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 : ✏ =
(12)
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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 Spring '09
 ZHU
 Force, M.

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