Lecture

Metal Structures: Stability and Lateral Stiffness

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In course

CIVIL-235: Design of steel structures

Ce cours permet de maitriser les aspects fondamentaux et pratiques du dimensionnement des structures en acier. Il traite des poutres, des poteaux, des assemblages, des cadres, des systèmes porteurs et des problèmes de stabilité. ...

Description

This lecture covers the stability and lateral stiffness of metal structures, focusing on criteria for stability and lateral rigidity of frames, as well as the effects of horizontal displacements. It also discusses the interaction verification formulas, critical lengths for spillage, and practical examples of instability calculations.

Instructor

Alain Nussbaumer

Expertise Metallic structuresStructural glassFatigue and fracture mechanicsAssessment of existing structuresUltra low cycle Teaching & PhD Past EPFL PhD Students Luís Costa Borges, Claire Acevedo, Nariman Maddah, Farshid Zamiri Akhlaghi, Manuel Santarsiero, Luca D'Angelo, Cláudio Alexandre Pereira Baptista, Albano António Sousa, Jagoda Cupac, Ardalan Hosseini, Martin Garcia, Hossein Heydarinouri, Jian Zhan Past EPFL PhD Students as codirector Marina Rocha Courses Design of steel structures CIVIL-2

Official source

Related concepts (32)

Critical exponent

Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

Critical phenomena

In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking.

Lyapunov stability

Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).

Metal

A metal (from Ancient Greek μέταλλον métallon 'mine, quarry, metal') is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typically ductile (can be drawn into wires) and malleable (they can be hammered into thin sheets). These properties are the result of the metallic bond between the atoms or molecules of the metal. A metal may be a chemical element such as iron; an alloy such as stainless steel; or a molecular compound such as polymeric sulfur nitride.

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