Strut and Tie Modelling
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12/10/2010
ACI Web Sessions The audio for this web session will begin momentarily and will play in its entirety along with the slides.
Design Using the Strut-and-Tie Method, Part 2(A) ACI Spring 2010 Xtreme Concrete Convention March 21 - 25, Chicago, IL
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Fall 2010 ACI Seminars
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1
12/10/2010
ACI Web Sessions This ACI Web Session includes four speakers presenting at the ACI Xtreme Concrete convention held in Chicago, IL, March 21st through 25th, 2010.
Design Using the Strut-and-Tie Method, Part 2(A)
Additional presentations will be made available in future ACI Web Sessions. Please enjoy the presentations.
ACI Spring 2010 Xtreme Concrete Convention March 21 - 25, Chicago, IL
Daniel Kuchma holds a B.A.Sc., M.A.Sc., and Ph.D., all in civil engineering, from the University of Toronto. Since 1997, he has been an Associate Professor in the department of Civil and Environmental Engineering at the University of Illinois, and has taught courses in structural dynamics, statics, reinforced concrete, and prestressed concrete. His work includes a variety of consulting projects involving offshore structures, hydroelectric dams, towers, buildings and specialty structures. Dr. Kuchma is an active member of ACI, and the Federation International de Beton (fib). He received a National Science Foundation CAREER Award on “Tools and Research to Advance the Use of Strut-andTie Models in Education and Design.” He is also a National Center for Supercomputing Applications Faculty Fellow and University of Illinois Collins Scholar.
Propped Cantilever with Opening Dan Kuchma Sukit Yindeesuk Tjen Tjhin University of Illinois
10
Design problem
Selected truss model
5625 kN
Externally and internally indeterminate truss
535 mm
5800 kN 5625 kN
A
B
C
2895 mm
D
L
K
O
M
Q
P
E
R
F
570 mm 11
H
1590 1015 mm mm
I 2030 mm
3659 kN
41 T 36 k
U G
4000 mm 3229.5 kN
S
N
J 1015 1350 mm mm
N
418.8 kN
49 degrees
12
2
12/10/2010
Outline of Presentation
ACI design; calculation of nominal capacity
Calculated plastic truss capacity
Calculated non-linear truss capacity
Predicted capacity and behavior by nonlinear finite element analysis
Reinforcement and strut/node dimensions selected to provide adequate capacity 46
3409 3265
2662 -486 3 3650
2535 15 4
3650 0 43
-4090
209 -2 54 3860
70
5615
821 52 0 -421 -45
Observations and Conclusions
69
7 94 -6
-38
Measured capacity and behavior by experimental testing
1243 -536 0 2083
-4
-7500 -3860 -3796 -79 2146 35
-38
Member forces determined assuming equal stiffness of member forces
-87 3716 3410
1582 1670 -305
ACI design; calculation of nominal capacity
144 1781 1828
-821
-949
13
Calculated plastic truss capacity
ACI design; calculation of nominal capacity
Occurs at top right tie; Pn = 7500 kN
Utilization rates shown in figure 0.452 0.039
0.02 1.01(O/S) 0.924
0.496
0.429
0.01
0.89 0.92
0.524
0.525
0.942 0.0 16 0.04
54
0.990 0.6 33
86
0.078 0. 03 3
Member stress-strain characteristics
0.227 1.01(O/S) 0. 07 0.054 5 0.
0.764
96 0.4
28 0.3
2 39 0.
0.343 0.69 8 0.774
0.4
0.520 0.188 0.185 0. 01 0.798
0.495
Nominal design strength taken as when first members reaches its capacity
0.039 0.483
14
0.035
15
Calculated plastic truss capacity
16
Calculated non-linear truss capacity
P = 9469 kN
Capacity reaches when a mechanism forms
P = 9301 kN
0.724
0.476 0.014
0.971 0.0 06
0.006
0.08
0.988 0.7 38 0.730
0.468
0.973 0.981 0.015
0.521
0.001 1.002 1.009
1.009 0.997 0.041
0.528
0.016 0. 07
0.714
11
17
0.985
0.988
0.047 0. 03 1 0.019
0.5
0.018
0.012 0.76 2
3 61
0.734
0.922 0.0 25 0.009
0 52 0.
