Design of composite haunch beams and connections for long span applications

DESIGN OF COMPOSITE HAUNCH BEAMS AND CONNECTIONS FOR LONG SPAN APPLICATIONS BY NG YIAW HEONG (BEng.(Hons.), MEng) DEPARTMENT OF CIVIL ENGINEERING A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NATIONAL UNIVERSITY of SINGAPORE 2004 ACKNOWLEDGEMENTS The author would like to take this opportunity to acknowledge various individuals for their guidance and encouragement in the course of this research. Firstly, the author would like to express his appreciation for the constant guidance and encouragement provided by his research supervisors, Professor N.E. Shanmugam and Associate Professor J.Y. Richard Liew. This research work would not have been completed without their continuous support. Secondly, the author is fortunate to have received moral support and understanding from Sze Ching; his wife and his parents. He would like to express gratitude to them. For the author’s years-old and 1-year-old sons, Yan Zhang and Ding Jie; the author could only apologize for not being able to keep them company most of the time especially during the final stage of the study. Last but not least, the assistance given by the lab officers during the experimental testing in the Concrete and Structural Laboratory, National University of Singapore is gratefully appreciated. This research project was funded by the National University of Singapore under a research grant (RP 930648). The support from Yongnam Engineering & Construction Pte Ltd, Singapore who supplied the test specimens is gratefully acknowledged. ii TABLE OF CONTENTS TITLE PAGE i ACKNOWLEDGEMENTS ii TABLE OF CONTENTS iii SUMMARY vi LIST OF TABLES vii LIST OF FIGURES xiii LIST OF SYMBOLS xiv CHAPTER INTRODUCTION 1.1 BACKGROUND 1.2 RESEARCH OBJECTIVES 1.3 SCOPE OF WORK 1.4 STRUCTURE OF THE THESIS CHAPTER LITERATURE REVIEW 2.1 BACKGROUND 2.2 INTERNAL FORCES AND MOMENTS IN CONTINUOUS COMPOSITE HAUNCH BEAM 2.3 GLOBAL ELASTIC ANALYSIS OF NON-SWAY FRAME 2.4 PLASTIC HINGE ANALYSIS OF NON-SWAY FRAME 2.4.1 Rigid-Plastic Analysis 2.4.2 Elastic-Plastic Analysis 2.5 ANALYSIS OF HAUNCH SECTION 1 9 11 12 14 15 16 16 CHAPTER EXPERIMENTAL INVESTIGATION - HAUNCH CONNECTION 3.1 GENERAL 3.2 MATERIAL PROPERTIES 3.2.1 Beam and column sections 3.2.2 Reinforcement bar 3.2.3 Concrete 3.3 FABRICATION OF TEST SPECIMENS 3.4 TEST SET-UP 21 21 22 22 23 23 24 25 iii 3.5 INSTRUMENTATION 3.6 TESTING PROCEDURE 3.7 DATA ASSESSMENT 3.7.1 Beam rotation, θb 3.7.2 Column rotation, θc 3.7.3 Connection rotation, φ 3.7.4 Inelastic Rotation, θie 3.8 JOINT STIFFNESS, RKI 3.9 JOINT ULTIMATE MOMENT, MU 3.10 JOINT ROTATIONAL CAPACITY, φCD 3.11 HAUNCH CONNECTION CAPACITY 3.12 HAUNCH TOE MOMENT CAPACITY 3.13 JOINT TEST RESULTS AND DISCUSSION 3.13.1 Comparison of test results 3.13.2 Connections H1 and H2 3.13.3 Connections H3 and H4 3.13.4 Connections H5 and H6 3.13.5 Connections H7 and H8 3.13.6 Connections H9 and H10 3.14 EFFECT OF SLAB REINFORCEMENT RATIO 3.15 EFFECTS OF HAUNCH LENGTH 3.16 CONCLUSIONS 26 26 28 28 28 28 29 29 29 30 30 31 31 32 32 34 36 37 38 40 40 41 CHAPTER EXPERIMENTAL INVESTIGATION - HAUNCH BEAM 4.1 INTRODUCTION 4.2 MATERIAL PROPERTIES 4.2.1 Beam and column sections 4.2.2 Reinforcement bar 4.2.3 Concrete 4.3 FABRICATION OF TEST SPECIMENS 4.4 TEST SET-UP 4.5 INSTRUMENTATION 4.6 TESTING PROCEDURE 