what is so great about ductility?
TRANSCRIPT
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A Tension-Controlled Open Web Steel Joist
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No joist will withstand sudden and catastrophic impact forces that exceed system capability. Flex-Joist design offers probability of high ductility and time delay under static gravity overload conditions.
DISCLAIMER:
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Improved Ductility and Reliability under Static
Gravity Overload
Purpose:
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Flex-Joist™ Engineered Limit States
Intentionally imbalanced member strength ratios Weaker components serve as “ductile fuse” Initial limit state of ductile yielding in primary tension members Other limit states inhibited until advanced state of collapse
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• Reduced Probability of Collapse
– Improved Structural Reliability
• Reduced Variance in Strength
• Reserve Inelastic Capacity
• Load Sharing with Adjacent Joists
What is so great about ductility?
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• Increased Probability of Safe Evacuation
– Slower Collapse Mechanism
– Sensory Warning via Large Inelastic Deflections
What is so great about ductility?
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What is so great about ductility?
Improved Structural Reliability: Reduced Variance in Strength
Influence of Variance on Reliability
Which population has the greatest probability of a value below 1.0?
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• Idealized parallel system sketch
• Load shared equally between components
What is so great about ductility?
Improved Structural Reliability: Load Sharing
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• Sudden Strength Loss (lack of ductile behavior)
• Load dumps to remaining components (progressive collapse)
• System strength limited by weakest component
• System variance equals variance of individual components population
What is so great about ductility?
Improved Structural Reliability: Load Sharing
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• Idealized parallel system sketch
• Load shared equally between components
• Elasto-Ductile system
What is so great about ductility?
Improved Structural Reliability: Load Sharing
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• Ductile behavior
• Weakest member continues to support plastic capacity after exceeding elastic limit
• System strength a function of average component strength
• System Variance:
• 𝑉𝑠 =𝑉
𝑛
What is so great about ductility?
Improved Structural Reliability: Load Sharing
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Compressive Buckling
Design Strength
Compression Element Buckling
Ultimate Strength
What is so great about ductility?
Slower Collapse Mechanism with Sensory Warning
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Compression Element Buckling
Tension Element Yield
Design Strength
Ultimate Strength
Ductile Tensile Yielding
What is so great about ductility?
Slower Collapse Mechanism with Sensory Warning
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Flex-Joist Load/Deflection Data Plot
When Loads Exceed Capacity of a Flex-Joist
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Flex-Joist™ Design Reliability Study
Ratio of Plastic Strength / Experimental Design Load From Villanova Data
Series Sample
LRFD
Design
Load (plf)
Fy Experi-
mental
(ksi)
Adjusted
Design
Critical
Load (plf)
Plastic
Strength
(plf)
Ratio
Plastic /
Adj Crit
Load
J1-1 568 1.01
J1-2 574 1.02
J1-3 567 1.01
J1-4 589 1.05
J1-5 592 1.06
J1-6 582 1.04
J2-1 1878 1.07
J2-2 1882 1.07
J2-3 1886 1.07
J2-4 1852 1.06
J2-5 1868 1.06
J2-6 1855 1.06
J3-1 582 1.01
J3-2 589 1.03
J3-3 567 0.99
J3-4 568 0.99
J3-5 572 1.00
J3-6 566 0.99
K-Series 418 60.3 560
LH-Series 1303 60.6 1755
Rod-Web-
Series420 61.5 574
Average 1.033
Std Dev 0.030
COV 0.029
Qty 18
All
Plastic Strength Ratio
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Flex-Joist™ Design Reliability Study
Steel Dynamics Roanoke Bar Division A529-50 merchant bar
May 2008 to October 2012 11546 samples / 4337 batches
Stat's
Yield
Stress
(psi)
Ratio
Yield
Stress /
50 ksi min
Average 56764 1.1353
Minimum 50000 1.0000
Maximum 76570 1.5314
Std Dev 3415.6 0.0683
COV 0.0602 0.0602
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Flex-Joist™ Design Reliability Study Structural Reliability Analysis: • φ = 0.90 • Live / Dead Load Ratio = 3
β = 3.2
𝛽 =ln
𝐶𝜑
𝜑𝑀𝑚𝐹𝑚𝑃𝑚
𝑉𝑀2+𝑉𝐹
2+𝐶𝑃𝑉𝑃2+𝑉𝑄
2
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Summary of Flex-Joist™ Design Characteristics
System β based on N = 4 statistically unlinked joists working in parallel
Criteria Std Joist Flex-Joist % Diff
Joist Strength Reliability β 2.6 3.2 22%
System Strength Reliability β 2.6 3.4 31%
Average ASD Test Strength Ratio 1.8 2.3 29%
Average Test Ductility Ratio 1.4 3.2 129%
Tension Limit State Probability Low High
Electronic Monitoring Suitable Okay Excellent
Average Relative Weight 100% 107%
Joist Performance Comparison
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• Approximately 30% higher Reliability Index (β). • Approximately 7% heavier, on average. • Clearly room for potentially reducing weight
while retaining superior reliability. – Subject to justification being provided to support a
higher φy value and/or lower Ωy value, in an ICC Engineering Services Report submittal.