5 60 0.
0.993 0.7 31
0.481 0.267 0.271 0. 01 3 0.959 69 0.3
0.743
0.994
0.115 0.639 0 .0 05 0.003
0
0.025 0.0 11
0.122 0.7 43
48 0.
0.999
0.919 97 0.5
63 0.3
7 52 0.
0.284 0. 03 3
0.
0.274
0.973
Similar demands as by plastic truss model
1.000
Capacity reaches when a mechanism forms
0.008 0.520 0.506
0.489 0.526 0.002
Non-linear stress-strain relationship
0.013 0.562 0.521
0.482
Very different distribution of demands
0.008
18
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12/10/2010
Predicted capacity and behavior by non-linear finite element analysis
Comparison of strength calculations
Predicted state of cracking at ultimate
P = 16622 kN
Pn Pu
19
20
Predicted capacity and behavior by non-linear finite element analysis
Predicted capacity and behavior by non-linear finite element analysis
Predicted distribution of steel stress at ultimate
Compressive Demand: ratio of compressive stress to compressive capacity at failure
P = 16622 kN
Stress (Steel): -truss at crack 46.06 64.52 82.98 101.43
119.89 138.35 156.81 175.27
193.73 212.18 230.64 249.10
267.56 286.02 304.48 322.93
341.39 359.85 378.31 396.77
Vital Signs: Fcm
415.23 433.68 452.14 470.60
0.04 0.08 0.13 0.17
0.21 0.25 0.29 0.33
0.38 0.42 0.46 0.50
0.54 0.58 0.63 0.67
0.71 0.75 0.79 0.83
21
Measured capacity and behavior by experimental testing
0.88 0.92 0.96 1.00 22
Measured capacity and behavior by experimental testing
Reinforcing cage
23
Test Setup
24
4
12/10/2010
Measured capacity and behavior by experimental testing
Comparison of strength calculations
Mode of failure
Pn Pu
25
Observations and Conclusions 1.
Truss member design forces in statically indeterminate strut-and-tie models depend on the relative stiffness of members
2.
Plastic truss capacity can be modestly larger than when the first member reaches its capacity
3.
Truss models cannot provide a good estimate of deformation; much softer than in reality
4.
Non-linear finite element analysis can predict well the behavior of complex STM designed regions
26
Questions
27
Hakim Bouadi is a Senior Associate with Walter P Moore & Associates in Houston, Texas, which provides structural, structural diagnostics, civil, traffic and transportation engineering, and parking consulting services to clients worldwide.
28
STM Design of two Link Beams at a Medium-Rise Building Hakim Bouadi, Ph.D., P.E. Asif Wahidi, Ph.D., P.E. WALTER P MOORE
5
12/10/2010
Outline
148'-0"
Building Overview
351'-0"
Building Overview Link Beam Overview Link Beam with Moderate Shear Link Beam with High Shear Conclusions
142'-0"
256'-0"
Hospital building Location: Las Vegas, Nevada Lateral design controlled by seismic forces
31
STM Design of two Link Beams at a Medium-Rise Building
31
WALTER P MOORE
32
STM Design of two Link Beams at a Medium-Rise Building
Building Overview
32
WALTER P MOORE
Shear Wall Overview
48'-7"
Shear walls with link beams above openings Link beam: deep beams per ACI 318 definition Review link beam at roof and at level 3
18'-0"
18'-0"
18'-0"
15'-0"
351'-0"
15'-0"
15'-0"
15'-0"
15'-0"
15'-0"
148'-0"
48'-7"
256'-0"
18'-0"
142'-0"
Plan size: about 500 ft by 400 ft Lateral resisting system: shear walls Controlling lateral loads: seismic forces
33
STM Design of two Link Beams at a Medium-Rise Building
33
WALTER P MOORE
34
STM Design of two Link Beams at a Medium-Rise Building
34
WALTER P MOORE
.