4.7 BEAM TEST RESULTS AND DISCUSSION 4.7.1 Beam Specimen B1 4.7.2 Beam Specimen B2 4.7.3 Beam Specimen B3 4.8 CONCLUDING REMARKS CHAPTER ANALYTICAL MODEL 5.1 GENERAL 5.2 COMPARISON OF PLASTIC HINGE ANALYSIS AND TEST RESULTS 5.3 ROTATION CAPACITY 5.3.1 General 5.3.2 Calculation of available rotation capacity of composite section 5.4 BEAM ANALYSIS 5.4.1 Composite Haunch Beam Properties 5.4.2 Composite Haunch Beam analysis 5.5 FINITE ELEMENT MODELLING 5.5.1 Nonlinear Analysis Software: - USFOS 59 59 60 60 61 61 61 62 65 65 66 66 69 71 73 105 105 105 108 108 109 111 111 115 116 116 iv 5.5.2 Modeling of Composite Haunch Beam 5.5.3 Results 5.6 LATERAL TORSIONAL INSTABILITY 5.6.1 General 5.6.2 Lateral Distorsional Buckling Design Method 116 117 117 117 118 CHAPTER DESIGN RECOMMENDATIONS AND DESIGN EXAMPLE 6.1 INTRODUCTION 6.2 DESIGN RECOMMENDATIONS 6.3 ELASTIC GLOBAL ANALYSIS 6.4 PLASTIC HINGE ANALYSIS 6.5 DESIGN PROCEDURE FLOW CHART 6.6 DESIGN EXAMPLE 131 131 131 133 135 138 140 CHAPTER CONCLUSIONS AND PROPOSALS FOR FUTURE WORK 7.1 GENERAL 7.2 BEHAVIOUR OF THE COMPOSITE HAUNCH CONNECTION 7.3 BEHAVIOUR OF THE COMPOSITE HAUNCH BEAM 7.4 SECTION PROPERTIES AND FRAME ANALYSIS 7.5 FUTURE WORK 141 141 141 142 142 144 APPENDIX A DESIGN EXAMPLE 146 REFERENCES 154 LIST OF PUBLICATIONS 160 v SUMMARY This thesis is concerned with the behaviour of steel-concrete composite haunch connections and beams. Experiments were carried out to investigate the moment rotation characteristics and ultimate capacity of these connections and beams. Details of the experiments giving information on test specimens, instrumentation, test set-up and test procedures are described. There are a total of 10 haunch connections and continuous composite haunch beam specimens tested to failure. Results obtained for connection moment capacity, rotation capacity and failure modes are presented. It is found that through proper design and detailing, these connections display the characteristics of a rigid connection. Optimum design of composite haunch beam can be achieved when plastic hinge occurred at haunch toes followed by at the mid-span to form a plastic collapse mechanism. Haunch toe could be designed as the weakest section to form a plastic hinge with suitable amount of reinforcement in the slab and range of haunch length. Experimental results show that composite haunch connection exhibits a ductile moment-rotation behaviour and is able to redistribute moment to the mid-span by loss of stiffness due to cracking of concrete slab and yielding of either steel reinforcement or cross section. Study also has been carried out to investigate the parameters that influence the stiffness, strength and rotation capacity of composite haunch connections. Design guidelines for composite haunch joints and beams are provided. vi LIST OF TABLES Chapter Table 2.1 Limits to redistribution of hogging moment to reduce (EC4) Table 2.2 Maximum redistribution of negative moment in composite haunch beam at ultimate limit state [Lawson 1989] Chapter Table 3.1 Details of joint test specimens Table 3.2 Summary of universal section properties and tensile test results Table 3.3 Summary of reinforcement bar properties and tensile test results Table 3.4 Summary of concrete cube test results Table 3.5 Summary of test results Chapter Table 4.1 Summary of