Designing Members For Torsion
Designing Members For Torsion
Designing Members For Torsion
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Copyright 2014
American Institute of Steel Construction
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AISC Webinar
February 12, 2015
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Course Description
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Learning Objectives
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Daniel Linzell
University of Nebraska, Lincoln
Acknowledgements
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Background - Torsion
What is it?
From Wikipedia
In solid mechanics, torsion is the twisting of an object due to an applied
torque, therefore is expressed in Nm or ftlbf. In sections perpendicular
to the torque axis, the resultant shear stress in this section is
perpendicular to the radius.
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Background - Torsion
From Your Undergrad Engineering Mechanics
Class Pure Torsion
x
M
TL
GJ
Torsion
d M
=
dx EI
Bending
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Background - Torsion
From Your Undergrad Engineering Mechanics Class?
How many cantilevered, solid round bars are used in steel
building structural elements? Not many most are like those
shown. Consequences?
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Background - Torsion
From Your Undergrad Engineering Mechanics Class?
Consequences? New worries with these sections shear flow,
shear center, determining J.
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Background - Torsion
From Your Undergrad Engineering Mechanics Class?
More consequences?
Pure (St. Venants) vs. Warping Torsion.
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Background - Torsion
Why Do We Care?
Even Though Publications We Use Say/Show This:
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Background - Torsion
Why Do We Care?
We Run Into Situations Like This:
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Background - Torsion
Why Do We Care?
AND too much twist can be a bad thing
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A Few Fundamentals
Terms You May (or May Not)
Know
Shear Flow
Again, Wiki:
The gradient of a shear stress force
through the body (in solid mechanics)
The flow induced by such a force gradient
(in a fluid)
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A Few Fundamentals
Terms You May (or May Not)
Know
Shear Center (Wiki!!)
An imaginary point on a section,
where a shear force can be applied
without inducing any torsion
Sometimes coincides with
centroid (center of area)
How establish? Look @ twist
equilibrium in-plane. No twist
occurs due to in-plane shears
that develop due to flexure
location where they cancel each
other out is shear center.
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A Few Fundamentals
Terms You May (or May Not) Know (NO
WIKI!!)
Pure (St. Venants) Torsion
Planar rotation of a structural element. Generates
in-plane shear stresses.
Warping Torsion
Tendency of portions of structural element to move
out of plane. If out of plane movement not
prevented, no stresses developed. If prevented,
generates BOTH in-plane shear stresses and stresses
normal to plane.
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A Few Fundamentals
Warping Torsion
Can also be seen as a force couple to each
flange
T
h
T
h
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A Few Fundamentals
Warping Torsion
Now lets look at the bottom flange
T
h
T
h
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A Few Fundamentals
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Pr M r Vr Tr
+ + 1.0
+
P
M
Tc
c Vc
c
Tr < 0.2 * Tc, ignore torsion.
Tc prescribed in Eqns. H3-2a or H3-2b.
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Fn = Fy
Shear yielding (Eqn. H3-8):
Fn = 0.6Fy
Buckling (Eqn. H3-9):
Fn = Fcr
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f n = a bx by w
f v = bx by t w
I-Shapes:
f n = a ( bx + by + w )
f v = bx + by + t + w
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t = Gt
G = shear modulus
t = element thickness
= Rate of change of
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ws =
ES ws
t
E = elastic modulus
Sws = warping statical moment at s
= hbf2tf /16
t = element thickness
= 3rd derivative of
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ws = EWns
E = elastic modulus
Wws = normalized warping function at s
= hbf/4
= 2nd derivative of
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w =
1.5Vf
bf t f
w =
Mf
Sf
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Bridges
AASHTO/NSBA G 13.1 Guidelines for Steel Girder Bridge Analysis (2011),
http://www.aisc.org/contentNSBA.aspx?id=20130
AISC/NSBA Steel Bridge Design Handbook,
http://www.aisc.org/contentNSBA.aspx?id=20244
General
Salmon, C.G., Johnson, J.E. and Malhas, F.A., Steel Structures Design and
Behavior, 5th Ed., Pearson Prentice Hall, 2009.
Young, W. and Budynas, R., Roarks Formulas for Stress and Strain, 7th Ed.,
McGraw Hill, 2001.
Your undergrad mechanics textbook
Your undergrad steel design textbook
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Example
Steel lintel beam spanning opening in a bearing wall building
Live load is neglected due to
arching action
2
L=15
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Example
(a) Define structural system
Span=15 ft.
W8x24
Fy=50 ksi
Boundary conditions?
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Example
(a) Define structural system
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Example
(a) Define structural system
Boundary conditions?
Moment
OR
Torsion
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Example
(a) Define structural system
Boundary conditions?
