Xây dựng mô hình giàn ảo (Developments in strut and tie method)

DEVELOPMENTS IN
STRUT-AND-TIE METHOD
AASHTO T-10 UPDATE

OGUZHAN BAYRAK, Ph.D., P.E.
Ferguson Structural Engineering Laboratory
The University of Texas at Austin
April 21, 2015


UNIVERSITY OF TEXAS
STRUT-AND-TIE MODELING RESEARCH

Brown et al.
(2002-2006)

Birrcher et al.
(2006-2009)

Williams et al.
(2009-2012)

Larson et al.
(2009-2013)

Design for Shear
Using STM

Strength and
Serviceability
Design of Deep

Beams Using STM

STM Guidebook with
Design Examples

Strength and
Serviceability
Design of
Inverted-T Beams
Using STM

DR. OGUZHAN BAYRAK

DEVELOPMENTS IN STRUT-AND-TIE MODELING

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UNIVERSITY OF TEXAS
STRUT-AND-TIE MODELING RESEARCH
5 Ph.D., 6 MS, 21 Undergraduates
Brown et al.
(2002-2006)

Birrcher et al.
(2006-2009)

David Birrcher, PhD
Michael Brown, PhD
Rob Tuchscherer, PhD

Ivan Ornelas, MS
Cameron Sankovich, MS Matt Huizinga, MS
Mike McCarthy, BS
Kyle Stueck, BS
Gary Lehman, BS
Annika Trevino, BS
Thomas Stablon, BS
Mike Ziemenski, BS
Brian Schnittker, BS
Erin O’Malley, BS
Patrick Harkin, BS
James Kleineck, BS
James Plantes, BS
Ryan Kalina, BS
David Wald, BS
Carlos Jordan, BS
DR. OGUZHAN BAYRAK

Williams et al.
(2009-2012)

Larson et al.
(2009-2013)

Chris Williams, MS
Dean Deschenes, MS

Nancy Larson, PhD
Eulalio Fernández, PhD
David Garber, MS

Michelle Wilkinson, BS
Laura Chimelski, BS
Daniel Bejarano, BS
Allison Lehman, BS
Michael Weyenberg, BS
Michael Carrell, BS
Alexander Peña, BS

DEVELOPMENTS IN STRUT-AND-TIE MODELING

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DEEP BEAM EXPERIMENTAL WORK

DR. OGUZHAN BAYRAK

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DEEP BEAM EXPERIMENTAL WORK
U. of Texas Research

A total of 37 deep beam tests
DR. OGUZHAN BAYRAK

DEVELOPMENTS IN STRUT-AND-TIE MODELING

Previous Research
that led to Code
Development

1 in. = 25.4 mm
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DEVELOPMENT OF STRUT-AND-TIE PROVISIONS

Experimental
Program (37 Tests)
Filtering

Evaluation
Deep Beam
Evaluation Database

STM Provisions

Literature Review

DR. OGUZHAN BAYRAK

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DEEP BEAM DATABASE:

ASSEMBLY AND FILTERING
Stage 1
filtering

Collection Database

905 tests

-

incomplete plate size
information

- 284 tests

-

subjected to uniform loads

- 7 tests

-

stub column failure

- 3 tests

-

f ′c < 2,000 psi

- 4 tests

Stage 2
filtering

Filtered Database

607 tests

-

bw < 4.5 in.

- 222 tests

-

bwd < 100 in.2

- 73 tests

-

d < 12 in.

- 13 tests

-

∑ρ┴ < 0.001

- 120 tests

Evaluation Database

179 tests

Representative of deep beams in the field
1 psi = 0.00689 MPa
DR. OGUZHAN BAYRAK

1 in. = 25.4 mm

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STRESS CHECKS PERFORMED
(1)
(2)
(3)
(4)

CCC Back Face
CCT Back Face
CCC Bearing Face
CCT Bearing Face

(5) CCC Strut-to-Node Interface
(6) CCT Strut-to-Node Interface
(7) Tie Reinforcement

(3)

CCC Node
(1)

(5)

(6)

(2)

(7)