concrete cube test results for beam specimen Table 4.2 Details of beam test specimens Chapter Table 5.1 Comparison of test results with Plastic Hinge Theory Table 5.2 Comparison of rotational capacity at Haunch Toe vii LIST OF FIGURES Chapter Figure 1.1 Haunch as Taper Section in Universal Beam Figure 1.2 Cutting of Taper Section in Universal Beam Chapter Figure 2.1 Cross Section of Continuous Composite Beam Figure 2.2 Sub-frame of Beam and Column in Non-sway Frames Analysis Figure 2.3 Relation between Haunch Beam Elastic Resistance and Parent Beam Plastic Resistance Figure 2.4 Distorsional Buckling of Composite Beam Chapter Figure 3.1 Building Plan Layout for Joint Specimens'Design Figure 3.2 Cruciform Joint Specimen Figure 3.3 Test Specimen Ready for Concrete Casting Figure 3.4 Typical Joint Test Specimen Figure 3.5 Joint Test Specimen Ready for Testing Figure 3.6 Instrumentation of Test Specimen Figure 3.7 Definition of Rotation in a Joint Figure 3.8 Moment-rotation Curve of Connection Figure 3.9 Stress-strain Block of Haunch Connection Figure 3.10(a) View after Failure of Specimen H1 and H2 Figure 3.10(b) View after Failure of Tension Bolt of Specimen H1 and H2 viii Figure 3.11 Moment-Rotation Curve of H1 and H2 Figure 3.12 View after Failure of H3 and H4 Figure 3.13 Moment-Rotation Curve of H3 Figure 3.13 Moment-Rotation Curve of H4 Figure 3.15 View after Failure of H5 Figure 3.16 Moment-Rotation Curve of H5 Figure 3.17 View after Failure of H6 Figure 3.18 Moment-Rotation Curve of H6 Figure 3.19 View after Failure of H7 Figure 3.20 Moment-Rotation Curve of H7 Figure 3.21 View after Failure of H8 Figure 3.21 Moment-Rotation Curve of H8 Figure 3.23 View after Failure of H9 Figure 3.24 Moment-Rotation Curve of H9 Figure 3.25 Premature Failure of H10 Figure 3.26 Comparison of Load-Displacement Curve of H2,H4 and H6 Figure 3.27 Comparison of Load-Displacement Curve of H3, H4, H7 and H8 Chapter Figure 4.1 Haunch Beam Test Specimen Figure 4.2 Wooden Formwork of Beam Test Specimen Figure 4.3 Beam Specimen Ready for Concrete Casting Figure 4.4 Beam Specimen Ready for Testing Figure 4.5 Isometric View of Haunch Beam Test Specimen ix Figure 4.6 Schematic Loading of Haunch Beam Test Specimen Figure 4.7 Loading Frame in Haunch Beam Test Specimen Figure 4.8 Loading Frame Connected to Hydraulic Actuator Figure 4.9 Larger Haunch Connection at Cantilever Beam Side Figure 4.10 Instrumentation of Beam Specimen Figure 4.11 View after Failure of Specimen B1 Figure 4.12 Load-Displacement Curve of Specimen B1 Figure 4.13 Inelastic Buckling in Compression Flange of the Beam B1 Figure 4.14 Crushing of Concrete Slab at Loading Point in Beam B1 Figure 4.15 Concrete Slab Cracking Pattern of the Beam B1 at Haunch Toe Figure 4.16 Strain Reading of Cross Section for Beam B1 at Left Haunch Toe at Different Load Stage Figure 4.17 Strain Reading of Cross Section for Beam B1 at Right Haunch Toe at Different Load Stage Figure 4.18 Strain Reading of Cross Section for Beam B1 at Left Loading Point at Different Load Stage Figure 4.19 Strain Reading of Cross Section for Beam B1 at Right Loading Point at Different Load Stage Figure 4.20 Strain Reading of Tension Reinforcement for Beam B1 at Left Haunch Toe at Different Load Stage Figure 4.21 Strain Reading of Tension Reinforcement for Beam B1 at Right Haunch Toe at