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From page 75... ... These examples cover the five sections of the proposed Guide Specification. Example 1: Calculation of the characteristic value of the strength of an FRP reinforcement system Example 2: Flexural strengthening of a T-beam in an unstressed condition Example 3: Flexural strengthening of a T-beam in a stressed condition Example 4: Shear strengthening of a T-beam using U-jacket FRP reinforcement Example 5: Shear strengthening of a rectangular beam using complete wrapping FRP reinforcing system Example 6: Strengthening of an axially loaded circular column. Read the entire page →
From page 76... ... Results are given in Table B1. It is also required to establish the linear load-strain relationship for use in the design following the recommended Guide Specifications. Read the entire page →
From page 77... ... B-2 Step 1: Examine the data set to find out if there is any outlier. To do so, the Maximum Normed Residual outlined in ASTM D7290 Standard Practice will be used. Read the entire page →
From page 78... ... B-3 inkipsx /09.2 16 22.221.2....95.187.1 inkips x s i i /092.0) Read the entire page →
From page 79... ... at 1% strain s xxi 5 15 1 3 7 10 4 9 11 8 13 6 12 2 14 16 1.87 1.95 2.00 2.01 2.08 2.09 2.1 2.1 2.1 2.12 2.12 2.14 2.14 2.17 2.21 2.22 2.39 1.52 0.98 0.87 0.11 0.00 0.11 0.11 0.11 0.33 0.33 0.54 0.54 0.87 1.30 1.41 Step 4 The sample size is greater than 10 and the coefficient of variation 15.0044.0 09.2 092.0COV , the composite material strength data meet the requirements of Article 1.4.3 of the Guide Specifications. Step 5 : Estimate the parameters of the two-parameter Weibull distribution from the following equations (See Commentary C1.4 of the Guide Specifications) Read the entire page →
From page 80... ... 0.1054 1.96 /x u kips in Step 7: Establish the FRP reinforcement strength-strain design relationship as shown in B-1. Strain Lo ad /u n it w id th 0.01 1.96 kip/in. Read the entire page →
From page 81... ... Reinforcing steel yield strength: 40yf ksi Girder dimensions and Steel Reinforcement: See Figure B.2 FRP reinforcement: Shop-fabricated carbon fiber/Epoxy composite plates Plate thickness, 0.039t Glass Transition Temperature: 165ogT F Tensile strain in the FRP reinforcement at failure: 0.013tufrp Tensile strength in the FRP reinforcement at 1% strain: 9.3 /frpP kips in Shear modulus of the adhesive = 185 ksi Structural Analysis Results under the New Loading For Strength I Load Combination: ftkipM D 239 and ftkipM IL 615 . For Fatigue Limit State: ftkipM IL 308 Special Notes Hydraulic jacking procedure of the bridge will be used so that strengthening is carried out in an unstressed condition. Read the entire page →
From page 82... ... B-7 24.5" 6" 7'-2" 7'-2" 18" Detail A # 4 8#11 Bundled 2" cover 18" Figure B-2 Bridge cross section at mid-span Read the entire page →
From page 83... ... Step 2: Establish the linear stress-strain relationship of the FRP reinforcement based on the design assumptions specified in Article 3.2 of the Guide and compute the tensile strength corresponding to a strain value of 0.005. Results are presented in Figure B.3 ./65.4) Read the entire page →
From page 84... ... 12) (39( 4 ins inbt inl Minimumb ws e e .86 inbe Assumptions: A rectangular stress block to represent the distribution of concrete compression stresses (Article 5.7.2.2 of AASHTO LRFD Bridge Design Specifications) Read the entire page →
From page 85... ... The nominal flexural strength of the girder can then be computed from .837,12 2 75.159.264048.12 2 inkipadfAM ysn Read the entire page →
From page 86... ... The factored moment for Strength I limit state is .500,16375,1) 615(75.123925.175.125.1 inkipftkipMMM ILDu For a preliminary estimate of the amount of FRP reinforcement necessary to resist 1,375 k-ft of moment, the following approximate design equation can be used: infunre orced u n FRP M MT h kipsTfrp 1625.30 12963375,1 frpbfrp bnNT Where n is the number of FRP reinforcement plates. Read the entire page →
