Design of FRP Systems for Strengthening Concrete Girders in Shear (2011) / Chapter Skim
Currently Skimming:
Attachment B - Recommended Design Guidelines for Concrete Girders Strengthened in Shear with FRP
Attachment B - Recommended Design Guidelines for Concrete Girders Strengthened in Shear with FRP
Pages 59-120
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 59... ...
A T T A C H M E N T B Recommended Design Guidelines for Concrete Girders Strengthened in Shear with FRP
|
From page 60... ...
CB2 The proposed design guidelines were based on the traditional reinforced concrete (RC) design principles adopted by the current AASHTO LRFD Bridge Design Specifications and the knowledge on the mechanical behavior of FRP obtained from work performed under the NCHRP Project 12-75.
|
From page 61... ...
ICRI 03733: Guide for Selecting and Specifying Materials for Repairs of Concrete Surfaces NCHRP Report 609: Recommended Construction Specifications Process Control Manual for Repair and Retrofit of Concrete Structures Using Bonded FRP Composites Relevant specifications and guidelines provided by FRP manufacturers should also be carefully reviewed prior to th e design of any strengthening syste m. B3 STRENGTHENING SCHEMES FRP shear reinforcement is commonly attached to a beam , as shown in Figure B3.1 with (a)
|
From page 62... ...
Comprehensive guidelines in this regard are provided in NCHRP Report 609, Recommended Construction Specifications and Process Control Manual for Repair and Retrofit of Concrete Structures Using Bonded FRP Composites CB4.2 Bond behavior of the FRP system is highly dependent on a sound concrete substrate and can significantly influence the integrity of the FRP strengthening system. Proper preparation and profiling of the concrete substrate is necessary to achieve optimum bond strength.
|
From page 63... ...
and approximate locations in structure Batch numbers, mixture ratios, mixing times, and qualitative descriptions of the appearance of all mixed resins, including primers, putties, saturants, adhesives, and coatings mixed for the day Observations of progress of cure of resins Conformance with installation procedures Location and size of any delaminations or air voids General progress of work Level of curing of resin in accordance with ASTM D3418. Adhesion strength B5 MATERIAL PROPERTIES OF FRP The following mechanical properties should be obtained from manufacturers or coupon tests in accordance with ASTM D3039.
|
From page 64... ...
Therefore, following the current reinforced concrete design principals, the nominal shear resistance ( nV ) is determined by adding the contribution of the FRP reinforcement to the contributions from concrete and internal transverse steel reinforcement: n c s fV V V V (B6-1)
|
From page 65... ...
where .670.066 3( ) 1.0f f fR E The effective strain, fe , is largely dependent on the failure modes as discussed in Appendix A - Sections A3 and A4.
|
From page 66... ...
B.7.2.3 Maximum Spacing of FRP Shear Reinforcement The clear spacing between externally bonded FRP shear reinforcement shall not exceed the maximum permitted spacing ( maxs ) in accordance with the current AASHTO LRFD Bridge Design Specifications, expressed as: If '0.125 thenu cv f max 0.8 24in.vs d (AASHTO 5.8.2.7-1)
|
From page 67... ...
67 The following six design examples are presented to illustrate use of the recommended guidelines: Example 1-1: RC T-beam without internal transverse steel reinforcement strengthened with FRP in U-wrap configuration without anchorage systems Example 1-2: RC T-beam without internal transverse steel reinforcement strengthened with FRP in U-wrap configuration with an anchorage system Example 2-1: RC T-beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration without anchorage systems Example 2-2: RC T-Beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration with an anchorage system Example 3-1: PC I-Beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration without anchorage systems Example 3-2: PC I-Beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration with an anchorage system A P P E N D I X Design Examples
|
From page 68... ...
The T-beams contain no transverse steel reinforcement. Additional details of the T-beam are provided in Figures 1 and 2.
|
From page 69... ...
Thickness tf := 0.0065 in. Failure strength ffu := 550 ksi Modulus of elasticity Ef := 33000 ksi Failure strain εfu ffu Ef := εfu = 0.017 in/in 3.
|
From page 70... ...
