Strut and Tie Part 1

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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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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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19

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


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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25

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


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)


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.


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



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Strut and Tie Part 1