Simplicity in application 2. Compatibility with tests of Dregions 3. Consistency with other sections of ACI 318 andor AASHTO LRFD 4. Compatibility with other codes or design recommendations STM provisions (with m < 2) calibrated for rectangular beams are also accurate when applied to invertedT beam design → Proposed 3dimensional model provides accurate results for invertedT beams
Trang 2UNIVERSITY OF TEXAS STRUT-AND-TIE MODELING RESEARCH
Design for Shear
Using STM
Strength and Serviceability Design of Deep Beams Using STM
Williams et al
(2009-2012)
STM Guidebook with Design Examples
Strength and Serviceability Design of Inverted-T Beams Using STM
Trang 3UNIVERSITY OF TEXAS STRUT-AND-TIE MODELING RESEARCH
Williams et al
(2009-2012)
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
5 Ph.D., 6 MS, 21 Undergraduates
Trang 4DEEP BEAM EXPERIMENTAL WORK
Trang 5U of Texas Research
Previous Research that led to Code Development
DEEP BEAM EXPERIMENTAL WORK
Trang 6DEVELOPMENT OF STRUT-AND-TIE PROVISIONS
Trang 7Collection Database 905 tests
- subjected to uniform loads - 7 tests
- stub column failure - 3 tests
DEEP BEAM DATABASE:
ASSEMBLY AND FILTERING
Trang 8STRESS CHECKS PERFORMED
CCT Node CCC Node
Trang 9NODAL STRESS CHECKS
lb
a
acosθ
lbsin θ θ
Bearing Face
Strut-to-Node Interface
Trang 10ν ACI 318 AASHTO LRFD Back Face 0.85 0.85
Bearing Face 0.85 0.85
Strut-to-Node Interface
NODAL EFFICIENCY FACTORS:
ACI 318 AND AASHTO LRFD*
* Reduction factors are not considered for clarity (φ = 1)
Trang 11Max = 9.80 Mean = 1.80 1.7% Unconservative COV = 0.58
No Unconservative = 6 Min = 0.87
Max = 11.77 Mean = 2.21 3.4% Unconservative COV = 0.69
COV = Coefficient of Variation = Standard Deviation/Mean
Trang 12RECOMMENDED STM PROVISIONS:
NODAL ZONE CONFINEMENT
Trang 13ACI 318/AASHTO LRFD NODAL ZONE
Trang 14RECOMMENDED STM PROVISIONS:
PERFORM STRUT CHECK AT NODE INTERFACE
Critical stresses exist at
nodal regions
Trang 15RECOMMENDED STM PROVISIONS:
BACK FACE CHECK
Bond Stress
Trang 16T C C
0.85
0.85
0.70
0.70
If the web crack control reinforcement requirement is not
satisfied, use ν = 0.45 for the strut-to-node interface
Trang 17RECOMMENDED STM PROVISIONS:
NODAL EFFICIENCY FACTORS*
ν ACI 318 AASHTO LRFD Proposed
Bearing Face 0.85 0.85 0.85
Strut-to-Node Interface
Trang 18EVALUATION OF RECOMMENDED PROVISIONS
0 20 40 60 80 100
PROPOSED STM PROVISIONS
No Unconservative = 1 Min = 0.73
Max = 4.14 Mean = 1.54 0.6% Unconservative COV = 0.28
Max = 9.80 Mean = 1.80 1.7% Unconservative COV = 0.58
No Unconservative = 6 Min = 0.87
Max = 11.77 Mean = 2.21 3.4% Unconservative COV = 0.69
N = 179
Trang 19fib (1999) was key in providing guidance for the recommended
provisions
Provisions Should Satisfy the Following Criteria (MacGregor, 2002)
1 Simplicity in application
2 Compatibility with tests of D-regions
3 Consistency with other sections of ACI 318 and/or AASHTO LRFD
4 Compatibility with other codes or design recommendations
DEVELOPMENT OF RECOMMENDED
STM PROVISIONS
Trang 20Max = 4.14 Mean = 1.54 0.6% Unconservative COV = 0.28
No Unconservative = 5 Min = 0.76
Max = 2.82 Mean = 1.55 2.8% Unconservative COV = 0.25
Trang 21CHANGE LIMIT OF NODAL ZONE CONFINEMENT
FACTOR BASED ON fib (1999)
Trang 22N = 179 tests
Design Provision Average
Experimental/Calculated No Unconservative % Unconservative † COV ††
ACI 318 STM 1.79 3 1.7% 0.58 AASHTO LRFD 2.21 6 3.4% 0.69
DATABASE EVALUATION
† “Unconservative” = Exper mental/Calculated Value < 1.0
†† COV = Coefficient of Variation = Standard Deviation/Mean
Trang 23STM APPLIES TO MORE THAN
Trang 24INVERTED-T STRADDLE BENT CAP
Ledge
Trang 25INVERTED-T EXPERIMENTAL WORK
Trang 26INVERTED-T EXPERIMENTAL WORK
A total of 33 inverted-T beam tests
Previous Research that led
to Code Development Present Study
1 in = 25.4 mm
Trang 273-Dimensional STM
Longitudinal STM
APPLICATION OF STM TO INVERTED-T BEAMS
Trang 281.85d
APPLICATION OF STM TO INVERTED-T BEAMS
Trang 29Cusens &
Besser (1985)
Shütt (1956)
Trang 30EVALUATION OF STRUT-AND-TIE PROVISIONS
FOR INVERTED-T BEAMS
Check Accuracy
of Deep Beam STM Provisions
Filtering
Trang 31INVERTED-T DATABASE:
ASSEMBLY AND FILTERING
Representative of inverted-T beams in the field
(ALL from present study)
- specimen did not fail - 10 tests
- incomplete plate size information - 10 tests
- no shear reinforcement - 2 tests
- complicated supports/geometry/reinforcement - 19 tests
- h /b w > 4 - 11 tests
- b w < 4.5 in - 9 tests
- tension- and compression-chord loaded - 9 tests
- torsional loads - 27 tests
Trang 32DATABASE EVALUATION
Inverted-T Beams Rectangular Deep Beams
(33 tests) (179 tests) Minimum 1.05 0.73 Maximum 2.17 4.14 Mean 1.50 1.54
% Unconservative † 0.0% 0.6%
Standard Deviation 0.33 0.43 Coefficient of Variation †† 0.22 0.28
† “Unconservative” = Exper mental/Calculated Value < 1.0
†† Coefficient of Variation = Standard Deviation/Mean
→ STM provisions (with m < 2) calibrated for rectangular beams are
also accurate when applied to inverted-T beam design
→ Proposed 3-dimensional model provides accurate results for
inverted-T beams
Trang 33QUESTIONS