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Lecture# Virtual Work in Structural Mechanics

Description

This lecture covers the concept of virtual work in structural mechanics, focusing on the principle of virtual work and its application to determine equilibrium states. The instructor explains how to use virtual displacements to analyze the behavior of mechanical systems, emphasizing the importance of smart choices in selecting virtual displacements. The lecture also discusses the advantages and disadvantages of applying the principle of virtual work, highlighting its relevance in solving statics problems with zero displacements. Examples and practical applications are provided to illustrate the theoretical concepts.

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Related concepts (416)

Work (physics)

In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when applied it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.

Force

In physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. It is measured in the SI unit of newton (N) and often represented by the symbol F.

Conservative force

In physics, a conservative force is a force with the property that the total work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero. A conservative force depends only on the position of the object.

Potential energy

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to the ancient Greek philosopher Aristotle's concept of potentiality. Common types of potential energy include the gravitational potential energy of an object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field.

Fictitious force

A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. It is related to Newton's second law of motion, which treats forces for just one object. Passengers in a vehicle accelerating in the forward direction may perceive they are acted upon by a force moving them into the direction of the backrest of their seats for instance.

Related lectures (1,000)

Virtual Work I

Covers virtual work, equilibrium conditions, and its application in problem-solving.

Virtual Work II: Examples of Potentials

Covers examples of potentials in virtual work for structural mechanics.

Structural Mechanics Principles: Equilibrium and Stability

Explores the principles of structural mechanics, including internal loads, equilibrium stability, and the superposition principle.

Virtual Work I: Introduction to Structural Mechanics

Introduces work, potential energy, and virtual work in structural mechanics, emphasizing equilibrium conditions and their application to solve problems.

Introduction to Structural Mechanics

Introduces structural mechanics concepts like distributed loads, centroids, and equilibrium in 2D and 3D.