Programa Flexion Aci440.2r

Readme File

GENERAL INFORMATION:

This program computes the ultimate flexural strength of reinforced-concrete (including prestressed) sections externally strengthened with Carbon Fiber Reinforced Polymer (CFRP) systems manufactured by SIKA Corp. The program also performs serviceability checks and it is applicable to rectangular and T-beams.The design procedures adopted in this program are in compliance with the American Concrete Institute (ACI) Committee 440 document, "Guide for theDesign and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures" (ACI 440.2R-02).

TO SUCCESSFULLY IMPLEMENT CFRP DESIGN WITH SPREADSHEET:

the solver box appears, or choose "OK" if you get this message: "The Active sheet is protected and therefore read only." If the SOLVERAdd-in is not installed on your machine, you will need to do install it first (go to "Tools/Add-Ins" menu and choose "Solver").

a) Loading information (flexural demand)b) Environment informationc) Initial Strains (Yes or No) and conditiond) Concrete substrate surface strength propertiese) Prestress section properties (if applicable)f) Existing section's propertiesg) CFRP system properties and configuration

This information can be input either by directly entering the values/properties in the white cells (by following the "comment cell" recommendations), or by using the input forms: press the "Enter Data" button, then follow the instructions on the screen. If an error ismade, corrections can be easily implemented by navigating through the form structure. At the end of the data entry, the program will performthe necessary design calculations, and the results will appear on the screen (all the spreadsheet cells will be updated).

button. The design calculations should then be automatically performed and all the cells in the spreadsheet will be updated. The easiest way to check whether or not the calculations are updated and correct is to examine the "equilibrium" cells in the spreadsheet. If they all equal zero,the calculations are correct; if not, then the spreadsheet calculations did not converge (due to an unreasonable input, for example), or, mostlikely, the solver function called by the macro did not execute (most likely because solver was not initially loaded).

NOTES:

1) To calculate the distance to the neutral axis (c), the program solves a quadratic or cubic equation. Even though the program makes the best possible guess in order to estimate the appropriate root, it is possible that a negative or exaggerated root for c will appear in the table. Therefore, all c values should be checked for possible calculation misinterpretations.

2) When the quadratic equation does not have meaningful roots (for instance when c exceeds h), the program will not be able to find a viable solution, and it will prompt the user in the appropriate cells. Again, a hand-calculation check is necessary.

3) When the equation for c based on one mathematical model either cannot be solved, or an inappropriate root for c is obtained, the calculations will not be affected if the state of stress is governed by the other mathematical model (based on the calculatedvalues for concrete strain). The program will then automatically use the other equation for determining c.

1) Load the "SOLVER" tool prior to execution of any calculation or data entry: from the "Tools" menu, choose "Solver", then press "cancel" once

2) Go to the appropriate workbook and units (CFRPMetric, CFRPEnglish).

3) Enter all the necessary input information. The input data are entered in the "user input" table (white boxes). They consist of the following:

4) Run the design calculations. If the calculations were not completed under the data entry procedure (see the above), then press the "Recalculate"

5) Observe the results. If a change in the input data is needed, repeat the procedure described in point 3 (or portion thereof).

Flexion -ACI 440.2R

CFRP System 230C w/ Sikadur Hex 330 Epoxy VERSION 3.0 TypeS

New loading conditions: Cross Section Properties: CFRP Properties: 0.90 include

k-ft 0.95 ###

k-ft ksi No. of strips/sheets: 0.85 ###

0.0 k-ft ksi No. of Sheet Layers: #DIV/0! N

0.0 k-ft ksi Sheet Width: in. creep rupture/fatigue factor 0.55 230C w/ Sikadur Hex 330 EpoxyEnvironment h = in. 0.00 in. Expected service conditions

Include Initial Condidions? d = in. 0.015 in.

Initially cracked? b = in. 99 ksi

ksi 0.85 8855 ksi ###Prestress? in. 0.000 ###Bonded ? in. NG ###

k span = in. 54 ksi Spacing Check: spacing > 0.2L or > 5h? ###ksi 0 ksi Spacing = #DIV/0! in. #DIV/0! ###

######

#DIV/0! k-ft #DIV/0! #DIV/0! #DIV/0! ###

#DIV/0! #DIV/0! #DIV/0! ###

#DIV/0! k-ft Steel rupture? #DIV/0! #DIV/0! ###

Unstrength. Check #DIV/0! #DIV/0! ###

#DIV/0!Rectangular section

Equilibrium c (in.)