Different Load Stage Figure 4.22 Strain Reading of Concrete Slab for Beam B1 at Left Loading Point at Different Load Stage Figure 4.23 Strain Reading of Concrete Slab for Beam B1 at Right Loading Point at Different Load Stage Figure 4.24 Load-Displacement Curve of Specimen B2 Figure 4.25 Inelastic Buckling of Compression Flange of the Beam B2 Figure 4.26 Crushing of Concrete Slab at Loading Point in Beam B2 x moment. It is necessary to understand the haunch connection behaviour and its application in sway frame. The finite element USFOS shows reasonable predictions of the behaviour of composite haunch beam as a structural frame. It could be further developed to zoom into the component design which is able predict the failure mode of the haunch beam construction system. Further development will be worthwhile because when reasonable accurate computer simulation is possible, full scale testing will be the least option for researchers to study the behaviour of any structural system. 145 APPENDIX A DESIGN EXAMPLE A) Design Data i) Structure Data A storey building size 24m x 72m as shown in Figure 3.1 braced against side-sway is considered in this design example. Main Beam Span : m (Composite Haunch Beam Rigid Connection) Secondary Beam Span : 12 m (Composite Beam Simply Supported) Storey Height : 4.2 m Column Base : Fixed Slab Thickness : 120 mm ii) Material Data: Shear Stud : Dia 19mm x 95mm as welded Concrete : fcu = 30N/mm2 , 2400 kN/m3 Slab thickness : 120mm Steel Grade : S275 iii) Design Loading Concrete Slab : 2.88 kN/m2 Construction Load : 0.50 kN/m2 Building Services : 0.70 kN/m2 Imposed Load : 5.00 kN/m2 Design Loading : 1.4 (2.88+0.7) + 1.6(5) = 13.01 kN/m2 Secondary beam self weight, say 0.50 kN/m. Design Load = 1.4 x 0.50 = 0.70 kN/m 146 Therefore, loading from secondary beam transferred to main beam, P = ((2.67m x 13.01kN/m2) + 0.70 kN/m) x 12m /2 = (41.74 kNm) x 12m/2 = 250 kN B) Plastic Design of Main Beam To form a plastic mechanism at the haunch toes and loading points: Lh A h L/3-L B L/3-Lh L/3 C D A Lh E F L/3-Lh Mph B C Mps Where, Mph = Plastic Moment Capacity at Haunch Toe (Hogging) Mps = Plastic Moment Capacity at Load point (Sagging) Moment about haunch toe, Mph + Mps = P (L/3-Lh) Therefore, to design the haunch beam, Mph + Mps P (L/3-Lh) > 147 Beam size - Span to Depth ratio 25 to 30 Using 30, D = 8000/30 = 266 mm Try UB 254 x 146 x 37 kg/m, plastic section for both sagging and hogging condition and hence is suitable for plastic design. A Data: Slab Thickness , Ds = Concrete strength, fcu = 30 N/mm2 Concrete Cover, Dc = 20 mm Effective width,sagging,Bes = 1400 mm Effective width,hogging,Beh 120 mm 1000 mm Number of rebars = 10 nos Diameter of rebar = 20 mm Area of rebar, Abar = Yielding strength of rebar = 10 Lever arm of rebar to beam flange, Dr = 90 mm Depth, D = 255.9 mm Width, B = 146.4 mm Flange thickness, T = 10.9 mm Web thickness, t = 6.4 mm Web depth, d = 218.9 mm Area = 4740 mm2 Yielding strength, fy = 275 mm2 13 Constant, (Pfix/Py)^(1/2) = Resistance of concrete flange, Rc = 5040 kN Resistance of steel flange, Rf = 439 kN Resistance of steel beam, Rs = 1304 kN Resistance of clear web depth, Rv = 385 kN Resistance of overall web depth,Rw = 426 kN Resistance of slender web, Ro = 428 kN 3142 mm2 460 N/mm2 12 Universal beam dimension B Calculation 148 Resistance