θ := 45 deg β := 2 The nominal shear resistance provided by the concrete, V c , is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: Assuming rectangular section behavior with no compression steel, the distance from the extreme compression fiber to the neutral axis, cc, may be calculated as: c c1 := A s ⋅fy 0.85⋅f' c ⋅b eff⋅β1 c c1 = 9.6 in.
|
From page 71... ...
v c := 0.0316⋅β⋅ f' c ⋅b v ⋅d v (vc) = 58 kips v s := 0 The nominal shear resistance provided by the internal steel reinforcement is:
|
From page 72... ...
Check_FRP_Needed := "NOT need shear reinforcement" if φ V n ≥ V u_crit⋅ "NEED shear reinforcement" otherwise Check_FRP_Needed = "NEED shear reinforcement" 5.2 Computation of Required Vf Vf_req := V u_crit φ − Vn Vf_req = 53.1 kips 5.3 Selection of FRP Strengthening Scheme U-wrap configuration is used without anchorage systems at the end of the sheets. The FRP sheets will be applied at 90 degree with respect to the longitudinal axis of the girder as shown in Figure 3.
|
From page 73... ...
αf := 90 degOrientation of FRP sheets Effective depth of FRP sheets df := d – hf Check if the selected spacing is acceptable or not Shear stress on concrete is: (LRFD Eqn.
|
From page 74... ...
Vf( ) 53.5 kips= Vf_check1 := "Change FRP Strengthening Scheme" if (Vf < Vf_req)
|
From page 75... ...
The FRP sheets are applied at 90 degrees with respect to the longitudinal axis of the member with the U-wrap configuration and without anchorage systems as shown in Figure 4. The final design is summarized as: Use number of plies of FRP sheets Use the width of FRP sheets Use the center-to-center spacing of FRP sheets sf = 15 in.
|
From page 76... ...
The T-beams contain no transverse steel reinforcement. Additional details of the T-beam are provided in Figures 1 and 2.
|
From page 77... ...
Thickness tf := 0.0065 in. Failure strength ffu := 550 ksi Modulus of elasticity Ef := 33000 ksi Failure strain εfu ffu Ef := εfu = 0.017 in/in 3.
|
From page 78... ...
(β := 2) The nominal shear resistance provided by the concrete, V c , is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: Assuming rectangular section behavior with no compression steel, the distance from the extreme compression fiber to the neutral axis, c c , may be calculated as: c c1 := A s ⋅fy 0.85⋅f' c ⋅b eff⋅β1 (cc1)
|
From page 79... ...
(V c ) = 58 kips The nominal shear resistance provided by the internal steel reinforcement is: V s := 0
|
From page 80... ...
DESIGN OF FRP SHEAR REINFORCEMENT 5.1 Check if FRP Reinforcement is Necessary or Not Strength reduction factor for shear (φ := 0.9) Check_FRP_Needed := "NOT need shear reinforcement" if φ⋅V n ≥ V u_crit "NEED shear reinforcement" otherwise Check_FRP_Needed = "NEED shear reinforcement" 5.2 Computation of Required Vf Vf_req := V u_crit φ Vn− Vf_req = 53.1 kips 5.3 Selection of FRP Strengthening Scheme U-wrap configuration is used with anchorage systems at the end of the sheets.
|
From page 81... ...
Orientation of FRP sheets αf := 90 deg Effective depth of FRP sheets df := d − hf df = 25.7 in. Check if the selected spacing is acceptable or not Shear stress on concrete is: v u V u_crit − φ⋅Vp φ⋅b v ⋅d v := (LRFD Eqn.
|
From page 82... ...
(Vf) = 56.1 kips Vf_check1 := "Change FRP Strengthening Scheme" if (Vf < Vf_req)
|
From page 83... ...
In addition, an anchorage system is installed. The final design is summarized as: Use number of plies of FRP sheets Use the width of FRP sheets wf = 5.5 in.
|
From page 84... ...
The T-beams contain transverse steel reinforcement spaced at 12 inches on center. Additional details of the T-beam are provided in Figures 1 and 2.
|
From page 85... ...
Longitudinal Reinforcement Yield strength fy := 60 ksi Modulus of elasticity E s := 29000 ksi 2.3. Internal Steel Shear Reinforcement Yield strength fyt := 60 ksi 2.4.
|
From page 86... ...
(β := 2) The nominal shear resistance provided by the concrete, V c , is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: Assuming rectangular section behavior with no compression steel, the distance from the extreme compression fiber to the neutral axis, c c , may be calculated as: c c1 := c c1( )
|
From page 87... ...
