1

NLTH-1

Title Verification of Fiber Model in MIDAS comparing with experimental results

Description To test the validity of Fiber Model in MIDAS, analytical results are compared with the experimental results of the reference 3, Cho (2004). A cantilever column was tested under the conditions of constant axial compression and cyclic lateral load reversals. The hollow column, H24-300, is cast out of concrete with compressive strength of 24MPa and reinforcing steel with yield strength of 300 MPa.

Verification Example

2

a) Specimen , H24-300

NLTH-1

3

b) Fiber Model

Structural geometry and analysis model

Different concrete models with different tie spacing are reflected in the fiber sections I and II. The center to center spacing of the ties is 50mm in the fiber section I and 100mm in the fiber section II.

Verification Example

4

Model Analysis Type

2-D Nonlinear Static Analysis

Unit System mm, N

Dimension Height 4500 mm

Element Beam element (linear beam + nonlinear beam assigned with fiber models)

Material In MIDAS, the modified Kent & Park concrete model and Menegotto-Pinto steel model for fiber elements are adopted to construct the fiber sections of the test model.

a) Concrete ; The parameters for the Kent & Park model are described as follows.

1'

s yh

c

fK

f

ρ= +

0 0 .00 2 Kε =

0.5

3 0.29 ' '0.75 0.002

145 ' 1000c

s

c h

Zf h

Kf s

ρ

=+

+ −−

0.004 0.9 ( / 300)u s yhfε ρ= +

NLTH-1

5

where,

0 Concrete strain at maximum stress; ε

Concrete compressive cylinder strength [MPa]' ; cf

Strength increase factor due to confinement; KStrain softening slope; Z

Yield strength of stirrups or ties [MPa]; yhfVol. ratio of hoop reinforcement to the vol. of core concrete

measured to outside of stirrups or ties

; sρ

Center to center spacing of stirrups or ties sets; hs

Width of core concrete measured to outside of stirrups or ties' ; h

Ultimate compressive strain of concrete

confined by stirrup-ties suggested by Scott et al.

; uε

Verification Example

6

The calculation of parameters for the Kent & Park concrete is described as follows. First, for the core concrete at the fiber section I ; For the cover concrete at the the fiber section I ;

0 0.002 0.002 1.217 0.002434Kε = = × =

0.530.268

3 0.29 ' '0.75 0.002

145 ' 1000c

s

c h

Zf h

Kf s

ρ

= =+

+ −−

' 3 0 .4 cf =

3 5 0 y hf =

(28.274 3720) / 50 (400 650 280 530) 0.018849

( 0.0 for cover concrete)sρ = × × × − × =

=

0.004 0.9 ( / 300) 0.023791u s yhfε ρ= + =

' 60, 50hh s= =

1 1.217'

s yh

c

fK

f

ρ= + =

0 0 .0 0 2 0 .0 0 2Kε = =

1 1'

s yh

c

fK

f

ρ= + =

0.5340.8

3 0.29 ' '0.75 0.002

145 ' 1000c

s

c h

Zf h

Kf s

ρ

= =+

+ −−

0.004 0.9 ( / 300) 0.004u s yhfε ρ= + =

NLTH-1

7

Secondly, the core concrete at the fiber section II;

For the cover concrete at the fiber section II;

0 0.002 0.002 1.109 0.002217Kε = = × =

1 1.109'

s yh

c

fK

f

ρ= + =

0.574.354

3 0.29 ' '0.75 0.002

145 ' 1000c

s

c h

Zf h

Kf s

ρ

= =+

+ −−

0.004 0.9 ( / 300) 0.013896u s yhfε ρ= + =

' 3 0 .4 cf =

3 5 0 y hf =

(28.274 3720) / 100 (400 650 280 530) 0.009425

( =0.0 for cover concrete)sρ = × × × − × =

' 60, 100hh s= =

0 0 .0 0 2 0 .0 0 2Kε = =

1 1'

s yh

c

fK

f

ρ= + =

0.5340.8

3 0.29 ' '0.75 0.002

145 ' 1000c

s

c h

Zf h

Kf s

ρ

= =+

+ −−

0.004 0.9 ( / 300) 0.004u s yhfε ρ= + =

Verification Example

8

b) Steel ; The Menegotto-Pinto steel model is used for the analytical steel model. The parameters are as follows. The yield strength of the steel is determined from material test data.

where,

350 [ ]yf M P a=

2205940 [ ]E N/mm=

0.02b =

; Yield Strength yf

; Young's Modulus E

; Stiffness Reduction Ratio b

σ [MPa]

