FRPpro™ Engineering Calculator
Using FRPpro™ FRP Design Software is a simple way to design reinforced concrete beam strengthening.
All engineering software calculations are based on recommendations of the American Concrete Institute (ACI) 440.2R-08, "Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures" and ACI 318-08, "Building Code Requirements for Structural Concrete." Users should understand the fundamentals of reinforced concrete design.
Table of Contents
Beam Geometry and Capacity
. You need to be running either: Windows XP, Windows Vista, Windows 7, or Windows 8. FRPpro software runs on the Microsoft Excel engine. FRPpro™ will not run unless you have Excel 2003, Excel 2007, or Excel 2010 on your computer.
At the top of the spreadsheet, notice the two colored cells: A yellow cell indicates that data entry here is required for the calculations. A green cell indicates that data entry here is not required for calculations, but is recommended so that you may add descriptive information to the printed solution.
Be careful to enter data in the units shown adjacent to each cell to assure the software calculates properly.
Enter your project information into the green cells at the top of the page. The project information entered here becomes the header on each printed page of the calculations.
FRPpro™ leaves much of the formatting of the printed pages up to you. A basic format is already installed in FRPpro, but you may add to the formatting if you wish.
Loadings and Corresponding Moments
The Beam length, l is an optional entry used to help describe the member. The calculation method does not use the beam length to compute any solutions; it only needs the existing and new bending moments entered later.
Note: This software does not calculate bending moments for you. These are entered directly into appropriate cells. There are plenty of low cost and free beam programs that can help you calculate maximum bending moments. One free version that we like is Atlas 2.0.
Beam width, b
is the width of the compression face of the beam to be analyzed. For rectangular shaped beams, b is the full width. For wall sections, enter a simple unit width such as 1,000 mm in SI units, or 12 inches in US units. For T-beams where the neutral axis falls in the flange, the beam width, b is the effective flange width.
Tip: For basement wall strengthening projects, the amount of vertical steel reinforcing is generally low. For basement walls, it can be advantageous to analyze the width of wall that equals one or two times the spacing of vertical steel. Say a reinforced concrete basement wall has vertical reinforcing every four feet (or one meter). Enter in the beam width, b as 48 inches (or 1,000 mm). In this example, you would then find the FRP system needed to strengthen a four-foot (or one meter) section of wall.
Effective depth, d
is the depth from the extreme compression fiber to the centroid of the steel tension reinforcement. For one layer of steel reinforcing, the effective depth, d is simply the depth from the compression side of the beam to the center of the reinforcing bars. For two or more layers of reinforcing steel, enter the distance from the compression side of the beam to the arithmetic average of all reinforcing layers.
Depth to FRP, df
is the depth from the extreme compression fiber to the centroid of the FRP system. Usually this is equal to the beam height, h where the FRP system is located solely on the tension side of the beam. However, in unusual cases where the FRP is located on the sides of the beam as well as the tension side, the arithmetic average of the FRP depths is entered.
The concrete compressive strength, f'c
is the specified compressive strength of the compression side of the beam. Enter the value in U.S. units of kips per square inch (ksi) or MPa in SI units.
The steel yield strength, fy
should be taken from building plans or for older beams where no documentation is available, it should be conservatively estimated considering the time period in which the structure was built. Sound engineering judgment should prevail.
The modulus of elasticity of steel, Es
of 29,000 ksi (U.S. units) or 200,000 MPa (SI units) is given for normal, nonprestressed reinforcing steel. You may override this value but will return to its default value when the FRPpro™ FRP Design software calculates the area of tension steel, As
FRP Design software is restarted.
Moment resistance of unstrengthened beam, ΦMn
is the flexural strength of the beam prior to strengthening with a FRP system.
Tip: A simple, online calculator to estimate the strength of beams can be found at Structural Software, Inc.
The area of tension steel, As in the beam is entered as the total area of tension steel in the beam.
Note: For your convenience, FRPpro™ FRP Design software provides a simple calculator for the area of tension steel, As below the Rebar Table and can be found by clicking on the tab of the same name at the bottom of your screen.
Manufacturer's Reported FRP System Properties
FRPpro™ FRP Design software requires you to enter the unfactored, design dead load moment, MDL
and the unfactored, design live load moment, MLL
that the strengthened beam will be required to resist.