Link Beam Overview
Roof Link Beam External forces applied at nodes Shear force equal to about:
4.25 f c ' bw d
Beam under constant shear and moment reversal Forces on nodes obtained from global lateral analysis Reduce forces to ends
35
STM Design of two Link Beams at a Medium-Rise Building
35
WALTER P MOORE
36
External nodes at location of wall reinforcement Horizontal tie at location of reinforcement Vertical tie at mid-span Improvement: Extend model into wall
STM Design of two Link Beams at a Medium-Rise Building
36
WALTER P MOORE
6
12/10/2010
Forces on Members
Design of Struts and Ties
Force resolved by analysis Check struts Design ties Check nodes Detailing
37
STM Design of two Link Beams at a Medium-Rise Building
37
WALTER P MOORE
Strut and tie dimensions from geometry Struts: fan shaped Capacity of struts checked at strut and at nodes Tie force resisted by reinforcement
38
Design of Struts and Ties
STM Design of two Link Beams at a Medium-Rise Building
38
WALTER P MOORE
Node Capacity
• Vertical tie: 8#5 stirrups As
Fu
fy
187 4 . 15 in 2 0 . 75 60
Nodal dimensions from geometry Node type CCT due to tension force in wall reinforcement Check capacity on each face
• Horizontal tie: 4 #7 As
Fu
fy
94.9 2.18 in 2 0.7560
• Develop beyond extended nodal zone
0.85 n f c' wb 0.75 0.85 0.8 5.5 8.5 12 286 kips
• Strut Fu 0.85 s f 'c b w 0.75 0.85 0.60 5.5 8.5 12 215 kips
39
STM Design of two Link Beams at a Medium-Rise Building
39
WALTER P MOORE
40
Node Capacity
STM Design of two Link Beams at a Medium-Rise Building
40
WALTER P MOORE
Design: Roof Link Beam,
Node type CTT due to tension force in wall reinforcement Check capacity on each face 0.85 n f c' wb 0.75 0.85 0.6 5.5 7 12 176 kips
41
STM Design of two Link Beams at a Medium-Rise Building
41
WALTER P MOORE
42
STM Design of two Link Beams at a Medium-Rise Building
42
WALTER P MOORE
7
12/10/2010
Link Beam at Level 3
Forces for Level 3 Link Beam
15'-0"
48'-7"
15'-0"
Shear force equal to about: 15'-0"
10 f c ' bw d
18'-0"
18'-0"
Design using STM Follow also Chapter 21 of ACI: Seismic Design/Detailing
Shear force equal to about:
10 f c ' bw d
Design using STM Follow also Chapter 21 of ACI: Seismic Design/Detailing
43
STM Design of two Link Beams at a Medium-Rise Building
43
WALTER P MOORE
44
Model for Level 3 Link Beam
STM Design of two Link Beams at a Medium-Rise Building
45
WALTER P MOORE
STM Design of two Link Beams at a Medium-Rise Building
44
WALTER P MOORE
Design for Level 3 Link Beam Forces resolved through geometry Symmetric design due to load reversal Tie force resisted by reinforcement (4#11 and 2#9) Strut force resisted by concrete and reinforcement
External nodes at location of wall reinforcement Transfer forces through “X” configuration
45
External nodes at location of wall reinforcement Horizontal tie at location of reinforcement Vertical tie at mid-span Improvement: Extend model into wall
46
Detailing for Level 3 Link Beam
STM Design of two Link Beams at a Medium-Rise Building
46
WALTER P MOORE
Summary for Level 3 Link Beam
development length of beyond extended nodal zone extended by 25% Minimum web reinforcement Appendix A ACI Chapter 21 (controls) Enclose Tie reinforcement with stirrups
47
STM Design of two Link Beams at a Medium-Rise Building
47
WALTER P MOORE
48
STM Design of two Link Beams at a Medium-Rise Building
48
WALTER P MOORE
8
12/10/2010
STM Design of two Link Beams at a Medium-Rise Building
Conclusions STM use for link beam design Different models are possible Model can be extended into the wall to follow force transfer Check detailing (in addition to design)
Thank you Hakim Bouadi, Ph.D., P.E. Asif Wahidi, Ph.D., P.E. WALTER P MOORE
49
STM Design of two Link Beams at a Medium-Rise Building
49
WALTER P MOORE
MIC-Earlington Heights Connector Metrorail
Richard Beaupre received his Bachelor of Science and Engineering from the University of Florida and his Master of Science from the University of Texas at Austin. While at the University of Texas he was involved in research pertaining to deviation saddle behavior and design for externally post-tensioned segmental concrete girder bridges. He is currently a senior bridge engineer for URS Corporation in Tampa, Florida, where he is responsible for design of steel and concrete bridges, ship impact designs, structural modeling, and quality control. He is experienced in design of major bridge structures, including cable-stayed, posttensioned segmental concrete and movable.