(dv3 := 0.72⋅hT) The nominal shear resistance provided by the internal steel reinforcement is: V s := A v ⋅fyt⋅dv⋅(cot(θ)
|
From page 88... ...
DESIGN OF FRP SHEAR REINFORCEMENT 5.1 Check if FRP Reinforcement is Necessary or Not Strength reduction factor for shear (φ := 0.9) Check_FRP_Needed := "NOT need shear reinforcement" if φ V n ≥ V u_crit⋅ "NEED shear reinforcement" otherwise Check_FRP_Needed = "NEED shear reinforcement" 5.2 Computation of Required Vf Vf_req := V u_crit φ − Vn Vf_req = 43 kips 5.3 Selection of FRP Strengthening Scheme U-wrap configuration is used with anchorage systems at the end of the sheets.
|
From page 89... ...
αf := 90 degOrientation of FRP sheets Effective depth of FRP sheets df := d – hf Check if the selected spacing is acceptable Shear stress on concrete is: (LRFD Eqn.
|
From page 90... ...
Vf( ) 44.1 kips= Vf_check1 := "Change FRP Strengthening Scheme" if (Vf < Vf_req)
|
From page 91... ...
Use number of plies of FRP sheets Use the width of FRP sheets Use the center-to-center spacing of FRP sheets sf = 12 in.
|
From page 92... ...
The T-beams contain transverse steel reinforcement spaced at 12 inches on center. Additional details of the T-beam are provided in Figures 1 and 2.
|
From page 93... ...
Longitudinal Reinforcement Yield strength fy := 60 ksi Modulus of elasticity E s := 29000 ksi 2.3. Internal Steel Shear Reinforcement Yield strength fyt := 60 ksi 2.4.
|
From page 94... ...
(β := 2) The nominal shear resistance provided by the concrete, V c , is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: Assuming rectangular section behavior with no compression steel, the distance from the extreme compression fiber to the neutral axis, c c , may be calculated as: c c1 := c c1( )
|
From page 95... ...
(dv3 := 0.72⋅hT) The nominal shear resistance provided by the internal steel reinforcement is: V s := A v ⋅fyt⋅dv⋅(cot(θ)
|
From page 96... ...
DESIGN OF FRP SHEAR REINFORCEMENT 5.1 Check if FRP Reinforcement is Necessary or Not Strength reduction factor for shear (φ := 0.9) Check_FRP_Needed := "NOT need shear reinforcement" if φ V n ≥ V u_crit⋅ "NEED shear reinforcement" otherwise Check_FRP_Needed = "NEED shear reinforcement" 5.2 Computation of Required Vf Vf_req := V u_crit φ − Vn Vf_req = 43 kips 5.3 Selection of FRP Strengthening Scheme U-wrap configuration is used with anchorage systems at the end of the sheets.
|
From page 97... ...
αf := 90 degOrientation of FRP sheets Effective depth of FRP sheets df := d – hf Check if the selected spacing is acceptable or not Shear stress on concrete is: (LRFD Eqn.
|
From page 98... ...
Vf( ) 45.9 kips= Vf_check1 := "Change FRP Strengthening Scheme" if (Vf < Vf_req)
|
From page 99... ...
Use number of plies of FRP sheets Use the width of FRP sheets Use the center-to-center spacing of FRP sheets sf = 16 in.
|
From page 100... ...
The bridge consists of five simply supported pretensioned I-beams spanning 42 feet and spaced at 7.5 feet on center. The I-beams are lightly reinforced with transverse steel reinforcement.
|
From page 101... ...
MATERIAL PROPERTIES 2.1. Concrete 2.1.1 Deck 2.1.1 I-Beam E cd = 3834 ksi Compressive strength f' cd := 4.0 ksi Modulus of elasticity E cd := 33⋅(1.5)
|
From page 102... ...
Total Area of the 14 strands Aps := 2.142 in.2 k := 0.28 for low-relaxation steel Yield strength fpy := 243 ksi Modulus of elasticity Eps := 28500 ksi 2.3. Internal Steel Shear Reinforcement Yield strength fyt := 60 ksi 2.4.
|
From page 103... ...
(b) Cross-Section of an Intermediate Beam Figure 2.
|
From page 104... ...
Calculation of Nominal Shear Resistance For this example, the simplified approach is followed. The nominal shear resistance provided by the concrete, V c , is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: The distance from the extreme compression fiber to the center of gravity of the strands at the midspan: Assuming rectangular section behavior with no compression steel, the distance from the extreme compression fiber to the neutral axis, cc , may be calculated as: a c := β1d⋅cc V u_crit := 100 kips dp := 34.6 in.
|
From page 105... ...