of reinforcement, Rr = 1445 kN Resistance of slender steel beam,Rn = 1346 kN d/t = 34.2 10 76*e/(1+Rr/Rv) = 16.0 11 76*e*/(1+Rc/Rv) = 5.4 Case : Plastic neutral axis in concrete slab (Sagging) Rc > Rw and Rs < Rc Mc = Rs*(D/2+Ds-Rs/Rc*Ds/2) = 303 kNm BS 5950: Part Case : Plastic neutral axis in concrete slab (Hogging) Rr > Rw and Rr > Rs Mc = Rs*(D/2 +Dr) = 284 kNm BS 5950: Part Try Haunch Length 5% of span, hence haunch length Lh = 0.05 x 8000 = 400 mm Check ultimate condition, Mph + Mps P (L/3-Lh) > 303 + 284 > 250(8/3-0.4) 587 567 = 1.04 > :- Ultimate condition satisfied Checking of lateral distorsional buckling of beam at haunch toe Refer to equation (Eq 5.14) in the thesis LT = 17.7 and refer to Table 16 of BS5950:2000, pb = 275 N/mm2 Therefore, no reduction to Rs to obtain the Mb = Mc = 284kNm Okay ! 149 C) Main Beam Elastic composite Properties I) Calculation of Moment Inertia, Ig (Sagging) Uncracked UB254 x 146 x 37kg/m Universal Beam Properties D = 255.9 mm B = 146.4 mm t = 6.4 mm T = 10.9 mm A = 4740.0 mm2 d = 218.9 mm Sxx = 484363.0 mm4 Ms = 0.0 kNm Steel Beam Inertia Moment Ixx = 55600000.0 mm4 Effective Width of Concrete (Sagging) Be = 1400.0 mm Overall slab depth Ds = 120.0 mm Depth of the deck profile Dp = 0.0 mm Modular Ratio αe αe = 13.2 Cross section area of steel beam A = 4750.0 mm2 Depth of steel beam D = 256.0 mm Ig = 1.93E+08 mm4 D) Main Beam Serviceability Deflection Check Design Load from Secondary Beam (Imposed Live Load Only) = 5.0 kN/m2 x 8/3 x 12m/2 = 80kN 150 80kN Lh L/3-Lh 80kN L/3-Lh L/3 Lh = 0.00772 PL3/EI = 0.00772 *80,000*80003/(205,000*1.93E08) = 8.0mm Max Deflection Hence, Span/Def = 8000/8 = 1000 > 360, Live Load Serviceability Deflection Okay! E) Haunch Connection Design Haunch Connection is designed to remain elastic. Therefore, the connection is to resist 1.1 time the haunch toe moment Mph. 250 kN V Lh L/3-Lh 250 kN L/3 322kNm V L/3-Lh Lh 322kNm V V 250 kN 1.1 Mps = 1.1 x 322kNm = 354 kNm Le = 400 mm Connection Moment = 250 kN x 0.4 + 354 kNm = 454 kNm Try M20 Grade 8.8 Bolts with 10T20 Tension Reinforcement 151 Rr = = 0.87 x 10 x 3.14 x 202/4 x 460 1256 kN Rb = = x 91.9 kN 184 kN Rhf = = 146 x 10.9 x 1.2 x 275 525 kN Column Web Bearing (Try column UC 203 x 203 x 60 kg/m) Pc = (b1 + n2) x tc x py b1 = = = Tbeam + 2Tplate 10.9 + 2x20 50.9 mm n2 = = = 2(Tcolumn + rcolumn) x 2.5 2(14.2 + 10.2) x 2.5 122 mm Therefore, Pc = (50.9 + 122) x 9.1 x 275 = 436 kN Column Web Buckling (Try column UC 203 x 203 x 60 kg/m) Pc = (b1 + n1) x tc x py n1 = = x 209.5/2 209 = = = 2.5 d/tcolumn 2.5 x 189.1/9.1 51.7 152 from Table 27(c) BS 5950: Part pc = 217 N/mm2 Therefore, Pc = (50.9+209.5) x 9.1 x 217 = 518 kN Comparing Rhf and Pc (Bearing or Buckling), Column Bearing Controlled So, Rhf is limited to 436 kN Rhw = = 234 x 6.4 x 1.2 x 275 494 kN Rf = = 146 x 10.9 x 1.2 x 275 525 kN (Limit to 436 kN Column Bearing Controlled) Rw = = 234 x 6.4 x 1.2 x 275 494 kN Rhf + Rhw + Rf + Rw < Rr + Rb , PNA at beam web ((yc - Dh) x 1.2 x 275)+ Rhf + Rhw + Rf = Rr + Rb ((yc - 256) x 1.2 x 275) + 436 + 494 + 436 = 1256 + 184 yc = 256 mm Take moment about reinforcement Mu = 525 (90+256+256-10.9/2) + 494 (90+256+234/2) + 525(90+256-10.9/2) = 313163 + 228722 + 178762 = 720647 kNmm = 721 kNm > 454 kNm Haunch Connection Moment Satisfied !! 