Finite elements for higher order steel–concrete composite beams

none4noThis paper presents finite elements for a higher order steel–concrete composite beam model developed for the analysis of bridge decks. The model accounts for the slab–girder partial interaction, the overall shear deformability, and the shear‐lag phenomenon in steel and concrete components. The theoretical derivation of the solving balance conditions, in both weak and strong form, is firstly addressed. Then, three different finite elements are proposed, which are characterised by (i) linear interpolating functions, (ii) Hermitian polynomial interpolating functions, and (iii) interpolating functions, respectively, derived from the analytical solution expressed by means of exponential matrices. The performance of the finite elements is analysed in terms of the solution con-vergence rate for realistic steel–concrete composite beams with different restraints and loading con-ditions. Finally, the efficiency of the beam model is shown by comparing the results obtained with the proposed finite elements and those achieved with a refined 3D shell finite element model.openGara F.; Carbonari S.; Leoni G.; Dezi L.Gara, F.; Carbonari, S.; Leoni, G.; Dezi, L

On the validity of the reduced Salpeter equation

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Salpeter approximations. We find that for $J\not{\hspace*{-1.0mm}=}0$ the solutions are strikingly similar for all constituent masses. For zero angular momentum states the full and reduced Salpeter equations give different results for small quark mass especially with a large additive constant coordinate space potential. We also show that $\frac{1}{m}$ corrections to heavy-light energy levels can be accurately computed with the reduced equation.Comment: Latex (uses epsf macro), 24 pages of text, 12 postscript figures included. Slightly revised version, to appear in Phys. Rev.

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.Comment: 23 pages, revte

On the instantaneous Bethe-Salpeter equation

We present a systematic algebraic and numerical investigation of the instantaneous Bethe-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector types. We explore stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge structure and stable solutions.Comment: Latex (uses epsf macro), 26 pages of text, 12 postscript figures included

A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context

In this paper we give a new derivation of the quark-antiquark potential in the Wilson loop context. This makes more explicit the approximations involved and enables an immediate extension to the three-quark case. In the $q\overline{q}$ case we find the same semirelativistic potential obtained in preceding papers but for a question of ordering. In the $3q$ case we find a spin dependent potential identical to that already derived in the literature from the ad hoc and non correct assumption of scalar confinement. Furthermore we obtain the correct form of the spin independent potential up to the $1/m^2$ order.Comment: 30 pages, Revtex (3 figures available as hard copies only), IFUM 452/F

Large Possible retardation effects of quark confinement on the meson spectrum II

We present the results of a study of heavy-light-quark bound states in the context of the reduced Bethe-Salpeter equation with relativistic vector and scalar interactions. We find that satisfactory fits may also be obtained when the retarded effect of the quark-antiquark interaction is concerned.Comment: 11 pages, RevTex, to appear in PR

Modal properties and seismic behaviour of buildings equipped with external dissipative pinned rocking braced frames

his paper deals with the seismic protection of building frames by means of external dissipative systems. Dampers and external framing system can be arranged in several configurations, involving different kinematic behaviours and seismic performances. This study analyses a recently-developed solution called “dissipative tower”, which exploits the rocking motion of a steel braced frame, hinged at the foundation level, for activating the dampers. This system aims at controlling both the global response and the local storey deformation of the frame, by using a reduced number of viscous dampers. A state space formulation of the dynamic problem is presented in general terms, together with the solution of the seismic problem via the modal decomposition method. A parametric study is carried out to evaluate the influence of the added damping and of the braced frame stiffness on the modal properties and seismic response of a benchmark reinforced concrete frame retrofitted with the external dissipative towers. It is shown that the addition of the towers yields a regularization and reduction of the drift demand along the building height, but it may induce significant changes, not always beneficial, in the distribution of internal actions of the frame and in the absolute storey accelerations

Bound q\bar q Systems in the Framework of the Different Versions of the 3-Dimensional Reductions of the Bethe-Salpeter Equation

Bound q\bar q systems are studied in the framework of different 3-dimensional relativistic equations derived from the Bethe-Salpeter equation with the instantaneous kernel in the momentum space. Except the Salpeter equation, all these equations have a correct one-body limit when one of the constituent quark masses tends to infinity. The spin structure of the confining qq interaction potential is taken in the form $x\gamma_{1}^{0}\gamma_{2}^{0}+(1-x)I_{1}I_{2}$, with $0\leq x \leq 1$. At first stage, the one-gluon-exchange potential is neglected and the confining potential is taken in the oscillator form. For the systems (u\bar s), (c\bar u), (c\bar s) and (u\bar u), (s\bar s) a comparative qualitative analysis of these equations is carried out for different values of the mixing parameter x and the confining potential strength parameter. We investigate: 1)the existence/nonexistence of stable solutions of these equations; 2) the parameter dependence of the general structure of the meson mass spectum and leptonic decay constants of pseudoscalar and vector mesons. It is demonstrated that none of the 3-dimensional equations considered in the present paper does simultaneously describe even general qualitative features of the whole mass spectrum of q\bar q systems. At the same time, these versions give an acceptable description of the meson leptonic decay characteristics.Comment: 22 pages, 5 postscript figures, LaTeX-file (revtex.sty

Heavy Quarkonium Potential Model and the 1P1{}^1P_1 State of Charmonium

A theoretical explanation of the observed splittings among the P~states of charmonium is given with the use of a nonsingular potential model for heavy quarkonia. We also show that the recently observed mass difference between the center of gravity of the ${}^3P_J$ states and the ${}^1P_1$ state of $c\bar{c}$ does not provide a direct test of the color hyperfine interaction in heavy quarkonia. Our theoretical value for the mass of the ${}^1P_1$ state is in agreement with the experimental result, and its E1 transition width is 341.8~keV. The mass of the $\eta_c'$ state is predicted to be 3622.3~MeV.Comment: 15 page REVTEX documen