LECTURE+1+COE-3001-A

Aerospace 3 normal stress i normal

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Unformatted text preview: InternaIonal (SI) 1/7/13 M. Mello/Georgia Tech Aerospace 4 NORMAL STRESS (II) COMPLEX STRESS CONCENTRATIONS ARISE AROUND HOLES AT THE ENDS OF THE BAR DASHED LINES REPRESENT PINS WHICH PASS THROUGH HOLES IN THE EYE BAR P 6= A d>b P 1/7/13 “RULE OF THUMB”: EQ 1- 1 IS ACCURATE ²་  EQUATION = IS ONLY VALID IF A FOR POINTS LYING AT A DISTANCE d > b WHERE “b” REPRESENTS THE LARGEST THE AXIAL FORCE P ACTS THROUGH THE LATERAL DIMENSION OF THE BAR. CENTROID OF THE CROSS- SECTIONAL AREA! FORMULA OTHERWISE GIVES THE AVERAGE ²་  STRESS IS THEN UNIFORMLY NORMAL STRESS WHEN THE STRESS IS DISTRIBUTED OVER THE CROSS SECTION NOT UNIFORMLY DISTRIBUTED OF THE BAR. 5 M. Mello/Georgia Tech Aerospace NORMAL STRAIN (I) NORMAL STRAIN : ✏ = (1-2) L ²་  DIMENSIONLESS ²་  TENSILE (ε > 0) ²་  COMPRESSIVE (ε < 0) lo u = ( l0 ) L ²་  original units of d and L are sIll sIll someImes retained… i.e., as ²་  mm/m, µm/m, in/in etc. ²་  1 microstrain = 1 µstrain = 1x10- 6 ²་  strain olen expressed as a % ²་  % strain = εx100 Change in length of any segment lo of a bar of iniIal length L which stretches or shrinks by δ u = l0 ( L ) = ✏ l0 ²་  Numerical values of strain are typically very small! ²་  Consider that a steel bar of initial length L=2m may stretch by δ=1.4mm when heavily loaded in tension. 1/7/13 1m 1.4mm( 1000mm ) ✏= = 700x10 2m M. Mello/Georgia Tech Aerospace 6 = 700µstrain 6 UNIFORM STRESS DISTRIBUTION ASSERTION : NORMAL STRESS σ IS UNIFORMLY DISTRIBUTED OVER THE CROSS SECTION IF THE LINE OF ACTION OF THE AXIAL FORCES PASSES THROUGH THE CENTROID OF THE CROSS- SECTIONAL AREA. PROOF : Let p1 represent the point in the cross secIon where the line of acIon of the forces intersects the cross secIon. Moments of force P about x and y axes: M x = P y M y = P x (mindful of cross product M = ~ ⇥ P ) ¯ ¯ ~ r ~ Z Z Moments of the distributed stresses: M x = M y = x (sum of moments of elemental force dA y dA acIng on infinitesimal area dA ) Z Z E...
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