Unstrengtened N/A #DIV/0! 0.0 #DIV/0! N/A 0.00300 #DIV/0! 6.84 N/A N/A N/A N/A N/A 0.00300 ###

0.0 #DIV/0! #DIV/0! #DIV/0! 0.01004 #DIV/0! #DIV/0! 5.33 0.0 #DIV/0! #DIV/0! N/A N/A #DIV/0! ###

#DIV/0! #DIV/0! 0.0 #DIV/0! #DIV/0! 0.00300 #DIV/0! 5.32 0.0 0.77 0.40 N/A N/A 0.00300 ###

Governing limit state #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! ####DIV/0! #DIV/0!

Service

N/A Unstngth.N/A

LOADING CONDITION Ts due to DL c (in.) Comment n_one =

Initial Conditions (DL) N/A #DIV/0! #DIV/0! #DIV/0! N/A #DIV/0! #DIV/0! #DIV/0! N/A #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! n_two =

Service, Strengthened #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! N/A #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

km =MD = As = in.2 environm. factor =ML = fy = yf =

1.2MD+0.85ML = Es = Overall f =

Mu = 1.4MD+1.7ML = f'c =

bf =

tf =

ffU =Pulloff ft^ from test = b1 = Ef =

hf = Af = in.2 Pulloff Check: ft^ from test > 200 psi?

bw =

Pe = Ffs =

fpsu = 0.8 fy =

f Mni = f Mni >1.2MD+ 0.85ML? fMn (k-ft) =

r or r W = r act < 0.75 r bal? Serviceability Check: fs < 0.8 fsy ?

Mcr = Creep Rupt./Fatigue Check: ffs < Ffs ?

Steel Rupture Check: es > er ?

Tf (k) TS (k) CC or CCf (k) ef ec eS Ccw (k) a or af g or gf aw gw ehc Wu

efe = km efu

ec = 0.003

Unbonded: fps limit met?

Tf (k) TS (k) Total CC (k) ef ec eS Tc (k) Itr (in.4) ff (ksi) fs (ksi) ecb

Econc =

CALCULATED FORCES, STRAINS, NEUTRAL AXIS, ETC., ULTIMATE LIMIT STATECALCULATED FORCES, STRAINS, NEUTRAL AXIS, ETC., ULTIMATE LIMIT STATE

REDUCTION FACTORSREDUCTION FACTORS

UNSTRENGTHENED SECTION CHECKUNSTRENGTHENED SECTION CHECK

ANALYSIS OF ELASTIC SECTION ANALYSIS OF ELASTIC SECTION

PULLOFF STRENGTH ANDSPACING CHECKSPULLOFF STRENGTH ANDSPACING CHECKS

USER INPUTUSER INPUT

STRENGTHENED BEAM CHECKSTRENGTHENED BEAM CHECK

OVERALL CHECKOVERALL CHECK

PRESTRESSED SECTION CONCRETE STRESS CHECKPRESTRESSED SECTION CONCRETE STRESS CHECK

Recalculate

Enter Data

Flexión -ACI 440.2R

CFRP System S512 VERSION 3.0 TypeSNew loading conditions: Cross Section Properties: CFRP Properties: 0.90 include

0.95 ###

kN-m MPa No. of strips/sheets: 0.85 ###

0 kN-m MPa No. of Sheet Layers: #DIV/0! N

0 kN-m MPa Sheet Width: mm Creep rupture/fatigue factor 0.55 230C w/ Sikadur Hex 330 EpoxyEnvironment h = mm 50 mm Expected service conditions

Include Initial Condidions? d = mm 1.2 mm

Initially cracked? b = mm 2660 Mpa

MPa 0.85 165000 MPa ###Prestress? mm 0 ###Bonded ? mm NG ###

kN span = m 1463 MPa Spacing Check: spacing > 0.2L or > 5h? ###Mpa 0 Mpa Spacing = #DIV/0! mm #DIV/0! ###

######

### kN-m #DIV/0! #DIV/0! #DIV/0! ###

#DIV/0! #DIV/0! #DIV/0! ###

### kN-m Steel rupture? #DIV/0! #DIV/0! ###

#DIV/0! #DIV/0! #DIV/0! ###

#DIV/0!Rectangular section

Equilibrium c (mm)

Unstrengtened N/A #DIV/0! 0 #DIV/0! N/A 0.00300 #DIV/0! 212 N/A N/A N/A N/A N/A 0.00300 ###

0 #DIV/0! #DIV/0! #DIV/0! 0.01451 #DIV/0! #DIV/0! 137 0 #DIV/0! #DIV/0! N/A N/A #DIV/0! ###

### #DIV/0! 0 #DIV/0! #DIV/0! 0.00300 #DIV/0! 137 0 0.77 0.40 N/A N/A 0.00300 ###

Governing limit state ### #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! ####DIV/0! #DIV/0!

Service Unstngth.