Richard Beaupre, PE Robert (Bob) Anderson, PE Velvet Bridges, PE URS Corporation Tampa, Florida
Diaphragm for a Segmental Concrete Bridge ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Introduction
Project Overview
• Many Areas of a Concrete Segmental Bridge can be Classified as a “D” Region – Pier Diaphragms – Interior Segment Diaphragms at Deviation Points for External Tendons – Openings in Flanges and Webs – Pile Caps ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
9
12/10/2010
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Superstructure Requirements
Miami Intermodal Center MIC-EARLINGTON HEIGHTS METRORAIL EXTENSION
• 130’ Spans in Miami Intermodal Center • 225’ Span to Clear the Miami River with a 40’ Vertical Clearance • 180’ Span for the South Florida Railroad Corridor • 256’ Span to Cross to SR112 and the Future Dade Expressway • Height Restrictions Set by FAA Airspace near MIA
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Superstructure Types
Guideway Structures Overview 72” Florida U-Beams - Single Track Guideway
• • • •
72” Florida Prestressed U-Beams Segmental Concrete Boxes 30” Cast-In-Place Concrete Slabs Single Track and Dual Track CrossSections
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Guideway Structures Overview 72” Florida U-Beams - Dual Track Guideway
ACI 2010, Chicago, IL
Guideway Structures Overview Single Track Guideway (Units 1 thru 4 & 14)
ACI 2010, Chicago, IL
10
12/10/2010
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Guideway Structures Overview
Diaphragm Example
Dual Track Guideway (Units 5 thru 9 & 11 thru 13)
• • • •
ACI 2010, Chicago, IL
Layout Function Boundary Forces Strut-Tie Model
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Diaphragm Example
Layout
• Unit 8
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Pier Diaphragm Function
Layout
• Transfer Loads from the Webs to the Support around Access Openings • Distribute Tendon Anchorage Forces to the Cross-section
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
11
12/10/2010
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Rapid Transit Live Load Vehicle • Full Live Load Weight of 120 kips • Train – 2 to 8 Vehicles
ACI 2010, Chicago, IL
Diaphragm Loadings
Shear Factored Loading Case Kips/Box (kN/Box)
(kN*m/Box)
Strength I (Maximum Shear)
3,291
(14,638)
21
(28)
Extreme Event III (Maximum Torsion)
2,634
(11,716)
5,355
(7,260)
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
Diaphragm Unit Loads for Shear
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
Diaphragm Unit Loads for Torsion
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Strut-Tie Model Steps • Step 1:
Determine strut-and-tie arrangement based on boundary forces
• Step 2:
Solve for the member forces
• Step 3:
Determine the amount of steel for ties
• Step 4:
Arrange tie steel
• Step 5:
Check anchorage zone for the ties
• Step 6:
Check diagonal struts
• Step 7:
Check nodal zones