– Limited applications until fire testing has been performed
Summary of Flex-Joist™ Design Characteristics
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Tension-Controlled Joist Limiting Design Factors
Conditions preventing the Bottom Chord and End Web from developing their tensile capacity:
Unusually high material Fy High compression under net uplift loads, axial loads, or end moments Unusually strict deflection criteria Minimum material size criteria Unnecessarily strict tension member slenderness criteria
Uniformly distributed loading on a 20K7 steel joist with a base length of 33’
Lowest Stress Highest Stress
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Tension Slenderness Ratio
Current SJI maximum slenderness ratios are based on the 1946 & 1949 AISC spec’s, as follows:
For main compression members…………………………………………120
For bracing and other secondary members in compression…200
For main tension members………………………………………………….240
For bracing and other secondary members in tension………...300
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Tension Slenderness Ratio
Remnants of the 1946 slenderness requirement carried over as far as the 8th edition (1980) AISC: The slenderness ratio, Kl/r, of compression members shall not exceed 200. The slenderness ratio, l/r, of tension members, other than rods, preferably should not exceed:
For main members……………………...………………..………..240 For lateral bracing members and other secondary members…300
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Tension Slenderness Ratio
Current (14th edition, 2010) AISC states in Section D1:
User Note: For members designed on the basis of tension, the slenderness ratio L/r preferably should not exceed 300. This suggestion does not apply to rods or hangers in tension.
There is no slenderness limit for members in tension.
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When safe and reliable is not enough… Increased reliability… Increased probability of time for safe evacuation…
www.newmill.com/flex
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1
Experimental Investigation of Open Web Steel Joists Designed for Tension-
Controlled Strength Limit State
Joseph Robert Yost, Ph.D., PE Associate Professor, Structural Engineering
Department of Civil and Environmental Engineering Villanova University
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2
Presentation Overview
1. Introduction and Methodology
2. Experimental Matrix
3. Load and Support Details
4. Test Results
5. Conclusions
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3
Research Program
• Experimental investigation of simply supported uniformly loaded open web steel joists subjected to gravity loading.
• Top chord in combined compression and bending.
• Bottom chord and end webs in axial tension.
• Interior webs alternating tension and compression.
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4
Member Limit States and Experimental Objective
Member strength limit states
• Top chord compression buckling
• Bottom chord and end webs tensile yield
• Interior webs alternating tension and compression
Load
Displacement
Compression buckling
Tension yielding
Experimental Objective
• Design and test series of OWSJ for tension controlled failure limit state.
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5
Methodology
• Design individual members so that tension yield of BC or EW occurs before compression buckling of TC or webs. Call tension-controlled design methodology.
• Over size compression members relative to strength demand.
• Define member Demand Capacity Ratio (DCR) as:
Tension-Controlled Design Methodology
• All compression members DCR < 1.0 (reserve strength)
• Critical tension member DCR = 1.0 (at failure)
• Other tension members DCR ≈ 1.0 (close to failure)
• Increase slenderness limit on tension members to 300
DCR = Required StrengthProvided Strength
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6
Tension-Controlled Design Term and Member Selection
rn = DCRn
DCRmax-tension =1.0Introduce relative strength term, r:
Relative Strength Ratios Used for Member Selection of Experimental Joists
Bottom C. and/or End Webs r = 1.0 (failure)
Interior Tension Webs r ≤ 0.95 (5% reserve strength)
Top Chord r ≤ 0.90 (10% reserve strength)
Compression Webs r ≤ 0.80 (20% reserve strength)
P P P P
P/2 (typ.)
P/4 (typ.)
P/8 (typ.)
