2.6 Print
SIKA CarboDur Composite Strengthening Systems

Use of Software FRP-Analysis

2.6 Print

A printout of both the user's input and the calculation results can be obtained through the window "Results". By using the window "Options" the user may select print fonts and the print setup.

The printout contains the following information, independently of the strengthening chosen (flexural, shear or confinement):

(a) user and project name, date & time (by demand);

(b) type of strengthening;

(c) type and geometry of cross section;

(d) material properties (concrete, steel and composite materials);

(e) type of application;

(f) strengthening requirements;

(g) required FRP dimensions (cross sectional area or thickness).

For the case of flexural strenthening, the moment capacity corresponding to every limit state, as well as the stresses in the concrete and steel (corresponding to SLS), and the governing failure mode are also printed. Moreover, information on the "cross section strain profile" for every limit state is given, if the user selects to see it at the solution stage. Finally, if the user selects the option "Input of FRP dimensions", the applied FRP dimensions as well as the number of strips or layers are printed. If the "Bond check" is performed, the corresponding results are also printed.


1.1 General
SIKA CarboDur Composite Strengthening Systems

Theoretical Background

1.1 General

Recent developments related to materials, methods and techniques for structural strengthening have been enormous.  One of today’s state-of-the-art techniques is the use of fibre reinforced polymer (FRP) composites, which are currently viewed by structural engineers as “new” and highly promising materials in the construction industry.  Composite materials for strengthening of civil engineering structures are available today mainly in the form of thin unidirectional strips (with thickness in the order of 1 mm) made by pultrusion, or flexible sheets or fabrics, made of fibres in one or at least two different directions, respectively (and sometimes pre-impregnated with resin).

The reasons why composites are increasingly used as strengthening materials of RC elements are: immunity to corrosion; low weight (about 1/4 of steel), resulting in easier application in confined space, elimination of the need for scaffolding and reduction in labour costs; very high tensile strength (both static and long-term, for certain types of FRP materials, e.g. those based on carbon fibres); stiffness which may be tailored to the design requirements; large deformation capacity; and practically unlimited availability in FRP dimensions.

The aim of this software is to assist the user in calculating the FRP dimensions required to provide (a) flexural strengthening, (b) shear strengthening and (c) confinement.  These three topics are treated in the next sections, which present the theoretical basis of the calculations.

The equations used in this programme are those given in the fib Bulletin 14 "Externally Bonded FRP Reinforcement for RC Structures".


1.2 Flexural Strengthening
SIKA CarboDur Composite Strengthening Systems

Theoretical Background	Use of Software FRP-Analysis

1.2 Flexural Strengthening

Reinforced concrete elements, such as beams, slabs and columns, may be strengthened in flexure through the use of FRP composites epoxy-bonded to their tension zones, with the direction of fibres parallel to that of high tensile stresses (member axis). The calculations described below address both the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS).

Ultimate Limit State

The calculations are based on the assumption that one of the following two desirable failure modes govern the behaviour:

(a)	following yielding of the internal tension steel reinforcement the concrete crushes in the compression zone;

     (b) following yielding of the internal tension steel reinforcement the FRP reaches a limiting strain, åf,lim, (this is a simplified way to treat debonding of the FRP in areas where flexure dominates the response, e.g. mid-span of simply supported beams).

The first step in the calculations is to find the initial strain, åo, that develops in the extreme fibre of the cross section when the strengthening operations take place  (Fig. 1.2.1).  This strain is the result of a moment Mo (service moment) acting at the critical cross section during strengthening (e.g. due to the self-weight of the structure), and may be calculated based on equilibrium of internal forces and moments.  For the example of Fig. 1.2.1, the results are given below.

Fig. 1.2.1	Initial situation – equivalent stress block approach: The moment Mo acting during strengthening results in the development of an initial strain åo at the extreme tensile concrete fibre.

Internal force equilibrium (initial situation):

(1.2.1)

Moment equilibrium (initial situation):

(1.2.2)

where xo is the depth of neutral axis from the extreme compressive fibre and fs1, fs2 are the stresses in the bottom and top steel reinforcement, respectively.

(1.2.3)

(1.2.4)

In the above equations fck is the characteristic (cylinder) strength of concrete, fyd is the yield stress of steel and á, k are factors determining the location and magnitude of the stress resultant in the concrete compression block.  These factors depend on the maximum compressive concrete strain, åco.

(1.2.5)

(1.2.6)

From the numerical solution of eqs. (1.2.1) and (1.2.2) we calculate the maximum compressive concrete strain, åco, and the neutral axis depth xo.  Finally, the initial strain åo is given as:

(1.2.7)

Once åo is calculated, the analysis of the critical cross section for the ULS (Ultimate Limit State) is performed on the basis of Fig. 1.2.2, which shows the strain profile and internal forces at the Ultimate Limit State.

Fig. 1.2.2	Analysis of rectangular cross section (strain profile and internal forces) for the ultimate limit state in bending.

Internal force equilibrium:

(1.2.8)

Resisting design moment:

(1.2.9)

where Af, Ef and åf is the cross section area, elastic modulus and strain of FRP reinforcement, respectively.  The FRP strain and the stress in the top steel reinforcement are given in terms of the maximum compressive concrete strain, åc, and the neutral axis depth as follows:

(1.2.10)

(1.2.11)

Note that the factors á and k in eqs. (1.2.8) and (1.2.9) are given as before, by eqs. (1.2.5) and (1.2.6), with åco replaced by åc.

