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method of joints and sections

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