CE5510 Advanced Structural Concrete Design - STRUT-AND-TIE METHODS - Assoc Prof Tan Kiang Hwee Department of Civil Engineering National University of Singapore 2/16/2004 In this lecture DEPARTMENT OF CIVIL ENGINEERING We will explore !the concept of strut-and-tie models !their applications to new construction (and strengthening works) 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING At the end of the lecture You should be able to !identify cases where strut-and-tie models are applicable or appropriate !formulate strut-and-tie models in structural concrete members !design the reinforcement according to the strut-and-tie models 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Contents !B- and D-regions !Concept of Strut-and-Tie Models • Geometric Layout • Design of Struts • Nodes and Nodal Zones • Design of Ties • Detailing 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING ! Design • • • • • • Examples for New Construction High Wall Corbel Dapped-Beam Transfer Girder Deep Beam with Opening (Stepped (Non-Prismatic) Beams) ! (Examples for Strengthening Works) • Dapped Beams • Beam with Openings or Recesses 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Main (B-) & Local (D-) regions D-region B-region 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Main (B-) regions !regions of relatively uniform stresses !Bernoulli hypothesis of linear strain distribution applies !internal forces or stresses are derived from statics !“Standard” methods of Codes apply 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Local (D-) regions !significantly non-linear strain distribution !near concentrated loads, corners, bends, openings and other discontinuities !internal flow of forces well described by strut-and-tie models !conventionally design by thumb-rule 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Concept of Strut-and-Tie Models ! Components ! concrete compression struts ! steel tension ties ! nodes (nodal zone) where struts and ties meet ! concrete Dual purpose ! describe essential aspects of structural behaviour ! provide tools for structural dimensioning 2/16/2004 steel  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Geometric Layout of strut-and-tie models Load path ? Boundary forces/stresses follows the flow of internal forces in the structure 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING 4T13 closed stirrups 4T13 U stirrups 2T13 1T13 U bar 4T20 welded to angle 2T13 U bars 2T20 U bars 4T25 bars 2/16/2004 178 mm  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Example - Transfer girder 11600 kN 3600 700 6850 140.4 kN/m 3600 700 2/16/2004 MacGregor b=700 mm fc’=35 MPa fy=410 MPa 10450 mm  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING 6579 kN 2/16/2004 Combined truss and strut action 6543 kN  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Right end: V=6543 - 11x(140.4x0.6) = 5616 kN ∴req’d Av=(5616/9)x103 ÷ (410x610) =2537 mm2/m ∴use φ 22 U-stirrups @ 300 mm c/c (2540 mm2/m) Left end: For K-UU, D= (624+84.2)/sin 280 = 1508 kN ∴req’d width w =D/(bfce) =D/(0.5bfc’) =123 mm For S-UU, w=65 mm 6579w = 94 mm Average kN →assume all struts to be 100 mm and lower tensile tie located at mid-height 2/16/2004 of truss node at UU ∴V transmitted by stirrups = 3x854 = 2562 kN = 39% of 6579 kN To ensure ductility, at least 30% of shear to be transmitted by stirrups; the rest by a major diagonal strut →try φ 22 U-stirrups @ 225 mm c/c (Avfyv=854 kN per 600 mm spacing) V transmitted by strut H-AA = 6579-2562-6x84.2 =3512 kN 6543 For H-AA, D = 5102 kN; w=416 mm kN Combined truss For E-AA, D = 1174 kN; w=96 mm and strut action  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Example - Deep beam with opening fyd=434 MPa fcd=17 MPa Schlaich 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Right side, complete model 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING left side, model 2/16/2004 left side, model  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Check concrete stresses: Stresses under bearing plates: σp=3000x103/(700x400) = 10.7 MPa < 1.0 fcd=17 MPa σA=1070x103/(500x400) = 5.4 MPa < 0.8 fcd=13.6 MPa σB=1930x103/(500x400) = 9.7 MPa < 0.8 fcd=13.6 MPa Required depth of compression zone: C=T= 1070 kN d ≥ 1070x103/(400x1.0fcd) = 135 mm < 400 mm ∴OK (Nodes taken 200 mm below top surface.) 2/16/2004  Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Check anchorage length of reinforcing bars Other critical anchorages - C, D 2/16/2004 > Anchorage length Tan K H, NUS DEPARTMENT OF CIVIL ENGINEERING Further reinforcement mesh on either face of wall stirrups 2/16/2004 nominal column reinforcement  Tan K H, NUS References ! ! ! ! DEPARTMENT OF CIVIL ENGINEERING J.G MacGregor, “REINFORCED CONCRETE: Mechanics and Design”, 3rd Ed., Prentice-Hall, 1997, Ch 18 A.H Nilson, D Darwin and C.W Dolan, “Design of Concrete Structures”, McGraw-Hill, 2003, pp K.H Reineck (Ed), “Examples for the Design of Structural Concrete with Strut-and-Tie Models”, ACI SP-208, 2002, 244 pp Strut-and-Tie Resource Web Site http://www.cee.uiuc.edu/kuchma/strut_and_ti e/STM/ 2/16/2004  Tan K H, NUS Further reading: ! ! ! ! ! DEPARTMENT OF CIVIL ENGINEERING J Schlaich, et al., “Toward a Consistent Design of Structural Concrete”, J of Prestressed Concrete Institute, V.32, No 3, 1987, pp.74-150 P Marti, “Basic Tools of Reinforced Concrete Beam Design”, ACI Journal, V 82, No 1, Jan-Feb 1985, pp 46-56 Tan, K.H and Naaman, A.E., "Strut-and-Tie Model for Externally Prestressed Concrete Beams", ACI Structural Journal, Vol 90, No 6, USA, November-December 1993, pp 683-691 Tan, K.H., “Shear Strengthening of Dapped Beams Using FRP Systems", Fifth International Symposium on Fibre Reinforced Plastics for Reinforced Concrete Structures (FRPRCS-5), Cambridge, UK, July 16-18, 2001, Vol 1, pp 249-258 Mansur, M.A., Tan, K.H and Weng, W., “Effects of Creating an Opening in Existing Beams”, ACI Structural Journal, Vol 96, No 6, USA, November-December 1999, pp 899-905 2/16/2004  Tan K H, NUS