Sam Eurocode UK Pretressed Beam Sample Report

8/10/2019 Sam Eurocode UK Pretressed Beam Sample Report

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Sample ReportPrecast Pre-tensioned Beam ExampleEurocodes UK NA


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Pre-tensioned Pre-stressed Beam

Bridge Design Example

1. Geometry & Basic Data ................................................................................................................... 5

2. Carriageway Configuration .................................................................................................. ...........9

3. Global Analysis Model ................................................................................................................... 13

4. Influence surfaces ......................................................................................................................... 17

a) Mid Span Sagging Moment ....................................................................................................... 19

b) Internal Support Hogging Moment ........................................................................................... 20

c) Internal Support Shear .............................................................................................................. 21

5. Traffic Loading Configuration ........................................................................................................ 23




6. Global Analysis Results .................................................................................................................. 29




7. Section Properties ......................................................................................................................... 37

a) Mid Span ................................................................................................................................... 39

b) Internal Support ........................................................................................................................ 41

8. Data Summary after Tendon Design ............................................................................................. 43

9. Temperature Gradient .................................................................................................................. 51

10. Shrinkage & Creep ........................................................................................................................ 55

11. Verification: Transfer Stresses ...................................................................................................... 63

12. Verification: SLS Bending - Mid Span ............................................................................................ 73

13. Verification: ULS Bending - Mid Span ........................................................................................... 93

14. Verification: SLS bendingPier .................................................................................................... 99

15. Verification: SLS bendingSupport ............................................................................................ 117

16. Verification: ULS Shear - Pier ...................................................................................................... 135

17. Verification: ULS Interface Shear ................................................................................................ 143

18. Verification: Web Shear Cracking ............................................................................................... 149

Appendix - National Annex NDP Values .............................................................................................. 157

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1.Geometry & Basic Data

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General Cross Section

Elevation

Plan

Grade C31/40 insitu concrete; Grade C50/60 precast concrete

Grade B500B reinforcement steel

Supports located 1m beneath soffit of slab

Reinforced Concrete diaphragm over supports

Cracked insitu concrete over central supports

Slab reinforcement over internal supports (6m either side)

Carriageway is 9.6 m wide with 1.2m footway on each side

Designed for vertical highway loading groups Gr1a with French National Annex NDP values

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Bestech Systems Limited2 Slaters CourtPrincess StreetKnutsfordWA16 6BW

Job: Sample ReportsJob No.: 6.5dCalc. By: dlg

Beam: Prestress Beam - Inner span 1 Checked:

Eurocode + UK NA

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

SAM v6.50d 02/02/2012 10:57:11 Page: 1 2012 Bestech Systems Ltd

USER NOTES

The design had been completed using the following process:

-

1) Four beams are created in SAM, two representing each span of the Y7 inner

beams and the other two representing the edge beams of each span (with the

upstand on the left hand side). At this stage all possible tendons are active.

The differential temperatue profile is also determied and entered for each of

the beams -

2) A line beam analysis is carried out to determine the bending moments and

shear forces atrributed to the dead load actions at each construction stage and

the secondary moments and shears for differential temperatuire and differential

shrinkage. Surfacing (SDL) actions are also established with the line beam

analysis

-

3) A grillage model of the bridge deck is created using the beams prepared in 1)

above. The grillage is to take account of the vertical level of each of the

component beam elements by way of member eccentricities. This will give rise to

a better distribution of effects but will intruduce (relatively small) axial

forces into the beams.

-

4) Traffic load patterns are established for max sagging, hogging and shear foreach node point along one of the central most beams, by using the load

optimisation. This will give rise to three envelopes for sagging, hogging and

shear.

-

5) The traffic live loads are transferred back to the table in the appropriate

beam file.

-

6) An alaysis at transfer is carried out and some tendons are removed and

debonded to reduce the compressive and tensile stresses to below limiting

values. (This can be done with the tendon optimisation facility if required).

Results output is produced for the mid span section

-

7) Other construction stages are checked at SLS Characteristic and ULS:STR to

check compliance with stress limits and Bending capacity. Results output is

produced for the mid span section.

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8) Bending moments (sagging and Hogging) due to the full traffic action (plus

other permanent and variable effects) ar checked for compliance at SLS and ULS.

Results output is produced for the mid span section.

-

9) Transverse and Longitudinal shear reinforcement requirements are

established and the results output for the most onerouse section as well as web

shear cracking checks at SLS

-

10) Other reports of results, such as differential temp and shrinkage are

produced and appended to the final report.

-11) Time dependant creep effects are accounted for using the simplified method

found in EN1992-2 Annex KK.7

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2.Carriageway Configuration

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Job: Sample ReportsJob No.: 6.5dCalc. By: DLG

Structure: 2 span grillage prestresses beam deck Checked:

Eurocodes + UK NA

Data File: J:\...\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44


Data Report

STRUCTURE

CARRIAGEWAYS

CW1: Carriageway

Carriageway is for road traffic loading.

It is aligned to design line DL1 and is single.

Primary carriageway has 2 lanes 4.0m wide.

Carriageway Offset 1 (m) Offset 2 (m)

Primary -4.0 4.0

Footway 1 -5.5 -4.0

Footway 2 4.0 5.5

Loaded Widths for:CW1

CF1: DefaultPrimary carriageway - Number of lanes: 2

Ref Offset Width Direction

1 0.0 3.0 with Chainage

2 3.0 3.0 against Chainage

CF2: Load Opt. (created by load optimisation)Primary carriageway - Number of lanes: 2








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Job: Sample ReportsJob No.: 6.5dCalc. By: DLG

Structure: 2 span grillage prestresses beam deck Checked:

Eurocodes + UK NA

Data File: J:\...\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44








1 -0.25 2.5 with Chainage










CF8: Load Opt. (created by load optimisation)

Primary carriageway - Number of lanes: 2Ref Offset Width Direction



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3.Global Analysis Model

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This is a view of the structure that is

modelled for the global analysishighlighting the beam considered for

design

The beam in isolation indicates the

cracked concrete slab over the

central pier, shown dotted

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4.Influence surfaces

a)

Mid Span Sagging Moment

b) Internal Support Hogging Moment

c) Internal Support Shear

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Job: Sample ReportsStructure: 2 span grillage prestresses beam deck

Eurocodes + UK NAData File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44

Job No.: 6.5dCalc. By: DLGChecked:

Result Type: Influence Surface Name: I7: BM55; My Sagging

Influence coefficients are expressed with respect to global axes.

Analysis Run: 01/02/2012 14:39:12

Results shown for: Influence Coefficients - DZ (m)

SAM v6.50dCopyright 2012 Bestech Systems Ltd 102/02/2012 11:14

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Result Type: Influence Surface Name: I25: BM60; My Hogging


Analysis Run: 06/02/2012 11:01:20



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Result Type: Influence Surface Name: I26: BM60; Shear z-


Analysis Run: 06/02/2012 11:01:20



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5.Traffic Loading Configuration

a)




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6.Global Analysis Results

a)




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Eurocodes + UK NAData File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d D...\2 span prestress beam deck .sst 02/02/2012 09:29:44


Result Type: Envelope Name: E1: GR1A; ULS STR/GEO Mem 49-60: My+

Result For: Beam Effect: Member End Actions

Moments at the member start end correspond with the local member axes directions. At the other end, moments are positive in the oppositedirection to the local member axes.With this convention, a positive y or z moment at each end denotes sagging.The table displays the enveloped effect and associated values. The enveloped effect is Member End Moments - My (kN.m).