ACI 2010, Chicago, IL
Torsion KipFt/Box
Pier Diaphragms Reference: Schlaich et. al., ”Towards a Consistent Design of Structural Concrete”, PCI Journal, Vol. 32, No. 3, May-June 1987
ACI 2010, Chicago, IL
12
12/10/2010
MIC-Earlington Heights Connector Metrorail
Model Members with Shear Unit Loads
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
Model Members with Torsion Unit Loads
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Material Properties
Results for Shear Only
• Concrete: f’c=8,500 psi (58.7 MPa) • Reinforcement: fy= 60,000 psi (414 MPa)
ACI 2010, Chicago, IL
Extreme Event III V=2634 k (11,716 kN)
Unit Force
Kips
(kN)
Kips
(kN)
1
0.450
740.9
(3295.3)
593.0
(2637.5)
2
0.267
439.4
(1954.4)
351.7
(1564.2)
3
0.267
4
439.4
(1954.4)
351.7
(1564.2)
0.450
740.9
(3295.3)
593.0
5
-0.792
-1302.7
(-5794.4)
-1042.6
(-4637.7)
6
-0.467
-768.5
(-3418.1)
-615.0
(-2735.7)
(2637.5)
7
-0.467
8
-768.5
(-3418.1)
-615.0
(-2735.7)
-0.792
-1302.7
(-5794.4)
-1042.6
(-4637.7)
9
-1.000
-1645.5
(-7319.2)
-1317.0
(-5858.0)
10
-1.000
-1645.5
(-7319.2)
-1317.0
(-5858.0)
11
-0.363
-596.5
(-2653.2)
-477.4
(-2123.5)
12
-0.363
-596.5
(-2653.2)
-477.4
(-2123.5)
13
0.000
0.0
(0.0)
0.0
14
0.000
0.0
(0.0)
0.0
(0.0)
15
1.020
1678.7
(7466.9)
1343.6
(5976.2)
16
0.001
0.9
(4.2)
0.7
(3.3)
17
1.020
1678.7
(7466.9)
1343.6
(5976.2)
18
0.001
0.9
(4.2)
0.7
(3.3)
(0.0)
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
Results for Torsion Only Member
Unit Force
1
-0.015
2
-0.009
Strength I T=21 k-ft (28 kN-m) Kips (kN) -0.3 (-1.4) -0.2
(-0.8)
MIC-Earlington Heights Connector Metrorail
Results for Shear and Torsion Combined
Extreme Event III T=5354 k-ft (7258 kN-m) Kips (kN) -81.1 (-360.8) -48.1
1
Strength I Kips (kN) 740.5 (3293.9)
(-214.0)
2
439.2
(1953.5)
Member
Extreme Event III Kips (kN) 511.8 (2276.7) 303.6
3
439.2
(1955.2)
0.015
0.3
(1.4)
81.1
(360.8)
4
741.2
(3296.8)
674.1
(2998.3)
5
-0.027
-0.6
(-2.5)
-142.6
(-634.4)
5
-1303.3
(-5796.8
-1185.3
(-5272.1)
(749.3)
6
-767.8
(-3415.1)
-446.6
(-1986.4)
0.009
0.2
(0.8)
48.1
6
0.031
0.7
(2.9)
168.5
7
-0.031
-0.7
(-2.9)
-168.5
7
(-749.3)
8
-769.1 -1302.1
(-3421.0)
399.8
(1350.2)
(214.0)
4
3
ACI 2010, Chicago, IL
Strength I V=3291 k (14,638 kN)
Member
-783.5
(1778.2)
(-3485.0)
8
0.027
0.6
(2.5)
142.6
(634.4)
(-5791.9)
-900.0
(-4003.3)
9
-0.105
-2.2
(-9.8)
-562.3
(-2501.2)
9
-1647.7
(-7329.0
-1879.3
(-8359.2)
10
0.105
2.2
(9.8)
562.3
(2501.2)
10
-1643.4
(-7309.4)
-754.7
(-3356.9) (-1833.0)
11
0.012
0.3
(1.1)
(290.5)
11
-596.8
(-2652.1)
-412.1
12
-0.012
-0.3
(-1.1)
-65.3
(-290.5)
12
-596.8
(-2654.4)
-542.7
13
0.086
1.8
(8.0)
458.5
(2039.3)
13
1.8
(8.0)
458.5
(2039.3)
14
-0.086
-1.8
(-8.0)
-458.5
(-2039.3)
14
-1.8
(-8.0)
-458.5
(-2039.3)
15
0.700
0.7
3.2
183.8
(817.5)
15
1679.4
(7470.1)
1527.4
(6793.8)
65.3
16
0.0
0.0
0.0
0.0
(0.1)
17
-0.700
-0.7
-3.2
-183.8
(-817.5)
18
-0.0
0.0
0.0
0.0
(-0.1)
(-2414.1)
16
0.9
(4.2)
0.8
(3.5)
17
1678.0
(7463.7)
1159.8
(5158.7)
18
0.9
(4.2)
0.7
(3.2)
ACI 2010, Chicago, IL