The solution of eqs. (1.2.8) and (1.2.9) is performed numerically through iterations, yielding the required FRP cross section Af.

Serviceability Limit State

For the SLS (Serviceability Limit State), the analysis of the critical cross section is performed, according to EC2, for the two possible load combinations:  Rare load, Quasi-permanent load.

For the case of Rare Load the calculations are performed as in the case of the ULS, with the following modifications:

(a) 0.85fcd in eq. (1.2.8) and in Fig. 1.2.2 is replaced by fck;

(b) Mrd is replaced by the acting moment (under the rare load combination) Mser,r;

(c) fyd (the tension steel stress) is replaced by fs1;

(d) the stress limitations are fs1 <= 0.8fyk (for steel) and óc <= 0.6fck, where the stress in the concrete is given by the following stress-strain relationship of concrete (for åc less than 0.002):

(1.2.12)

   For the case of Quasi-permanent Load the calculations are performed as in the case of the ULS, with the following modifications:

(a) 0.85fcd in eq. (1.2.8) and in Fig. 1.2.2 is replaced by fck;

(b) Mrd is replaced by the acting moment (under the quasi-permanent load combination) Mser,q-p;

(c) fyd (the tension steel stress) is replaced by fs1;

(d) åc in eqs. (1.2.5) – (1.2.6) is replaced by åc/(1+ö), where ö is the creep coefficient;

(e) the stress limitations are fs1 <= 0.8fyk (for steel) and óc <= 0.45fck, where the stress in the concrete is given by equation (1.2.12), with åc replaced by åc/(1+ö).

Bond check

For user-defined dimensions of the FRP cross section geometry (n strips of width bf and thickness tf placed in m layers, n/m should be an integer if m > 1) the programme calculates the maximum force, Nbd,max, that can be carried by the total number of strips, and the associated bond length, lbd,max, before debonding of the external reinforcement initiates at the ends (anchorage zone), see Fig. 1.2.3.  These calculations are based on the following equations:

(1.2.13)

(1.2.14)

where:

(1.2.15)

b = beam width [note that b/(n/m) equals the spacing of strips if the number of layers >1]

fctd = design value of the tensile strength of the substrate in N/mm2, that is the tensile strength of concrete near the surface

lbd,max is in mm, Nbd,max is in N, bf and tf are in mm, Ef is in N/mm2.

Fig. 1.2.3   Bending moment envelope line and definition of bond length corresponding to section A.

At each cross section (say A), equilibrium and strain compatibility equations yield the tensile force Nfd,A carried by each strip.  If this force does not exceed Nbd,max, then the bond check is verified, that is failure of the anchorage is not expected, provided that the appropriate bond length lbd will be available.  The bond length corresponding to Nfd,A is calculated as follows:

(1.2.16)

It was mentioned above that Nfd,A is the tensile force carried by the FRP.  This is calculated by multiplying the cross sectional area Af by the product of elastic modulus times strain, Efåf, where åf results through cross section equilibrium and compatibility.  The equations in this case are identical to those used in the ULS, with the provision that the tensile steel reinforcement may not be yielding.  Hence the same formulas used for the ULS apply, with:

(a) Mrd replaced by the design value of the bending moment acting at section A, Msd,A;

(b) fyd replaced by fsd1;

(c) åo taken approximately equal to that corresponding to Mo, times the reduction factor (Msd,A/Msd). This implies the assumption that the bending moment during strengthening at cross section A, Mo,A , is equal to Mo (acting at the critical section) reduced by the factor Msd,A/Msd (note that Msd is acting at the critical section).


1.3 Shear Strengthening
SIKA CarboDur Composite Strengthening Systems

Theoretical Background	Use of Software FRP-Analysis

1.3 Shear Strengthening

Shear strengthening of RC members using FRP may be provided by bonding the external reinforcement with the principal fibre direction as parallel as practically possible to that of maximum principal tensile stresses, so that the effectiveness of FRP is maximised.  For the most common case of structural members subjected to lateral loads, the maximum principal stress trajectories in the shear-critical zones form an angle with the member axis that may be taken roughly equal to 45o.  However, it is normally more practical to attach the external FRP reinforcement with the principal fibre direction perpendicular to the member axis (Fig. 1.3.1).

Fig. 1.3.1	Examples of shear strengthening with: (a) closed (properly anchored) jackets; (b) discrete strips anchored in the compression zone; and (c) open jackets.

Closed jackets (Fig. 1.3.1a) or properly anchored strips (Fig. 1.3.1b) are always preferable compared with open jackets (Fig. 1.3.1c), as in the latter case the FRP debonds prematurely and is, therefore, of reduced effectiveness.

The external FRP reinforcement may be treated in analogy to the internal steel (accepting that the FRP carries only normal stresses in the principal FRP material direction), assuming that at the ultimate limit state in shear (concrete diagonal tension) the FRP develops an effective strain in the principal material direction, åf,e which is, in general, less than the tensile failure strain, åfu.  The effective strain depends on the degree of FRP debonding when the shear capacity of the RC is reached, that is on the type of anchorage (properly anchored FRP, e.g. closed jackets, versus poorly anchored FRP, i.e. open jackets).  Hence, the shear capacity of a strengthened element may be calculated as follows (e.g. in Eurocode 2 format):

(1.3.1)

where Vfd, the contribution of FRP to the member’s shear capacity, is given by the following expression.

