinkage strain = -0.0003
Percentage occurring before in situ = 25.0 %
Shrinkage strain occurring now = -0.0003*0.25
= -0.000075
——————————————————————————————————————————————————————————————
shrinkage loss
height No of area force moment
mm tendons mm² kN kN.m
——————————————————————————————————————————————————————————————
60.0 17 150.0 38.25 2.295
110.0 14 150.0 31.5 3.465
1040.0 2 150.0 4.5 4.68
——————— ————————— —————————
TOTAL 33 74.25 10.44

Moment about the centroid of the precast beam:


Msh = 10.44-(74.25*0.55819)
= -31.00596 kN.m
Corresponding stresses:
top stress = 74.25/480.412+-31.006/1.56852E8
= 0.1545546+-0.197676

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 3
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

= -0.0431 N/mm²
bottom stress = 74.25/480.412+-31.006/-1.5787E8
= 0.1545546+0.1964058
= 0.35096 N/mm²

CREEP LOSS Clause 6.7.2.5. - before in situ cast

Cube strength at transfer fci = 60.0 N/mm²


Basic creep value = -0.000048 per N/mm²
One-third of cube strength fci /3 = 20.0 N/mm²
Maximum stress in beam at transfer = 23.2964 N/mm²
Max stress > fci /3 therefore the basic creep is modified:
(23.2964-20.0)
modified creep = -0.000048 * [ 1 + ———————————————————— *0.25 ]
((0.5*60.0)-20.0)
= -5.196E-5 per N/mm²

Percentage occurring before in situ = 25.0 %


Creep occurring now = -5.2E-5*0.25
= -1.299E-5 per N/mm²

stress at top of precast beam = 2.74329 N/mm²


stress at bottom of precast beam = 22.5374 N/mm²
depth of precast beam = 1120.0 mm
————————————————————————————————————————————————————————————————————
concrete creep loss
height No of area E stress force moment
mm tendons mm² kN/mm² N/mm² kN kN.m
————————————————————————————————————————————————————————————————————
60.0 17 150.0 200.0 21.477 142.2712 8.5362722
110.0 14 150.0 200.0 20.5934 112.34382 12.35782
1040.0 2 150.0 200.0 4.15715 3.2398141 3.3694067
——————— ————————— —————————
TOTAL 33 257.85483 24.263499

Moment about the centroid of the precast beam:


Mcr = 24.263499-(257.85483*0.55819)
= -119.6697 kN.m
Corresponding stresses:
top stress = 257.85483/480.4125+-119.6697/1.569E8
= 0.5367363+-0.762945
= -0.2262 N/mm²
bottom stress = 257.85483/480.412+-119.6697/-1.579E8
= 0.5367363+0.7580423
= 1.29478 N/mm²

Erection of beam Loading


Bending moment from erection loadcase at current span location:
MApplied = 1081.6 kN.m
Corresponding stresses:
top stress = 1081.6/1.5685E8
= 6.89566 N/mm²
bottom stress = 1081.6/-1.579E8
= -6.8513 N/mm²

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 4
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

Remove the dead load applied for transfer calculations


Msw = -958.04 kN.m
Corresponding stresses:
top stress = -958.04/1.5685E8
= -6.1079 N/mm²
bottom stress = -958.04/-1.579E8
= 6.06865 N/mm²

Construction stage 1A Loading


MApplied = 641.7775 kN.m
Corresponding stresses:
top stress = 641.7775/1.5685E8
= 4.09161 N/mm²
bottom stress = 641.7775/-1.579E8
= -4.0653 N/mm²

SHRINKAGE LOSS - after in situ cast


Total design shrinkage strain = -0.0003
Percentage occurring after in situ = 75.0 %
Shrinkage strain occurring now = -0.0003*0.75
= -0.000225
——————————————————————————————————————————————————————————————
shrinkage loss
height No of area force moment
mm tendons mm² kN kN.m
——————————————————————————————————————————————————————————————
60.0 17 150.0 114.75 6.885
110.0 14 150.0 94.5 10.395
1040.0 2 150.0 13.5 14.04
——————— ————————— —————————
TOTAL 33 222.75 31.32

Moment about the centroid of the composite beam:


