Exploring Beam Deflection: Area Moment, Moment of Inertia & Center of Gravity

[blamoi]

Homework Statement

Hey

In my assignment I am writing about beamdeflection, but there's some things i really can find out how to do.
I need to explain area moment, moment of inertia and the center of gravity, i need to explain this with the help of integration.

Under her I've inertet the whole assigment, sorry for bad english, its google translate:
Problem Formulation
Explain the use of beams for building construction in a historical perspective as well as for the two
requirements normally will dimension the following (strength and deflection).
Derive the expression for the maximum stress in a cross-section, and for two different bar case
expression to determine the maximum deflection - explains including area moments
center of gravity and inter timo elements using integral calculus and use the theory of a self-selected
profile of adequate complexity.

can someone please help make notation, or give me some reading stuff i can use

Homework Equations

The Attempt at a Solution

 

[Valkarie]

Area Moment: Area moment is a measure of the stiffness of a beam, which is determined by the shape, size, and material of the beam. It is the product of the area times the moment of inertia of the cross sectional area at a particular point along the length of the beam. It is used to calculate the bending moment of the beam at that point, which determines the amount of deflection the beam will experience when a force is applied to it.Moment of Inertia: Moment of inertia is a measure of a beam's resistance to bending or twisting. It is defined as the sum of the products of the mass of each particle multiplied by the square of its distance from the axis of rotation. It is used to calculate the moment of force in a beam, which is used to calculate the deflection of the beam when a force is applied.Center of Gravity: The center of gravity is the point at which the entire mass of the beam is considered to be concentrated. It is determined by taking the sum of the products of each particle's mass multiplied by its distance from the axis of rotation. It is used to calculate the moment of force in a beam, which is used to calculate the deflection of the beam when a force is applied.Integral Calculus: Integral calculus is a branch of mathematics that deals with the calculation of areas and volumes using integrals. It is used to calculate the area moments and center of gravity of a beam, which are used to calculate the moment of force in a beam and its deflection when a force is applied.