Analysis Run: 01/02/2012 14:48:20

Results shown for: Member End Moments - My (kN.m)


New Selection

Member End MomentsMember End ForcesReference

Mz (kN.m)OriginMy (kN.m)Mx (kN.m)Fz (kN)Fy (kN)Fx (kN)Joint Member 182.2866C1184.23525.4402226.5307647.25736-55.914245349

100.8609C9335.77319.73986271.168133.06124-35.846835449

51.87468C9343.283623.78223133.497822.6683-22.257845450

-1.920841C171012.892-2.971709488.1098-2.69283354.621675550

4.310352C17992.37411.268835207.1184-2.86377520.416045551

7.980115C251519.030.4258882341.2957-3.10870628.149615651

8.499461C251506.3874.64540112.84226-2.2136399.6565855652

11.38605C331867.6183.409645271.0804-3.99245312.550145752

10.30689C331859.0247.16562-53.32979-1.9583221.5448865753

11.96043C412039.2325.880492209.6595-3.6849422.670425853

11.81908C412035.9778.95645-115.5332-0.77581320.79649235854

10.77256C492042.0857.473753138.1745-2.4877742.1202915954

12.77409C492045.3819.730765-183.480.745568311.215135955

FactoredFactorsUnfactoredLoad

TotalOtherLanegrAlphaPsiGammaTypeRef

Compilation : C49: BM55; My Sagging; GR1A; ULS STR/GEO (SUM=2045.38)

234.83491110.6111.35285.1668LM1 UDL SystemL57

66.862931112.211.3522.51277LM1 UDL SystemL59

12.778711111.359.465714Footway: UDL System (Footway)L121

31.604811111.3523.41097Footway: UDL System (Footway)L122

232.891610.277777812.211.35282.2928LM1 UDL SystemL123

584.233110.66666671111.35649.1479LM1 Tandem SystemL124

882.1748111111.35653.4628LM1 Tandem SystemL125

My=2045.3811925.46

-17.79333C571895.57.51426177.735880.79824715.520786055

-16.04987C571907.1512.884023-247.2278-2.98801633.820526056

-15.22928C651621.2725.464101-6.8347880.828261230.53476156

-16.90568C651638.5770.3388024-346.8961-3.61068560.012716157

-10.54859C731210.068-0.6692659-110.8182-4.71520648.377496257

-17.32338C731230.844-5.560555-465.8913-10.9215582.864696258

-3.139501C81651.3091-4.188907-134.3832-7.79754728.104176358

-11.63125C81681.349-5.459631-505.8134-12.0478352.215756359

4.864394C8961.63301-7.84137-151.3374-9.6556325.6309566459

12.16619C8967.45666-8.120834-406.9595-13.5708611.729366460

20.18539C977.586888-6.696705-16.30567-9.464386-20.19546560

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Result Type: Envelope Name: E2: GR1A; ULS STR/GEO Mem 49-60: My-


Moments at the member start end correspond with the local member axes directions. At the other end, moments are positive in the oppositedirection to the local member axes.With this convention, a positive y or z moment at each end denotes sagging.The table displays the enveloped effect and associated values. The enveloped effect is Member End Moments - My (kN.m).

Analysis Run: 01/02/2012 14:48:20

Results shown for: Member End Moments - My (kN.m)


New Selection


Mz (kN.m)OriginMy (kN.m)Mx (kN.m)Fz (kN)Fy (kN)Fx (kN)Joint Member -0.3055404C2-540.7185-2.139213427.03255.094982157.88875349

-19.1692C10-203.0551-4.97695207.85785.170721137.66415449

-1.098864C10-224.4301-4.123625210.5464.67488799.322145450

-0.04289707C26-70.21469-0.1607472-30.588310.125463-2.6128395550

0.2566332C26-69.16653-0.5053211-30.842540.4065817-0.88858475551

-0.5195683C26-128.0478-0.5053211-30.842540.4065817-0.88858475651

0.5482784C26-126.6603-0.8808424-31.263120.78352131.5138165652

-1.782311C42-189.36610.08934582-33.712691.110892.1639335752

0.3427496C42-186.3882-0.4991898-34.776291.5861327.5409485753

-2.733323C58-252.8444-0.4645858-34.816471.6257697.4986075853

0.4624202C58-248.9295-1.132049-36.421222.13799214.866245854

-3.609668C74-318.4683-1.130482-36.502142.12158214.809315954

0.6104634C58-313.4238-1.896179-38.681392.68995124.707025955

-4.508079C74-387.4718-1.896578-38.800912.66461124.705346055

0.7231245C74-381.0251-2.795453-41.874923.2060237.703976056

-5.397487C74-460.9685-2.795453-41.874923.2060237.703976156

0.8188211C74-453.6171-3.869674-45.787753.64199154.369216157

-6.134068C74-541.0301-3.869674-45.787753.64199154.369216257

0.7229482C74-531.9109-5.391563-50.554853.47563674.17496258

-5.145004C82-656.2544-4.804924-90.500552.98982395.309836358

0.5380956C82-610.4323-8.621091-95.091971.956679117.81486359

24.02131C90-888.0567-23.02836-266.468-26.16291150.70056459

8.108403C90-883.7671-19.99131-270.5991-36.96983154.14736460

13.65186C98-1286.162-9.477075-469.0165-15.75881190.19576560



Compilation : C98: BM60; My Hogging; GR1A; ULS STR/GEO (SUM=-1286.16)

-33.735841112.211.35-11.35887LM1 UDL SystemL24

-0.39762381111.35-0.2945362Footway: UDL System (Footway)L210




-256.41731110.6111.35-311.375LM1 UDL SystemL214

-421.5176111111.35-312.2353LM1 Tandem SystemL215

-257.305110.277777812.211.35-311.8849LM1 UDL SystemL216

-268.358910.66666671111.35-298.1766LM1 Tandem SystemL217

-16.807251112.211.35-5.659007LM1 UDL SystemL218

My=-1286.162-1274.408

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Result Type: Envelope Name: E9: GR1A; ULS STR/GEO Mem 50-60: Sh z


Forces at the member start end correspond with the local member axes directions. At the other end, forces are positive in the opposite directionto the local member axes.With this convention, a positive axial force at each end denotes compression.The table displays the enveloped effect and associated values. The enveloped effect is Member End Forces - Fz (kN).

Analysis Run: 01/02/2012 14:48:20

Results shown for: Member End Forces - Fz (kN)


New Selection


Mz (kN.m)My (kN.m)Mx (kN.m)OriginFz (kN)Fy (kN)Fx (kN)Joint Member -15.82357-433.2182-2.585628C105525.8172-1.96579114.29165349

-13.9471468.69836-2.585628C105525.8172-1.96579114.29165449

-3.45443440.00968-1.151738C105512.9767-1.62522260.945635450

-0.35173761019.329-1.151738C105512.9767-1.62522260.945635550

-3.804586674.19852.064739C113426.0225-3.65579733.789145551

3.1746611487.5142.064739C113426.0225-3.65579733.789145651

-4.9924961064.6314.608999C121352.5722-4.87726114.187575652

4.3186381737.7244.608999C121352.5722-4.87726114.187575752

-4.7388151238.8065.606502C129289.4707-4.6132971.8361645753

4.0683861791.4315.606502C129289.4707-4.6132971.8361645853

-3.2237641243.9065.591374C137233.3123-3.216076-0.73896025854

2.916011689.325.591374C137233.3123-3.216076-0.73896025954

-10.564141703.8993.502448C146-292.0244-2.01351213.776225955

-6.7201651146.3983.502448C146-292.0244-2.01351213.776226055

11.652621668.2016.038212C154-363.17345.12856738.658466056

1.861671974.86716.038212C154-363.17345.12856738.658466156

11.475341443.0394.055623C162-428.09125.96815775.811426157

0.08159752625.77434.055623C162-428.09125.96815775.811426257

7.8264551053.7221.035365C170-500.86014.032943110.66546258

0.127203697.53511.035365C170-500.86014.032943110.66546358

1.894806489.9939-1.563676C178-583.3914-0.4487549114.0696359

2.751519-623.7527-1.563676C178-583.3914-0.4487549114.0696459

4.316139-294.7813-6.772206C186-655.6394-2.10465286.188196460



Compilation : C186: BM60; Shear z-; GR1A; ULS STR/GEO (SUM=-655.64)

-4.82031112.211.35-1.622997LM1 UDL SystemL231

-5.7299051112.211.35-1.929261LM1 UDL SystemL425




-60.6132110.277777812.211.35-73.47056LM1 UDL SystemL470

-128.986710.66666671111.35-143.3186LM1 Tandem SystemL471

-97.321591110.6111.35-118.1804LM1 UDL SystemL472

-352.5574111111.35-261.1537LM1 Tandem SystemL473

-0.073897681112.211.35-0.02488137LM1 UDL SystemL474

-0.41446371112.211.35-0.1395501LM1 UDL SystemL475

Fz=-655.6394-603.6339

6.325115-920.6156-6.772206C186-655.6394-2.10465286.188196560

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7.Section Properties

a)

