presentation-moment capacity of damaged beams
TRANSCRIPT
![Page 1: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/1.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 1/25
Moment Capacity of Moment Capacity of Damaged GirdersDamaged Girders
Andrea V. Ch Andrea V. Ch áá vezvez , New Mexico State University,, New Mexico State University,NSFNSF --REU 2004REU 2004 August 6, 2004 August 6, 2004
Research Advisor:Research Advisor: Dr. Harry W. ShentonDr. Harry W. Shenton
![Page 2: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/2.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 2/25
ObjectiveObjective
•• Analyze bridge girders that have bent flanges Analyze bridge girders that have bent flanges
•• Assume damaged girder is in perfect plastic Assume damaged girder is in perfect plasticregion and calculate plastic moment before andregion and calculate plastic moment before andafter damage occursafter damage occurs
•• Develop plastic moment ratioDevelop plastic moment ratio
![Page 3: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/3.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 3/25
Types of Damage to GirdersTypes of Damage to Girders
Severe Case
Our research will focus on aless severe case
Photo courtesy of Connecticut Department of TransportationBureau of Engineering and Highway Operations Division of Research
Photo courtesy of paper on Engineered HeatStraightening
![Page 4: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/4.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 4/25
The Focus for this ResearchThe Focus for this Research
DamagedUndamaged
U P M
D P M
( )θ
U P
D P
M
M
![Page 5: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/5.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 5/25
Assumptions Assumptions
•• Deck is nonDeck is non --compositecomposite
•• Perfect PlasticityPerfect Plasticity
•• Shear and fatigue not addressed in this studyShear and fatigue not addressed in this study
•• Nonsymmetrical BendingNonsymmetrical Bending
![Page 6: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/6.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 6/25
Analysis of Plasticity Analysis of Plasticity
•• Defining the Plastic RegionDefining the Plastic Region
Figure courtesy of Mechanics of Materials (2 nd edition)Gere, Timoshenko
2
)( 21 y y A Z M y
y p
+==
σ σ
y1
A1
A2
y2c2
c1
![Page 7: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/7.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 7/25
Analysis of Nonsymmetrical Bending Analysis of Nonsymmetrical Bending
22
)( 21 YAd d YA
y y A Z M T
y y p
==+
==σ
σ
Figure courtesy of Advanced Mechanics of Materials 5 th edition-Boresi, Schmidt,Sidebottom
![Page 8: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/8.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 8/25
ConstraintsConstraints
•• Shift in Neutral Axis (which divides theShift in Neutral Axis (which divides the
cross section into two equal areas)cross section into two equal areas)
•• Centroids of areas must be alignedCentroids of areas must be alignedverticallyvertically
![Page 9: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/9.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 9/25
Model of Girder Before DamageModel of Girder Before Damage
Load applied
C 1
C 2
N.A.
![Page 10: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/10.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 10/25
Model of Girder After DamageModel of Girder After Damage
Load applied
N.A.θ
![Page 11: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/11.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 11/25
Choosing a ModelChoosing a Model
![Page 12: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/12.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 12/25
Section PropertiesSection Properties
•• Determine the effect of its dimensionsDetermine the effect of its dimensions
•• Calculate the two equal areasCalculate the two equal areas•• Calculate the plastic momentCalculate the plastic moment
•• Locating the neutral axisLocating the neutral axis
![Page 13: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/13.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 13/25
Plastic Moment RatioPlastic Moment Ratio
•• RecallRecall
•• Ratio is needed for comparisonRatio is needed for comparison
•• Performance of Calculations basedPerformance of Calculations basedonon
22
)( 21 YAd y y A M y
p=
+=
σ
U
p
D p
M
M
( )( ) U
p
D p
U
D
M
M
y y
y y y y =
+
+
→+
21
2121
![Page 14: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/14.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 14/25
Plastic Moment RatioPlastic Moment Ratio
TOP BOT x x=
d
θ
m
Bot y
Bot x
Important:
•m=n
•All thicknesses “t”
are the sameTop x
Top y
n
b
Dm y
![Page 15: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/15.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 15/25
Calculating the Plastic Moment RatioCalculating the Plastic Moment Ratio
22
sin28
22
2cos22
22
222
d b
md bd
y
d b
mbmbb
x
BOT
BOT
+
++
=
+
−++−
=
θ
θ
d
θ
b-m
m
d/2
y
x
Bot y
Bot x b
![Page 16: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/16.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 16/25
Calculating the Plastic Moment RatioCalculating the Plastic Moment Ratio
Top x
Top y
d
n
d/2
b-mb
yx
22
8
22
2
2
2
d b
d md y
d b
mbm x
TOP
TOP
+
+
=
+
+−=
![Page 17: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/17.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 17/25
Calculating the Plastic Moment RatioCalculating the Plastic Moment Ratio
2cos32
−
++−=
θ bbm
22
2
22
2cos22
22
22
d b
mbmd
b
mbmbb
x x TOP BOT
+
+−=
+
−++−
=
θ
•Recall
•Solve for m
![Page 18: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/18.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 18/25
![Page 19: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/19.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 19/25
Calculating the Plastic Moment RatioCalculating the Plastic Moment Ratio
d b
d db
d b
bd bd
y
yU
m
D
m
+
+
+
++−
=
42
44
cos32sin2
2
22
θ θ
b
d
2=γ
Solve for ratio
γ θ and
Make ratio dependent on only two variables
where
![Page 20: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/20.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 20/25
2
2
2+8
cos+34+sin2==
γγ
θ γθ γ
y
y
M
M U
m
Dm
U P
D P
Calculating the Plastic Moment RatioCalculating the Plastic Moment Ratio
![Page 21: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/21.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 21/25
Results of the Plastic Moment RatioResults of the Plastic Moment Ratio
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 1 0
1 5
2 0
2 5
3 0
3 5
4 0
4 5
5 0
5 5
6 0
6 5
7 0
7 5
8 0
8 5
9 0
Angle θ (degrees)
r a t i o o
f Y
m D / Y
m U = M
p D / M
p U
0.5
1
23
4
5
10
γ of values
![Page 22: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/22.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 22/25
ConclusionsConclusions
••The relative moment capacity decreases for The relative moment capacity decreases for decreasing gammadecreasing gamma
•• As the angle increases the ratio will decrease As the angle increases the ratio will decrease
••The larger the bend of the flange the lower theThe larger the bend of the flange the lower the
capacitycapacity••The shallower the crossThe shallower the cross --section the lower the plasticsection the lower the plasticmoment capacitymoment capacity
![Page 23: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/23.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 23/25
Future GoalsFuture Goals
•• Vary the thicknesses for the girder Vary the thicknesses for the girder
•• Calculate the ratio based on varying thicknessesCalculate the ratio based on varying thicknesses
•• Apply new ratio to any girder Apply new ratio to any girder
•• Help DOT with field situations in a timely manner Help DOT with field situations in a timely manner
![Page 24: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/24.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 24/25
![Page 25: Presentation-Moment Capacity of Damaged Beams](https://reader035.vdocument.in/reader035/viewer/2022062504/577cd7db1a28ab9e789fd7df/html5/thumbnails/25.jpg)
7/27/2019 Presentation-Moment Capacity of Damaged Beams
http://slidepdf.com/reader/full/presentation-moment-capacity-of-damaged-beams 25/25
QuestionsQuestions
Thank You!Thank You!
Contact Info: [email protected]