Chap4 Structures

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method of joints and sections

Text of Chap4 Structures

  • Engineering Mechanics: Statics

    Chapter 4: Structures

  • Statically Determinate Structure

    Do not have more supporting constraints than are necessary to maintain equilibrium

    This chapter focus on trusses, frames and machines

    Truss = A framework composed of members joined at their

    ends to form a rigid structure

    When the members lie in a single plane = a plane truss

  • Simple Trusses

    Basic element of a plane truss = triangle

    Three bars joined by pins at their ends

    constitute a rigid frame (noncollapsible)

    Structures built from a basic triangle are known

    as simple trusses

    Truss members = Two-force members

  • Simple Trusses

    Assumptions

    All external forces are applied at the joints. (If consider

    weight, apply half of the magnitude at each end)

    The members are joined together by pin connections

    Two approaches for force analysis

    Method of joints

    Method of sections

  • Method of Joints

    Used to find the forces in the truss members

    Analysis steps

    Draw FBD of a joint

    Use and to find the member forces

    Begin analysis with a joint where

    at least one known load exists

    Not more than two unknown forces are present

    xF = 0 yF = 0

  • Method of Joints Special conditions

    Zero-force member

    (a) Three members two collinear + one noncollinear

    (b) Two noncollinear members

    Two pairs of collinear members forces in each pair equal and opposite

    Choice of reference axis

  • Problem 4/20

    A snow load transfers the forces shown to the upper joints of a

    Howe roof truss. Neglect any horizontal reactions at the

    supports and solve for the forces in all members

    Problem 4/21

  • Method of Sections

    Take advantage of moment equation of equilibrium

    Not necessary to proceed with the calculation from joint to joint until the member in question has been reached

    Procedures

    1. Determine external reactions by considering whole truss (R1 & R2)

    2. An imaginary section (dashed line) is passed

    through the truss

    3. To determine BC use

    To determine FE use

    To determine BE use

    EM = 0

    BM = 0

    yF = 0

  • Sample Problem 4/4

    Calculate the force in member CD and member DJ of the roof

    truss illustrated. Neglect any Horizontal components of force at

    the supports

  • Structures which contain one or more multi-force members

    Frame = Structure designed to support loads

    Machine = Structure which transforms input actions (forces or couples)

    to output actions

    Frames and Machines

  • Determine the force supported by the roller at E.

    Ans E = 150 N

    Problem 4/71

  • The elements of a floor jack are shown in the figure. The figure CDFE is a parallelogram. Calculate the force in the hydraulic cylinder AB corresponding to the 10-kN load supported as shown. What is the

    force in link EF?

    Problem 4/80