Mid Span

b) Internal Support

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Eurocode + UK NA



Design code: EN 1992-2:2005 with UK National Annex (modified)Analysis: Section Properties EN 1990 Equation 6.14 SLS CharacteristicExposure Class: XD1, XD2, XS1, XS2, XS3 Section Ref 1 at 10.5m from left end of beam

Section Ref: 1 "Section 1"

depth of precast beam = 1300.0 mm

total depth of section = 1470.0 mm

Section properties are detailed below in the following sequence:

PRECAST BEAM ALONECOMPOSITE BEAM TO STAGE 1

PRECAST BEAM ALONEElastic section properties

area, Ac = 5.372E5 mm

height to centroid, za = 576.039 mm

overall depth, h = 1300.0 mm

2nd moment of area, Iyy = 9.2977E10 mm

section modulus at bottom, Wb = 9.2977E10 / -576.04

-1.6141E8 mm

section modulus at top, Wt = 9.2977E10 / (1300.0-576.039)

1.28428E8 mm

COMPOSITE BEAM

COMPOSITE BEAM TO STAGE 1

Elastic section properties

Area centroid Sy Iyy Iyy (z=0)

mm mm mm mm mm

Precast beam 537225.68 576.0392 1.0 3.09463E8 9.2977E10 2.7124E11

Stage 1 i.s. 388869.57 1372.4329 1.057 5.04816E8 1.18215E9 6.9401E11

TOTAL 905051.14(transformed) 8.14279E8 9.6525E11

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Eurocode + UK NA



height to centroid = 8.14279E8/9.051E5

= 899.705 mm

Iyy = 9.6525E11 - (9.051E5*899.705)

= 2.3264E11 mm

ELASTIC SECTION PROPERTIES SUMMARY TABLE

Level Iyy zna W

mm mm mm mm

Precast beam only

Precast beam B 0.0 9.2977E10 576.0392 -1.6141E8

T 1300.0 1.28428E8

In situ to stage 1

Precast beam B 0.0 2.3264E11 899.70476 -2.5857E8

T 1300.0 5.81164E8

In situ Stage 1 B 1270.0 6.64191E8

T 1470.0 4.31262E8

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Eurocode + UK NA



Design code: EN 1992-2:2005 with UK National Annex (modified)Analysis: Section Properties EN 1990 Equation 6.14 SLS CharacteristicExposure Class: XD1, XD2, XS1, XS2, XS3 Section Ref 2 at 21m from left end of beam

Section Ref: 2 "Section 2"

depth of precast beam = 1300.0 mm

total depth of section = 1470.0 mm

Section properties are detailed below in the following sequence:

PRECAST BEAM ALONECOMPOSITE BEAM TO STAGE 1

PRECAST BEAM ALONEElastic section properties

area, Ac = 5.372E5 mm

height to centroid, za = 576.039 mm

overall depth, h = 1300.0 mm

2nd moment of area, Iyy = 9.2977E10 mm

section modulus at bottom, Wb = 9.2977E10 / -576.04

-1.6141E8 mm

section modulus at top, Wt = 9.2977E10 / (1300.0-576.039)

1.28428E8 mm

COMPOSITE BEAM

COMPOSITE BEAM TO STAGE 1

Elastic section properties

Area centroid Sy Iyy Iyy (z=0)

mm mm mm mm mm

Precast beam 537225.68 576.0392 1.0 3.09463E8 9.2977E10 2.7124E11

Stage 1 i.s. 388869.57 1372.4329 1.057 5.04816E8 1.18215E9 6.9401E11

Rft in IS 1 4908.7385 1407.5 0.211 3.2698E7 907471.06 4.6E10

TOTAL 928282.4(transformed) 8.46977E8 1.0113E12

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Eurocode + UK NA



height to centroid = 8.46977E8/9.283E5

= 912.413 mm

Iyy = 1.0113E12 - (9.283E5*912.413)

= 2.3848E11 mm

ELASTIC SECTION PROPERTIES SUMMARY TABLE

Level Iyy zna W

mm mm mm mm

Precast beam only

Precast beam B 0.0 9.2977E10 576.0392 -1.6141E8

T 1300.0 1.28428E8

In situ to stage 1

Precast beam B 0.0 2.3848E11 912.41288 -2.6137E8

T 1300.0 6.1529E8

In situ Stage 1 B 1270.0 7.05066E8

T 1470.0 4.52167E8

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8.Data Summary after Tendon Design

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Eurocode + UK NA



DATA SUMMARY

ANALYSIS TYPE: EN 1992-2 Pre-tensioned Prestressed BeamWith UK National Annex (modified)

BEAM DETAILS

Span:Total length of pre-tensioned beam : 21 m

Distance from left support to beam end face : 0 m

Distance from right support to beam end face : 0 m

Total distance between supports : 21 m

Beam section varies along length of beam.

Number of different sections : 2

No. of longitudinal construction stages : 2No. of superimposed construction stages : 1

Section 1

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Eurocode + UK NA



Precast beam:

Precast beam is standard section: Y7 Beam

Property set: 2 "C40/50 Ecm 35.2 "

Age of beam at transfer: 4.0 days

Corresponding concrete strength at transfer: 23.8094 MPa

In situ concrete - stage 1A:

In situ is from standard section:

- width : 2.0 m

- depth : 0.2 m

Property set: 1 "C31/40 Ecm 33.3 "Age of beam when stage 1A concrete is cast: 60 days

Shear resistance width: 216.0 mm

Section 2

Precast beam:

Precast beam is standard section: Y7 Beam


Age of beam at transfer: 4.0 days

Corresponding concrete strength at transfer: 23.8094 MPa

In situ concrete - stage 1B:In situ is from standard section:

- dimensions (m) : 2.0 0.0

0.2 0.0

0.0 0.0


Age of beam when stage 1B concrete is cast: 60 days

Shear resistance width: 216.0 mm

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Eurocode + UK NA



Tendons:

y-zcoordinates area transmission coeffients draw-in property

mm mm 1 2 p1 1 p2 mm mm/beam ref

-275.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-225.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-175.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-125.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-75.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded

0.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded

75.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded125.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

175.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

225.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

275.0 60.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-75.0 110.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded

-25.0 110.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded

25.0 110.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded

75.0 110.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Debonded

-25.0 210.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

25.0 210.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-25.0 260.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

25.0 260.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

-80.0 1200.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

80.0 1200.0 150.0 1.0 0.19 3.2 1.0 1.2 16.0 3.0 4 Full stress

Debonded Tendons:

y-zcoordinates distance from left end (m)

mm start end

-75.0 60.0 2.0 19.0

0.0 60.0 2.0 19.0

75.0 60.0 2.0 19.0

-75.0 110.0 2.5 18.5 -25.0 110.0 2.5 18.5

25.0 110.0 2.5 18.5

75.0 110.0 2.5 18.5

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Reinforcement:

y-zcoordinates diameter Property Start End Length

mm mm ref m m m

900.0 1407.5 25.0 3 15.0 21.0 6.0

700.0 1407.5 25.0 3 15.0 21.0 6.0

500.0 1407.5 25.0 3 15.0 21.0 6.0

300.0 1407.5 25.0 3 15.0 21.0 6.0

100.0 1407.5 25.0 3 15.0 21.0 6.0

-100.0 1407.5 25.0 3 15.0 21.0 6.0

-300.0 1407.5 25.0 3 15.0 21.0 6.0 -500.0 1407.5 25.0 3 15.0 21.0 6.0

-700.0 1407.5 25.0 3 15.0 21.0 6.0

-900.0 1407.5 25.0 3 15.0 21.0 6.0

Location of sections

Position along span

from left support: Section

dimension (m) proportion

0.0 0.0 1 "Section 1"

18.0 0.857 1 "Section 1"

18.0 0.857 2 "Section 2"

21.0 1.0 2 "Section 2"

