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    Chapter 4 Centroid - Distr. Forces

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    kamal touileb
    This document discusses centroids and distributed forces. It introduces the concepts of concentrated versus distributed forces and defines centers of mass and centroids. It then covers determining centroids for lines, areas, and volumes. Several sample problems are worked through calculating centroids and distributed loads on beams. Theorems of Pappus are presented for calculating the surface area generated by revolving a plane curve. More sample problems calculate volumes and load distributions on beams.

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    Chapter 4 Centroid - Distr. Forces

    Uploaded by

    kamal touileb
    24 views33 pages
    This document discusses centroids and distributed forces. It introduces the concepts of concentrated versus distributed forces and defines centers of mass and centroids. It then covers determining centroids for lines, areas, and volumes. Several sample problems are worked through calculating centroids and distributed loads on beams. Theorems of Pappus are presented for calculating the surface area generated by revolving a plane curve. More sample problems calculate volumes and load distributions on beams.

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    chapter 4 Centroid - distr. forces

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    This document discusses centroids and distributed forces. It introduces the concepts of concentrated versus distributed forces and defines centers of mass and centroids. It then covers determining centroids for lines, areas, and volumes. Several sample problems are worked through calculating centroids and distributed loads on beams. Theorems of Pappus are presented for calculating the surface area generated by revolving a plane curve. More sample problems calculate volumes and load distributions on beams.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    24 views33 pages

    Chapter 4 Centroid - Distr. Forces

    Uploaded by

    kamal touileb
    This document discusses centroids and distributed forces. It introduces the concepts of concentrated versus distributed forces and defines centers of mass and centroids. It then covers determining centroids for lines, areas, and volumes. Several sample problems are worked through calculating centroids and distributed loads on beams. Theorems of Pappus are presented for calculating the surface area generated by revolving a plane curve. More sample problems calculate volumes and load distributions on beams.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 33

    Chapter 4

    Centroids &
    Distributed forces
    Introduction
     In the previous chapters we treated
    all forces as concentrated along their
    lines of action and at their points of
    application.
     “concentrated” forces do not exist in
    the exact sense, since every external
    force applied mechanically to a body
    is distributed over a finite contact
    area, however small.
    Introduction

    Volume Distribution
    Line Distribution Area Distribution
    CENTERS OF MASS AND
    CENTROIDS
     Center of Mass
    Determining the Center of
    Gravity
    Determining the Center of Gravity
    Centroids of Lines, Areas,
    and Volumes
     Centroids of Lines
    Centroids of Lines, Areas,
    and Volumes
     Centroids of Areas:
    Centroids of Lines, Areas,
    and Volumes
     Centroids of Volumes
    Sample Problem
    Sample Problem
    Sample Problem
    Centroid of semicircular&
    quarter-circular
    Composite Bodies and
    Figures; Approximations
    Sample Problem
    Sample Problem
    Solution
    Theorems of Pappus
    A very simple method exists for calculating the surface area generated
    by revolving a plane curve about a nonintersecting axis in the plane of
    the curve
    Theorems of Pappus
    Theorems of Pappus
     Ifa line or an area is revolved
    through an angle θ less than 2π, we
    can determine the generated
    surface or volume by replacing 2π
    by θ
    Sample Problem
     Determinethe volume V and surface area A of
    the complete torus of circular cross section.
    Sample Problem
     Calculate the volume V of the solid generated by
    revolving the 60-mm right triangular area through
    180 about the z-axis. If this body were constructed
    of steel, what would be its mass m?
    Solution
    Beams—External Effects

    Beams are structural


    members which offer
    resistance to bending
    due to applied loads.
    This analysis requires
    the application of the
    principles of statics.
    Types of Beams
    Distributed Loads
    Sample Problem
     Determine the equivalent concentrated load(s) and
    external reactions for the simply supported beam
    which is subjected to the distributed load shown.
    Problem 1
     Calculate the
    supporting force
    Ra and moment
    Ma at A for the
    loaded cantilever
    beam.
    Problem 2

     Determine
    the reactions
    at A and B for
    the loaded
    beam.
    Problem 3

    Determine the
    reactions at A for
    the cantilever
    beam subjected to
    the distributed and
    concentrated
    loads.
    Problem 4
     Findthe reaction at
    A due to the
    uniform loading
    and the applied
    couple.
    Problem 5
     Determine the
    reactions at A and B
    for the beam
    subjected to a
    combination of
    distributed and point
    loads.
    Problem 6
    Determine the force and moment reactions
    at A for the beam which is subjected to
    the load combination shown.

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