(1.3.2)

In the above equation Ef is the elastic modulus of FRP, b is the width of the cross section, d is the static (or effective) depth, á is the angle between the principal FRP fibre orientation and the longitudinal axis of the member, åfd,e is the design value of the effective FRP strain and ñf is the FRP reinforcement ratio, equal to (2tf/b)siná for continuously bonded FRP of thickness tf, or (2tf/b)(bf/sf) for FRP reinforcement in the form of strips or sheets of width bf (perpendicular to the fibre orientation) at a spacing sf (axis to axis of strips along the member axis). Equation (1.3.2) may be solved for the thickness of FRP required to provide a shear resistance equal to Vfd.

The effective FRP may be estimated as follows:

•	Fully wrapped or properly anchored CFRP or GFRP:

(1.3.3a)

•	Fully wrapped or properly anchored AFRP:

(1.3.3b)

•	Open FRP jackets (e.g. side or U-shaped sheets):

  (1.3.4)

In the above, fcm is the mean compressive strength of concrete in N/mm2, Ef is taken in kN/mm2, k is a constant relating the characteristic to the mean value of the effective FRP strain (default: k = 0.8) and ãf is the FRP material safety factor.  The ãf factor depends on the type of FRP material as well as on the failure mode governing shear design.  The first term in eqs. (1.3.3a), (1.3.3b) and (1.3.4) corresponds to FRP fracture (when the member’s shear capacity is reached), hence the use of ãf,f (= 1.20 for CFRP, 1.25 for AFRP, 1.30 for GFRP), the second term in eq. (1.3.3) corresponds to FRP debonding, hence the use of ãf,b (= 1.30), and the last term is taken (with ãf,l = 1.25) if it is desired to limit the FRP strain in order to to maintain the integrity of concrete and secure activation of the aggregate interlock mechanism.  It should be noted that these FRP material factors may be changed through Options.


1.4 Confinement
SIKA CarboDur Composite Strengthening Systems

Theoretical Background	Use of Software FRP-Analysis

1.4 Confinement

The main objectives of confinement are: (a) to enhance concrete strength and deformation capacities, (b) to provide lateral support to the longitudinal reinforcement and (c) to prevent the concrete cover from spalling.  In the case of circular columns, these goals can be achieved by applying external FRP jackets, either continuously all over the surface or discontinuously as strips.  In the case of rectangular columns, the confinement can be provided with rectangular-shaped reinforcement, with corners rounded before application.  Note that rectangular confining reinforcement is less effective (but still possible) as the confinement action is mostly located at the corners and a significant jacket thickness needs to be used between corners to restrain lateral dilation and rebar buckling.

The stress-strain response of FRP-confined concrete is illustrated schematically in Fig. 1.4.1.  The figure displays a nearly bilinear response with a sharp softening and a transition zone at a stress level that is near the strength of unconfined concrete, fco.  After this stress the tangent stiffness changes a little, until the concrete reaches its ultimate strength fcc when the jacket reaches tensile failure at a stress ff,e and a corresponding strain åfu,e, which is, in general, less than the uniaxial tensile strength åfu.  This reduction is attributed to several reasons, including: (a) the triaxial state of stress in the FRP (due to axial loading and confining action, but also due to bending, e.g. at corners of low radius); and (b) the quality of execution (potential local ineffectiveness of some fibres due to misalignment, and overstressing of others; damaged fibres at sharp corners or local protrusions etc).

Fig. 1.4.1	Stress-strain curves for plain (unconfined) and FRP-confined concrete.

For rectangular cross sections with dimensions b and h (b>=h), Fig. 1.4.2, the effect of FRP confinement may be calculated based on the following expressions for the confined concrete strength fcc and the corresponding strain åcu:

Fig. 1.4.2	Rectangular cross section with radius R at corners.

(1.4.1)

(1.4.2)

where

(1.4.3)

(1.4.4)

(1.4.5)

 	(1.4.6)

(1.4.7)

(1.4.8)

     (confinement effectiveness coefficient)	(1.4.9)

Eco = initial elastic modulus of concrete, åco = 0.002 (strain corresponding to fco), Ag = gross sectional area of concrete = bh-(4-ð)R2.

Note that for circular cross sections of diametre D confined with strips of width bf at a spacing sf, ke is given as follows:

(1.4.10)


2.1 General
SIKA CarboDur Composite Strengthening Systems

Use of Software FRP-Analysis

2.1 General

The software package FRP-Analysis may be used as a user friendly, simple and reliable design tool for the selection of required FRP dimensions to provide flexural strengthening, shear strengthening or confinement in Reinforced Concrete sections.  Essentially, the software is divided in two procedures.  The first one is related to definitions of input data, solution options and print options, whereas the second involves presentation of results, selection of appropriate number of FRP strips or layers and printing.  Between the two distinct procedures lies the numerical solutions algorithm.