PROPERTIES DETAILS

ref: 1 Type: Concrete - Parabola-RectangleName: C31/40 Ecm 33.3

Design Code Part : EN 1992-2

Characteristic strength fck: 31.875 MPa

fc

k

,

c

u

b

e: 40.0 MPa

modulus of elasticity Ecm: 33.314469 GPa

Elastic modulus - long term : 13.325787 GPa

Ultimate compressive strain cu: 0.0035

Tensile strength fctm: -3.015931 MPa

Cement Class : N - Normal and rapid hardening

Contains Silica Fume : No

Coefficient of thermal expansion: 0.00001 /C

Density : 24.0 kN/m

Density increase for rft. : 1.0 kN/m

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ref: 2 Type: Concrete - Parabola-RectangleName: C40/50 Ecm 35.2

Design Code Part : EN 1992-2

Characteristic strength fck: 40.0 MPa

fck,cube: 50.0 MPa

modulus of elasticity Ecm: 35.220462 GPa

Elastic modulus - long term : 14.088185 GPaUltimate compressive strain cu: 0.0035

Tensile strength fctm: -3.508821 MPa

Cement Class : N - Normal and rapid hardening

Contains Silica Fume : NoCoefficient of thermal expansion: 0.00001 /C

Density : 24.0 kN/mDensity increase for rft. : 1.0 kN/m

ref: 3 Type: Reinforcing Steel - HorizontalName: Grade 500 Es 200.0

Yield strength fyk: 500.0 MPa

modulus of elasticity Es: 200.0 GPa

Characteristic strain limit uk: 0.025

Density : 77.0 kN/m

ref: 4 Type: Prestressing Steel - HorizontalName: Grade 1600 Ep 195.0

tensile strength fpk: 1860.0 MPa

0,1% proof stress fp0,1k: 1600.0 MPa

modulus of elasticity Ep: 195.0 GPa

Relaxation loss after 1000 hours: 8.0 %Relaxation Class : 1

Density : 77.0 kN/m

ANALYSIS DATA

Data for loss calculations:

Shrinkage strain is calculated from the data provided

Creep coefficient is calculated from the data provided

Differential shrinkage is calculated from the data provided

Percentage of total long term loss which occurs before the section is made composite is 30.18

%

Age at start of drying shrinkage = 1.0 day

Ambient relative humidity = 80.0 %

Ambient temperature = 20.0 C

Maximum Curing temperature = 20.0 C

Creep calculations are based upon EN 1992-1-1

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Data for shear calculations:

Material property for transverse reinforcement: Grade 500 Es 200.0

Angle between concrete strut and beam axis, = 35.0

Angle between shear reinforcement and beam axis, = 90.0

Enhancement close to supports is ignoredSurface condition for precast / in-situ interface = Smooth

Longitudinal force ratio is calculated

Angle for compression strut in slab, f = 26.0

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9.Temperature Gradient

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DIFFERENTIAL TEMPERATUREEN 1991-1-5:2003 Figure 6.2 non-linear Temperature Profile

EN 1991-1-5:2003 Figure 6.2 non-linear Temperature Profile

Figure 6.2c: Type 3b. Concrete Beams

Surfacing : surfaced

Surfacing thickness : 0.1 m

Top warmer than bottom Bottom warmer than top

height m Temperature C height m Temperature C

0.0 13.5 0.0 -8.376

0.15 3.0 0.25 -0.56

0.4 0.0 0.45 0.0

1.27 0.0 1.02 0.0 1.47 2.5 1.22 -1.03

1.47 -6.488

Relaxing Forces

Moment Axial

kN.m kN

Heating Temperature difference -413.8371 -1015.993

Cooling Temperature difference 143.38408 976.55933

Note: The reinforcement has been ignored in the calculation of the above relaxing moments

Self Equilibrating Stresses

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Rectangle

Distance to top Stress - MPa

of section - m Heating Cooling

0.0 2.4760279 -1.437326

0.15 -0.769597

0.2 -0.885352 0.5291631

Y7 Beam

Distance to top Stress - MPaof section - m Heating Cooling

0.17 -0.862578 0.2475882

0.25 1.0791869

0.4 -1.425518

0.45 1.1531531

1.02 0.8018382

1.22 0.3157990

1.27 0.1221205

1.47 1.358411 -1.760619

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10. Shrinkage & Creep

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DIFFERENTIAL SHRINKAGE MODIFIED BY CREEP - Primary Load effects

Section Reference: 2 "Section 2"

Evaluate the shrinkage strains using EN 1992-1-1 clause 3.1.4(6)

Shrinkage in precast at time t =

Age of concrete at time considered, t= Age of concrete at loading, t0 = 4.0 days

Age of concrete at start of drying, ts = 1.0 days

Relative humidity of enviroment, RH = 80.0 %Average temperature, Ta = 20.0 C

Type of cement = Class Nfor which, EN1992-1-1 Annex B.1(2) = 0.0

Annex B.2(1) ds1 = 4.0

Annex B.2(1) ds2 = 0.12

3.1.2(6) s= 0.25Characteristic strength of concrete, fck = 40.0 MPa

Mean compressive strength at 28 days (Table 3.1),fcm = fck + 8.0 = 48.0 MPa

Mean comp. strength at 4.0 days (3.1.2(6) ),fcm(t0) = fcm.exp[s.(1-(28/t0)]

= 48.0*exp[0.25*(1-(28/4.0)] = 31.809 MPaConstant value from Annex B.2(1) fcm0 = 10.0 MPa

Total Shrinkage:cs = cd + ca (3.8)

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Drying Shrinkage - Expression (3.9):

cd(t) = ds(t,ts).kh.cd,0

ds(t,ts) = 1.0 for t=

From Table 3.3:kh = 0.79438

From Annex B, Expression (B.11):

cd,0 = 0.85[(220+110.ds1).(exp(-ds2.fcm/fcm0)].10-6.RH

RH = 1.55[1.0-(RH/100)] (B.12)

= 0.7564For cement class N,

ds1 = 4

ds2 = 0.12

hence,

cd,0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10-6*0.7564

= 238.54*10-6

and,

cd(t) = 1.0*0.79438*238.54*10-6

= 189.491*10-6

Autogenous Shrinkage - Expression (3.11):

ca(t) = a

s(t).ca()

as(t) = 1.0 for t=

ca() = 2.5*(fck-10.0)*10-6

= 75.0*10-6

hence,

ca(t) = 1.0*75.0*10-6

= 75.0*10-6

Total Shrinkage:

cs = cd(t) + ca(t)

= 189.49131 + 75.0

= 264.49131*10

-6

Shrinkage in in-situ concrete at time t=

Age of concrete at time considered, t= Age of concrete at loading, t0 = 4.0 days




Annex B.2(1) ds1 = 4.0

Annex B.2(1) ds2 = 0.12

3.1.2(6) s= 0.25

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Characteristic strength of concrete, fck = 31.875 MPa

Mean compressive strength at 28 days (Table 3.1),fcm = fck + 8.0 = 39.875 MPa










RH = 1.55[1.0-(RH/100)] (B.12)


ds1 = 4

ds2 = 0.12

hence,

cd,0 = 0.85[(220+110*4.0)*exp(-0.12*39.88/10.0)]*10-6*0.7564

= 262.969*10-6

and,

cd(t) = 1.0*0.79438*262.969*10-6

= 208.897*10-6


ca(t) = as(t).ca()

as(t) = 1.0 for t=

ca() = 2.5*(fck-10.0)*10-6

= 54.6875*10-6

hence,

ca(t) = 1.0*54.6875*10-6

= 54.6875*10-6

Total Shrinkage:

cs = cd(t) + ca(t)

= 208.89738 + 54.6875

= 263.58488*10-6

Shrinkage in precast at time in-situ is placed (t= 60 days)

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Age of concrete at time considered, t= 60.0 daysAge of concrete at loading, t0 = 4.0 days




Annex B.2(1) ds1 = 4.0

Annex B.2(1) ds2 = 0.12

3.1.2(6) s= 0.25

Characteristic strength of concrete, fck = 40.0 MPaMean compressive strength at 28 days (Table 3.1),fcm = fck + 8.0 = 48.0 MPa






ds(t,ts) = (t-ts)/[(t-ts)+0.04h0] (3.10)

t-ts = 60.0-1.0

= 59.0 daysds(t,ts) = 59.0/(59.0+0.04255.62)

= 0.26519From Table 3.3:

kh = 0.79438



RH = 1.55[1.0-(RH/100)] (B.12)


ds1 = 4

ds2 = 0.12

hence,

cd,0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10-6*0.7564

= 238.54*10-6

and,

cd(t) = 0.26519*0.79438*238.54*10-6

= 50.2528*10-6

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ca(t) = as(t).ca()

as(t) = 1-exp(-0.2t) (3.13)