From page 87... ... (86) 992.5c c eC f cb kips Tension Force in the tension steel: Strain in the steel: 001379.0 000,29 4000418.000122.0 6 659.26 E f c cd y ycs Figure B-7 Strain and stress diagrams for the reinforced concrete T-beam externally reinforced with bonded carbon fiber FRP reinforcement Read the entire page →
From page 88... ... 16,500 . r M kip in kip in Increase the width of the FRP reinforcement to 17 .frpb in and re-compute the flexural resistance rM . Read the entire page →
From page 89... ... cy y c y frp s y ys fA k2c frpT cC d ' 2 (0.9 ) av cf f Figure B-8 Strain and stress distribution in the T-beam when tension steel reinforcement yield By satisfying the conditions of force equilibrium and strain compatibility, the strain in the FRP reinforcement when the steel tensile reinforcement yields can be found numerically to be 0.0016yfrp . Read the entire page →
From page 90... ... B-10 FRP reinforcement Detail Step 8: Check fatigue load combination limit state For the fatigue load combination: .772,2231) 308(75.075.0 inkipftkipM IL Determine the cracking moment: t g rcr y IfM with ksiff cr 474.09.324.024.0 ' Section Properties: 4096,78 inI g inyt 4.20 78,096(0.474) Read the entire page →
From page 91... ... B-16 Neglect the concrete part in tension and calculate the moment of inertia of an equivalent transformed FRP section: From the FRP reinforcement load-strain data: / 4.65 / (0.039) 23,850 0.005 frp b frp frp frp frp f N t E ksi Modular ratio for the concrete: 3,594 0.15 23,850 c c frp E n E Modular ratio of the steel: 29,000 1.2 23,850 s s frp E n E Based on the modular ratios for the concrete and for the steel, an equivalent FRP transformed section is constructed as shown below with the neutral axis assumed to lie in the flange. Read the entire page →
From page 92... ... 2 2 2 frp s frp s s c e w s c w frp s s c e w s c w nt t zA h n A d n b b t n b z A n A n b b t n b z z 2 2 ( ) 2 ( 2 2 0 frp s frp s s c e w s frp s s c e w s c w c w nt tA h n A d n b b tA n A n b b t z z n b n b By substituting all parameters into the above equation, the following equation is obtained 2 57.9 476.4 0z z Which has a positive solution 7.31 .z in The moment of inertia of the equivalent transformed FRP section can be computed to be 48,345 .TI in Strain in the concrete, steel reinforcement, and FRP reinforcement, respectively, due to the fatigue load combination: '(231) Read the entire page →
From page 93... ... 0.117(1.5) 0.740 0.065 3.9 0.128 23,850 0.125peel f ksi ksi Provide mechanical anchors at the FRP reinforcement ends. Read the entire page →
From page 94... ... SOLUTION Step 1: Determine if the FRP reinforcement material is in compliance with Section 2 of the Guide Specification and be sure that the glass transition temperature is higher than the maximum design temperature plus 40oF. Based upon the location of the bridge (State of Georgia) Read the entire page →
From page 95... ... (30.5 6.82) 1.41 48,104 D N bo cr M h y ksi I At the time of installing the externally bonded FRP reinforcement, the dead load initial strain at the bottom surface is: 1.41 0.00039 3,594 bo bo cE Read the entire page →
From page 96... ... 4.28 / . 0.01 N kip in To estimate the amount of FRP reinforcement necessary to resist 1,375 k-ft of moment, the following approximate design equation can be used: infunre orced u n frp M MT h kipsTfrp 1625.30 ) Read the entire page →
From page 97... ... Reinforcing steel yield strength: 40yf ksi Girder dimensions and Steel Reinforcement: See Figure B-12 FRP reinforcement: Shop-fabricated carbon fiber/Epoxy composite plates Plate thickness, 0.039t Glass Transition Temperature: 165ogT F Tensile strain in the FRP reinforcement at failure: 0.013tufrp Tensile strength in the FRP reinforcement at 1% strain: 9.3 /frpP kips in kipsVD 24 , kipsV IL 61 Read the entire page →
