What is so great about ductility?

A Tension-Controlled Open Web Steel Joist

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:

Improved Ductility and Reliability under Static

Gravity Overload

Purpose:

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

• 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?

• Increased Probability of Safe Evacuation

– Slower Collapse Mechanism

– Sensory Warning via Large Inelastic Deflections



Improved Structural Reliability: Reduced Variance in Strength

Influence of Variance on Reliability

Which population has the greatest probability of a value below 1.0?

• Idealized parallel system sketch

• Load shared equally between components


Improved Structural Reliability: Load Sharing

• 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



• Idealized parallel system sketch

• Load shared equally between components

• Elasto-Ductile system



• 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



Compressive Buckling

Design Strength

Compression Element Buckling

Ultimate Strength


Slower Collapse Mechanism with Sensory Warning

Compression Element Buckling

Tension Element Yield

Design Strength

Ultimate Strength

Ductile Tensile Yielding


Slower Collapse Mechanism with Sensory Warning

Flex-Joist Load/Deflection Data Plot

When Loads Exceed Capacity of a Flex-Joist

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

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

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

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

• 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

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

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


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


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.

When safe and reliable is not enough… Increased reliability… Increased probability of time for safe evacuation…

www.newmill.com/flex

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

2

Presentation Overview

1. Introduction and Methodology

2. Experimental Matrix

3. Load and Support Details

4. Test Results

5. Conclusions

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.

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.

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

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'

7





4. Test Results

5. Conclusions

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.

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)

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

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

12





4. Test Results

5. Conclusions

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

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)


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

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)


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

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

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

18




4. Test Results

5. Conclusions


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

Documents

What is so great about ductility?