Calculate the distance from the extreme compression face to the center of gravity of the strand, de at the location, d v away from the centerline of the support. etr := 2⋅4 + 4⋅4 + 23 206.4 206.4 d v_trial− + 2 ⋅2 + 23 206.4 206.4 d v_trial− + 4 ⋅2 + 23 206.4 206.4 d v_trial−( )
|
From page 106... ...
DESIGN OF FRP SHEAR REINFORCEMENT 5.1 Check if FRP Reinforcement is Necessary or Not Strength reduction factor for shear (φ := 0.9) Check_FRP_Needed := "NOT need shear reinforcement" if φ V n ≥ V u_crit⋅ "NEED shear reinforcement" otherwise Check_FRP_Needed = "NEED shear reinforcement" 5.2 Computation of Required Vf Vf_req := V u_crit φ − Vn Vf_req = 33.8 kips
|
From page 107... ...
Use number of plies of FRP sheets nf := 1 Use the width of FRP sheets wf := 8 in.
|
From page 108... ...
= 1.238 × 10−3 Vf_check1 := "Change FRP Strengthening Scheme" if (Vf < Vf_req) "Provided FRP Strength Large Enough" otherwise Vf_check1 = "Provided FRP Strength Large Enough" Check_Spacing := "Acceptable" if sf ≤ smax "NOT_Acceptable_Change_the_Spacing" otherwise Check_Spacing = "Acceptable"
|
From page 109... ...
The final design is summarized as: Use number of plies of FRP sheets Use the width of FRP sheets Use the center-to-center spacing of FRP sheets sf = 12 in.
|
From page 110... ...
110 Figure 4. Final design of FRP strengthening.
|
From page 111... ...
The bridge consists of five simply supported prestensioned I-beams spanning 42 feet and spaced at 7.5 feet on center. The I-beams are lightly reinforced with transverse steel reinforcement.
|
From page 112... ...
β1b := 0.85 if f'cb ≤ 4 0.65 if f' cb ≥ 8 0.85 − 0.05⋅ otherwise β1b = 0.7 2.1.1 I-Beam Compressive strength f' cb := 7.0 ksi 2.2. Prestressing Strands Specified tensile strength fpu := 270 ksi Yield strength fpy := 243 ksi Modulus of elasticity Eps := 28500 ksi Diameter = 0.5 in.
|
From page 113... ...
Failure strength ffu := 550 ksi Modulus of elasticity Ef := 33000 ksi Failure strain εfu := ffu Ef εfu = 0.017 in./in.
|
From page 114... ...
Calculation of Nominal Shear Resistance For this example, the simplified approach is followed. The nominal shear resistance provided by the concrete, V c , is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: The distance from the extreme compression fiber to the center of gravity of the strands at the midspan: V u_crit := 100 kips dp := 34.6 in.
|
From page 115... ...
= 2.11 in. The effective shear depth d v is taken as the distance, measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure; it need not be taken to be less than the greater of 0.9d e or 0.72h (LRFD Article5.8.2.9)
|
From page 116... ...
5.8.3.3-3) The nominal shear resistance provided by the internal steel reinforcement is: V s := A v ⋅fyt⋅dv⋅(cot(θ)
|
From page 117... ...
FRP strengthening scheme. Use number of plies of FRP sheets nf := 1 Use the width of FRP sheets wf := 4 in.
|
From page 118... ...
if vu < 0.125⋅f'cb min(0.4⋅dv, 12) otherwise s max = 21.9 Check_Spacing := "Acceptable" if sf ≤ smax "NOT_Acceptable_Change_the_Spacing" otherwise Check_Spacing = "Acceptable" 5.4 Calculation of Shear Resistance of FRP, Vf The FRP reinforcement ratio is: ρf := 2⋅nf⋅wf⋅tf b v ⋅sf (Attachment A Eqn.
|
From page 119... ...
Vf( ) 36.1 kips= Vf_check1 := "Change FRP Strengthening Scheme" if (Vf < Vf_req)
|
From page 120... ...
Final design of FRP strengthening. Use number of plies of FRP sheets Use the width of FRP sheets Use the center-to-center spacing of FRP sheets sf = 12 in.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.