strut and tie part 1
TRANSCRIPT
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Design Using the Strut-and-Tie
Method, Part 1
ACI Spring 2010 Xtreme Concrete Convention
March 21 - 25, Chicago, IL
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ACI Web Sessions
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March 21st through 25th, 2010.
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Please enjoy the presentations.
Design Using the Strut-and-Tie
Method, Part 1
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 pre-
stressed 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-and-
Tie Models in Education and Design. He is also a National
Center for Supercomputing Applications Faculty Fellow and
University of Illinois Collins Scholar.
10
Dan Kuchma
The STM Design Process and
ACI Requirements
University of Illinois at Urbana-Champaign
11
Basis of the Strut-and-Tie Method
B (Beam) and D (Discontinuity) Regions
Basis of the Strut-and-Tie Method
Applications of Strut-and Tie Method
The STM Design Process
ACI Code Provisions for Design Using the STM
Challenges to Design by the STM
12
D
DBBB DDD
D
BB
B
B B
B
B
DD
D
D DD
D
h1
h1
h2h2
h2
h3
h4
h4
h3
h4
Reg io n St rai n Co nd it io n Des ig n Pr oc ed ur e
B
(Beam or Bernoulli)
D
(Discontinuity or
Disturbed)
Sectional
C om pl ex Emp ir ical , FEM, STM
Reg io n St rai n Co nd it io n Des ig n Pr oc ed ur e
B
(Beam or Bernoulli)
D
(Discontinuity or
Disturbed)
Sectional
C om pl ex Emp ir ical , FEM, STM
B-Regions and D-Regions
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CSA A23.3-84
CEB-FIP Model Code 90
AASHTO LRFD 94
ACI 318-02
ACI Code Prov is ions for Design us ing the STM
20
T
C
T
C
C C
P
P
2
>A f Ts y
P
2
>
Af
C
c
cu
>A f Ts y
>
Af
C
c
cu
Struts, Ties, and Nodal Zones (Joints)
ACI Code Provisions for Design using the STM
21
Struts -- Compression Members
Design Strength of Struts = Fns where Fns = fcs Acsfcs = 0.85sfc
s = 1.00 for prismatic struts in uncracked compression zones
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 = 0.40 for struts in tension members
s = 0.60 for other cases
*crack control reinforcement requirement is visini 0.003
= 0.75 for all elements of truss
ACI Code Prov is ions for Design us ing the STM
fcw
fc
22
Compressive Stress Limit fcs = 0.85sfc
= 0.85 = 0.51
= 0.85
= 0.51 = 0.51 = 0.64
ACI Code Provisions for Design using the STM
s = 1.0s = 0.60s = 0.75 s = 1.0 s = 0.60
23
Ties Tension Members
Capacity of combined ordinary
and bonded prestressing steel:
Components o f Strut-and-Tie Models
Fnt
= Ats
fy
+ Atp
(fse
+fp)
Note that the tie reinforcement must be spread over a
large enough area such that the tie force divided by
the anchorage area is less than the limiting stress for
that nodal zone.
24
ACI Code Prov is ions for Design using the STM
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Nodal Zones (Joints)
Design Strength of Each Nodal Zone Face = Fnn where Fnn = fcn
Area on Face of Nodal Zone perpendicular to the line of action of the
associated strut or tie force. Again fcn = 0.85nfc
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
ACI Code Prov is ions for Design using the STM
26
ACI Code Provisions for Design using the STM
Dimensions of Nodal Zones
27
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
28
This method involves imagining that an internal truss, consisting of
concrete struts and steel ties, carries the load through a D(Discontinuity)
Region to its supports. With this idealization, structural design involves
detailing reinforcement to serve as the ties, and checking that the capacity
of the struts and joints (nodal zones) are sufficient to carry the imposed
load.