OR
Torsion
Twist fixed
Warping free
Twist fixed
Warping fixed
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Example
(b) Find member demand shear V, moment M,
torsion T, and axial force P Moment
Live load is neglected due to
arching action
Torsion
2
L=15
pfacade=40 lb/ft2
= 60
pmasonry=60 lb/ft2
15
4
1
= 150
15
15
4
1
= 225
15
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Example
(b) Find member demand shear V, moment M,
torsion T, and axial force P Moment
Torsion
wmasonry
wsnow
Wfacade
= 1.4
= 1.4 150
+ 225
8 in.
= 1.4 150
+ 225
= 3.9
15
8
= 14.8
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Example
(b) Find member demand shear V, moment M,
torsion T, and axial force P Moment
Torsion
wmasonry
wsnow
Wfacade
= 1.4 150
8
= 0.14
12
8 in.
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Example
(c) Calculate angle of twist, derivatives
Moment
Torsion
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Example
(d) Check normal stresses P+M+T
Demand stresses (bending)
Moment
Torsion
f n = a ( bx + by + w )
14.8
(12 / )
82.7
7.93
2 = 8.5
x
y
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Example
(d) Check normal stresses P+M+T
Demand stresses (torsion)
Moment
Torsion
f n = a ( bx + by + w )
w = EWno
y
Torsion
x
x
y
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Example
(d) Check normal stresses P+M+T
0.75 =
11200
0.35
0.14
15(12)
= 4.11
43.8
= 2.68 5 rad/in2
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Example
(d) Check normal stresses P+M+T
Demand stresses (torsion)
Moment
Torsion
f n = a ( bx + by + w )
= 2.08 5
w = EWno
= 29000
x
2.68 5
= 9.5
x
y
12.2
= 0 (8.5
+ 0 + 9.5
) = 18.0
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Example
(d) Check normal stresses P+M+T
Moment
Beam capacity
Torsion
Fn = Fy
Buckling (Eqn. H3-9):
Fn = Fcr
fn T Fn
=
= 50
Example
(e) Check shear stresses V+T
OK
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Moment
Torsion
f v = bx + by + t + w
by =
y
VuQw
I x tw
Direct shear
3.9
82.7
(11.6 )
= 2.23
(0.245 )
y
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
Shear stresses from
Torsion
x
y
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
Shear stresses from
= 1.70 3
x
= 11200
0.245
1.70 3
= 4.67
y
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
= 2.23
+ 0 + 4.67
+ 0 = 6.90
x
y
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
ws =
y
Torsion
x
x
y
'''
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
ws =
y
= 7.90 7
x
29000
(7.94
4) (7.90
0.4
= 0.45
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
t = Gt f
Torsion
x
y
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
t = Gt f
= 1.70 3
x
= 11200
0.4
1.70 3
= 7.62
y
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Example
(e) Check shear stresses V+T
Moment
Torsion
f v = bx + by + t + w
= 0 + 0 + 7.62
+ 0.46
= 8.08
x
y
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Example
(e) Check shear stresses V+T
Moment
Web/flange capacity
Torsion
Fn = 0.6Fy
fv T Fn
= 0.6 = 30
Fv=0.9(30 ksi) = 27 ksi
Fv = 8.08 ksi (flange) Fv = 27.0 ksi
OK
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References
AASHTO/NSBA G 13.1 Guidelines for Steel Girder Bridge Analysis (2011)
Domalik, D.E., Shura, J.F. and Linzell, D.G., Design and Field Monitoring of Horizontally Curved Steel Plate Girder Bridge,
Transportation Research Record, Journal of the Transportation Research Board No. 1928, pp. 83-91, 2005.
Salmon, C.G., Johnson, J.E. and Malhas, F.A., Steel Structures Design and Behavior,,5th Ed., Pearson Prentice Hall, Upper Saddle
River, NJ, 2009.
Seaburg, P.A. and Carter, C. J. AISC Steel Design Guide Series #9, Torsional Analysis of Structural Steel Members, American
Institute of Steel Construction, Chicago, IL, 2003.
http://www.news.com.au/national-news/melbourne-teacher-under-investigation-over-alleged-punishments/story-e6frfkvr1226035003739
http://www.gestech.net/shaft_torsional_failure1.htm
http://www.proactivefluidpower.com/shaft_failures.htm
http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=me&chap_sec=02.2&page=theory
http://www.transtutors.com/homework-help/mechanical-engineering/torsion/shafts-circular-section.aspx
http://www.renovateforum.com/f83/hhow-much-can-c-purlin-span-shed-frame-53666/
http://www.structuremag.org/article.aspx?articleid=527
http://faculty.kirkwood.edu/jlopez/details/floor004.jpg
http://www.gostructural.com/magazine-article-gostructural.com-4-2010structural_detailing_solutions_to_avoid_thermal_bridging-7838.html
http://www.pascalsteel.com/content/girts-and-panel-metal-building
http://alviassociates.com/awards
http://appliedconceptengineering.com.au/construction/structural/rounded-steel-frames
http://orthostreams.com/wp-content/uploads/2013/02/OilRig_OilRig_WEB.jpg
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