When the programme starts, the user is asked to provide “Data Input” for one of the following three cases: flexural strengthening (ULS and SLS), shear strengthening, confinement.  When all data are provided, the user may either proceed to the “Solution” or initialise the input parametres through the “New Input” option.  During the data input definitions, the programme checks for the validity of input parametres and provides warnings if incorrect actions are taken.  Through a series of “Options” the user may define print-related information, or even change the default values for FRP material safety factors. Finally, the commands “Open” and “Save” provide the possibility to the user to keep track of the various strengthening projects, whose input data are loaded and saved by demand.

By clicking “Solution”, the programme’s “heart”, that is the solution procedure is activated. When the solution procedure is finished, the results are provided in terms of the FRP cross sectional area (in case of flexural strengthening) or total FRP thickness (in case of shear strengthening or confinement) required for a given problem.  For the case of flexural strengthening additional information is provided regarding the degree of strengthening (moment capacity after strengthening divided by that before strengthening), the strain profile (e.g. neutral axis depth, concrete, steel and FRP strains) during strengthening as well as that after strengthening, the ductility, the failure mode, the acting moment before strengthening (at the SLS) and the maximum achievable acting moment (at the SLS). Finally, the user has the option to input dimensions of real FRP products (e.g. thickness and width of strips in the case of flexural strengthening, thickness of each layer in the case of shear strengthening or confinement) and the programme responds with the calculation of number of strips or layers and the corresponding capacity (flexural, shear or confinement).


2.2 Flexural Strengthening
SIKA CarboDur Composite Strengthening Systems

Use of Software FRP-Analysis        	Theoretical Background

2.2 Flexural Strengthening

DATA INPUT

The user needs to provide input as described in the following.

Type of Cross Section

The option “T-beam” is selected for T-shaped cross sections or “Rectangular beam” for rectangular sections.  The last option covers also the case of slabs.

Cross Section Geometry

Width b :  input the width in m.

Height h :  input the height in m.

Effective width beff :  input the effective width in m (only in the case of T-beams).

Slab thickness hf :  input the slab thickness in m (only in the case of T-beams).

Concrete

The user has the option either to select the strength class of concrete (if known) or to input the mean strength (fcm) in N/mm2.  The assumed relationship between the two is: fck = fcm – 1.64*5. Moreover, the user has the option to input the creep coefficient (estimated according to EC2 procedures), which is used in the Serviceability Limit State verification for quasi-permanent loads. The default value of 2.5 is assumed here.

Composite Materials

By clicking the button "Sika CarboDur Properties", properties of the various CarboDur systems are provided for consultation.

Elastic modulus Ef :  Input the elastic modulus of FRP in kN/mm2 (provided by the material supplier).

Limiting strain åf,lim :  Input the limiting strain of the FRP (non-dimensional quantity !).  Beyond this value, the FRP may debond in the areas of high bending moments (flexural cracks).  Suggested (default) value = 0.008.

Steel Reinforcement

Elastic modulus Es : Input the elastic modulus of the longitudinal steel reinforcement in kN/mm2. The default value is 200 kN/mm2.

Characteristic yield stress fyk :  Input the characteristic yield stress of the longitudinal steel reinforcement in N/mm2, e.g. 500 for steel S500.

Top As2 :  Input the total cross sectional area of the steel reinforcement in the compression zone (if present) (in mm2).

At distance d2 :  Input the distance from the centroid of As2 to the extreme compressive fibre of the cross section (in m).

Bottom Ás12 :  Input the total cross sectional area of the second layer (if present) of steel reinforcement in the tension zone (in mm2).

At distance d12 :   Input the distance from the centroid of As12 to the extreme tensile fibre of the cross section (in m).

Bottom Ás11 :  Input the total cross sectional area of the first layer of steel reinforcement in the tension zone (in mm2).

At distance d11 :   Input the distance from the centroid of As11 to the extreme tensile fibre of the cross section (in m).

Bending Moments

Bending moment during strengthening Ìï :  Input the bending moment applied to the cross section during strengthening (service moment), that is the moment that develops e.g. due to gravity loads when the strengthening process takes place (in kNm).

Required design moment after strengthening Ìsd :  Input the design value of the resisting bending moment after strengthening (in kNm) for the Ultimate Limit State verification.

Acting moment - Rare load Ìser,r :  Input the bending moment acting at the critical cross section due to the rare load combination of the Serviceability Limit State (in kNm).

Acting moment - Quasi-permanent load Ìser,q-p :  Input the bending moment acting at the critical cross section due to the quasi-permanent load combination of the Serviceability Limit State (in kNm).

Commands

Solution :  The programme checks for input errors and provides the solution.

New Input :  All input data values may be initialized through this command.

Help :  Activates the help facility.

Options :  Activates the options described in Section 2.5.

Save :  Saves all the input data in a file.

Open :  Opens a data file, where input data may have been saved.

About … :  Activates the programme’s introductory window.

Exit :  Exits the programme.

Information Line

The following information is shown:  Project     Name     Company     Date     Time

The first three fields are provided by the user through “Options”, “General”.

In the last two fields the date and time are provided by the system.

***General Remarks***

For each input value provided by the user the programme checks if this value is a “reasonable” one (e.g. not too high, not too low) and provides a warning if this is not the case.  Warnings are also provided if the user inputs wrong characters (e.g. a letter instead of a number) or if he/she forgets to fill a box.  Additional checks are made by the programme (and the corresponding warnings are provided) if a combination of values does not make sense (e.g. the effective width of a slab cannot be less than the beam’s width).