= 1.0-exp(-0.2*60.0)= 0.78758

ca() = 2.5*(fck-10.0)*10-6

= 75.0*10-6

hence,

ca(t) = 0.78758*75.0*10-6

= 59.0686*10-6

Total Shrinkage:

cs = cd(t) + ca(t)

= 50.252794 + 59.068556

= 109.32135*10-6

Summary of data

Section is composite from t= 60 daysat time t= 60 days:

shrinkage strain in precast concrete, a = 109.321 x10-6

at time t=

shrinkage strain in precast concrete, b = 264.491 x10-6

shrinkage strain in in-situ concrete, c = 263.585 x10-6

differential shrinkage strain,diff = c - ( b - a )

= 263.585 - (264.491-109.321) = 108.415 x10-6

creep coefficient, = 2.00881

1 - e(-)

creep reduction factor = = 0.43102

2nd moment of area of transformed section, Iyy = 2.33E11 mm

height of centroid, za = 899.705 mm

total transformed area, Ac = 9.051E5 mm

elastic modulus of precast concrete, Ec,p = 35.2205 GPa

elastic modulus of in situ concrete, Ec,i = 33.3145 GPa

modular ratio n0 = Ec,p / Ec,i= 35.2205/33.3145= 1.05721

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Stage 1 In-situ

area of concrete : 3.889E5 mmheight to centroid : 1372.43 mmforce required to restrain shrinkage:

Ac..Ec,i.diff = 3.889E5*0.65982*33.3145*108.415 x10-6

= 605.383 kNcorresponding moment = 605.383*(1372.43-899.705)

= 286.182 kN.m (sagging)

self equilibrating stress in precast beam:

top of beam = P/Ac +M/Wt= 605.38331/905051.14 + 286.18174/5.81164E8= 1.1613224 MPa

soffit of beam = P/Ac +M/Wb= 605.38331/905051.14 + 286.18174/-2.5857E8= -0.437889 MPa

self equilibrating stress in stage 1 concrete:at top = ( P/Ac +M.(zt-za)/Iyy + .diff.Ec,p )/

= (605.38331/905051.14 +286.18174*570.29524/2.3264E11 +0.4310270*-1.084E-4*35.220462 ) /1.0572122

= -0.260490 MPa

at bottom = ( P/Ac +M.(zb-za)/Iyy + .diff.Ec,c )/

= (605.38331/905051.14 +286.18174*370.29524/2.3264E11 +0.4310270*-1.084E-4*35.220462) /1.0572122

= -0.493208 MPa

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11.

Verification: Transfer Stresses

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Design code: EN 1992-2:2005 with UK National Annex (modified)Analysis: Stresses at Transfer EN 1990 Equation 6.14 SLS Characteristic Section Ref 1 at 10.5m from left end of beam

Section details:Ref 1 "Section 1"at 0.5 x span = 10.5 m from left end of beam

Analysis:Stresses at TransferServiceability Limit State: Characteristic - EN 1990 Equation 6.14

ACTUAL STRESSES IN PRECAST BEAM

No. of tendons fully bonded at this section: 21No. of tendons fully debonded at this section: 0No. of tendons deflected at this section: 0

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Maximum Stressing Force - EN 1992-1-1 Clause 5.10.2.1(1)PFor tendon property Grade 1600 Ep 195.0

k1.fpk = 0.8*1860.0 = 1488.0 MPa

k2.fp0,1k = 0.9*1600.0 = 1440.0 MPa

Wedge draw-in loss Clause 5.10.4(1)(i)draw-in strain = 0.003/21.0

= 1.43E-4loss = Ep . strain

= 195.0*1.43E-4

= 27.8571 MPa

Heat Curing Clause 5.10.4(1)(ii)(Note)Concrete is cured at ambient temperature

Immediate Losses - EN 1992-1-1 Clause 5.10.4

height No of fp k1/k2 draw-in heat cure area initial force

mm tendons MPa MPa MPa mm kN

60.0 11 1600.0 0.9 27.8571 0.0 150.0 2330.0357

110.0 4 1600.0 0.9 27.8571 0.0 150.0 847.28571

210.0 2 1600.0 0.9 27.8571 0.0 150.0 423.64286 260.0 2 1600.0 0.9 27.8571 0.0 150.0 423.64286

1200.0 2 1600.0 0.9 27.8571 0.0 150.0 423.64286

TOTAL 21 4448.25

In accordance with clause 5.10.9(1), for SLS, the Characteristic value must be used.With rinf = 1.0, Pk,inf = 4448.25 kN

Friction Clause 5.10.4(1)(i)All tendons are straight in this beam.

Initial Relaxation Clause 5.10.4(1)(ii)

Loss is calculated from clause 3.3.2(7)For tendon property Grade 1600 Ep 195.0relaxation loss at 1000 hours, 1000 = 8.0 %

= pi / fpk= 1440.0-27.8571-0.0/1860.0= 0.75921

time after tensioning = 96.0 hoursfor Class 1 relaxation, use Expression (3.28)

5.39 . 1000 . e6.7

. [t/1000]0.75(1-)

. 10-5

= 5.39 * 8.0 * 161.863 * 0.65495 * 10-5

= 0.04571

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relaxation After relaxation

height No of area x loss force momentmm tendons pi % kN kN kN.m

60.0 11 2330.04 4.57 106.51239 2223.5233 133.4114

110.0 4 847.286 4.57 38.731779 808.55394 88.940933

210.0 2 423.643 4.57 19.365889 404.27697 84.898163

260.0 2 423.643 4.57 19.365889 404.27697 105.11201

1200.0 2 423.643 4.57 19.365889 404.27697 485.13236

TOTAL 21 4244.9082 897.49487

Moment about the centroid of the precast beam:Mr = 897.49487-(4244.9082*0.5760392)

= -1547.739 kN.mCorresponding stresses:top stress = 4244.9082/537225.68+-1547.739/1.2843E8

= 7.9015362+-12.05139= -4.149853 MPa

bottom stress = 4244.9082/537225.68+-1547.739/-1.614E8= 7.9015362+9.5890175= 17.490554 MPa

Self weight moment:

c.s.a. = 5.372E5 mmdensity = 24.0 kN/m + 1.0 kN/m + 1.0 kN/m = 26.0 kN/m

[1]

self weight = 5.372E5*26.0= 13.9679 kN/m

beam length = 21.0 mdistance = 10.5 mMsw = 0.5*13.9679*10.5*(21.0-10.5)

= 769.979 kN.mCorresponding stresses:top stress = 769.979/1.2843E8

= 5.9954 MPabottom stress = 769.979/-1.614E8

= -4.7704 MPa

Elastic Deformation - Clause 5.10.4(1)(iii)stress at top of precast beam = 1.84555 MPastress at bottom of precast beam = 12.7201 MPadepth of precast beam = 1300.0 mmelastic modulus of concrete at transfer = 31.1307 GPa

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height No of conc conc tendon tendontendons stress strain force moment

mm MPa kN kN.m

60.0 11 12.21824 3.925E-4 126.28096 7.5768575

110.0 4 11.79999 3.79E-4 44.348407 4.8783248

210.0 2 10.96348 3.522E-4 20.602262 4.326475

260.0 2 10.54523 3.387E-4 19.816291 5.1522358

1200.0 2 2.682055 8.615E-5 5.0400412 6.0480495

TOTAL 21 216.08796 27.981943

Moment about the centroid of the precast beam:Med = 27.981943-(216.08796*0.5760392)

= -96.49319 kN.mhence,top stress = 1.8455-216.08796/537.22568--96.49319/1.2843E8

= 1.8455-0.4022294--0.751339= 2.1946575 MPa

bottom stress = 12.72-216.08796/537.22568--96.49319/-1.614E8= 12.72-0.4022294-0.5978237= 11.720096 MPa

After a further 2 iterations of the above process, the top and bottom stresses are as follows:top stress = 2.16502461 MPa

bottom stress = 11.7912468 MPa

Max Prestress Force after transfer - EN 1992-1-1 Clause 5.10.3.(2)

For tendon property Grade 1600 Ep 195.0k7.fpk = 0.75*1860.0 = 1395.0 MPa

k8.fp0,1k = 0.85*1600.0 = 1360.0 MPa

Maximum tendon stress after transfer = 1329.4 MPawhich is not greater than 1360.0 and therefore OK.