The software calculates the design service load moment, MS
and the design factored moment, MU
. The strength factors are based on ACI 318-08, section 9.2.1 for dead and live loads. The design factored moment, MU
value can be entered directly for other load combinations such as for wind, snow and earthquake loads.
It is recommended that the moment resistance of the unstrengthened beam be equal to or greater than the unstrengthened moment limit.
ΦMn = (ΦRn)existing [2-1]
FRPpro™ FRP Design software calculates this for you. If Equation 2-1 is true, the software shows "OK" (without the quotes) below the calculation. If Equation2-1 is untrue, the FRPpro™ FRP Design software shows "UNDERSTAND THE RISK."
Note: The unstrengthened moment limit, (ΦRn)existing is an important consideration in the use of structure after FRP strengthening. According to the American Concrete Institute (ACI) 440.2R-08, a structural member should have enough strength, after physical damage to a FRP strengthening system, to resist the dead load and a small portion of the live load to avoid catastrophic collapse. Physical damage could be from mechanical means of from fire.
Calculate the FRP System Design Material Properties
Enter the FRP manufacturer and product. The FRP manufacturer and product names are not used in the calculations but should be listed for reference.
Next, choose from the drop-down list whether the FRP product lists the properties of the textile only or of the laminated system.
Note: Manufacturers report either the properties of the laminated FRP system (textile embedded within the matrix) or the textile alone. A laminated system is defined as the combination of fibers embedded in a polymer matrix, such as a prepreg to pultruded product. Some manufacturers list laminated properties for textiles or unidirectional fabrics that have been tested after wetting out with polymer matrix and cured.
The next entry is also a drop-down list to select the FRP system fiber type. Select the appropriate fiber. The fiber type determines the creep rupture stress limit in Step 17 as a percent of the effective fiber stress.
Follow with the entry of the manufacturer's reported FRP system ultimate tensile strength, f*fu
, tensile modulus of elasticity, Ef
, and the ultimate strain at break or rupture strain, ζ*fu
In the table following, the product name is entered for you in the FRP column as you entered it before. Under the ply thickness, tf
column, enter the thickness of the textile or laminate ply. Next, enter the ply width, wf
in the next column.
In the next two columns, it is important to distinguish between ply layers and ply groups. Ply layers, nf
are defined as the number of FRP system plies that are bonded on top of each other. Ply groups, mf
are defined as the number of separate, FRP system plies that are bonded directly to the beam substrate. Ply groups can have one or more layers of FRP. FRPpro™ FRP Design software assumes the number of ply layers in each ply group is the same.
You may enter up to three lines of ply width, layer, and group combinations, however, only the product named with entered strength, modulus, and rupture strain will be used in the calculations.
Existing Beam Conditions
The FRP system is given a partial reduction factor based on the environment in which the system will perform. Select and enter the appropriate environmental reduction factor, CE
based on the following table:
Environmental Reduction Factor, CE
Exposure Condition|| ||Fiber Type|| |
Interior Exposure||0.95|| 0.85|| 0.75|
An aggressive environment is considered a location where prolonged exposure to high humidity, freeze-thaw cycles, salt water, or alkalinity is expected.
Tip: If the FRP system is coated after installation, the coating has shown by testing to decrease the effects of environmental conditions, and the coating is maintained for the life of the FRP system, an environmental reduction factor representing the protected environment of the FRP system can be used (ACI 440.2R-08, section 9.4).
FRPpro™ FRP Design software calculates the ultimate tensile stress, ffu
and strain, εfu
based on the environmental reduction factor entered.
Existing Strain on the Beam Soffit
FRPpro™ FRP Design software calculates the ratio of the equivalent rectangular compressive stress block depth, β1
and the modulus of elasticity of concrete, Ec
based on the concrete compressive strength entered in Step 1. The software then calculates the modular ratio of elasticity between the reinforcing steel and concrete, ns.
Note: Beginning in Step 5, FRPpro™ FRP Design software automates the remaining calculations. No calculation steps are hidden; therefore, the engineer or designer can easily validate each step and verify that design assumptions are correct.
Design Strain of the FRP System
A small strain will exist on the beam due to the dead load imposed on it at the time of FRP system installation. This initial substrate strain, εbi
is excluded from the strain in the FRP in Step 9. To find the initial substrate strain FRPpro™ FRP Design software first calculates the cracked beam section moment of inertia and the depth to the cracked neutral axis.
