Analysis and modelling of the seismic behaviour of high ... - Ingegneria
Analysis and modelling of the seismic behaviour of high ... - Ingegneria
Analysis and modelling of the seismic behaviour of high ... - Ingegneria
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4. SEISMIC RESPONSE OF PARTIAL-STRENGTH COMPOSITE JOINTS<br />
The two material constants are linked to <strong>the</strong> Mohr-Coulomb constants, viz. <strong>the</strong><br />
cohesion <strong>and</strong> <strong>the</strong> angle <strong>of</strong> internal friction, by matching <strong>the</strong> fictitious tensile strength<br />
ft <strong>and</strong> <strong>the</strong> biaxial compressive strength f’bc <strong>of</strong> concrete according to transformation<br />
formulae in Chen (1982). Moreover, a non-associated flow rule is exploited. The<br />
strain-hardening <strong>behaviour</strong> <strong>of</strong> concrete is governed by means <strong>of</strong> <strong>the</strong> stress-strain<br />
law <strong>of</strong> concrete in uniaxial compression or uniaxial tension, complemented with<br />
appropriate post-peak s<strong>of</strong>tening rules. In detail, <strong>the</strong> tension-s<strong>of</strong>tening <strong>behaviour</strong> <strong>of</strong><br />
concrete related to its progressive fracturing or tension-stiffening <strong>behaviour</strong> owing<br />
to <strong>the</strong> presence <strong>of</strong> reinforcements is reproduced with exponential decay curves<br />
(Stevens et al, 1991). Confining effects owing to transversal reinforcements <strong>and</strong><br />
pr<strong>of</strong>iled-steel sheeting are considered in <strong>the</strong> compression regime by means <strong>of</strong> <strong>the</strong><br />
model <strong>of</strong> M<strong>and</strong>er et al. (1988). The concrete model does not embody <strong>the</strong> specific<br />
fracture energy Gf, to overcome mesh-dependent results (Hilleborg et al, 1976).<br />
However, as <strong>the</strong> concrete slab is moderately reinforced both in <strong>the</strong> longitudinal <strong>and</strong><br />
transversal direction, <strong>the</strong> mesh-dependency is small. Moreover, <strong>the</strong> FE analyses<br />
account for steel nonlinearities using <strong>the</strong> von Mises yield criterion. Isotropic<br />
hardening is assumed for <strong>the</strong> analyses. In <strong>the</strong> analysis <strong>the</strong> measured stress-strain<br />
properties <strong>of</strong> <strong>the</strong> materials obtained by tensile test were used. The elastic modulus<br />
<strong>and</strong> <strong>the</strong> Poisson’s ratio were assumed as E=210000 <strong>and</strong> ν=0.3, respectively.<br />
Longitudinal rebars in <strong>the</strong> slab are assumed to be made with a hardening elasto-<br />
plastic material <strong>and</strong> modelled using discrete two-noded beam elements for 3D<br />
models. The discrete representation <strong>of</strong> <strong>the</strong> reinforcements is adopted because <strong>the</strong><br />
influence <strong>of</strong> bond-slip is <strong>of</strong> interest. Thereby, dimensionless bond-link elements are<br />
adopted to connect concrete <strong>and</strong> steel nodes. In detail, <strong>the</strong> bond stress-slip relation<br />
is modulated according to <strong>the</strong> law proposed in Stevens et al. (1991). Friction<br />
between <strong>the</strong> structural steel <strong>and</strong> <strong>the</strong> concrete slab is not modelled because it has<br />
little influence on <strong>the</strong> substructure responses. Elastic <strong>and</strong> inelastic convergence<br />
studies have been conducted to evaluate <strong>and</strong> arrive at <strong>the</strong> final mesh for <strong>the</strong> finite<br />
element models.<br />
The reaction force vs. <strong>the</strong> controlled displacement is illustrated in Figure 4.39,<br />
where <strong>the</strong> numerical simulations are compared to <strong>the</strong> envelope curve <strong>of</strong> <strong>the</strong> cyclic<br />
experimental response. One may observe that experimental data <strong>and</strong> numerical<br />
prediction are in a good agreement. Under sagging bending moment <strong>the</strong> specimen<br />
yield strength is well captured as expected; moreover <strong>the</strong> numerical simulation<br />
captures very well <strong>the</strong> hardening branch <strong>of</strong> <strong>the</strong> experimental response, both in term<br />
<strong>of</strong> strength <strong>and</strong> stiffness; this indicates a satisfactory <strong>behaviour</strong> <strong>of</strong> <strong>the</strong> numerical<br />
model. The model clearly shows <strong>the</strong> evolution <strong>of</strong> <strong>the</strong> distribution <strong>of</strong> <strong>the</strong> principal<br />
stresses <strong>of</strong> compression in <strong>the</strong> slab for <strong>the</strong> specimen subjected both under sagging<br />
<strong>and</strong> hogging bending moment.<br />
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