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Assoc Prof Tan Kiang Hwee Department of Civil EngineeringCE5510 Advanced Structural Concrete Design - STRUT-AND-TIE METHODS... formulate strut-and-tie models in structural concrete mem

Assoc Prof Tan Kiang Hwee Department of Civil Engineering

CE5510 Advanced Structural

Concrete Design

- STRUT-AND-TIE METHODS

! the concept of strut-and-tie models

! their applications to new construction

(and strengthening works)

At the end of the lecture

You should be able to

! identify cases where strut-and-tie

models are applicable or appropriate

! formulate strut-and-tie models in

structural concrete members

! design the reinforcement according to

the strut-and-tie models

! Design Examples for New Construction

• High Wall

• Corbel

• Dapped-Beam

• Transfer Girder

• Deep Beam with Opening

• (Stepped (Non-Prismatic) Beams)

! (Examples for Strengthening Works)

• Dapped Beams

• Beam with Openings or Recesses

! regions of relatively uniform stresses

! Bernoulli hypothesis of linear strain

! near concentrated loads, corners,

bends, openings and other

! Components

! concrete compression

struts

! steel tension ties

! nodes (nodal zone) where

struts and ties meet

 Tan K H, NUS

2/16/2004

Boundary forces/stresses

Load path

?

Geometric Layout of strut-and-tie models

follows the flow of internal forces in the structure

! Major requirements

! S-T model must be in equilibrium with applied

loads ( statically admissible field )

! Strength of struts, ties and nodal zones must

equal or exceed forces in these members ( safe )

! Sufficient to consider only axes of struts and ties in

the early design stage ; need to consider widths in

general

! Struts must not overlap each other

! Ties may cross struts or other ties

! Angle between a strut and a tie joined at a node

should not be less than 25 degrees.

boundary and compute

force resultants on each

Elastic stress trajectories

Some rules

for estabilshing strut-and tie

model

Agreement with Crack Pattern

××××

Truss 2 can form only if truss

1 does not fail prematurely

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2/16/2004

Exercise 1

! Explore the application of strut-and-tie

model in the design of anchorage zone

Exercise 2

! A T-beam is post-tensioned with a cable anchored at

the centroid of the section at its end Given that the

area of the flange is one-third of the overall

cross-section, explain by sketching in the following figures,

how you would obtain the required reinforcement to

resist bursting tension in the web due to the

prestressing force

 Tan K H, NUS

2/16/2004

! Compression struts

! line along centre-line of strut

! strut with width

! Tension ties

! band of steel reinforcement

! anchorage (hooks, development length)

! Nodes

! bounded by compressive forces (CCC)

! anchoring one tension tie (CCT)

! anchoring more than one tie (CTT, TTT)

Elements of strut-and-tie model

Forces in struts and ties

In general,

φ F n ≥ F u

φ : strength reduction factor

F n : nominal strength of the member

F u : force in the member due to factored

loads

(to ensure same load capacity as FIP

Recommend-ations, consistency between AC1 1999 and 2002

Codes, & consistency between B-and D- regions)

• Transverse tensile strains

! Confinement from surrounding

concrete (e.g pile caps)

Prismatic strut

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2/16/2004

Bottle-shaped strut

! Draw truss to transmit forces

! use of elastic analysis , crack patterns

! equilibrium of forces, width of struts,

anchorage of ties

! Provide steel reinforcement for ties &

check concrete stresses in struts and

nodes where necessary

Example 1 –

Column on wall 187

187

263 565

534 534

1 0

0 m

m

1.80 MPa 4.67

MPa

267

2T13 each face

2T13 each face 3T13 each face

474 530 745

785 kN 158

b=406 mm h=508 mm d=457 mm

241 mm

w=1732/ (0.61f c ’)

=200mm

100 mm

Final layout

486 x 486mm

229

356 406

3T25

2T13

3T13 closed stirrups 4T25

Example 3 - Dapped ends

516

516

37

37 553

compute steel required in ties

U bars 4T25 bars

178 mm

Example 4 - Transfer girder

 Tan K H, NUS

2/16/2004

Combined truss and strut action

6543 kN 6579

kN

Combined truss and strut action

6543 kN

∴ V transmitted by stirrups

= 3x854 = 2562 kN = 39% of 6579 kN

V transmitted by strut H-AA

= 6579-2562-6x84.2 =3512 kN For H-AA, D = 5102 kN; w=416 mm.

For E-AA, D = 1174 kN; w=96 mm.

 Tan K H, NUS

2/16/2004

Example 5 - Deep beam with opening

f cd =17 MPa

f yd =434 MPa

Schlaich

left side, model 1

left side, model 2

 Tan K H, NUS

2/16/2004

 Tan K H, NUS

2/16/2004

Check concrete stresses:

Stresses under bearing plates:

Other critical anchorages

- C, D

Check anchorage length of reinforcing

bars

 Tan K H, NUS

2/16/2004

Further reinforcement

mesh on either face of wall

nominal column reinforcement stirrups

! J.G MacGregor, “REINFORCED

CONCRETE: Mechanics and Design”, 3rd

Ed., Prentice-Hall, 1997, Ch 18.

! A.H Nilson, D Darwin and C.W Dolan,

“Design of Concrete Structures”, McGraw-Hill,

2003, pp.

! K.H Reineck (Ed), “Examples for the Design

of Structural Concrete with Strut-and-Tie

Models”, ACI SP-208, 2002, 244 pp.

http://www.cee.uiuc.edu/kuchma/strut_and_ti

 Tan K H, NUS

2/16/2004

Further reading:

1987, pp.74-150.

ACI Journal, V 82, No 1, Jan-Feb 1985, pp 46-56.

No 6, USA, November-December 1993, pp 683-691.

Plastics for Reinforced Concrete Structures (FRPRCS-5),

Cambridge, UK, July 16-18, 2001, Vol 1, pp 249-258

6, USA, November-December 1999, pp 899-905