When “Solution” is selected, the programme performs a number of checks.  Warning messages are provided when the required design moment after strengthening is too high (so that the section cannot be strengthened, no matter how much FRP is provided) or too low (that is less than the resisting design moment before strengthening).

RESULTS

Upon completion of the solution process, the “Results” window provides the following.

Ultimate Limit State

Resisting design moment before strengthening Ìrd,o :  This is the value of the resisting design moment calculated without the use of FRP.

Required FRP cross section for ULS Af :  Total FRP cross sectional area to be added to the tension face in order to verify the ULS.

Resisting design moment after strengthening Ìrd :  This is the value of the resisting design moment corresponding to the above FRP cross section Af. Note that this value might be slightly different from the one input by the user, due to round-off errors.

Degree of strengthening Ìrd/Ìrd,ï :  The ratio of the resisting design moment after strengthening to that before strengthening.

Serviceability Limit State - Rare Load

Moment capacity before strengthening Mser,r,o :  This is the value of the moment capacity calculated without the use of FRP.  A warning will be provided if the bending moment during strengthening Mo is higher than Mser,r,o.

Required FRP cross section for SLS Af :  Total FRP cross sectional area to be added to the tension face in order to verify the SLS for the Rare Load combination.

Moment capacity Mser,r :  Value of the moment capacity corresponding to the above FRP cross section Af. Note that this value might be slightly different from the one input by the user, due to round-off errors.

Steel stress fs11 :  Stress in the extreme tension steel reinforcement for the SLS verification under the Rare Load combination.

Concrete stress óc :  Maximum stress in the concrete for the SLS verification under the Rare Load combination.

Note that for the SLS verification under the Rare Load combination either the steel or the concrete stress has reached its respective limiting value. For the steel stress the limiting value is 0.8fyk and for the maximum concrete stress the limiting value is 0.6fck. If Mser,r is lower than Mser,r,o, no FRP is needed for the SLS verification under the Rare Load combination, and in this case none of the above materials reaches its respective limiting value.

Serviceability Limit State - Quasi-permanent Load

Moment capacity before strengthening Mser,q-p,o :  This is the value of the moment capacity calculated without the use of FRP.  A warning will be provided if the bending moment during strengthening Mo is higher than Mser,q-p,o.

Required FRP cross section for SLS Af :  Total FRP cross sectional area to be added to the tension face in order to verify the SLS for the Quasi-permanent Load combination.

Moment capacity Mser,q-p :  Value of the moment capacity corresponding to the above FRP cross section Af. Note that this value might be slightly different from the one input by the user, due to round-off errors.

Steel stress fs11 :  Stress in the extreme tension steel reinforcement for the SLS verification under the Quasi-permanent Load combination.

Concrete stress óc :  Maximum stress in the concrete for the SLS verification under the Quasi-permanent Load combination.

Note that for the SLS verification under the Quasi-permanent Load combination either the steel or the concrete stress has reached its respective limiting value. For the steel stress the limiting value is 0.8fyk and for the maximum concrete stress the limiting value is 0.45fck. If Mser,q-p is lower than Mser,q-p,o, no FRP is needed for the SLS verification under the Quasi-permanent Load combination, and in this case none of the above materials reaches its respective limiting value.

Flexural Strengthening - Final

Design is controlled by :  the Limit State controlling the design (corresponding to the maximum of the three Af values, calculated for ULS, SLS - Rare Load, SLS - Quasi-permanent Load) is provided here.

Final required FRP cross section Af :  The maximum of the three Af values (calculated for ULS, SLS - Rare Load, SLS - Quasi-permanent Load) is provided here.

Commands

Cross section strain profile :  Activates a window with the deformation characteristics of the cross section, both graphically and with numbers.

Initial Situation During Strengthening (Mo)

•   Depth of neutral axis :  depth of neutral axis (in m) during strengthening (due to Mo).

•   Top fibre strain :  strain in the extreme concrete compressive fibre during strengthening (due to Mo).

•   Top steel strain :  strain in the top steel reinforcement during strengthening (due to Mo).

•   Bottom steel strain :  strain in the bottom steel reinforcement during strengthening (due to Mo).

•   Bottom fibre strain :  strain in the extreme concrete tensile fibre during strengthening (due to Mo).

Ultimate Limit State (Mrd)

•   Depth of neutral axis :  depth of neutral axis (in m) when Mrd is reached.

•   Top fibre strain :  strain in the extreme concrete compressive fibre when Mrd is reached.  If this value equals 0.0035, compressive crushing of the concrete occurs.

•   Top steel strain :  strain in the top steel reinforcement when Mrd is reached.

•   Bottom steel strain :  strain in the bottom steel reinforcement when Mrd is reached.

•   FRP strain :  strain in the FRP when Mrd is reached.  If this value equals the limiting strain åf,lim (default = 0.008), debonding of the FRP occurs.

Fail: The failure mode assosiated to ULS is reported.

Ductility (for ULS)

The ratio of neutral axis depth is calculated and compared with the maximum value provided by EC2. A statement is provided related to the ductility requirement.

Serviceability Limit State - Rare Load (Mser,r)

•   Depth of neutral axis :  depth of neutral axis (in m) corresponding to Mser,r.