ε

36.997

30.4

0.002434

6.08

0.002

Core Concrete

Cover Concrete

0.2 Kfc’

σ [MPa]

ε

33.714

30.4

0.002217

6.08

0.002

Core Concrete

Cover Concrete

0.2 Kfc’

σ [MPa]

ε

350

Stress-Strain relation at Fiber section I Stress-Strain relation at Fiber section II

Stress-Strain relation of Steel Model

Kfc’

fc’

Kfc’

fc’

NLTH-1

9

Element Property The rectangular section and detailed rebars of the cantilever column used for the experiment are shown below. To consider its confinement effect, the concrete cover zones and the core concrete zone are separately considered in the analytical model.

Rebar and Fiber Division of the Column Section

Concrete Cover

Core Concrete

Verification Example

10

Boundary Condition Node 1 ; Constrain all DOFs. (Fixed node)

Load Case The loading for this specimen consists of a cyclic lateral load and an axial compression load equivalent to 10% of the compressive strength of the section of the specimen, which was kept constant during the experiment.

Cyclic lateral displacement load

The cyclic loading is implemented by using sequential analysis of one-directional displacement loadings. Each one-directional displacement is loaded up to the same magnitude as the experimental displacement.

-200

-150

-100

-50

0

50

100

150

200

250

300

Displacement

[mm]

24 (450 700 480 230) 0.1 491040axialF N= × × − × × =

NLTH-1

11

Results The figure below shows the comparison of lateral force and displacement histories between experiment and analysis by MIDAS.

Experimental and Analytical Load-Displacement Relation It was found that the analytical results agreed well with the experimental result up to the drift ratio of 6 %. Beyond drift ratio 6%, both tensile and compressive failure took place in the specimen, which became extremely unstable.

-200

-150

-100

-50

0

50

100

150

200

-200 -150 -100 -50 0 50 100 150 200 250 300

D isp la cemen t [mm]

La t er a l

Fo r ce[kN ]

MIDAS Experiment

Drift Ratio 4% 2% 2% 4% 6%

Verification Example

12

The stress – strain histories of the cover, core concrete and steel are plotted as below. And the analytical results of the maximum moment and curvature at the bottom fiber section are also plotted below in which the pinching effect is well taken into account by the analysis.

Stress-Strain results of Concrete Cover Stress-Strain results of Core Concrete

Stress-Strain results of Steel Moment and Curvature Relation

-3.5E+01

-3.0E+01

-2.5E+01

-2.0E+01

-1.5E+01

-1.0E+01

-5.0E+00

0.0E+00

5.0E+00

-2E-02 -1E-02 0E+00 1E-02 2E-02

Strain

Stress

[MPa]

-4.0E+01

-3.5E+01

-3.0E+01

-2.5E+01

-2.0E+01

-1.5E+01

-1.0E+01

-5.0E+00

0.0E+00

5.0E+00

-2E-02 -1E-02 -5E-03 0E+00 5E-03 1E-02

Strain

Stress

[MPa]

-6E+02

-4E+02

-2E+02

0E+00

2E+02

4E+02

6E+02

8E+02

-2E-02 0E+00 2E-02 4E-02 6E-02

Strain

Stress

[MPa]

-8E+08

-4E+08

0E+00

4E+08

8E+08

-2E-04 -1E-04 0E+00 1E-04 2E-04

Curvature [rad/mm]

My

[N.mm]

NLTH-1

13

References

1. Fabio Taucer, et al., “A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures”, EERC-91/17, College of Engineering, University of California at Berkeley,1991. 2. Kent, D.C., and Park, R., “ Flexural Members with Confined Concrete”, Journal of the Structural Division, ASCE, 97(ST7), 1971. 3. Keun-Ho Cho, “An Experimental and Analytical Study on the Seismic Behavior of RC Piers using High-Strength Concrete and High-Strength Rebars”, Master’s Thesis, Seoul National University, 2004. 4. Menegotto, M. and Pinto, P.E., “ Method of Analysis for Cyclically Loaded Reinforced Concrete Plane Frames Including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending”, Proceedings, IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads”, Lisbon, 1973, pp.15-22. 5. Scott, B.D., Park, R. and Priestley, M.J.N., “Stress-Strain Behavior of Concrete Confined by Overlapping Hoops at Low and High Strain Rates”, ACI Journal, Vol. 79, No. 1, 1982, pp.13-27.