Design of Metal Building Roof Purlins Including System Reliability Effects

Final Project ReportThis report provides a framework to incorporate structural system reliability effects in the design of roof purlins in a typical metal building. Today every roof purlin is considered as a separate component and the effect of spatial variation in the demand loads and potential redistribution and load sharing in the roof system capacity are ignored in design. Component reliability is established by first-order reliability methods implemented through load and resistance factor design. Based on recent work in loading bearing cold-formed steel framing systems the load and resistance factor design framework is extended from components to systems through an additional resistance factor to account for system influence. An archetypical metal building is designed and selected for this study. Monte Carlo simulations of a segment of the metal building roof are performed with consideration of both randomness in the demands and capacity and employing geometric and material nonlinearity in the response model of the roof. The simulations indicate that the system effect in metal building roofs is beneficial, and increases in the design capacity when evaluated against demands may be appropriate. Sensitivity to the target reliability (allowed probability of failure), deflection limits, and modeling assumptions are observed and discussed. Preliminary factors to account for roof system reliability are provided.Metal Building Manufacturers Association (MBMA

Cyclic Performance and Behavior Characterization of Steel Deck Sidelap and Framing Connections

A wide variety of steel deck sidelaps and framing connections have been experimentally studied to characterize the cyclic performance required in seismic evaluation of steel deck diaphragms. This study intends to provide cyclic test results of common steel deck connections including screw nestable and top arc seam sidelaps; and powder actuated fasteners, arc spot weld, and arc seam weld framing connections. A total of 24 sidelap and 36 framing connection tests have been performed in the Thin-Walled Structures Laboratory at Johns Hopkins University by NBM Technologies. The connection test results have been used to parameterize a nonlinear hysteretic spring element (i.e. utilizing the Pinching04 material model) applicable to modeling of the connections in high fidelity steel deck diaphragms to evaluate the seismic behavior of the steel deck diaphragm in rigid wall flexible diaphragm buildings, where inelasticity and ductility of the building system are intended to be derived largely from the diaphragm and the connections. Finally, the test results have been compared to AISI 310 and DDM04 connection strength and stiffness predictions. This experimental program is a task within a larger effort, i.e. “Advancing Seismic Provisions for Steel Diaphragm in Rigid Wall - Flexible Diaphragm Buildings” by NBM Technologies. The object of the larger effort is to investigate alternative seismic design provisions for conventionally designed steel diaphragms in Rigid Wall - Flexible Diaphragm Buildings

Extensions of AdS_5 x S^5 and the Plane-wave Superalgebras and Their Realization in the Tiny Graviton Matrix Theory

In this paper we consider all consistent extensions of the AdS_5 x S^5 superalgebra, psu(2,2|4), to incorporate brane charges by introducing both bosonic and fermionic (non)central extensions. We study the Inonu-Wigner contraction of the extended psu(2,2|4) under the Penrose limit to obtain the most general consistent extension of the plane-wave superalgebra and compare these extensions with the possible BPS (flat or spherical) brane configurations in the plane-wave background. We give an explicit realization of some of these extensions in terms of the Tiny Graviton Matrix Theory (TGMT)[hep-th/0406214] which is the 0+1 dimensional gauge theory conjectured to describe the DLCQ of strings on the AdS_5 x S^5 and/or the plane-wave background.Comment: 27 pages, LaTe

Holographic Charged Fluid with Anomalous Current at Finite Cutoff Surface in Einstein-Maxwell Gravity

The holographic charged fluid with anomalous current in Einstein-Maxwell gravity has been generalized from the infinite boundary to the finite cutoff surface by using the gravity/fluid correspondence. After perturbing the boosted Reissner-Nordstrom (RN)-AdS black brane solution of the Einstein-Maxwell gravity with the Chern-Simons term, we obtain the first order perturbative gravitational and Maxwell solutions, and calculate the stress tensor and charged current of the dual fluid at finite cutoff surfaces which contains undetermined parameters after demanding regularity condition at the future horizon. We adopt the Dirichlet boundary condition and impose the Landau frame to fix these parameters, finally obtain the dependence of transport coefficients in the dual stress tensor and charged current on the arbitrary radical cutoff $r_c$. We find that the dual fluid is not conformal, but it has vanishing bulk viscosity, and the shear viscosity to entropy density ratio is universally $1/4\pi$. Other transport coefficients of the dual current turns out to be cutoff-dependent. In particular, the chiral vortical conductivity expressed in terms of thermodynamic quantities takes the same form as that of the dual fluid at the asymptotic AdS boundary, and the chiral magnetic conductivity receives a cutoff-dependent correction which vanishes at the infinite boundary.Comment: 19 pages, v2: references added, v3: typos corrected, v5: typos corrected, version accepted for publication in JHE