•   Top fibre strain :  strain in the extreme concrete compressive fibre corresponding to Mser,r.

•   Top steel strain :  strain in the top steel reinforcement corresponding to Mser,r.

•   Bottom steel strain :  strain in the bottom steel reinforcement corresponding to Mser,r.

•   Bottom fibre strain :  strain in the extreme concrete tensile fibre corresponding to Mser,r.

•   FRP strain :  strain in the FRP corresponding to Mser,r.

Serviceability Limit State - Quasi-permanent Load (Mser,q-p)

•   Depth of neutral axis :  depth of neutral axis (in m) corresponding to Mser,q-p.

•   Top fibre strain :  strain in the extreme concrete compressive fibre corresponding to Mser,q-p.

•   Top steel strain :  strain in the top steel reinforcement corresponding to Mser,q-p.

•   Bottom steel strain :  strain in the bottom steel reinforcement corresponding to Mser,q-p.

•   Bottom fibre strain :  strain in the extreme concrete tensile fibre corresponding to Mser,q-p.

•   FRP strain :  strain in the FRP corresponding to Mser,q-p.

Input of FRP dimensions :  Activates a window where the user may input the dimensions (width and thickness, in mm) of FRP materials (values refer to a single strip) to be used for the specific strengthening project. By clicking the button Sika CarboDur Properties, properties of the various CarboDur systems are provided for consultation. By clicking Calculation, the number of strips required and the corresponding FRP area (final cross section) are calculated. The user has the option to override the required number of strips, by providing the applied number in the appropriate field.

•	Solve and return :  The window “Results” is activated with updated information, based on the new (applied) FRP cross section. Note that ALL values are updated (e.g. even if the SLS controls, values corresponding to the ULS are provided too, and vice versa).  The FRP area is now called “applied”.

•	Return (without solution) :  The window “Results”, as it was before the input of FRP dimensions, is activated again.

Bond Check :  When the user has selected the FRP dimensions and the number of strips (n), this button activates a window where the bond check is performed.

Section's Properties

•	Substrate tensile strength fctm :  Input the mean value of the concrete tensile strength near the surface (in N/mm2). The default value is calculated based on the characteristic value of the compressive strength. However, more realistic values could be obtained through pull-off testing.

•	Design moment at section A  Msd,A :  Input the bending moment acting in cross section A (in kNm). The calculations will provide the required bond length lbd corresponding to this particular cross section, that is, how far from this section the FRP should extend, in addition to the horizontal displacement of the bending moment diagram aL.

Steel Reinforcement at Section A

•	Elastic modulus Es : Input the elastic modulus (in kN/mm2) of the longitudinal steel reinforcement crossing section A. The default value is the one provided for the critical cross section verifications.

•	Characteristic yield stress fyk :  Input the characteristic yield stress (in N/mm2) of the longitudinal steel reinforcement crossing section A. The default value is the one provided for the critical cross section verifications.

•	Top As2 :  Input the total cross sectional area of the steel reinforcement in the compression zone (if present) of section A (in mm2). The default value is the one provided for the critical cross section verifications.

•	At distance d2 :  Input the distance from the centroid of As2 to the extreme compressive fibre of the cross section A (in m). The default value is the one provided for the critical cross section verifications.

•	Bottom Ás12 :  Input the total cross sectional area of the second layer (if present) of steel reinforcement in the tension zone of section A (in mm2). The default value is the one provided for the critical cross section verifications.

•	At distance d12 :   Input the distance from the centroid of As12 to the extreme tensile fibre of the cross section A (in m). The default value is the one provided for the critical cross section verifications.

•	Bottom Ás11 :  Input the total cross sectional area of the first layer of steel reinforcement in the tension zone of section A (in mm2). The default value is the one provided for the critical cross section verifications.

•	At distance d11 :   Input the distance from the centroid of As11 to the extreme tensile fibre of the cross section A (in m). The default value is the one provided for the critical cross section verifications.

FRP Arrangement

•	Total number of n strips is placed in m layers :  The number of strips n has been calculated from the previous step. Given this number, the user will decide about the number of layers m. For instance, if a total of two strips are needed, and they do not fit one next to the other, they will be placed one on the top of the other, so that m=2. The number of layers m should be provided here as input by the user. Note that if m>1, the total number of strips divided by the number of layers should be an integer, so that the strips can be divided evenly! If the condition is not fulfilled, the user is warned through a message, so that a new selection of FRP dimensions should be made resulting in n/m=integer.

Calculation

By clicking Calculation, the programme provides the total tensile force carried by FRP in section A, Nfd,A, the corresponding value of the maximum force, Nbd,max, so that debonding (anchorage failure) does not occur, the bond length, lbd,max, corresponding to Nbd,max and, if the bond check is OK, (Nfd,A<Nbd,max), the bond length required to transmit the force Nfd,A. If the bond check is NOT OK, a couple of suggestions are provided: the user should increase the FRP cross section (this solution is not so likely to be successful), and/or use a mechanical anchorage at the FRP ends.

Help :  Activates the help facility.

Return :  Activates the Data Input window, in case modifications to the input data need to be made.

Print :  A printout of the results is obtained.

Exit :  Exits the programme.