Msh = 31.32-(222.75*0.79458)
= -145.673 kN.m
Corresponding stresses:
top stress = 222.75/747.357+-145.67/5.04479E8
= 0.2980503+-0.288759
= 0.00929 N/mm²
bottom stress = 222.75/747.357+-145.67/-2.0661E8
= 0.2980503+0.7050694
= 1.00312 N/mm²

CREEP LOSS Clause 6.7.2.5. - after in situ cast


creep = -5.196E-5 per N/mm²
Percentage occurring after in situ = 75.0 %
Creep occurring now = -5.2E-5*0.75
= -3.897E-5 per N/mm²

stress at top of precast beam = 7.83957 N/mm²


stress at bottom of precast beam = 15.3915 N/mm²
depth of precast beam = 1120.0 mm
————————————————————————————————————————————————————————————————————

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 5
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

concrete creep loss


height No of area E stress force moment
mm tendons mm² kN/mm² N/mm² kN kN.m
————————————————————————————————————————————————————————————————————
60.0 17 150.0 200.0 14.9869 297.83619 17.870171
110.0 14 150.0 200.0 14.6498 239.7592 26.373512
1040.0 2 150.0 200.0 8.37899 19.590119 20.373724
——————— ————————— —————————
TOTAL 33 557.18551 64.617407

Moment about the centroid of the composite beam:


Mcr = 64.617407-(557.18551*0.79458)
= -378.1119 kN.m
Corresponding stresses:
top stress = 557.18551/747.3569+-378.1119/5.045E8
= 0.7455413+-0.749509
= -0.004 N/mm²
bottom stress = 557.18551/747.357+-378.1119/-2.066E8
= 0.7455413+1.8300928
= 2.57563 N/mm²

Superimposed dead load 1 Loading


MApplied = 305.96395 kN.m
Corresponding stresses:
top stress = 305.96395/5.0448E8
= 0.60649 N/mm²
bottom stress = 305.96395/-2.066E8
= -1.4809 N/mm²

SDL non-structural concrete etc. Loading


MApplied = 354.55862 kN.m
Corresponding stresses:
top stress = 354.55862/5.0448E8
= 0.70282 N/mm²
bottom stress = 354.55862/-2.066E8
= -1.7161 N/mm²

Live load BM 1 Loading


MApplied = 1852.8906 kN.m
Corresponding stresses:
top stress = 1852.8906/5.0448E8
= 3.67288 N/mm²
bottom stress = 1852.8906/-2.066E8
= -8.9681 N/mm²

——————————————————————————————————————————
PERMISSIBLE STRESSES IN PRECAST BEAM
——————————————————————————————————————————
Compression
Clause 6.3.2.2 Table 22
0.4*fcu = 0.4 * 60.0
= 24.0 N/mm²
Clause 7.4.3.2
for ductile failure, this may be increased by 25%
ie permissible compression stress = 1.25 * 24.0

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 6
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

= 30.0 N/mm²
Tension
Clause 6.3.2.4 (a)(1)
Permissible tension stress = 0.0 N/mm²

———————————————————————————————————————————————
PERMISSIBLE STRESSES FOR IN SITU CONCRETE
———————————————————————————————————————————————
Compression
Clause 4.1.1.3 Table 2
char. strength of in situ concrete = 40.0 N/mm²
stress limitation factor = 0.5
permissible compression stress = 0.5*fcu
= 0.5 * 40.0
= 20.0 N/mm²
Tension
Clause 7.4.3.3
Flexural tensile stresses are to be limited by cracking considerations in
accordance with clause 5.8.8.2.
However, no tensile stress is present at this section.