N/A N/A

LOADING CONDITION Ts due to DL c (mm) Comment n_one =

Initial Conditions (DL) N/A #DIV/0! #DIV/0! #DIV/0! N/A #DIV/0! #DIV/0! #DIV/0! N/A #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! n_two =

Service, Strengthened ### #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! N/A #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

km =MD = As = mm2 Environmental factor =ML = fy = yf =


Mu = 1.4MD+1.7ML = f'c =

bf =

tf =


hf = Af = mm2 Pulloff Check: ft^ from test > 1.38 MPa?

bw =

Pe = ffs =

fpsu = 0.8 fy =

f Mni = f Mni >1.2MD+ 0.85ML? fMn (kN-m) =




Tf (kN) TS (kN) CC or CCf (kN) ef ec eS Ccw (kN) a or af g or gf aw gw ehc Wu

efe = km efu

ec = 0.003

Unbonded: fps limit met?

Tf (kN) TS (kN) Total CC (kN) ef ec eS Tc (kN) Itr (mm4) ff (MPa) fs (MPa) ecb

Econc =










Recalculate

Enter Data

To Convert FromEnglish Units to Metric Units

Force 1 k equals 4.44822 kNPressure 1 ksi equals 6.89475 MpaLength 1 in. equals 25.4 mmArea 1 equals 645.16Moment 1 k-ft. equals 1.35582 kN-m

To ConvertMetric Units to English Units

Force 1 kN equals 0.22481 kPressure 1 Mpa equals 0.14504 ksiLength 1 mm equals 0.0397 in.Area 1 equals 0.00155Moment 1 kN-m equals 0.73756 k-ft.

in.2 mm2

mm2 in.2

CFRP Properties

Page 5

Metric UnitsType E (MPa)* Elongation at break

CarboDur S512 2800 165000 0.0169CarboDur S812 2800 165000 0.0169Carbodur S1012 2800 165000 0.0169

SikaWrap 103C w/ Sikadur Hex 300 Epoxy 717 65087 0.0110SikaWrap 103C w/ Sikadur Hex 306 Epoxy 668 58021 0.0115SikaWrap 230C w/ Sikadur Hex 330 Epoxy 715 61012 0.0117

English UnitsType E (ksi)* Elongation at break

CarboDur S512 406 23900 0.0169CarboDur S812 406 23900 0.0169Carbodur S1012 406 23900 0.0169

SikaWrap 103C w/ Sikadur Hex 300 Epoxy 104 9447 0.0110SikaWrap 103C w/ Sikadur Hex 306 Epoxy 97 8421 0.0115SikaWrap 230C w/ Sikadur Hex 330 Epoxy 104 8855 0.0117

* Based on mean test value minus two standard deviations

flu (MPa)*

flu (ksi)*

CFRP Properties

Page 6

b (mm) t (mm)50.00 1.20080.00 1.200

100.00 1.200N/A 1.016N/A 1.016N/A 0.381

b (in) t (in)1.97 0.0473.15 0.0473.94 0.047N/A 0.040N/A 0.040N/A 0.015

2.3.2 TEXT EXAMPLEAnexo E-8

CFRP System 103C w/ Sikadur Hex 300 Epoxy VERSION 3.0

New loading conditions: Existing Beam Properties: CFRP Properties: 0.90

30.0 kN-m 1000 0.95

50.0 kN-m 414 MPa No. of strips/sheets: 1 0.85

79 kN-m 199950 Mpa No. of Sheet Layers: 1 0.90

127 kN-m 34.5 Mpa Sheet Width: 300 mm Creep rupture/fatigue factor 0.55

Environment Interior h = 300 mm 300 mm

Include Initial Condidions? Y d = 270 mm 1.0 mm

Initially cracked? N b = 1000 mm 681 Mpa

1.39 MPa 0.80 65087 MPa

Prestress? N 300 mm 305

Bonded ? N 1000 mm OK

700 kN span = 8.00 m 375 MPa Spacing Check: spacing > 0.2L or > 5h?

1862 Mpa 331 Mpa Spacing = 1000 mm OK

98 kN-m OK 137 OK

0.003704 OK OK

58.2 kN-m Steel rupture? OK OK

Unstrength. Check OK OK

OK

Equilibrium c (mm)

Unstrengtened N/A 414 414 0.00 N/A 0.00300 0.04293 18 N/A N/A N/A N/A N/A N/A

187 414 601 0.00 0.00942 0.00129 0.00841 34 0 0.51 0.36 N/A N/A N/A

465 414 879 0.00 0.02346 0.00300 0.02132 33 0 0.77 0.40 N/A N/A N/A

Governing limit state 187 414 601 0.00 0.00942 0.00129 0.00841 34 0 0.51 0.36 N/A N/A N/A

Service

N/A

LOADING CONDITION Equilibrium c (mm) Comment

Initial Conditions (DL) N/A 11 149 0 N/A 0.000070 0.00005 153 138.2 2351208623 N/A 11 0.00007 Uncracked