13
12/10/2010
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Ties 1 to 4 – Top Tie According to ACI 318 equation A-1 Fnt>Fut. Where: Fut = Factored Design Force = 741 k (3,297 kN) = 0.75 (Section 9.3.2.6) Fnt = Nominal Strength of a Tie Where no prestressing steel is used, Fnt = Atsfy (Section A.4.1) Using 1 row of 11 – # 11 diameter reinforcing bars.
Tie 13 – Diagonal Tie Similarly for Tie 14 (depending on direction of torsion), Fut = Factored Design Force = 459 k (2,039 kN) = 0.75 (Section 9.3.2.6) Using 10 – # 9 diameter reinforcing diagonal bars. Ats 10 bars 1.00 in 2 10.0 in 2 (6,452 mm2 )
Fnt 0.75 10.0 in 2 60 ksi 450 k (2,669 kN) 459 k (2,039 kN)
Ats 1 rows 11 bars 1.56 in 2 17.2 in 2 (10,064 mm2 )
Fnt 0.75 17.2 in 2 60 ksi 774 k (3443 kN) 741 k (3297 kN)
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Ties 15 and 17 – Hanging Up Tie
Main Tie Reinforcing
Fut = Factored Design Force = 1679 k (7,470 kN) = 0.75 (Section 9.3.2.6) Using 28 – # 8 diameter reinforcing web bars plus 11 - # 11 bars (continue Tie 1 to 4 reinforcement) Ats 28 bars 0.79 in 2 17 . 2 in 2 39.3 in 2 (25,368 mm 2 )
Fnt 0.75 39.3 in 2 60 ksi 1,768 k (7,864 kN) 1,679 k (7,470 kN)
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Nodal Zone Detail at Bearing Support
Strut 14 According to ACI 318 equation A-1 Fns>Fus Where: Fus = Factored Design Force = -459 k (-2,039 kN) = 0.75 (Section 9.3.2.6) Fns = Nominal Strength of a Strut = fceAcs Further, f ce 0.85 s f 'c Where: s 0.60 (Section A.3.2.2 (b) – bottle shaped struts without reinforcing of A.3.3.1) Therefore, f ce 0.85 0.60 8500 psi 4335 psi (29.9 MPa) Multiply the allowable compressive stress of a strut by the area of concrete available to carry the stress which is limited by the access opening (width is 4.9 in). Acs 4.9 in 28.9 in 141.6 in 2 (0.09 m 2 )
Fns 0.75 4335 psi 141.6 in 2 / 1000 460 k (2,048 kN) 459 k (2,039 kN)
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
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MIC-Earlington Heights Connector Metrorail
Nodal Check at Member 9
MIC-Earlington Heights Connector Metrorail
Total Diaphragm Reinforcement
According to ACI 318 equation A-1 Fnn>Fun Where: Fun = Factored Design Force = 0.75 (Section 9.3.2.6) Fnn = Nominal Strength of a Node = fceAnz Further, f ce 0.85 n f 'c Where: n 1.0 (Section A.5.2.2 – Nodes bounded by struts and bearing area) Therefore,
f ce 0.85 1.0 8500 psi 7225 psi (49.9 MPa) Multiply the allowable compressive stress on a face of a nodal zone by the area of concrete based on the geometry of the node. Fun = Factored Design Force = 1,879 k (8,359 kN) Anz 28.9 in 39.5 in 1142 in 2 (0.74 m 2 ) (Area of Bearing)
Fnn 0.75 7225 psi 1142 in 2 / 1 000 6188 k (27,525 kN) 1,879 k (8,359 kN)
ACI 2010, Chicago, IL
ACI 2010, Chicago, IL
MIC-Earlington Heights Connector Metrorail
MIC-Earlington Heights Connector Metrorail
Diaphragm Cracking
