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Simplicity in application 2. Compatibility with tests of Dregions 3. Consistency with other sections of ACI 318 andor AASHTO LRFD 4. Compatibility with other codes or design recommendations STM provisions (with m < 2) calibrated for rectangular beams are also accurate when applied to invertedT beam design → Proposed 3dimensional model provides accurate results for invertedT beams
DEVELOPMENTS IN STRUT-AND-TIE METHOD AASHTO T-10 UPDATE OGUZHAN BAYRAK, Ph.D., P.E Ferguson Structural Engineering Laboratory The University of Texas at Austin April 21, 2015 UNIVERSITY OF TEXAS STRUT-AND-TIE MODELING RESEARCH Brown et al (2002-2006) Birrcher et al (2006-2009) Williams et al (2009-2012) Larson et al (2009-2013) Design for Shear Using STM Strength and Serviceability Design of Deep Beams Using STM STM Guidebook with Design Examples Strength and Serviceability Design of Inverted-T Beams Using STM DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING UNIVERSITY OF TEXAS STRUT-AND-TIE MODELING RESEARCH Ph.D., MS, 21 Undergraduates Brown et al (2002-2006) Birrcher et al (2006-2009) David Birrcher, PhD Michael Brown, PhD Rob Tuchscherer, PhD Ivan Ornelas, MS Cameron Sankovich, MS Matt Huizinga, MS Mike McCarthy, BS Kyle Stueck, BS Gary Lehman, BS Annika Trevino, BS Thomas Stablon, BS Mike Ziemenski, BS Brian Schnittker, BS Erin O’Malley, BS Patrick Harkin, BS James Kleineck, BS James Plantes, BS Ryan Kalina, BS David Wald, BS Carlos Jordan, BS DR OGUZHAN BAYRAK Williams et al (2009-2012) Larson et al (2009-2013) Chris Williams, MS Dean Deschenes, MS Nancy Larson, PhD Eulalio Fernández, PhD David Garber, MS Michelle Wilkinson, BS Laura Chimelski, BS Daniel Bejarano, BS Allison Lehman, BS Michael Weyenberg, BS Michael Carrell, BS Alexander Peña, BS DEVELOPMENTS IN STRUT-AND-TIE MODELING DEEP BEAM EXPERIMENTAL WORK DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING DEEP BEAM EXPERIMENTAL WORK U of Texas Research A total of 37 deep beam tests DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING Previous Research that led to Code Development in = 25.4 mm DEVELOPMENT OF STRUT-AND-TIE PROVISIONS Experimental Program (37 Tests) Filtering Evaluation Deep Beam Evaluation Database STM Provisions Literature Review DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING DEEP BEAM DATABASE: ASSEMBLY AND FILTERING Stage filtering Collection Database 905 tests - incomplete plate size information - 284 tests - subjected to uniform loads - tests - stub column failure - tests - f ′c < 2,000 psi - tests Stage filtering Filtered Database 607 tests - bw < 4.5 in - 222 tests - bwd < 100 in.2 - 73 tests - d < 12 in - 13 tests - ∑ρ┴ < 0.001 - 120 tests Evaluation Database 179 tests Representative of deep beams in the field psi = 0.00689 MPa DR OGUZHAN BAYRAK in = 25.4 mm DEVELOPMENTS IN STRUT-AND-TIE MODELING STRESS CHECKS PERFORMED (1) (2) (3) (4) CCC Back Face CCT Back Face CCC Bearing Face CCT Bearing Face (5) CCC Strut-to-Node Interface (6) CCT Strut-to-Node Interface (7) Tie Reinforcement (3) CCC Node (1) (5) (6) (2) (7) CCT Node (4) DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING NODAL STRESS CHECKS ϕ𝐹𝑛 > 𝐹𝑢 lb where Bearing Face Back Face ϕ𝐹𝑛 = ϕ · 𝑓𝑐𝑢 · 𝐴𝑐𝑛 a θ 𝑓𝑐𝑢 = 𝑚 · 𝜈 · 𝑓 ′ 𝑐 lbsinθ ws Strut-to-Node Interface acosθ DR OGUZHAN