Service, Strengthened 20 296 316 0 0.00101 0.000398 0.00148 58 N/A 430313138 66 296 N/A Cracked



Mu = 1.4MD+1.7ML = f'c =

bf =

tf =



bw =

Pe = ffs =

fpsu = 0.8 fy =





Tf (kN) TS (kN) CC or CCf (kN) ef ec eS Ccw (kN) a or af g or gf aw gw ehc

efe = km efu

ec = 0.003











2.3.4.4. TEE SECTIONAnexo E-8

CFRP System S512 VERSION 3.0


77.7 kN-m 1282 0.95







1.39 MPa 0.85 165000 MPa





216 kN-m OK 293 OK

0.003023 OK OK



OK

Equilibrium c (mm)


225 530 755 0.00 0.00758 0.00124 0.00773 61 0 0.49 0.35 N/A N/A N/A

616 530 1146 0.00 0.02074 0.00300 0.02044 59 0 0.77 0.40 N/A N/A N/A


Service

N/A


Initial Conditions (DL) N/A 179 179 0 N/A 0.000172 0.00070 92 N/A 1664737597 N/A 140 N/A Cracked




Mu = 1.4MD+1.7ML = f'c =

bf =

tf =



bw =

Pe = ffs =

fpsu = 0.8 fy =






efe = km efu

ec = 0.003











2.3.4.5 UCSDAnexo E-8



0.6 kN-m 213 0.95







1.39 MPa 0.85 165000 MPa





6 kN-m OK 16 OK

0.005478 OK OK



OK

Equilibrium c (mm)


150 88 238 0.00 0.00758 0.00246 0.00553 25 0 0.73 0.38 N/A N/A N/A

174 88 262 0.00 0.00877 0.00300 0.00641 26 0 0.77 0.40 N/A N/A N/A


Service

N/A






Mu = 1.4MD+1.7ML = f'c =

bf =

tf =



bw =

Pe = ffs =

fpsu = 0.8 fy =






efe = km efu

ec = 0.003











2.3.4.1. PRESTRESSAnexo E-8



230.0 kN-m 600 0.95







1.39 MPa 0.80 165000 MPa

Prestress? Y 120 mm 60

Bonded ? Y 200 mm OK



625 kN-m OK 645 OK

0.001231 OK OK



OK

Equilibrium c (mm)


75 1084 1159 0.00 0.00758 0.00115 0.01199 97 0 0.46 0.35 N/A N/A N/A

295 1110 1405 0.00 0.02976 0.00300 0.03063 71 0 0.77 0.40 N/A N/A N/A


Service

OK

LOADING CONDITION Ts due to DL c (mm) Comment

Initial Conditions (DL) N/A 723 699 24 N/A 0.000104 0.00603 307 N/A 14530983144 N/A 1206 -0.00012 Prestressed

Service, Strengthened 2 742 720 24 0.00022 0.000244 0.00619 308 N/A 14617367366 37 1237 0.00010 Prestressed



Mu = 1.4MD+1.7ML = f'c =

bf =

tf =



bw =

Pe = ffs =

fpsu = 0.8 fy =






efe = km efu

ec = 0.003











2.3.4.2. RECT BEAMAnexo E-8

CFRP System 103C w/ Sikadur Hex 300 Epoxy VERSION 3.0


422.0 kN-m 4415 0.95







1.39 MPa 0.85 65087 MPa





1666 kN-m OK 1875 OK

0.008919 OK OK



OK

Equilibrium c (mm)


249 1826 2076 0.00 0.00942 0.00246 0.00893 230 0 0.73 0.38 N/A N/A N/A

317 1826 2144 0.00 0.01200 0.00300 0.01163 226 0 0.77 0.40 N/A N/A N/A


Service

N/A


Initial Conditions (DL) N/A 428 428 0 N/A 0.000222 0.00049 345 N/A 26409782593 N/A 97 N/A Cracked




Mu = 1.4MD+1.7ML = f'c =

bf =

tf =



bw =

Pe = ffs =

fpsu = 0.8 fy =






efe = km efu

ec = 0.003











2.3.4.3. SLABAnexo E-8



50.0 kN-m 2500 0.95







1.39 MPa 0.85 165000 MPa





158 kN-m OK 198 OK

0.003571 OK OK



OK

Equilibrium c (mm)


300 1034 1334 0.00 0.00758 0.00118 0.00654 25 0 0.47 0.35 N/A N/A N/A

898 1034 1932 0.00 0.02267 0.00300 0.01996 23 0 0.77 0.40 N/A N/A N/A


Service

N/A






Mu = 1.4MD+1.7ML = f'c =

bf =

tf =



bw =

Pe = ffs =

fpsu = 0.8 fy =






efe = km efu

ec = 0.003











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Programa Flexion Aci440.2r