Concept of StressesAFnmGiven F as the force transmitted across A, a stress traction vectorcan be defined ast = lim △F//AAA->0Units: Pa (N/m2), 1 MPa = 106 Pa, 1 GPa = 109 Pa11
m t ζ Units: Pa (N/m2 ), 1 MPa = 106 Pa, 1 GPa = 109 Pa. m 0 lim A t F A Given ΔF as the force transmitted across ΔA, a stress traction vector can be defined as F A n Concept of Stresses 11
General Stress State of a Point00xx0rO虹dzdxVAll stress components shown in the above figure are positive12
ζxx ζyy ζzz ζxy ζxz ζzx ζzy ζyx ζyz ζzz ζxx ζyy ζyx ζyz ζzy ζzx ζxz ζxy dx dz dy x y z All stress components shown in the above figure are positive. General Stress State of a Point 12
Stresses Acting on Cross SectionsTransverseLongitudinalRAssumption: stresses are uniformly distributed on the cross sectionsof axially loaded bars (Saint-Venant's Principle)dA=oAFn =LodA=αlA13
FN ζ N d d A A F A A A Longitudinal Transverse F F FN A Assumption: stresses are uniformly distributed on the cross sections of axially loaded bars (Saint-Venant’s Principle) Stresses Acting on Cross Sections 13
Saint-Venant's Principle.Loads transmitted through rigidplates result in uniform distributionofstressandstrain.Concentrated loads result in largestresses in the vicinity of the loadapplication point.Stressand strain distributionsbecomeuniform at a relatively short distancefrom theload application pointsSaint-Venant's Principle:Stress distribution may be assumedindependentofthemodeofloadCmin=0.198QaeOmin=0.668gaveOmim=0.9730aveapplicationexcept intheimmediateOmx=2.5750aveOmax=1.3870aveOmax =1.027Cavevicinity of loadapplicationpoints14
• Loads transmitted through rigid plates result in uniform distribution of stress and strain. • Saint-Venant’s Principle: Stress distribution may be assumed independent of the mode of load application except in the immediate vicinity of load application points. • Stress and strain distributions become uniform at a relatively short distance from the load application points. • Concentrated loads result in large stresses in the vicinity of the load application point. Saint-Venant’s Principle 14
Sample ProblemFNA22AH民A = 2AO A2 = 20 A115
FN A 1 2 2 1 2 2 A A A A Sample Problem 15