The dynamics of quark-gluon plasma and AdS/CFT

In these pedagogical lectures, we present the techniques of the AdS/CFT correspondence which can be applied to the study of real time dynamics of a strongly coupled plasma system. These methods are based on solving gravitational Einstein's equations on the string/gravity side of the AdS/CFT correspondence. We illustrate these techniques with applications to the boost-invariant expansion of a plasma system. We emphasize the common underlying AdS/CFT description both in the large proper time regime where hydrodynamic dynamics dominates, and in the small proper time regime where the dynamics is far from equilibrium. These AdS/CFT methods provide a fascinating arena interrelating General Relativity phenomenae with strongly coupled gauge theory physics.Comment: 35 pages, 3 figures. Lectures at the 5th Aegean summer school, `From gravity to thermal gauge theories: the AdS/CFT correspondence'. To appear in the proceedings in `Lecture Notes in Physics

Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory

The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in N=4 SYM theory and their gravity duals. Moreover, using our half BPS solutions, we show how the tiny graviton Matrix theory and the mass deformed D=3, N=8 superconformal field theories are related to each other.Comment: 40 pages, 12 figures, v

Electrified plasma in AdS/CFT correspondence

We construct new gravity backgrounds holographic dual to neutral plasma with U(1) global symmetry in the presence of constant electric field, considering its full back-reactions to the metric. As the electric field and the induced current cause a net energy in-flow to the system, the plasma is continually heated up and the corresponding gravity solution has an expanding horizon. After proposing a consistent late-time expansion scheme, we present analytic solutions in the scheme up to next-leading order, and our solutions are new time-dependent solutions of 5D asymptotic AdS Einstein-Maxwell(-Chern-Simons) theory. To extract dual CFT stress tensor and U(1) current from the solutions, we perform a rigorous holographic renormalization of Einstein-Maxwell-Chern-Simons theory including full back-reactions, which can in itself be an interesting addition to literatures. As by-products, we obtain interesting modifications of energy-momentum/current Ward identities due to the U(1) symmetry and its triangle anomaly.Comment: 27 pages, no figure, v3, minor typos fixed, matches with published versio

Phase diagram for non-axisymmetric plasma balls

Plasma balls and rings emerge as fluid holographic duals of black holes and black rings in the hydrodynamic/gravity correspondence for the Scherk-Schwarz AdS system. Recently, plasma balls spinning above a critical rotation were found to be unstable against m-lobed perturbations. In the phase diagram of stationary solutions the threshold of the instability signals a bifurcation to a new phase of non-axisymmetric configurations. We find explicitly this family of solutions and represent them in the phase diagram. We discuss the implications of our results for the gravitational system. Rotating non-axisymmetric black holes necessarily radiate gravitational waves. We thus emphasize that it would be important, albeit possibly out of present reach, to have a better understanding of the hydrodynamic description of gravitational waves and of the gravitational interaction between two bodies. We also argue that it might well be that a non-axisymmetric m-lobed instability is also present in Myers-Perry black holes for rotations below the recently found ultraspinning instability.Comment: 1+22 pages, 3 figures. v2: minor corrections and improvements, matches published versio

Universal thermal and electrical conductivity from holography

It is known from earlier work of Iqbal, Liu (arXiv:0809.3808) that the boundary transport coefficients such as electrical conductivity (at vanishing chemical potential), shear viscosity etc. at low frequency and finite temperature can be expressed in terms of geometrical quantities evaluated at the horizon. In the case of electrical conductivity, at zero chemical potential gauge field fluctuation and metric fluctuation decouples, resulting in a trivial flow from horizon to boundary. In the presence of chemical potential, the story becomes complicated due to the fact that gauge field and metric fluctuation can no longer be decoupled. This results in a nontrivial flow from horizon to boundary. Though horizon conductivity can be expressed in terms of geometrical quantities evaluated at the horizon, there exist no such neat result for electrical conductivity at the boundary. In this paper we propose an expression for boundary conductivity expressed in terms of geometrical quantities evaluated at the horizon and thermodynamical quantities. We also consider the theory at finite cutoff outside the horizon (arXiv:1006.1902) and give an expression for cutoff dependent electrical conductivity, which interpolates smoothly between horizon conductivity and boundary conductivity . Using the results about the electrical conductivity we gain much insight into the universality of thermal conductivity to viscosity ratio proposed in arXiv:0912.2719.Comment: An appendix added discussing relation between boundary conductivity and universal conductivity of stretched horizon, version to be published in JHE