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Shanmugam, N.E., Ng, Y.H. and Liew, J.Y.R. (2002) "Behaviour of Composite Haunch Beam Connection", Engineering Structures, Vol. 24, 1451-1463 50. SCI/BSCA Connection Group (1995) "Joints in Steel Construction – Moment Connections", Steel Construction Institute, United Kingdom. 51. Tehami, M. (1997) "Local Buckling in Class Continuous Composite Beams", Journal of Construction in Steel Research, Vol. 43, Nos.1-3, 141-159. 52. Trahair, N.S. and Kitipornchai, S. (1972) "Buckling of Inelastic I-Beams under Moment Gradient", Journal of the Structural Division, Proceedings of the ASCE, Vol. 99, No. ST11, Nov, 991-1004. 53. Trahair, N.S. (1983) "Inelastic Lateral Buckling of Beams, Beams and Beam Columns-Stability and Strength", ed. by Narayanan, R., Applied Science Publishers, London and New York 1983, 35-69. 54. Uy, B. and Liew, J.Y.R., (2003) “Composite Steel-Concrete Structures”, The Civil Engineering Handbook, ed. by Chen, W.F. and Liew, J.Y.R., CRC Press, 51-1/62. 159 LIST OF PUBLICATIONS 1. Shanmugam, N.E., Ng, Y.H, Richard Liew, J.Y., Behaviour of Composite haunch beam connection, Engineering Structures 24(2002), pp 1451-1463. 2. Ng, Y.H., N.E. Shanmugam, Richard Liew, J.Y. and Yu, C.H., Haunch Connections in Composite Construction, Proceeding of the Fifth Pacific Structural Steel Conference, 13-16 October 1998, Seoul, South Korea, pp. 717-722. 3. Richard Liew, J.Y., Ng, Y.H. and N.E. Shanmugam, Design of Haunch Composite Connections for Long-Span Beam Construction, Connections in Steel Structures IV: Behaviour Strength and Design, edited by Roberto Leon and W.S. Eastering, Chicago: AISC 2002, pp. 424-433. 4. Ng, Y.H., N.E. Shanmugam and Richard Liew, J.Y., Tests To Failure of Continuous Composite Haunch Beams, Proceeding of the International Conference on Structural and Foundation Failures August 2-4, 2004, Singapore. 5. Ng, Y.H., N.E. Shanmugam and Richard Liew, J.Y., Behaviour of Composite Haunch Beam, Journal of Constructional Steel Research (Accepted for Publication) 160 [...]... analysis 1.3 Scope of works In this thesis, literature related to composite haunch connections and composite haunch beams are reviewed The scope of literature study is not only limited to haunch connections Non -haunch connections were also studied and comparisons made between haunch and non -haunch composite connections A series of composite haunch connections and composite continuous haunch beams were tested... model And finally, design guidelines for composite haunch beam are provided 5 1.4 Structure of the Thesis The thesis contains seven chapters Chapter 1 gives the general description of the advantages of composite construction and in particular composite haunch beam construction The need for further research on composite haunch beam construction in long span application is presented and the objectives and. .. transition of the beam flanges to the intended reduced section at a given location, the haunch connection strengthens the connection and allows the formation of plastic hinges at a designated location (Iwankiw, 1997) Haunch composite beams are designed in a similar manner to continuous beams of uniform section (Lawson and Rackham, 1989) The critical section for design is at the haunch toe, and the depth of. .. in the diagram Haunch beams are designed by assuming a rigid moment