Structural Mechanics: Systems of Forces

In course

Description

This lecture covers systems of forces in 2D and 3D, including moments, couples, and the principle of moments. It also delves into rectangular components of vectors, moments about points and axes, and stress and strain in 2D elasticity. The lecture progresses to discuss space trusses, equilibrium in 2D and 3D, frames, machines, distributed forces, beam bending, and virtual work. Additionally, it explores the concept of torque, Varignon's theorem, and the effect of force-couple systems. The lecture concludes with examples illustrating the application of these concepts in real-world scenarios.

Instructors (2)

Official source

https://mediaspace.epfl.ch/media/0_b3vwgerl

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Related concepts (195)

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.

Couple (mechanics)

In mechanics, a couple is a system of forces with a resultant (a.k.a. net or sum) moment of force but no resultant force. A better term is force couple or pure moment. Its effect is to impart angular momentum but no linear momentum. In rigid body dynamics, force couples are free vectors, meaning their effects on a body are independent of the point of application. The resultant moment of a couple is a special case of moment. A couple has the property that it is independent of reference point.

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.

Centrifugal force

In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parallel to the axis of rotation and passing through the coordinate system's origin. If the axis of rotation passes through the coordinate system's origin, the centrifugal force is directed radially outwards from that axis.

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.