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