BAYRAK ν = nodal efficiency factor m = confinement modification factor DEVELOPMENTS IN STRUT-AND-TIE MODELING NODAL EFFICIENCY FACTORS: ACI 318 AND AASHTO LRFD* CCC Node CCT Node CTT Node * DR OGUZHAN BAYRAK ν ACI 318 AASHTO LRFD Back Face 0.85 0.85 Bearing Face 0.85 0.85 Strut-to-Node Interface 0.64 when ρ > ρmin Back Face 0.68 0.75 Bearing Face 0.68 0.75 Strut-to-Node Interface 0.64 when ρ > ρmin Back Face 0.51 0.65 Bearing Face 0.51 0.65 Strut-to-Node Interface 0.64 when ρ > ρmin 0.51 when ρ < ρ 0.85 0.51 when ρ < ρ 0.51 when ρ < ρ Reduction factors are not considered for clarity (φ = 1) DEVELOPMENTS IN STRUT-AND-TIE MODELING 10 DEVELOPMENT OF RECOMMENDED STM PROVISIONS Provisions Should Satisfy the Following Criteria (MacGregor, 2002) Simplicity in application Compatibility with tests of D-regions Consistency with other sections of ACI 318 and/or AASHTO LRFD Compatibility with other codes or design recommendations fib (1999) was key in providing guidance for the recommended provisions DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 19 DATABASE EVALUATION: fib (1999) VS RECOMMENDED PROVISIONS fib (1999) STM Conservative No Tests 80 100 N = 179 No Unconservative = Min = 0.76 Max = 2.82 Mean = 1.55 60 40 2.8% Unconservative COV = 0.25 20 Conservative 80 No Tests 100 PROPOSED STM PROVISIONS N = 179 No Unconservative = Min = 0.73 Max = 4.14 Mean = 1.54 60 40 0.6% Unconservative COV = 0.28 20 0 Experimental/Calculated DR OGUZHAN BAYRAK 12 10 11 Experimental/Calculated DEVELOPMENTS IN STRUT-AND-TIE MODELING 20 CHANGE LIMIT OF NODAL ZONE CONFINEMENT FACTOR BASED ON fib (1999) CONFINEMENT MODIFICATION FACTOR: 45 deg 𝑚= 𝐴2 𝐴 45 deg Loaded Area A1 45 deg Loaded Area A1 A2 is measured on this plane Plan Elevation The confinement modification factor, m, can be applied to all faces of the nodal region DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 21 DATABASE EVALUATION N = 179 tests Design Provision Average No Unconservative Experimental/Calculated % Unconservative† COV†† ACI 318 STM 1.79 1.7% 0.58 AASHTO LRFD 2.21 3.4% 0.69 fib (1999) 1.55 2.8% 0.25 PROPOSED (with m < 4) 1.51 0.6% 0.22 † “Unconservative” = Exper mental/Calculated Value < 1.0 †† COV = Coefficient of Variation = Standard Deviation/Mean DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 22 STM APPLIES TO MORE THAN DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 23 INVERTED-T STRADDLE BENT CAP Ledge DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 24 INVERTED-T EXPERIMENTAL WORK DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 25 INVERTED-T EXPERIMENTAL WORK Present Study Previous Research that led to Code Development A total of 33 inverted-T beam tests DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING in = 25.4 mm 26 APPLICATION OF STM TO INVERTED-T BEAMS 3-Dimensional STM Longitudinal STM Cross-Sectional STM DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 27 APPLICATION OF STM TO INVERTED-T BEAMS Hanger Tie P/2 Hanger Reinforcement P/2 Ledge Reinforcement Ledge Tie Diagonal Strut Cross-Sectional STM Diagonal Strut 45 Load Spread 2.50d 1.85d Longitudinal STM DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 28 INVERTED-T DATABASE 118 in Graf & Brenner (1943) In-Service In-Service In-Service Current Study Leonhardt & Furlong & Walther (1966) Ferguson (1971) In-Service