Simplified models/procedures for estimation of ... - ELSA - Europa

37where:vxyV= (10.5)b ⋅ dvFrom Equations (10.2), (10.3) and (10.4) ε 1 can be expressed as:* 2ε = ε + ⎡⎣ε + ε ⎤1 x x x⎦⋅cotθ⎛ v⎞*xyε x = 0.002 ⋅ 1− 1− ⋅ ( tanθ + cotθ) ⋅ ( 0.8 + 170 ⋅ε1)⎜ ′⎟⎝fc⎠(10.6)Considering the MCFT as a truss model with a concrete contribution equal to the transversecomponent of the shear stresses v ci transferred across the crack (see Figure 70), the shear strengthmay be expressed as:Av⋅ fvyV = Vs + Vc = ⋅dv ⋅ cotθ+ vci ⋅b⋅dvsAv⋅ fvy= ⋅d ⋅ cotθ+ f ⋅cotθ⋅b⋅dsSubstituting Equation (9.19) into Equation (10.7):v c1v(10.7)whereAv⋅ fvyV = ⋅dv ⋅ cotθ+ β ⋅ fc′⋅b⋅ dv(10.8)s0.33⋅cotθ0.18β = ≤1+ 500 ⋅ε24 ⋅ w1 0.3 +a + 16(MPa,mm)(10.9)In order to use Equation (10.8) for the evaluation of the required amount of transversereinforcement, it is necessary to determine appropriate values of θ and β which must satisfyEquation (10.6). These values are generally given as function of the longitudinal strain ε x andshear stress level ν xy /f ’ c in the form of tables or diagrams. The values given as example in Table23 ensure that the tensile strain in the stirrups is at least equal to 0.002 and that the compressivestress f c2 does not exceed the crushing strength f c2max of concrete. In determining these values itwas assumed that the amount and spacing of the stirrups would limit the crack spacing to about300 mm.13. CYCLIC LOAD MODELING THROUGH THE MCFTIt is worth discussing why some codes have maintained an approach based on the truss modeleven when more rational methods exist, such as the MCFT, which is now adopted, for example,in the Canadian, Norwegian and AASHTO LRFD codes. As observed in Duthinh and Carino[1996], the reason may be behind the fact that a whole generation of engineers has learned andused methods based on the truss approach. However, design engineers should take into account