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Lecture

Cutting Principle: Internal Forces and Equilibrium

In course

CIVIL-124: Statics (for GC)

Ce cours a pour but de développer une compréhension des modèles statiques de structures. Il présente l'étude du jeu des forces dans les constructions isostatiques formées de barres, poutres et câbles. ...

Description

This lecture covers the cutting principle in statics, where a solid is cut to analyze internal forces. The concept of equilibrium for fragments is explained, along with the synthesis of internal forces. The lecture also discusses the nature of internal forces, stress distribution, and force-displacement associations.

Instructors (2)

Emmanuel Denarié

Emmanuel Denarié is a civil engineer, with a PhD in Materials Science. He worked for 3 years in a civil engineering company where he was in charge of the design of structures and the maintenance of bridges. He has 30 years’ experience on research and applications in the field of building materials, advanced concretes, and rehabilitation of reinforced concrete structures. He is since 2000 senior scientist and lecturer in the Laboratory for Maintenance and Safety of structures, at Ecole Polytechnique Fédérale de Lausanne (EPFL), in charge of research and development activities on the application of concretes and advanced cementitious materials to the improvement of existing and new structures. In 2013, under the lead of Emmanuel Denarié, in cooperation with CEREMA, Subdivision des Phares et Balises from Lorient, and Lafarge, a turret at sea (Le Cabon, Brittany, France) was reinforced by a cast on site 60 mm thick UHPFRC shell. The strain hardening mix was developed jointly with Lafarge. This successful application in extreme conditions of access and restraint of the substrate (thin ring geometry) opened the way to large-scale industrial applications of UHPFRC for the reinforcement of existing structures.

Katrin Beyer

Since 2017 Associate Professor, School of Architecture, Civil and Environmental Engineering (ENAC), EPFL. Head of the Earthquake Engineering and Structural Dynamics (EESD) Laboratory 2010-2017 Assistant Professor, EPFL. 2008-2010 Post-doctoral researcher, ETH Zürich. 2003-2007 Ph.D., Roseschool / Università di Pavia, Italy. 2001-2003 Ove Arup & Partners, Advanced Technology and Research Group, London. 2001 Diploma, Civil engineering, ETH Zürich.

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Related concepts (32)

Economic equilibrium

In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers.

General equilibrium theory

In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts with the theory of partial equilibrium, which analyzes a specific part of an economy while its other factors are held constant.

Comparative statics

In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter. As a type of static analysis it compares two different equilibrium states, after the process of adjustment (if any). It does not study the motion towards equilibrium, nor the process of the change itself. Comparative statics is commonly used to study changes in supply and demand when analyzing a single market, and to study changes in monetary or fiscal policy when analyzing the whole economy.

Competitive equilibrium

Competitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium, introduced by Kenneth Arrow and Gérard Debreu in 1951, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices.

Chemical equilibrium

In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products.

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