Furlong & Ferguson (1971) Cusens & Besser (1985) In-Service Shütt (1956) Zhu et al (2003) Current Study Current Study Galal & Fereig & Sekar (2008) Smith (1977) Fereig & Furlong & Furlong & Furlong & Smith (1977) Ferguson (1971) Mirza (1974) Mirza (1974) Taylor (1960) DR OGUZHAN BAYRAK Tan, et al (1997) 12 in Fereig & Fereig & Fereig & Fereig & Smith (1977) Smith (1977) Smith (1977) Smith (1977) Ferguson (1956) DEVELOPMENTS IN STRUT-AND-TIE MODELING in = 25.4 mm 29 EVALUATION OF STRUT-AND-TIE PROVISIONS FOR INVERTED-T BEAMS Experimental Program (33 Tests) Filtering Inverted-T Beam Evaluation Database Evaluation Literature Review DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING Check Accuracy of Deep Beam STM Provisions 30 INVERTED-T DATABASE: ASSEMBLY AND FILTERING Stage filtering Collection Database - Stage filtering Filtered Database - specimen did not fail incomplete plate size information no shear reinforcement complicated supports/geometry/reinforcement h /b w > - b w < 4.5 in - tension- and compression-chord loaded - torsional loads Inverted-T Database 130 tests - 10 tests - 10 tests - tests - 19 tests 89 tests - 11 tests - tests - tests - 27 tests 33 tests Representative of inverted-T beams in the field (ALL from present study) in = 25.4 mm DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 31 DATABASE EVALUATION Inverted-T Beams (33 tests) Rectangular Deep Beams (179 tests) Minimum 1.05 0.73 Maximum 2.17 4.14 Mean 1.50 1.54 † 0.0% 0.6% Standard Deviation 0.33 0.43 0.22 0.28 % Unconservative †† Coefficient of Variation † “Unconservative” = Exper mental/Calculated Value < 1.0 †† Coefficient of Variation = Standard Deviation/Mean → STM provisions (with m < 2) calibrated for rectangular beams are also accurate when applied to inverted-T beam design → Proposed 3-dimensional model provides accurate results for inverted-T beams DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT-AND-TIE MODELING 32 QUESTIONS [...]... Coefficient of Variation = Standard Deviation/Mean DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 22 STM APPLIES TO MORE THAN DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 23 INVERTED-T STRADDLE BENT CAP Ledge DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 24 INVERTED-T EXPERIMENTAL WORK DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 25 INVERTED-T EXPERIMENTAL WORK... Development A total of 33 inverted-T beam tests DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 1 in = 25.4 mm 26 APPLICATION OF STM TO INVERTED-T BEAMS 3-Dimensional STM Longitudinal STM Cross-Sectional STM DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 27 APPLICATION OF STM TO INVERTED-T BEAMS Hanger Tie P/2 Hanger Reinforcement P/2 Ledge Reinforcement Ledge Tie Diagonal Strut Cross-Sectional... (1997) 12 in Fereig & Fereig & Fereig & Fereig & Smith (1977) Smith (1977) Smith (1977) Smith (1977) Ferguson (1956) DEVELOPMENTS IN STRUT- AND- TIE MODELING 1 in = 25.4 mm 29 EVALUATION OF STRUT- AND- TIE PROVISIONS FOR INVERTED-T BEAMS Experimental Program (33 Tests) Filtering Inverted-T Beam Evaluation Database Evaluation Literature Review DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING Check... the nodal region DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 13 RECOMMENDED STM PROVISIONS: PERFORM STRUT CHECK AT NODE INTERFACE Critical stresses exist at nodal regions DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 14 RECOMMENDED STM PROVISIONS: BACK FACE CHECK Bond Stress DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 15 RECOMMENDED STM PROVISIONS: NODAL EFFICIENCY... 