TOTAL LOSS OF PRESTRESS SUMMARYInitial stressing force = 4448.25 kNPrestress after all transfer losses = 4043.05 kN

Corresponding loss = 9.11 %

LIMITING STRESSES IN PRECAST BEAM

Compression

EN 1992-1-1 Clause 3.1.2(5) & 3.1.2(6)For transfer at t= 4.0 days

fck(t) = fcm(t) - 8.0

fcm(t) = c

c(t).fcm Equation 3.1

cc(t) = exp{s[1-(28/t)]} Equation 3.2

for Class N cement, s= 0.25

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hence cc(t) = exp{0.25[1.0-28/4.0)]}

= 0.66269fcm = fck + 8.0 (from Table 3.1)

= 48.0 MPafcm(t) = 0.66269*48.0

= 31.8094and fck(t) = 31.8094 - 8.0 MPa

= 23.8094 MPa

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TRANSMISSION LENGTH

Bond stress at release, EN 1992-1-1 Clause 8.10.2.2(1)fbpt = p1.1.fctd(t) Expression (8.15)

wherefctd(t) = ct.0.7fctm(t)/c

fctm(t) = -2.3253 MPa[2]

ct = 1.0 - from EN 1992-1-1/3.1.6(2)

tendon type coefficient, p1 = 3.2

bond condition coefficient, 1

= 1.0

hencefctd(t) = 1.0*0.7*-2.3253/1.5

= -1.0851 MPa

andfbpt = 3.2*1.0*-1.0851

= -3.4724 MPa

Basic transmission length, EN 1992-1-1 Clause 8.10.2.2(2)lpt = 1.2..pm0/fbpt Expression (8.16)

wherespeed of release coefficient, 1 = 1.0

tendon surface coefficient, 2 = 0.19

nominal diameter of tendon, = 16.0 mmtendon stress after release, pm0 = 1440.0 MPa

hencelpt = 1.0*0.19*16.0*1440.0 / 3.47242

= 1.26068 m

Design value of transmission length, EN 1992-1-1 Clause 8.10.2.2(3)lpt1 = 0.8*lpt

= 0.8*1.26068

= 1.00854 m

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SLS STRESS SUMMARY TABLE

Concrete Stresses (MPa)

force moment In situ PrecastkN kN.m top bottom top bottom

CHARACTERISTIC PERMANENT ACTIONS AND PRESTRESS

Prestress[3]

4244.91 -1547.7 -4.1499 17.4906

Self Weight 769.979 5.9954 -4.7704

Prestress + Self Weight 1.84555 12.7201

Elastic Def -201.86 89.2851 0.31947 -0.9289

TRANSFER 4043.05 -688.47 2.16502 11.7912

SLS FLEXURE

Precast Curvature Deflection

Stress E Strain (x10-6) (mm)

(MPa) (x10

-6

) (rad/m) Here Max.

After TransferT2.16502 ET 69.5462 -237.86 14.6578 14.6578

B11.7912 378.765

Curvatures here are derived from precast section height: 1300.0mm

ET = Elastic Modulus at Transfer = 31130.7MPa

[EN1992-1-1 Clauses 3.1.3-(3) and 3.1.2-(6) with age 4 days]

________[1] Refer to EN 1991-1-1 Table A.1 Notes 1) and 2)

[2] For the derivation of this value refer to the limiting stress calculations for transfer

[3] includes draw-in and initial relaxation

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Steel Composite Bridge Design Example

12. Verification: SLS Bending - Mid Span

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Design code: EN 1992-2:2005 with UK National Annex (modified) EN 1990 Equation 6.14 SLS CharacteristicExposure Class: XD1, XD2, XS1, XS2, XS3Load case: Traffic gr1a TS - for Bending design 1 Section Ref 1 at 10.5m from left end of beam

WARNING - A reduction of flange width to allow for shear lag effects may be appropriate for thisbeam. SAM makes no allowance for this.Refer to EN 1992-1-1/5.3.2.1

Section details:Ref 1 "Section 1"at 0.5 x span = 10.5 m from left end of beam

Analysis:Traffic Actions: Bending for gr1a, loading I.D. 1At time considered, t= Serviceability Limit State: Characteristic - EN 1990 Equation 6.14

ACTUAL STRESSES IN PRECAST BEAM

No. of tendons fully bonded at this section: 21No. of tendons fully debonded at this section: 0No. of tendons deflected at this section: 0

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Maximum Stressing Force - EN 1992-1-1 Clause 5.10.2.1(1)PFor tendon property Grade 1600 Ep 195.0

k1.fpk = 0.8*1860.0 = 1488.0 MPa

k2.fp0,1k = 0.9*1600.0 = 1440.0 MPa

Wedge draw-in loss Clause 5.10.4(1)(i)draw-in strain = 0.003/21.0

= 1.43E-4loss = Ep . strain

= 195.0*1.43E-4

= 27.8571 MPa

Heat Curing Clause 5.10.4(1)(ii)(Note)Concrete is cured at ambient temperature

Immediate Losses - EN 1992-1-1 Clause 5.10.4

height No of fp k1/k2 draw-in heat cure area initial force

mm tendons MPa MPa MPa mm kN

60.0 11 1600.0 0.9 27.8571 0.0 150.0 2330.0357

110.0 4 1600.0 0.9 27.8571 0.0 150.0 847.28571

210.0 2 1600.0 0.9 27.8571 0.0 150.0 423.64286 260.0 2 1600.0 0.9 27.8571 0.0 150.0 423.64286

1200.0 2 1600.0 0.9 27.8571 0.0 150.0 423.64286

TOTAL 21 4448.25

In accordance with clause 5.10.9(1), for SLS, the Characteristic value must be used.With rinf = 1.0, Pk,inf = 4448.25 kN

Friction Clause 5.10.4(1)(i)All tendons are straight in this beam.

Initial Relaxation Clause 5.10.4(1)(ii)

Loss is calculated from clause 3.3.2(7)For tendon property Grade 1600 Ep 195.0relaxation loss at 1000 hours, 1000 = 8.0 %

= pi / fpk= 1440.0-27.8571-0.0/1860.0= 0.75921

time after tensioning = 96.0 hoursfor Class 1 relaxation, use Expression (3.28)

5.39 . 1000 . e6.7

. [t/1000]0.75(1-)

. 10-5

= 5.39 * 8.0 * 161.863 * 0.65495 * 10-5

= 0.04571

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relaxation After relaxation

height No of area x loss force momentmm tendons pi % kN kN kN.m

60.0 11 2330.04 4.57 106.51239 2223.5233 133.4114

110.0 4 847.286 4.57 38.731779 808.55394 88.940933

210.0 2 423.643 4.57 19.365889 404.27697 84.898163

260.0 2 423.643 4.57 19.365889 404.27697 105.11201

1200.0 2 423.643 4.57 19.365889 404.27697 485.13236

TOTAL 21 4244.9082 897.49487

Moment about the centroid of the precast beam:Mr = 897.49487-(4244.9082*0.5760392)

= -1547.739 kN.mCorresponding stresses:top stress = 4244.9082/537225.68+-1547.739/1.2843E8

= 7.9015362+-12.05139= -4.149853 MPa

bottom stress = 4244.9082/537225.68+-1547.739/-1.614E8= 7.9015362+9.5890175= 17.490554 MPa

Self weight moment:

c.s.a. = 5.372E5 mmdensity = 24.0 kN/m + 1.0 kN/m = 25.0 kN/m

[1]

self weight = 5.372E5*25.0= 13.4306 kN/m

beam length = 21.0 mdistance = 10.5 m

Msw = 0.5*13.4306*10.5*(21.0-10.5)

= 740.364 kN.mCorresponding stresses:top stress = 740.364/1.2843E8


= -4.5869 MPa

Elastic Deformation - Clause 5.10.4(1)(iii)stress at top of precast beam = 1.61496 MPastress at bottom of precast beam = 12.9036 MPadepth of precast beam = 1300.0 mmelastic modulus of concrete at transfer = 31.1307 GPa

