Curved Beam Stress Analysis -...
1
C:\Bill\BEI\~ME311\2011\WebStuff\CurvedBeams.doc Curved Beam Stress Analysis 1) Draw a very good picture. Show r i , r o , Area Show the applied Force, F 2) Calculate the centroidal radius, R, based on the section type. (Hamrock § 4.5.3) Rectangular: 2 o i r r R + = Circular: c i r r R + = 3) Compute the neutral radius, r n , based on the section type. Rectangular: ) ln( i o i o n r r r r r - = Circular: 2 2 2 c n r R R r - + = 4) Compute the eccentricity, e = R - r n 5) Compute the moment about the centroidal radius, R. Here M = F x L, not F x R, because the force is not through the center of curvature. 6) Calculate the distances from the neutral axis to the inner and outer surfaces: c i = r n – r i and c o = r o – r n . 7) Calculate the stresses at the inside and outside surfaces: i i i Aer Mc = σ and o o o Aer Mc - = σ , where A = the section area 8) Add or subtract any P/A stresses (using superposition). Rectangular: b r r F i o ) ( - = σ Circular: 2 c r F π σ = 9) As a check, compare the answer to MC / I for a straight beam with neutral axis on the centroid and see if it makes sense. F R L r i r o e r i r o R r n r i r c b Centroidal radius, R Neutral radius, rn
Transcript of Curved Beam Stress Analysis -...
C:\Bill\BEI\~ME311\2011\WebStuff\CurvedBeams.doc
Curved Beam Stress Analysis
1) Draw a very good picture.
� Show ri, ro, Area � Show the applied Force, F
2) Calculate the centroidal radius, R,
based on the section type. (Hamrock § 4.5.3)
Rectangular: 2
oirr
R+
= Circular: cirrR +=
3) Compute the neutral radius, rn, based on the section type.
Rectangular: )ln(
io
io
n
rr
rrr
−= Circular:
2
22
c
n
rRRr
−+
=
4) Compute the eccentricity, e = R - rn
5) Compute the moment about the centroidal radius, R. Here M = F x L, not F x R, because the force is not through the center of curvature.
6) Calculate the distances from the neutral axis to the inner and outer surfaces:
ci = rn – ri and co = ro – rn.
7) Calculate the stresses at the inside and outside surfaces:
i
i
i
Aer
Mc=σ and
o
o
o
Aer
Mc−=σ , where A = the section area
8) Add or subtract any P/A stresses (using superposition).
Rectangular: brr
F
io)( −
=σ Circular: 2
cr
F
π
σ =
9) As a check, compare the answer to MC / I for a straight beam with neutral axis on the centroid and see if it makes sense.
F R
L
ri
ro
e
ri ro
R rn
ri rc
b
Centroidal radius, R
Neutral radius, rn
![The geodesic flow of a nonpositively curved graph manifold · 2018. 7. 24. · arXiv:math/9911170v1 [math.DG] 22 Nov 1999 The geodesic flow of a nonpositively curved graph manifold](https://static.fdocument.org/doc/165x107/5fdba015c36b0c2af5295c4f/the-geodesic-iow-of-a-nonpositively-curved-graph-manifold-2018-7-24-arxivmath9911170v1.jpg)