connection between the beams and columns Depth and length of a haunch are chosen so that they result in an economical method of transferring moment into the column and in a reduction of beam depth to a practical minimum Haunch composite beams in which steel beams are designed to act in conjunction with a concrete slab of definite width... (Hamada 1976) and the results have shown that the majority of beams failed as a result of local buckling Tests have shown that the width-thickness ratio for the flange of the steel section and the amount of longitudinal slab reinforcement are significant factors affect local flange buckling Therefore, it is 3 important to find out the factors that affect the design of haunched composite beams so that... to the composite beams and distributes shrinkage strains and prevents serious cracking of concrete Besides the advantages mentioned above, a strong demand for large columnfree space in buildings in recent times has necessitated further research into the behaviour of haunch beams since they are considered to be an efficient and economical form for long span construction This system is able to offer more... haunch connections in long- span composite construction a study has been undertaken by the author on the behaviour of haunch connections 2.2 Internal forces and moments in continuous composite haunch beam The internal forces and moments in a continuous haunch composite beam may generally be determined using either: a) Global elastic analysis or 11 b) Plastic hinge analysis 2.3 Global elastic analysis of. .. study also includes the behaviour of the composite haunch connection and haunch beam illustrated by their moment-rotation curves The effects of parameters such as reinforcement ratio, haunch length and the moment-rotation curve are investigated Analytical models for the prediction of moment resistance Mu, rotational capacity u and rotational stiffness Ki of the composite haunch beam are established Results... Length of the beam (including the haunch) λ = Slenderness of the beam length between restraints L = Length between hinges at both ends Le = Span of the beam between the end of the haunches Li = Length between maximum moment and adjacent point of inflection λLT = Equivalent Slenderness Lp = Plastic region of the flange Mhe = Elastic Moment Resistance of Haunch Section Mhu = Moment capacity of composite haunch. .. (Aribert and Raoul, 1992, Cosenza et al., 1995a, Climenhaga and Johnson, 1972a, Couchman, 1996, Dekker et al., 1995, Fabbrocino et al., 2001, Hamada and Longworth, 1976, Hamada and Longworth, 1974, Hope-Gill and Johnson, 1976, Johnson and Chen, 1991, Kemp and Dekker, 1991, Leon, 1990, Liew et al., 2001, Lukey and Adams, 1969, Price and Anderson, 1992, Tehami, 1997) have proposed design methods for simple . DESIGN OF COMPOSITE HAUNCH BEAMS AND CONNECTIONS FOR LONG SPAN APPLICATIONS BY NG YIAW HEONG (BEng.(Hons.), MEng) DEPARTMENT OF CIVIL ENGINEERING . Connections H3 and H4 34 3.13.4 Connections H5 and H6 36 3.13.5 Connections H7 and H8 37 3.13.6 Connections H9 and H10 38 3.14 EFFECT OF SLAB REINFORCEMENT RATIO 40 3.15 EFFECTS OF HAUNCH LENGTH. mid -span to form a plastic collapse mechanism. Haunch toe could be designed as the weakest section to form a plastic hinge with suitable amount of reinforcement in the slab and range of haunch