——————————————————————————————————————————————————————————————————————
SLS STRESS SUMMARY TABLE
——————————————————————————————————————————————————————————————————————
———————————————————————————————————————————————————————
Concrete Stresses (N/mm²)
force moment In situ Precast
kN kN.m top bottom top bottom
———————————————————————————————————————————————————————

Prestress[1] 6818.93
-2847.5 -3.9602 32.2313
Self Weight 958.039 6.10791 -6.0687
——————————————————————————————————————————————————————
Prestress + Self Weight 2.14773 26.1627

Elastic Def -570.46 265.039 0.50230 -2.8663


——————————————————————————————————————————————————————
TRANSFER 6248.48 -1624.4 2.65004 23.2964

Rem. Relax. -86.316 36.0444 0.05013 -0.4079


Shrinkage B -74.25 31.006 0.04312 -0.3509
Creep B -257.85 119.67 0.22620 -1.2948
Erection 123.561 0.78775 -0.7826
In situ 1A 641.777 4.09161 -4.0653
Shrinkage A -222.75 145.673 0.14482 -0.008 -0.0093 -1.0031
Creep A -557.19 378.112 0.40008 0.00342 0.00397 -2.5756
SDL 305.964 0.84323 0.52225 0.60649 -1.4809
SDL: conc etc 354.559 0.97716 0.60520 0.70282 -1.7161
Diff. Shr. 1 413.23 175.796 -0.3723 -0.5568 0.90139 -0.2979
Diff. Shr. 2 0.0 0.0 0.0 0.0 0.0
————————————————————————————————————————————————————
TOTAL DEAD 2.3653 1.12288 10.0542 9.32096

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 7
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

LIVE LOADS

Live load BM 1 Comb 1 1852.89 5.10656 3.16276 3.67288 -8.9681


———————————————————————————————————————————

TOTAL DEAD LOAD + LIVE LOAD

Live load BM 1 Comb 1 7.47187 4.28564 13.7271 0.35281


———————————————————————————————————————————

——————————————————————————————————————————————————————————————————————
SLS FLEXURE
BS 5400:4:1990 Appendix A.2 calculated for uncracked sections
——————————————————————————————————————————————————————————————————————
The deflections are calculated from integration of the curvatures along the
beam, using the parameters detailed below:
(Note that the reported values of deflections for live loadings are
exaggerated when these are derived from enveloped effects)

Elastic Modulus at Transfer, ET = 36.0 kN/mm²


Intermediate Term Elastic Modulus, EI = 28.8 kN/mm²
creep factor, φ =(ES /EL )-1 = 1.0
Creep before in situ cast, pbic = 25.0 %
EI = ES /(1+(φ.pbic))
Effective Elastic Modulus for time dependant effects, EE = 24.0 kN/mm²
creep factor, φ =(ES /EL )-1 = 1.0
Creep before in situ cast, pbic = 25.0 %
Ageing factor, χ = 0.8
EE = ES .(pbic + ((1-pbic)/ (1 + χ.φ)))
Long Term Elastic Modulus, EL = 18.0 kN/mm²
Short Term Elastic Modulus, ES = 36.0 kN/mm²

Precast section height = 1120.0 mm

—————————————————————————————————————————————
Precast Curvature Deflection
Stress E Strain (x10-6 ) (mm)
(N/mm²) (x10-6 ) (rad/m) Here Max.
—————————————————————————————————————————————

At Transfer T 2.65004 ET 73.6121 -512.06 38.2315 38.2315


B 23.2964 647.121

At Erection T 3.75725 EI 130.46 -517.82 39.4972 39.4972


B 20.4599 710.415

Long-term Dead T 10.0542


B 9.32096

Dead Stress Increment T 7.40421 EE 308.509 795.373 -55.774 -55.774


B -13.975 -582.31

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 8
Job: Bridge Sungai Muda Job No.: 148
Beam: TMbeam- 26m Calc. By: Aqila
Checked:
Data File: \\zar-storage\Eng\2. PROJECTS\31. Paya Keladi\TMBeam26mRev.sam 6/5/2025 2:25:09 PM

Design code: BS 5400-4:1990


Serviceability Limit State Load Combination 1
Prestress Classification: Class 1 - clause 4.1.1.1.
Load case: Live load BM 1
Section Ref 1 at 13m from left end of beam

—————————————————————————
Total Dead Load deflection 277.556 -16.277 -16.277
—————————————————————————

Live load BM 1 Comb 1 T 3.67288 ES 102.024 313.517 -21.921 -21.921


B -8.9681 -249.12
—————————————————————————
Extreme in-service 591.074 -38.198 -38.198
—————————————————————————

________
[1] includes initial relaxation

End

SAM v6.60e
Copyright © 2025 Bestech Systems Ltd 6/5/2025 15:30 9

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