The nominal compressive strength of the strut can be taken as a stress
limit times the area of the strut. The strength of the ties is equal to the
yield strength of the reinforcement. The strength of each have of a nodal
region can be taken as equal to the perpendicular area of the face to the
direction of the applied loading times the appropriate stress limit. In all
cases, the design strength will be taken as phi times the nominal strength
and this must be greater than the factored applied load.
The (phi) factor for concrete struts, steel ties, and nodal zones shall be
taken as 0.75.
Summary of the Strut-and-Tie Design Method
Leonard De Rooy is Professor and Department
Chair in the Civil and Environmental
Engineering department at Calvin College in
Grand Rapids, Michigan. He holds a B.S.E
from Calvin College and an M.S.E in Civil
Engineering from the University of Michigan.
He is a licensed professional engineer in thestate of Michigan. Mr. De Rooy also spent 13 years as a
Structural Engineer for URS Greiner, where his work included
structural design and retrofit of industrial structures, multistory
steel structures, multistory concrete structures, theaters, and
large high school complexes. He was involved in the design of
Calvin College DeVries Hall, a four-story concrete waffle slab
structure.
Examples for Design of Structural
Concrete with Strut and Tie Models
Example 3: Strut-and-Tie Design and
Detailing of Foundation Grade Beam
Presented by:
Leonard P. De RooyCalvin CollegeGrand Rapids, Michigan
Co-Authored by:
Bob Anderson, URS Corporation
Tim Den Hartigh, URS Corporation
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Site Constraints
Existing Site Constraints
Caissons for building 2 placed when building1 was built.
60 sanitary sewer
Matching existing floors
floor 1 and 2
Parking deck
Location of tower crane.
Structural Model
Used FEM for our modeling.
Input data file > 27,400 lines
Approx 500 load cases
2 models
cracked and uncracked
Modeling
Modeling
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Grade Beams Grade Beams
Grade Beams Grade Beams
Grade Beams
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Nodal Zone Node N-4
Node N-4
= 0.75 ACI 318-05 Section 9.3.2.6
n = 0.80 (one tie) ACI 318-05 Section A.5.2.2
Fnn = fce Anz ACI 318-05 Section A.5
fce = 0.85 n fc ACI 318-05 Section A.5.2
fce = 0.85 x 0.80 x 5,000 psi = 3,400 psi (23.4 MPa)
Node N-4 Left Face (Force Due to Member E-3)
Factored Design Force = Fut= 4,788 k (21,300 kN)
Anz = 32 in. x 90 in. = 2 ,880 in.2 (1,858,100 mm2)
Fnn = fce AnzFnn = 0.75 x 3,400 psi x 2,880 in.
2
Fnn = 7,344,000 lbs = 7,344 k (32,670 kN)
7,344 k > 4,788 k => OK (32,670 kN > 21,300 kN)
Node N-4 Bottom Face (Force Due to member E-13)
Factored Design Force = Fut= 6,148 k (27,350 kN)
An = 48 in. x 90 in. = 4 ,320 in.2 (2,787,100 mm2)
Fnn = fce AnzFnn = 0.75 x 3,400 psi x 4,320 in.
2
= 11,016,000 lbs. = 11,016 k (49,000 kN)
11,016 k > 6,148 k => OK (49,000 kN > 27,350 kN)
Node N-4 Top Face (Force Due to Col umn lo ad)
Factored Design Force = Fut
= 3,857 k (17,160 kN)
An
= 42 in. x 42 in. = 1 ,764 in.2 (1,138,100 mm2)
Note: the transverse strut-and-tie model converts this area from the
42 in. (1,070 mm) diameter column to an area of
42 in. (1,070 mm) x 90 in. (2,290 mm).
Using the smaller area here is a conservative check.
Fnn = fce AnzFnn = 0.75 x 3,400 psi x 1,764 in.
2
= 4,498,200 lbs. = 4,498 k (20,000 kN)
= 4,498 k > 3,857 k => OK (20,000 kN > 17,160 kN)
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Alternate Load Path
Final Design Final Design
Final Design Final Design
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Final Design Final Design
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