Summary • Strut-Tie Procedures can be Effectively Utilized for Diaphragm Design • Shear and Torsion Forces are Redirected into Support through the Diaphragm around the Access Opening • After Solving the Truss Forces, Ties can be Designed and Detailed • Struts and Nodes need to be Checked
ACI 2010, Chicago, IL
Daniel Kuchma holds a B.A.Sc., M.A.Sc., and Ph.D., all in civil engineering, from the University of Toronto. Since 1997, he has been an Associate Professor in the department of Civil and Environmental Engineering at the University of Illinois, and has taught courses in structural dynamics, statics, reinforced concrete, and prestressed concrete. His work includes a variety of consulting projects involving offshore structures, hydroelectric dams, towers, buildings and specialty structures. Dr. Kuchma is an active member of ACI, and the Federation International de Beton (fib). He received a National Science Foundation CAREER Award on “Tools and Research to Advance the Use of Strut-andTie Models in Education and Design.” He is also a National Center for Supercomputing Applications Faculty Fellow and University of Illinois Collins Scholar.
ACI 2010, Chicago, IL
Future of ACI STM Provisions and Guidelines Dan Kuchma
University of Illinois at Urbana-Champaign 90
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Location of STM Provisions in ACI318-14?
Appendix A of ACI318-08
Location of Provisions in ACI318-14
Available Guideline Documents
Challenges to Design by the STM
ACI 445 Committee Document
Appendix A of ACI318-08: Basic Rules
P C A
C
c
f cu
C
>C
T
C
As fy > T
P 2
T P 2
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92
Appendix A of ACI318-08: Basic Rules
Appendix A of ACI318-08: Explanatory Materials
Design Strength of Struts = Fns where Fns = f ce Area of Strut and f ce = 0.85 sfc s = 1.00 for prismatic struts in uncracked compression zones s = 0.40 for struts in tension members s = 0.75 when struts may be bottle shaped and crack control reinforcement* is included s = 0.60 when struts may be bottle shaped and crack control reinforcement* is not included s = 0.60 for all other cases
32 Figures
*crack control reinforcement requirement is vi si n i 0.003
Design Strength of Ties = Fnt where Fnt = Ast fy + Atp(f se + Δfp) Note that the tie reinforcement mu st be spread over a large enou gh area su ch that the tie force divided by the anchorage area (where the height is twice the distance from the edge of the region to the centroid of the reinforcement) is less than the limiting stress for that nodal zone. Design Strength of Each Nodal Zo ne Face = Fnn where F nn = f ce Area on Face of Nodal Zo ne (perpendicular to the line of action of the associated strut or t ie force) Again fce = 0.85 nf c n = 1.00 in nodes bounded by struts and bearing areas n = 0.80 in nodes anchoring a tie in one direction only n = 0.60 in nodes anchoring a tie in more than one direction
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Location of STM Provisions in ACI318-14?