From page 98... ... B-23 Figure B-12 Beam geometry and reinforcement SOLUTION Step 1: Calculate Nominal Shear Strength of Reinforced Concrete T-beam In accordance with Article 5.8.2.9 of the AASHTO LRFD Bridge Design Specifications (2007) The effective web width: 18 .vb in The effective shear depth: h d D Maximumd e CT v c 72.0 9.0 & cCTD & = Distance between the resultants of the tensile and compressive forces due to flexure ed = Effective depth from extreme compression fiber to the centroid of the tensile force in the tensile reinforcement -- Article 5.7.3.3.1 of AASHTO (2007) Read the entire page →
From page 99... ... Because the minimum transverse reinforcement requirement of Article 5.8.2.5 of AASHTO (2007) is met and the girder is neither prestressed nor axially loaded, the values of and can be determined by the simplified procedures of Article 5.8.3.4.1 of the AASHTO LRFD Bridge Design Specifications (AASHTO, 2007) Read the entire page →
From page 100... ... (25.72) 0 451.4 c s p n c v v p V V V kips V Minimum f b d V kips 92.08nV kips Step 2: Estimate the amount of FRP reinforcement needed to increase the shear strength to 156 kips kipsVVV ILDu 1376175.12425.175.125.1 137 (0.9) Read the entire page →
From page 101... ... In either case, intermittent or continuous reinforcement, the nominal shear strength provided by the externally bonded FRP shear reinforcement shall satisfy Article 4.3.5 stipulating, frpwcfrps dbfVV '8 kipsdbfV frpwcfrp 967,6) 5.24(189.38834 ' kipsV frp 933,634967,6 In both cases, the provision of Article 4.3.5 of the Guide is satisfied. Read the entire page →
From page 102... ... Type: Reinforced concrete Concrete compression Strength: ksifc 9.3' Reinforcing steel yield strength: 60yf ksi P Read the entire page →
From page 103... ... at a strain of 0.01. SOLUTION Step 1: Calculate nominal shear strength of the reinforced concrete member and Check compliance with Article 1.4.4 of the proposed Guide Specifications In accordance with Article 5.8.2.9 of the AASHTO LRFD Bridge Design Specifications (2007) Read the entire page →
From page 104... ... Because the minimum transverse reinforcement requirement of Article 5.8.2.5 of AASHTO (2007) is met and the girder is neither prestressed nor axially loaded, the values of and can be determined by the simplified procedures of Article 5.8.3.4.1 of the AASHTO LRFD Bridge Design Specifications (AASHTO, 2007) Read the entire page →
From page 105... ... Thus, proceed with strengthening using externally bonded FRP shear reinforcement wrapped around the member. Step 2: Estimate the amount of FRP reinforcement needed to increase the shear strength to 156 kips kipsVVV ILDu 275) Read the entire page →
From page 106... ... B-31 117.2 4,268frpV kips kips The provision of Article 4.3.5 of the Guide is satisfied. Calculate the factored shear resistance 0.9 35.2 187.2 0.65(117.2) Read the entire page →
From page 107... ... FRP reinforcement: Field-fabricated carbon fiber/Epoxy composites Dry fabric weight: 9 oz/yd2 Glass Transition Temperature: 165ogT F Thickness of a single layer after curing: 0.0397 .in Tensile strength of a single layer FRP reinforcement at 1% strain: 3.8 / .frpP kips in 42 " 16 # 8 Bars # 3 ties at 12 in. spacing 2" Figure B-14 Reinforcement details of a circular column Read the entire page →
From page 108... ... 3,255 r nP P kips Step 2: Compute the FRP reinforcement strength at a strain of 0.004. Read the entire page →
From page 109... ... Accordingly, the column axial strength is computed as follows: ksi k fksi D Nf e cfrp frpl 33.11 1 2 611.0 42 ) Read the entire page →

From page 75...

... These examples cover the five sections of the proposed Guide Specification. Example 1: Calculation of the characteristic value of the strength of an FRP reinforcement system Example 2: Flexural strengthening of a T-beam in an unstressed condition Example 3: Flexural strengthening of a T-beam in a stressed condition Example 4: Shear strengthening of a T-beam using U-jacket FRP reinforcement Example 5: Shear strengthening of a rectangular beam using complete wrapping FRP reinforcing system Example 6: Strengthening of an axially loaded circular column.