0.75 0.70 Bearing Face 0.68 0.75 0.70 Strut- to-Node Interface 0.64 when ρ > ρmin Back Face 0.51 0.65 Bearing Face 0.51 0.65 Strut- to-Node Interface 0.64 when ρ > ρmin 0.51 when ρ < ρ min 0.85 𝑓𝑐 𝑓𝑐 0.51 when ρ < ρ min 0.51 when ρ < ρ min 𝑓𝑐 𝑓𝑐 𝑓𝑐 2 2 2 2 2 Reduction factors are not considered for clarity (φ = 1) DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 17 EVALUATION OF RECOMMENDED PROVISIONS... = Standard Deviation/Mean DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 11 RECOMMENDED STM PROVISIONS: NODAL ZONE CONFINEMENT DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 12 ACI 318/AASHTO LRFD NODAL ZONE CONFINEMENT FACTOR CONFINEMENT MODIFICATION FACTOR: 45 deg 𝑚= 𝐴2 2 𝐴 45 deg Loaded Area A1 45 deg Loaded Area A1 2 1 A2 is measured on this plane Plan Elevation The confinement... Diagonal Strut Cross-Sectional STM Diagonal Strut 45 Load Spread 2.50d 1.85d Longitudinal STM DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 28 INVERTED-T DATABASE 118 in Graf & Brenner (1943) In- Service In- Service In- Service Current Study Leonhardt & Furlong & Walther (1966) Ferguson (1971) In- Service Furlong & Ferguson (1971) Cusens & Besser (1985) In- Service Shütt (1956) Zhu et al (2003)... control reinforcement requirement is not satisfied, use ν = 0.45 for the strut- to-node interface DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 16 RECOMMENDED STM PROVISIONS: NODAL EFFICIENCY FACTORS* CCC Node CCT Node CTT Node * ν ACI 318 AASHTO LRFD Proposed Back Face 0.85 0.85 0.85 Bearing Face 0.85 0.85 0.85 Strut- to-Node Interface 0.64 when ρ > ρmin Back Face 0.68 0.75 0.70 Bearing Face... Accuracy of Deep Beam STM Provisions 30 INVERTED-T DATABASE: ASSEMBLY AND FILTERING Stage 1 filtering Collection Database - Stage 2 filtering Filtered Database - specimen did not fail incomplete plate size information no shear reinforcement complicated supports/geometry/reinforcement h /b w > 4 - b w < 4.5 in - tension- and compression-chord loaded - torsional loads Inverted-T Database 130 tests - 10 tests... tests - 9 tests - 9 tests - 27 tests 33 tests Representative of inverted-T beams in the field (ALL from present study) 1 in = 25.4 mm DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 31 DATABASE EVALUATION Inverted-T Beams (33 tests) Rectangular Deep Beams (179 tests) Minimum 1.05 0.73 Maximum 2.17 4.14 Mean 1.50 1.54 † 0.0% 0.6% Standard Deviation 0.33 0.43 0.22 0.28 % Unconservative †† Coefficient ... DEVELOPMENTS IN STRUT- AND- TIE MODELING 11 RECOMMENDED STM PROVISIONS: NODAL ZONE CONFINEMENT DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 12 ACI 318/AASHTO LRFD NODAL ZONE CONFINEMENT... DEVELOPMENTS IN STRUT- AND- TIE MODELING 13 RECOMMENDED STM PROVISIONS: PERFORM STRUT CHECK AT NODE INTERFACE Critical stresses exist at nodal regions DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING... Variation = Standard Deviation/Mean DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 22 STM APPLIES TO MORE THAN DR OGUZHAN BAYRAK DEVELOPMENTS IN STRUT- AND- TIE MODELING 23 INVERTED-T STRADDLE