2.3 Shear Strengthening
SIKA CarboDur Composite Strengthening Systems

Use of Software FRP-Analysis        	Theoretical Background

2.3 Shear Strengthening

DATA INPUT

The user needs to provide input as described in the following.

Method of Anchorage

The option “Closed jacket” or “Open jacket” is selected, depending on the type of strengthening system used.  Shear strengthening of columns where all four sides are accessible is typically of the closed-type.  Moreover, shear strengthening of T-beams with mechanical anchorage systems that ensure perfect anchorage of the FRP in the compression zone may be considered of the closed-type too.  This is the case, for instance, with the Carboshear elements, if sufficient anchorage length is available through the slab.  For these particular elements, if the anchorage length is less than 400 mm, it is recommended to take as solution that corresponding to the average of “Closed jacket” and “Open jacket”, that is to run the programme for both cases and adopt the average solution.

Cross Section Geometry

Width b :  Input the width in m.

Static depth d :  Input the static (or effective) depth, that is the distance from the centroid of the tension steel reinforcement to the extreme compressive fibre, in m.

Angle between fibres direction and member axis :  Input the angle (degrees) formed between the principal fibre direction in the FRP and the axis of the RC member.  In most cases this angle is 90 degrees.

Concrete

The user has the option either to select the strength class of concrete (if known) or to input the mean strength in N/mm2.  The assumed relationship between the two is: fck = fcm – 1.64*5.

Composite Materials

By clicking the button "Sika CarboDur Properties", properties of the various CarboDur systems are provided for consultation.

Elastic modulus Ef :  Input the elastic modulus of FRP in kN/mm2 (provided by the material supplier).

Ultimate tensile strain åfu :  Input the ultimate tensile strain (failure strain) of the FRP (non-dimensional quantity !).  Typically provided by the material supplier.

Limiting strain åf,lim :  Input the limiting strain of the FRP (non-dimensional quantity !).  Exceeding this value would imply large cracks and hence reduced contribution from the concrete to the shear capacity (reduced aggregate interlock).  Suggested (default) value = 0.006.

Type of fibres :  Select the type of fibres of the FRP material.  This is related to material safety factors.

Type of Application

The use of continuous jacket or discrete strips may be selected here.  In the latter case the width and spacing (axis to axis !) of the strips should be provided (in m).  The spacing should be such that a potential shear crack should cross at least one strip.  As a simple rule, a maximum spacing of 0.8*d is adopted here.

Increase of Shear Capacity

Additional shear Vfd :  Input the shear force (in kN) to be carried by the FRP.

Commands

Solution :  The programme checks for input errors and provides the solution.

New Input :  All input data values may be initialized through this command.

Help :  Activates the help facility.

Options :  Activates the options described in Section 2.5.

Save :  Saves all the input data in a file.

Open :  Opens a data file, where input data may have been saved.

About … :  Activates the programme’s introductory window.

Exit :  Exits the programme.

Information Line

The following information is shown:  Project     Name     Company     Date     Time

The first three fields are provided by the user through “Options”, “General”.

In the last two fields the date and time are provided by the system.

***General Remarks***

For each input value provided by the user the programme checks if this value is a “reasonable” one (e.g. not too high, not too low) and provides a warning if this is not the case.  Warnings are also provided if the user inputs wrong characters (e.g. a letter instead of a number) or if he/she forgets to fill a box.  Additional checks are made by the programme (and the corresponding warnings are provided) if a combination of values does not make sense (e.g. the spacing of discrete strips cannot be less than their width).

RESULTS

Upon completion of the solution process, the “Results” window provides the following.

Required FRP thickness tf :  The total thickness of the FRP jacket is provided.

Additional shear Vfd :  This is the value of the force corresponding to the FRP jacket of thickness tf.  Note that this value might be slightly different from the one input by the user, due to round-off errors.

Commands

Input of FRP dimensions :  Activates a window where the user may input the thickness (in mm) of a single layer of the FRP material to be used for the specific strengthening project. By clicking the button Sika CarboDur Properties, properties of the various CarboDur systems are provided for consultation. By clicking Calculation, the number of layers required is calculated. The user has the option to override the required number of layers, by providing the applied number, in the appropriate field.

•	Solve and return :  The window “Results” is activated with updated information, based on the new FRP thickness. Note that the FRP thickness is now called “applied”.

•	Return (without solution) :  The window “Results”, as it was before the input of FRP dimensions, is activated again.

Help :  Activates the help facility.

Return :  Activates the Data Input window, in case modifications to the input data need to be made.

Print :  A printout of the results is obtained.

Exit :  Exits the programme.


2.4 Confinement
SIKA CarboDur Composite Strengthening Systems

Use of Software FRP-Analysis        	Theoretical Background

2.4 Confinement

DATA INPUT

The user needs to provide input as described in the following.

Type of Cross Section

The option “Rectangular” is selected for rectangular cross sections or “Circular” for circular sections.

Cross Section Geometry

Width b :  Input the width in m (for rectangular cross sections).

Height h :  Input the height in m (for rectangular cross sections).

Radius at corner R :  Input the radius at the corners of the cross section in m (for rectangular cross sections).

Diametre D :  Input the diametre in m (for circular cross sections).

Concrete

The user has the option either to select the strength class of concrete (if known) or to input the mean strength in N/mm2.  The assumed relationship between the two is: fck = fcm – 1.64*5.