Separate appendix like in ACI318-08
Separate 318 referenced document
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Available Guideline Documents
Basic rules put into main body of code and “application guidelines” in a separate document
95
Design Examples
SP-208
Second SP
Textbook Materials
Journal Papers
fib Bulletin 3
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Challenges to Design by the STM
Selection of Shape of the STM Model
Determination of Member Forces in Indeterminate Models
Design for Multiple Load Cases
Uncertainty in Nodal Zones Dimensions
Time Consuming Geometric Calculations
Selecting What Needs to be Checked and Not Checked
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Performance under Overloads
Challenges to Design by the STM
Selection of Shape of the STM Model
97
Challenges to Design by the STM
98
Challenges to Design by the STM
Selection of Shape of the STM Model
Selection of Shape of the STM Model
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100
Challenges to Design by the STM
Challenges to Design by the STM
Selection of Shape of the STM Model
Determination of Member Forces in Indeterminate Models
Design for Multiple Load Cases
Uncertainty in Nodal Zones Dimensions
Time Consuming Geometric Calculations
Selecting What Needs to be Checked and Not Checked
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Performance under Overloads
Selection of Shape of the STM Model
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102
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Challenges to Design by the STM
Challenges to Design by the STM
Selection of Shape of the STM Model
Selection of Shape of the STM Model
Determination of Member Forces in Indeterminate Models
Determination of Member Forces in Indeterminate Models
Design for Multiple Load Cases
Uncertainty in Nodal Zones Dimensions
Time Consuming Geometric Calculations
Selecting What Needs to be Checked and Not Checked
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Performance under Overloads
5800 kN 535 mm
5625 kN
A
B
C L
K
2895 mm
D
O
M
Q
P
E
R
570 mm
41 T 36 k
U G
H
1590 1015 mm mm
I 2030 mm
3659 kN
N
F
4000 mm 3229.5 kN
S
J 1015 1350 mm mm
N
418.8 kN
49 degrees
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104
Challenges to Design by the STM
Challenges to Design by the STM
Selection of Shape of the STM Model
Selection of Shape of the STM Model
Determination of Member Forces in Indeterminate Models
Determination of Member Forces in Indeterminate Models
Design for Multiple Load Cases
Design for Multiple Load Cases
Uncertainty in Nodal Zones Dimensions
Uncertainty in Nodal Zones Dimensions
Time Consuming Geometric Calculations
Time Consuming Geometric Calculations
Selecting What Needs to be Checked and Not Checked
Selecting What Needs to be Checked and Not Checked
Designing for Good Performance Under Service Loads
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Validity of Design in Complex Models
Performance under Overloads
Performance under Overloads
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106
Challenges to Design by the STM
Challenges to Design by the STM
Designing for Good Performance Under Service Loads
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Validity of Design in Complex Models
Performance under Overloads
Performance under Overloads
107
108
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Challenges to Design by the STM
Challenges to Design by the STM
Designing for Good Performance Under Service Loads
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Validity of Design in Complex Models
Performance under Overloads
Performance under Overloads
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110
Challenges to Design by the STM
Challenges to Design by the STM
45% of Pn
68% of Pn
Designing for Good Performance Under Service Loads
Designing for Good Performance Under Service Loads
Validity of Design in Complex Models
Validity of Design in Complex Models
Performance under Overloads
Performance under Overloads
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Content of Potential ACI Committee 445 Document
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Click on the text below to go to the web page.
Selection of model shape
Examples of good strut-and-tie model shapes for a large number of common design situations
Guidance for complex shapes
Use of predictions of stress trajectories and topology optimization
Selecting relative member stiffness in indeterminate situations
Design for multiple load cases and load reversals
Determination of nodal zone geometries
Determination of what to check and not to check
Evaluation of performance under service loads; minimum reinforcement recommendations
Validation of ACI code-calculated capacity
Other design requirements
Seminar Schedule
Online CEU Program
Bookstore
Web Sessions
ACI eLearning
Conventions
Concrete Knowledge Center
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