2P 2P
4.5' 8' 8' 8' 4.5'
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7
Presentation Overview
1. Introduction and Methodology
2. Experimental Matrix
3. Load and Support Details
4. Test Results
5. Conclusions
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8
P P P P
P/2 (typ.)
P/4 (typ.)
P/8 (typ.)
2P 2P
4.5' 8' 8' 8' 4.5'
K-Series x 6 identical samples
LH-Series x 6 identical samples
K-Series Rod Web x 6 identical samples
Sample Count
33 ft.
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9
Experimental Matrix
All 18 samples
• Designed for tension control strength limit state
• Simply supported and subjected to uniform load
• Monotonically tested to failure
• Top chord laterally braced at 2 ft. intervals
Bottom Chord & End Webs
Top Chord Tension Webs
CompressionWebs
K 6 20K7 J1-1,2,3,4,5,6LH 6 28LH11 J2-1,2,3,4,5,6RW 6 16K9 J3-1,2,3,4,5,6
1.00 0.90 0.95 0.80
Experimental Matrix
Series NBase SJI
DesignationExperimental
ID
Maximum Relative Strength Ratio (ρ)
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P P P P
P/2 (typ.)
P/4 (typ.)
P/8 (typ.)
2P 2P
4.5' 8' 8' 8' 4.5'
Cylinder #1
Cylinder #2
Cylinder #3
Cylinder #4
1 ft
(typ.)
10
P P P P
P/2 (typ.)
P/4 (typ.)
P/8 (typ.)
2P 2P
4.5' 8' 8' 8' 4.5'
Uniform Load Condition
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11
P P P P
P/2 (typ.)
P/4 (typ.)
P/8 (typ.)
2P 2P
4.5' 8' 8' 8' 4.5'
Cylinder #1
Cylinder #2
Cylinder #3
Cylinder #4
1 ft
(typ.)
Load Distribution Unit Detail
Distribution Unit
Load Distribution Unit
Hydraulic Cylinder
Distribution Beam
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12
Presentation Overview
1. Introduction and Methodology
2. Experimental Matrix
3. Load and Support Details
4. Test Results
5. Conclusions
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0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12
Load
(lb/
ft)
Midspan Displacement (in)
J1-1 J1-2 J1-3 J1-4 J1-5 J1-6 DL = 43 lb/ft
Unloading to adjust test apparatus.
Yield in BC or End Web
LRFD Design Capacity = 418 lb/ft
13
K-Series Results
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0
250
500
750
1000
1250
1500
1750
2000
2250
0 1 2 3 4 5 6 7 8 9 10 11 12
Load
(lb/
ft)
Midspan Displacement (in)
J2-1 J2-2 J2-3 J2-4 J2-5 J2-6
Unloading to adjust test apparatus
DL = 77 lb/ft
Yield in BC
Strain Hardening
LRFD Design Capacity= 1303 lb/ft
14
LH-Series Results
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0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9 10 11 12
Load
(lb/
ft)
Midspan Displacement (in)
J3-1 J3-2 J3-3 J3-4 J3-5 J3-6
DL = 45 lb/ft
Unloaded to adjust test apparatus
Yield of BC and End Web
Apparent strain hardening
LRFD Design Capacity = 420 lb/ft
15
Rod-Web Series Results
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16
D = design strength
Y = yield strength
P = plastic strength
U = ult. strength
Strength Ratios
1.29 1.28 1.26
1.39 1.44
1.37
1.49 1.52
1.63
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
K (J1) LH (J2) Rod Web (J3)
Ave
rage
Stre
ngth
Rat
io (-
)
Joist Series
Y/D P/D U/D
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17
Deflection Ratios (U/Y)
2.83
3.79
3.15
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1 2 3 4 5 6 Average
Dis
plac
emen
t Rat
io U
/ Y (-
)
Sample
K-Series LH-Series Rod-Web-Series
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18
1. Introduction and Methodology
2. Experimental Matrix
3. Load and Support Details
4. Test Results
5. Conclusions
Presentation Overview
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19
• The tension-controlled yield limit state was successfully achieved with all 18 test samples.
• Relative strength factors of 0.80 for compression web, and 0.90 for top chord was sufficient to prevent primary limit state compression failure.
• Reserve strength relative to design capacity. Y-to-D strength ratios = 1.30, P-to-D strength ratio = 1.40, and U-to-D strength ratio = 1.50.
• Significant ductility with average deflection ratios of U-to-Y = 2.8, 3.8 and 3.2 for K-, LH-, and RW-Series.
Conclusions