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height No of conc conc tendon tendontendons stress strain force moment

mm MPa kN kN.m

60.0 11 12.38261 3.978E-4 127.97976 7.6787854

110.0 4 11.94843 3.838E-4 44.906297 4.9396927

210.0 2 11.08007 3.559E-4 20.821353 4.3724841

260.0 2 10.64589 3.42E-4 20.005455 5.2014182

1200.0 2 2.483314 7.977E-5 4.6665732 5.5998878

TOTAL 21 218.37943 27.792268

Moment about the centroid of the precast beam:Med = 27.792268-(218.37943*0.5760392)

= -98.00285 kN.mhence,top stress = 1.615-218.37943/537.22568--98.00285/1.2843E8

= 1.615-0.4064947--0.763094= 1.9715546 MPa

bottom stress = 12.904-218.37943/537.22568--98.00285/-1.614E8= 12.904-0.4064947-0.6071768= 11.889955 MPa

After a further 2 iterations of the above process, the top and bottom stresses are as follows:top stress = 1.94149211 MPa

bottom stress = 11.9620665 MPa

Max Prestress Force after transfer - EN 1992-1-1 Clause 5.10.3.(2)

For tendon property Grade 1600 Ep 195.0k7.fpk = 0.75*1860.0 = 1395.0 MPa

k8.fp0,1k = 0.85*1600.0 = 1360.0 MPa

Maximum tendon stress after transfer = 1330.61 MPawhich is not greater than 1360.0 and therefore OK.

ACTIONS DURING EXECUTIONErection of beam Loading

Bending moment from erection loadcase at current span location:MApplied = 738.00575 kN.m

Corresponding stresses:top stress = 738.00575/1.2843E8


= -4.5723 MPa

Remove the dead load applied for transfer calculationsMsw = -740.36 kN.m

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Corresponding stresses:top stress = -740.36/1.2843E8

= -5.7648 MPabottom stress = -740.36/-1.614E8

= 4.58693 MPa

Construction stage 1A LoadingMApplied = 512.3149 kN.m

Corresponding stresses:

top stress = 512.3149/1.2843E8= 3.98911 MPa

bottom stress = 512.3149/-1.614E8= -3.174 MPa

Construction stage 1B LoadingMApplied = 21.87451 kN.m



= -0.1355 MPa

Time Dependent Losses - EN 1992-1-1 Clause 5.10.6

Simplified method using Expression (5.46)

Pc+s+r =Ap.p,c+s+r

cs.Ep + 0.8pr + Ep/Ecm.(t,t0).c,QPp,c+s+r =

1 + Ep/Ecm.Ap/Ac(1+Ac/Ic.zcp)[1+0.8(t,t0)]

The calculated loss is apportioned partly to the precast beam alone and partly to the fullcomposite section.

For in-situ cast at 60 days, the proportion of the loss occurring before the in-situ is castis calculated to be 28.63 %

Losses are calculated for time t=

Age of concrete at end of curing, ts = 1.0 days

Age of concrete at transfer, t0 = 4.0 days

Age is adjusted for expression (B.5) (for cement type & temperature)- for cement class N ( = 0)

adjusted t0 = t0,T . [(9/(2+t0,T1.2

)+1)>=0.5 Expression (B.9)

= 4.0 * [(9/(2+4.01.2

)+1]0

= 4.0 days

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Age of concrete at time considered, t =EN 1992-1-1/3.3.2(8) for relaxation, tis taken as 500,000 hours

Concrete age coefficient (Expression (3.2)), cc:

cc(t) = fcm(t)/fcm Expression (3.1)

= exp{s[1-(28/t)]} Expression (3.2)Coefficient for Class N cement, s= 0.25

cc(t0) = exp{0.25[1.0-(28/4.0)]} = 0.66269

cc(t) = exp{0.25} = 1.28403

Characteristic strength of concrete, fck = 40.0 MPa

Mean compressive strength of concrete, fcm = 40.0 + 8.0

(from Table 3.1) = 48.0 MPafcm0 = 10.0 MPa

fcm(t0) = cc(t0) . fcm = 31.8094 MPa

Ambient relative humidity = 80.0 %Notional size of member, h0 = 2Ac/u = 2*9.051E5/7245.89

= 249.811 mmModulus of elasticity of concrete at 28 days, Ecm = 35.2205 GPa

Modulus of elasticity of concrete at time considered,

Ecm(t) = cc(t)0.3

. Ecm Expressions (3.5) & (3.1)

= 1.284030.3

* 35.2205= 37.9636 GPa

Area of concrete cross section, Ac = 9.05E5 mm

Perimeter of concrete cross section, u= 7245.9 mmNotional size, h0 = 2*Ac/u= 2*9.051E5/7245.89 = 249.81 mm

Creep coefficient for concrete - EN 1992-1-1 clause 3.1.4 and Annex B.1(t,t0) = 0 . c(t,t0) Expression (B.1)

= RH . (fcm) . (t0) . c(t,t0) Expression (B.2)

for fcm > 35.0 MPa

1-RH/100RH = [ 1 + . 1 ] .2 Expression (B.3b)

0.1*h00.33

1 = [35.0/48.0]0.7 = 0.80163

2 = [35.0/48.0]0.2

= 0.93878

3 = [35.0/48.0]0.5

= 0.85391

RH = [1.0 + (1.0-0.8) / (0.1*249.8110.33

) * 0.80163]*0.93878

= 1.17777

(fcm) = 16.8/fcm Expression (B.4)

= 16.8/48.0= 2.42487

For Permanent LoadsIn the absence of heat curing t0,T = 4.0 days

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age is adjusted for expression (B.5) (for cement type and temperature)- for cement class N ( = 0)

9.0

t0 = t0,T . [ + 1.0 ] >=0.5 Expression (B.9)

2.0 + t0,T1.2

9.0

= 4.0 * [ + 1.0 ]0

2.0 + 4.01.2

= 4.0 day

(t0) = 1/(0.1+t00.2

) Expression (B.5)

= 1/(0.1+4.00.2

)= 0.70446

c(t,t0) = 1.0 for time t =

hence from (B.1) and (B.2):(t,t0) = 1.17777*2.42487*0.70446

= 2.01193

Check for creep non-linearity EN 1992-1-1 clause 3.1.4(4)

At the level of the centroid of the tendons, the compressive stress in the concrete at time t0

= 8.31165 MPa.This does not exceed 0.45*fck(t0), i.e. 18.0 MPa, so non-linear creep is not considered

Shrinkage Strain for concrete - EN 1992-1-1 clause 3.1.4(6)








RH = 1.55[1.0-(RH/100)] (B.12)


ds1 = 4

ds2 = 0.12

hence,

c

d

,

0

= 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10

-6

*0.7564= 238.54*10

-6

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and,

cd(t) = 1.0*0.80018*238.54*10-6

= 190.877*10-6


ca(t) = as(t).ca()

as(t) = 1.0 for t=

ca() = 2.5*(fck-10.0)*10-6

= 75.0*10-6

hence,ca(t) = 1.0*75.0*10

-6

= 75.0*10-6

Total Shrinkage:

cs = cd(t) + ca(t)

= 190.87688 + 75.0

= 265.87688*10-6

Further Relaxation Clause 5.10.6(1)(b)

Loss is calculated from clause 3.3.2(7)For tendon property Grade 1600 Ep 195.0

relaxation loss at 1000 hours, 1000 = 8.0 %

time after tensioning = 500000.0 hours = 0.75921 (as calculated for initial

relaxation loss above)for Class 1 relaxation, use Expression (3.28)

5.39 . 1000 . e6.7

. [t/1000]0.75(1-)

. 10-5

= 5.39 * 8.0 * 161.863 * 3.07185 * 10-5

= 0.21440With the initial relaxation deducted, the variation in tendon stress from relaxation becomes:

p

r

/ p

i

= 0.21440 - 0.04571= 0.16868

Summary of the above for Expression (5.46):

Estimated shrinkage strain cs = 265.877 x10-6

Creep coefficient at t for loading at t0 (t,t0) = 2.01193

Relaxation, pr = 238.212 MPa

Modulus of elasticity for prestressing steel Ep = 195.0 GPa

Modulus of Elasticity for concrete Ecm = 37.9636 GPa

Area of all prestressing Ap = 3150.0 mm

Area of concrete section Ac = 9.051E5 mm

Second moment of area of concrete section Ic = 2.33E11 mm

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Ep/Ecm = 195.0/37.9636 = 5.1365

Ep/Ecm.Ap/Ac = 5.1365*3150.0/9.051E5 = 0.01788

Ac/Ic = 9.051E5/2.33E11 = 3.8904

In the table below the following vary with tendon height:c,QP = Stress in concrete adjacent to tendons

zcp = Section centre of gravity to tendons

(t,t0) = Creep Coefficient (if non-linear creep is considered)

shrink relax creep denomheight cs.Ep (t,t0) Ep/Ecm..