CCT Node
(4)
DR. OGUZHAN BAYRAK

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NODAL STRESS CHECKS
ϕ𝐹𝑛 > 𝐹𝑢
lb

where

Bearing Face
Back Face

ϕ𝐹𝑛 = ϕ · 𝑓𝑐𝑢 · 𝐴𝑐𝑛

a
θ

𝑓𝑐𝑢 = 𝑚 · 𝜈 · 𝑓 ′ 𝑐

lbsinθ

ws

Strut-to-Node
Interface

acosθ

DR. OGUZHAN BAYRAK

ν = nodal efficiency factor
m = confinement modification
factor

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NODAL EFFICIENCY FACTORS:
ACI 318 AND AASHTO LRFD*
CCC Node

CCT Node

CTT Node

*
DR. OGUZHAN BAYRAK

ν

ACI 318

AASHTO LRFD

Back Face

0.85

0.85

Bearing Face

0.85

0.85

Strut-to-Node
Interface

0.64 when ρ > ρmin

Back Face

0.68

0.75

Bearing Face

0.68

0.75

Strut-to-Node
Interface

0.64 when ρ > ρmin

Back Face

0.51

0.65

Bearing Face

0.51

0.65

Strut-to-Node
Interface

0.64 when ρ > ρmin

0.51 when ρ < ρ min

0.85

0.51 when ρ < ρ min

0.51 when ρ < ρ min

Reduction factors are not considered for clarity (φ = 1)
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DATABASE EVALUATION:
ACI 318 AND AASHTO LRFD
ACI 318 STM
Conservative

No. Tests

80
60

N = 179

40

100
No. Unconservative = 3
Min = 0.87
Max = 9.80
Mean = 1.80

1.7% Unconservative
COV = 0.58

80

No. Tests

100

AASHTO LRFD STM

60

N = 179

40

20

20

0

0
0 1 2 3 4 5 6 7 8 9 10 11 12

Conservative

No. Unconservative = 6
Min = 0.87
Max = 11.77
Mean = 2.21
3.4% Unconservative
COV = 0.69

0 1 2 3 4 5 6 7 8 9 10 11 12

Experimental/Calculated

Experimental/Calculated

COV = Coefficient of Variation = Standard Deviation/Mean

DR. OGUZHAN BAYRAK

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RECOMMENDED STM PROVISIONS:
NODAL ZONE CONFINEMENT

DR. OGUZHAN BAYRAK

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ACI 318/AASHTO LRFD NODAL ZONE
CONFINEMENT FACTOR
CONFINEMENT MODIFICATION FACTOR:
45 deg

𝑚=

𝐴2

2

𝐴

45 deg

Loaded Area

A1

45 deg

Loaded Area A1
2

1

A2 is measured on this plane

Plan

Elevation

The confinement modification factor, m, can be
applied to all faces of the nodal region
DR. OGUZHAN BAYRAK

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RECOMMENDED STM PROVISIONS:
PERFORM STRUT CHECK AT NODE INTERFACE

Critical stresses exist at
nodal regions

DR. OGUZHAN BAYRAK

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RECOMMENDED STM PROVISIONS:
BACK FACE CHECK

Bond
Stress

DR. OGUZHAN BAYRAK

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RECOMMENDED STM PROVISIONS:
NODAL EFFICIENCY FACTORS
C

C
0.85
0.85

T

C

C

C

C
0.70

T

C

0.70

C

CCC Node

CCT Node

More Concrete
Efficiency
(Stronger)

T

CTT Node
Less Concrete
Efficiency

(Weaker)

If the web crack control reinforcement requirement is not
satisfied, use ν = 0.45 for the strut-to-node interface
DR. OGUZHAN BAYRAK