Composite Materials

By clicking the button "Sika CarboDur Properties", properties of the various CarboDur systems are provided for consultation.

Elastic modulus Ef :  Input the elastic modulus of FRP in kN/mm2 (provided by the material supplier).

Ultimate tensile strain åfu :  Input the ultimate tensile strain (failure strain) of the FRP (non-dimensional quantity !).  Typically provided by the material supplier.

Effective ultimate strain åfu,e :  Input a reduction factor (default = 0.9) which multiplies the ultimate tensile strain of the FRP to give the effective ultimate strain in the circumferential direction.  This reduction is related to the multiaxiality of stresses in the FRP and the quality of execution.

Type of Application

The use of continuous jacket or discrete strips may be selected here.  In the latter case the width and spacing (axis to axis !) of the strips should be provided (in m).  A warning is provided if the user specifies discrete strips as a means of confining rectangular cross sections.  The effectiveness of confinement in this case is very small, and hence not recommended.

Requirements

The user has the option to select (a) increase of the concrete strength from fco (= fcm) to fcc or (b) increase of the concrete ultimate strain to a value åcu, or both.

Mean strength after strengthening fcc:  Input the strength of FRP-confined concrete (target value after strengthening) in N/mm2.

Ultimate axial strain after strengthening åcu:  Input the ultimate axial strain of FRP-confined concrete (target value after strengthening), dimensionless value.

Commands

Solution :  The programme checks for input errors and provides the solution.

New Input :  All input data values may be initialized through this command.

Help :  Activates the help facility.

Options :  Activates the options described in Section 2.5.

Save :  Saves all the input data in a file.

Open :  Opens a data file, where input data may have been saved.

About … :  Activates the programme’s introductory window.

Exit :  Exits the programme.

Information Line

The following information is shown:  Project     Name     Company     Date     Time

The first three fields are provided by the user through “Options”, “General”.

In the last two fields the date and time are provided by the system.

***General Remarks***

For each input value provided by the user the programme checks if this value is a “reasonable” one (e.g. not too high, not too low) and provides a warning if this is not the case.  Warnings are also provided if the user inputs wrong characters (e.g. a letter instead of a number) or if he/she forgets to fill a box.  Additional checks are made by the programme (and the corresponding warnings are provided) if a combination of values does not make sense (e.g. the radius at the corners of a rectangular section cannot be more than half of the small side).

RESULTS

Upon completion of the solution process, the “Results” window provides the following.

Required FRP thickness tf :  The total thickness of the FRP jacket is provided.

Mean strength after strengthening fcc:  This is the value of the strength of FRP-confined concrete corresponding to the FRP jacket of thickness tf.  Note that this value might be different from the one input by the user due to: (a) round-off errors (only slight differences are expected in this case); (b) the fact that if the option “Ultimate axial strain after strengthening” has been selected, the FRP thickness is controlled by this requirement (i.e. larger FRP thickness is required to satisfy the strain requirement than the strength).

Ultimate axial strain after strengthening åcu:  This is the value of the ultimate axial strain of FRP-confined concrete corresponding to the FRP jacket of thickness tf.  Note that this value might be different from the one input by the user due to: (a) round-off errors (only slight differences are expected in this case); (b) the fact that if the option “Mean strength after strengthening” has been selected, the FRP thickness is controlled by this requirement (i.e. larger FRP thickness is required to satisfy the strength requirement than the strain).

Commands

Input of FRP dimensions :  Activates a window where the user may input the thickness (in mm) of a single layer of the FRP material to be used for the specific strengthening project. By clicking the button Sika CarboDur Properties, properties of the various CarboDur systems are provided for consultation. By clicking Calculation, the number of layers required is calculated. The user has the option to override the required number of layers, by providing the applied number in the appropriate field.

•	Solve and return :  The window “Results” is activated with updated information, based on the new FRP thickness. Note that the FRP thickness is now called ''applied''.

•	Return (without solution) :  The window “Results”, as it was before the input of FRP dimensions, is activated again.

Help :  Activates the help facility.

Return :  Activates the Data Input window, in case modifications to the input data need to be made.

Print :  A printout of the results is obtained.

Exit :  Exits the programme.


2.5 Options
SIKA CarboDur Composite Strengthening Systems

Use of Software FRP-Analysis

2.5 Options

General

Names for the user, the company and the project may be provided through this option.  A choice can be made whether these data should be included in the printout or not.

Print/Flexure

“Print Options” includes the “Print Setup” (type of printer, properties, paper etc.) and the “Fonts” (font, style, size, to be selected for the printout).

“Flexural Strengthening”: If the box “Solution for desirable failure modes only” is ticked (strongly recommended), the programme will provide a solution (for the ULS) only if one of the two desirable failure modes (steel yielding + concrete crushing, steel yielding + FRP at limiting strain) is activated (if this is not possible, a warning will inform the user that the cross section is over-reinforced !).  If the box “Solution for desirable failure modes only” is not ticked, the programme will provide a solution regardless of the failure mode (which could be of the concrete crushing type, without yielding of the tension steel reinforcement !).

FRP Material Safety Factors

These factors are described in Section 1.3 (theoretical background – shear strengthening). The default values given here may be modified by the user.