Ap 0.8pr c,QP zcp Pc+s+rmm mm MPa MPa MPa MPa mm kN

60.0 1650.0 51.846 190.57 2.012 8.605 88.927 839.705 1.175 465.43833

110.0 600.0 51.846 190.57 2.012 8.5109 87.954 789.705 1.16 170.90467

210.0 300.0 51.846 190.57 2.012 8.3226 86.008 689.705 1.133 86.962166

260.0 300.0 51.846 190.57 2.012 8.2284 85.035 639.705 1.121 87.637686

1200.0 300.0 51.846 190.57 2.012 6.4583 66.742 -300.3 1.063 87.248992

Total force loss: 898.19184Total moment loss: 192.47246

Mcsr = 192.47246-(898.19184*0.8997047)

= -615.635 kN.m

Corresponding stresses - before composite:top stress = ( 898.192/5.372E5+-615.64/1.284E8 )* 0.286

= ( 1.6719079+-4.793611 )* 0.286= -0.893716 MPa

bottom stress = ( 898.192/5.372E5+-615.64/-1.61E8 )* 0.2862= ( 1.6719079+3.8141679 )* 0.286= 1.5706162 MPa

- after composite:top stress = ( 898.192/9.051E5+-615.64/5.812E8 )*(1.0- 0.286)

= ( 0.9924210+-1.059313 )*(1.0-0.286)

= -0.047742 MPabottom stress = ( 898.192/9.051E5+-615.64/-2.59E8 )*(1.0-0.286 )

= ( 0.9924210+2.3809161 )*(1.0-0.286)= 2.4075798 MPa

Surfacing 1 LoadingMApplied = 99.65918 kN.m



= -0.3854 MPa

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Traffic gr1a TS - for Bending design 1 LoadingMApplied = 934.3025 kN.m

PApplied = -43.8224 kN

Corresponding stresses:top stress = -43.8224/905051.1 + 934.3025/5.8116E8

= -0.0484 + 1.60764= 1.55922 MPa

bottom stress = -43.8224/905051.1 + 934.3025/-2.586E8= -0.0484 + -3.613= -3.6618 MPa

Traffic gr1a UDL - for Bending design 1 LoadingMApplied = 324.4073 kN.m

PApplied = -4.365749 kN

Corresponding stresses:top stress = -4.365749/905051.1 + 324.4073/5.8116E8

= -0.0048 + 0.55820= 0.55337 MPa

bottom stress = -4.365749/905051.1 + 324.4073/-2.586E8= -0.0048 + -1.255= -1.2594 MPa

Traffic gr1a Footway - for Bending design 1 LoadingMApplied = 19.32731 kN.m

PApplied = 1.418796 kN

Corresponding stresses:top stress = 1.418796/905051.1 + 19.32731/5.8116E8

= 0.00157 + 0.03326= 0.03482 MPa

bottom stress = 1.418796/905051.1 + 19.32731/-2.586E8= 0.00157 + -0.075= -0.0732 MPa

TOTAL LOSS OF PRESTRESS SUMMARY

Initial stressing force = 4448.25 kNPrestress after all losses at t= = 3142.75 kN

Corresponding loss = 29.3 %

LIMITING STRESSES IN PRECAST BEAM

Compression

EN 1992-2 Clause 7.2(102)k1.fck = 0.6*40.0

= 24.0 MPaIn the presence of confinement or increase in cover this may be increased by up to 10%, i.e

to:

= 26.4 MPa

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Tension

Tension is governed by crack width considerations, and reinforcement provided for crackwidth control.

Exposure Class is XD1, XD2, XD3, XS1, XS2, XS3 ...... for which decompression is checked for the Frequent combination of loads.

Decompression requires all of the tendon to be at least 65.0 mm above the level of theneutral axis.

LIMITING STRESSES FOR IN SITU CONCRETE

Compression

EN 1992-2-2 Clause 7.2(102)To avoid longitudinal cracking, compressive stress is limited to:

c = k1.fck= 0.6*31.875= 19.125 MPa

Tension

Tension is governed by crack width considerations, and reinforcement provided for crackwidth control.

EN 1992-1_1 Clause 7.3However, no tensile stress is present at this section.

TRANSMISSION LENGTH

Bond stress at release, EN 1992-1-1 Clause 8.10.2.2(1)fbpt = p1.1.fctd(t) Expression (8.15)

wherefctd(t) = ct.0.7fctm(t)/c

fctm(t) = -2.3253 MPa[2]

ct = 1.0 - from EN 1992-1-1/3.1.6(2)

tendon type coefficient, p1 = 3.2

bond condition coefficient, 1

= 1.0

hencefctd(t) = 1.0*0.7*-2.3253/1.5

= -1.0851 MPa

andfbpt = 3.2*1.0*-1.0851

= -3.4724 MPa

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Basic transmission length, EN 1992-1-1 Clause 8.10.2.2(2)lpt = 1.2..pm0/fbpt Expression (8.16)

wherespeed of release coefficient, 1 = 1.0

tendon surface coefficient, 2 = 0.19

nominal diameter of tendon, = 16.0 mmtendon stress after release, pm0 = 1440.0 MPa

hencelpt = 1.0*0.19*16.0*1440.0 / 3.47242

= 1.26068 m

Design value of transmission length, EN 1992-1-1 Clause 8.10.2.2(3)lpt1 = 0.8*lpt

= 0.8*1.26068= 1.00854 m

STRUCTURAL EFFECTS OF TIME DEPENDENT BEHAVIOUREN 1992-2 Annex KK.7

Age of concrete at first loading, t0 = 4.0 days

Age of concrete when first composite, tc = 60.0 days

Age of concrete at time considered, t= Creep coefficient when first composite, (tc,t0) = 0.89250

Final creep coefficient, (,t0) = 2.00881

Creep coefficient increment, (,tc) = 1.20422

Specified value of Ageing coefficient, = 0.8

From Expression (KK.119):(,t0) - (tc,t0) 2.00881-0.89250

= 1 + .(,tc) 1.0 + 0.8*1.20422

= 0.56856

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SLS STRESS SUMMARY TABLE

Concrete Stresses (MPa)

force moment In situ PrecastkN kN.m top bottom top bottom

CHARACTERISTIC PERMANENT ACTIONS AND PRESTRESS

Prestress[3]

4244.91 -1547.7 -4.1499 17.4906

Self Weight 740.364 5.76481 -4.5869

Prestress + Self Weight 1.61496 12.9036

Elastic Def -203.96 90.6953 0.32653 -0.9415

TRANSFER 4040.95 -716.68 1.94149 11.9621

Cr+Sh+Rlx B -257.14 176.251 0.89371 -1.5706

Erection -2.3584 -0.0184 0.01461

In situ 1A 512.315 3.98911 -3.174

In situ 1B 21.8745 0.05072 0.03293 0.03764 -0.0846

0.0 0.0 0.0 0.0 0.0

TOTAL PERMANENT EFFECTS, S0 6.8436 7.14742

Cr+Sh+Rlx A -641.05 439.384 0.34886 -0.0084 0.04774 -2.4076

TOTAL PERMANENT EFFECTS, S0, 0.39958 0.0245 6.89134 4.73984

CREEP REDISTRIBUTION according to EN 1992-2 Annex KK.7

Construction On Centering,Sc =G+P1 +P2

PermanentG 606.626 1.40663 0.91333 1.04381 -2.3461

PrestressP1 -2584.1 -5.992 -3.8906 -4.4465 9.99388[4]

3780.83 3.95141 3.95141 4.17748 4.17748

PrestressP2 2329.9 5.40251 3

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