Estimate the Depth of the Neutral Axis
If the calculated design strain, εfd
on the FRP system exceeds 90 percent of the ultimate tensile strain, εfu
FRP rupture controls the design and the lower of the two strains is used as εfd
. Conversely, if the calculated design strain is less than or equal to 90 percent of the ultimate tensile strain, FRP debonding controls the design and the calculated design strain is used in subsequent calculations.
FRPpro™ FRP Design software calculates the design strain of the FRP system and determines if FRP system rupture or debonding controls the design.
Effective Strain in the FRP, Concrete, and Steel
Estimating the depth of the neutral axis after application of the FRP system is an iterative process. First, an estimate of the depth to the neutral axis, cest
is entered in Step 8.
Stress in the Reinforcing Steel and FRP
FRPpro™ FRP Design software calculates the FRP system effective strain, εfe
, the concrete strain, εc
, and the reinforcing steel strain, εs
Internal Force Resultants and Equilibrium Check
The software then calculates the steel stress, fs
and FRP stress, ffe
Adjust cest until Force Equilibrium is Satisfied
Next, the concrete strain, ε'c
corresponding to its compressive strength, f'c
, is calculated and used to find the ratio of the equivalent rectangular compressive stress block depth, β1
, and subsequently the ratio of average concrete stress, α1
. Force equilibrium is verified by checking the initial estimate of the depth to the neutral axis, c
Flexural Strength Components
If the value c
does not equal cest
, enter a different value as cest
in Step 8 or use the button to automate the iterative process:
When the button is pushed, FRPpro™ FRP Design software converges the values of c
to equality. The button does not appear on printed results.
Design Flexural Strength of the Section
FRPpro™ FRP Design software calculates the steel and FRP contributions to bending resistance. From the results shown here, you can begin to see the effect of the FRP strengthening addition to the design beam.
Reinforcing Steel Stress Check
The software indicates whether the nominal moment capacity, ΦMn
of the strengthened beam is greater or equal to the design factored moment, MU
. If this is true, the software displays, "OK" (without the quotes). If this is not true, the software displays, "DESIGN FAILS".
The strength reduction factor for reinforced concrete, Φ
, is calculated in accordance with ACI 318-08, figure R9.3.2 and based on the strain of the reinforcing steel found in Step 10. The recommended strength reduction factor for FRPs, Ψf
is taken as 0.85 (ACI 440.2R-08, section 10.2.10).
FRP Creep Rupture Limit Check
FRPpro™ FRP Design software calculates the stress in the reinforcing steel at the design service load moment, MS
. and compares that to the yield strength of the steel. ACI recommends that the reinforcing steel stress at the service load moment is less than 80 percent of the yield strength (ACI 440.2R-08, equation 10-14).
Tip: If the service load causes the stress in the reinforcing steel to exceed 80 percent of the yield stress, either:
1. Revise the FRP system; or,
2. Compute the deflection and crack width of the strengthened beam at the service load. If the deflection and crack width criteria meet the code requirements of ACI 318-08 then continue with the selected FRP strengthening system.
Summary of Results
FRPpro™ FRP Design software compares the service load stress level in the FRP system, ff,s
to the recommended "sustained plus cyclic service load (creep rupture) stress limits" based on the FRP system fiber type selected in Step 3. The limits recommended for each fiber type is shown below:
Sustained plus Cyclic Service Load (Creep Rupture) Stress Limits|
Creep Rupture Stress Limit2||0.55ffu||0.30ffu||0.20ffu||0.15ffu|
1"BasBar™ BFRP Design Guide", ReforceTech, AS, Royken, Norway, May 13, 2013, revision B. ReforceTech basalt bars only, 50-year design life.|
2ACI 440.2R-08, table 10.1 for Carbon, Aramid and Glass fiber-based FRPs.
™ FRP Design software provides two results tables. First, a summary of unstrengthened, strengthened and required moment resistance of the beam, and the strength reduction factors used in calculating the strengthened beam. Second, a summary of the input table entered in Step 4 is shown.
You have a FRP strengthened beam, documented with ACI recommended practices.
Still have Questions?|
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