Engineering Mechanics: Engineering Mechanics: Statics Statics

Chapter 4: Structures

Statically Determinate Statically Determinate StructureStructure

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 TrussesSimple 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 TrussesSimple 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 JointsMethod 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 JointsMethod 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 4/20Problem 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 SectionsMethod 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

Procedures1. Determine external reactions by

considering whole truss (R1 & R2)2. An imaginary section (dashed line) is

passed through the truss3. To determine BC use

To determine FE useTo determine BE use

EM =0 BM =0

yF =0

Sample Problem 4/4Sample 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 MachinesFrames and Machines

Determine the force supported by the roller at E. Ans E = 150 N

Problem 4/71Problem 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 4/80Problem 4/80