OpentubeintorsioE ytd
a t.FI
iismm
ifI.IT
Shearstress
FilIIII
For a solidcylindersubjecttotorqueloading Complementary
ShearStressesFlow
Shearstrain r Shearstress
Resultanttorque
y
T GJ z
Torsionalconstant J frfyi.gg
butif wehavea noncircular weseeWARPINS outofplanedistortion
Boundary
condition Tzn O freesurface
equatingforcesin s n
to i toxy
SEEIN
TzuSA TzySAcost TexSAsiny 0
rateottwist
Tzy Tax21 0
s
yO imm.fi.it i ijgana
aTw a
ylO'z ci
horizontal
u
displacement
v koxloz
dlngo
cnet.my
Hax 0 0
0
by 0
exy Oz
02 0
f
Halite Egg
esekiflo ty.cat
Ezx
ty 0 Tax GEzx
E
g
l
internalequilibriumofnonzerostresse
603Ey where
z
issatisfied.fi
F 0
Eyz 6012
Flay isthe stressFunction
2if 0 B.EEytEnditon
25tyfyfy.is 0 1
24.25 1 4.25 1
2 2 25 2521 0
87 21 2 10 1 24 0 5 2
p F 2
igii.isEinItreesurtace
, Torqueresultant T fff.tzyx
Txzyldxd T
GOff.atxtfIyydxdy
JFdx
Consider xdx Fdx
M eAnalogy thestress
functionF
to
free
surface
behaves in thesame asathinmembrane
under a constantway pressure andsimilarly fIyydy
Fdg
ne
t F 260 ffaFd
dy and J 2ffaFdxdy
i
profiled stressfunctionFis approximatelyconstant
midline exceptdcornersandends
alongthe
Iot.FIIIEEarst contours
pzF 2 becomes 3 2
J 2 aFdxdy
F AtBn n F o
Tsz_GO an th n
tz
Tsz 260m
J 2ff dnds i Flu tI 12
n J IfEds
3
Is
60 t
Igt
i
ClosedTubeinTorsion
noaxialfontofplanetconstraint Oz 0
q
t crosssectionshaperemainsconstantcos0
fr enforced
byhavingribsandspacers
shearstressis constantacrossthickness q Tszt Tzst
9 22Sz forceequilibrium 0 and It _0 i.e g constunderpuretorsion
gives Its
T 2Aq BredtBath Formula
ddIz O yIaq ds and enclosed
bythemidlineotthesectanway
J g4
, CLOSED SECTION'T OPEN SECTION
underthesame
torqueloading Imax GO't
gFEINT where OEI and YESTER
I 6J
F zIat I Tma Ft I t
Lopen 3 I
O ds ed get
G sections shearstresses
GJ
open seemuchhigher
O E
undertasionwhen
comparedtoclosed
sections
z
0 21121
yq 36
_O 3
I
Korea.se
EassiEeIdianhpigahIiiitioideiestiiisotn
OpenTubeinhear
s
Tszt2 Ss stresses are constant
along wallthickness
qzz assuming
thismeanswecannothave torsionltwist
any
9eahqeaihongIEEEE.si
lopenseotonramdg.ugki
2 Forceequilibriumgives
t2T 0
which
gives q.FI soytds andsimilartyg FyIyfoxtds
yasasIfIiYfipalaanxeds
freee.dges s Oands S
enforce
9 0 Dx
Dy
a t.FI
iismm
ifI.IT
Shearstress
FilIIII
For a solidcylindersubjecttotorqueloading Complementary
ShearStressesFlow
Shearstrain r Shearstress
Resultanttorque
y
T GJ z
Torsionalconstant J frfyi.gg
butif wehavea noncircular weseeWARPINS outofplanedistortion
Boundary
condition Tzn O freesurface
equatingforcesin s n
to i toxy
SEEIN
TzuSA TzySAcost TexSAsiny 0
rateottwist
Tzy Tax21 0
s
yO imm.fi.it i ijgana
aTw a
ylO'z ci
horizontal
u
displacement
v koxloz
dlngo
cnet.my
Hax 0 0
0
by 0
exy Oz
02 0
f
Halite Egg
esekiflo ty.cat
Ezx
ty 0 Tax GEzx
E
g
l
internalequilibriumofnonzerostresse
603Ey where
z
issatisfied.fi
F 0
Eyz 6012
Flay isthe stressFunction
2if 0 B.EEytEnditon
25tyfyfy.is 0 1
24.25 1 4.25 1
2 2 25 2521 0
87 21 2 10 1 24 0 5 2
p F 2
igii.isEinItreesurtace
, Torqueresultant T fff.tzyx
Txzyldxd T
GOff.atxtfIyydxdy
JFdx
Consider xdx Fdx
M eAnalogy thestress
functionF
to
free
surface
behaves in thesame asathinmembrane
under a constantway pressure andsimilarly fIyydy
Fdg
ne
t F 260 ffaFd
dy and J 2ffaFdxdy
i
profiled stressfunctionFis approximatelyconstant
midline exceptdcornersandends
alongthe
Iot.FIIIEEarst contours
pzF 2 becomes 3 2
J 2 aFdxdy
F AtBn n F o
Tsz_GO an th n
tz
Tsz 260m
J 2ff dnds i Flu tI 12
n J IfEds
3
Is
60 t
Igt
i
ClosedTubeinTorsion
noaxialfontofplanetconstraint Oz 0
q
t crosssectionshaperemainsconstantcos0
fr enforced
byhavingribsandspacers
shearstressis constantacrossthickness q Tszt Tzst
9 22Sz forceequilibrium 0 and It _0 i.e g constunderpuretorsion
gives Its
T 2Aq BredtBath Formula
ddIz O yIaq ds and enclosed
bythemidlineotthesectanway
J g4
, CLOSED SECTION'T OPEN SECTION
underthesame
torqueloading Imax GO't
gFEINT where OEI and YESTER
I 6J
F zIat I Tma Ft I t
Lopen 3 I
O ds ed get
G sections shearstresses
GJ
open seemuchhigher
O E
undertasionwhen
comparedtoclosed
sections
z
0 21121
yq 36
_O 3
I
Korea.se
EassiEeIdianhpigahIiiitioideiestiiisotn
OpenTubeinhear
s
Tszt2 Ss stresses are constant
along wallthickness
qzz assuming
thismeanswecannothave torsionltwist
any
9eahqeaihongIEEEE.si
lopenseotonramdg.ugki
2 Forceequilibriumgives
t2T 0
which
gives q.FI soytds andsimilartyg FyIyfoxtds
yasasIfIiYfipalaanxeds
freee.dges s Oands S
enforce
9 0 Dx
Dy