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RECOMMENDED STM PROVISIONS:
NODAL EFFICIENCY FACTORS*
CCC Node

CCT Node

CTT Node

*

ν

ACI 318

AASHTO LRFD

Proposed

Back Face

0.85

0.85

0.85

Bearing Face

0.85

0.85

0.85

Strut-to-Node
Interface

0.64 when ρ > ρmin

Back Face

0.68

0.75

0.70

Bearing Face

0.68

0.75

0.70

Strut-to-Node
Interface

0.64 when ρ > ρmin

Back Face

0.51

0.65

Bearing Face

0.51

0.65

Strut-to-Node
Interface

0.64 when ρ > ρmin

0.51 when ρ < ρ min

0.85

𝑓𝑐

𝑓𝑐

0.51 when ρ < ρ min

0.51 when ρ < ρ min

𝑓𝑐
𝑓𝑐
𝑓𝑐

2

2
2
2
2

Reduction factors are not considered for clarity (φ = 1)

DR. OGUZHAN BAYRAK

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EVALUATION OF RECOMMENDED PROVISIONS
ACI 318 STM
Conservative

No. Tests

80

60

N = 179

40

100
No. Unconservative = 3
Min = 0.87
Max = 9.80
Mean = 1.80

80

No. Tests

100

AASHTO LRFD STM

1.7% Unconservative
COV = 0.58

Conservative

60

N = 179

40

20

20

0

0
0 1 2 3 4 5 6 7 8 9 10 11 12

No. Unconservative = 6
Min = 0.87
Max = 11.77
Mean = 2.21
3.4% Unconservative
COV = 0.69

0 1 2 3 4 5 6 7 8 9 10 11 12

Experimental/Calculated

Experimental/Calculated

PROPOSED STM PROVISIONS
100

Conservative

No. Tests

80

N = 179

No. Unconservative = 1
Min = 0.73
Max = 4.14
Mean = 1.54

60
40

0.6% Unconservative
COV = 0.28

20
0

0

1

2

3

4

5

6

7

8

9

10 11 12

Experimental/Calculated
DR. OGUZHAN BAYRAK

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DEVELOPMENT OF RECOMMENDED
STM PROVISIONS
Provisions Should Satisfy the Following Criteria (MacGregor, 2002)
1.

2.
3.
4.

Simplicity in application
Compatibility with tests of D-regions
Consistency with other sections of ACI 318 and/or AASHTO LRFD
Compatibility with other codes or design recommendations

fib (1999) was key in providing
guidance for the recommended
provisions

DR. OGUZHAN BAYRAK

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DATABASE EVALUATION:
fib (1999) VS. RECOMMENDED PROVISIONS
fib (1999) STM
Conservative

No. Tests

80

100

N = 179

No. Unconservative = 5
Min = 0.76
Max = 2.82
Mean = 1.55

60
40

2.8% Unconservative
COV = 0.25

20

Conservative

80

No. Tests

100

PROPOSED STM PROVISIONS
N = 179

No. Unconservative = 1
Min = 0.73
Max = 4.14

Mean = 1.54

60
40

0.6% Unconservative
COV = 0.28

20
0

0
0

1

2

3

4

5

6

Experimental/Calculated

DR. OGUZHAN BAYRAK

7

8

9

0 12
1
10 11

2

3

4

5

6

7

8

9

Experimental/Calculated

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CHANGE LIMIT OF NODAL ZONE CONFINEMENT
FACTOR BASED ON fib (1999)
CONFINEMENT MODIFICATION FACTOR:
45 deg

𝑚=

𝐴2

2

𝐴

4

45 deg

Loaded Area
A1

45 deg

Loaded Area A1
2

1

A2 is measured on this plane

Plan

Elevation

The confinement modification factor, m, can be
applied to all faces of the nodal region
DR. OGUZHAN BAYRAK

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DATABASE EVALUATION
N = 179 tests
Design Provision

Average
No. Unconservative
Experimental/Calculated

% Unconservative†

COV††

ACI 318 STM

1.79

3

1.7%

0.58

AASHTO LRFD

2.21

6

3.4%

0.69

fib (1999)

1.55

5

2.8%

0.25

PROPOSED (with m < 4)

1.51

1

0.6%

0.22

† “Unconservative”

= Exper mental/Calculated Value < 1.0
†† COV = Coefficient of Variation = Standard Deviation/Mean

DR. OGUZHAN BAYRAK

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STM APPLIES TO MORE THAN

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INVERTED-T STRADDLE BENT CAP

Ledge

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INVERTED-T EXPERIMENTAL WORK

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