Experimental study on fiber-reinforced concrete panels subjected to shear, Finite Element Modeling - Tesi

Lai/Vecchio) provided comparable levels of accuracy. In cyclic loading the Walraven

model appears to be more accurate and stable. In constant rotation lag models, the lag

should be taken as 10° for unreinforced elements, 7.5° for uniaxially reinforced

elements and 5° for biaxially reinforced elements.

6.5 Modeling Elements

In this paragraph, the model sequence previous described, is analyzed, and results are

shown to prove the reliability of the FE Program. 247

6. FINITE ELEMENT MODELING

6.5.1 Steel Fiber Reinforced Concrete Beams

The experimental beam done by Minelli in 2005, where 11 FRC beams with

a = 1090 mm d = 435 mm

dimensions of and discussed in his PhD thesis “plain and

Fiber reinforced concrete beams under shear loading: Structural behavior and design

aspect”, is here represented in numerical model with the VecTor2 program, to better

understand the behavior of the Steel fibers, and to see if the previsions done with the

program were acceptable and correctly captured the experimental program done.

Following the correct dimension of the element, the right percentage of fiber inserted,

and their properties, many attempts were done to understand how program works and to

improve the response of that beam.

Following properties of the beams used in the FE Program are shown in the listed

tables: Beam Properties

2 Ø 24 = 905 mm²

Reinforcement Area 1.04%

Reinforcement Ratio Table 6.1: Beam Properties.

Cement Properties

0 4 4 7

123 5 56 5

Content

[kg/m³] [mm] [MPa] [MPa] [MPa]

345 20 24.8 2.30 31,400

Table 6.2: Concrete Properties.

Reinforcement and Fiber Properties

Reinforcement Fiber

4 ; <

4

4 7 4 7

89 4 4

6,123

86 8 56 5 [mm]

[mm] [MPa] [MPa] [MPa]

[kg/m³] [MPa] [mm]

345 20 24.8 2.30 31,400 1100 30 0.60

Table 6.3: Reinforcement and Fiber Properties. 248

6. FINITE ELEMENT MODELING

The following Figure 6.8 shows the correct dimension of the beams tested in this

research and how the load were applied:

Figure 6.8: Geometry and reinforced details of the specimen.

Taking advantage from symmetry, half of the beams was modeled with an overall

length of 480 mm x 2225 mm; the thickness of beam was 200 mm, as shown in the

previous figure.

The mesh depicted was deemed to be the most efficient, whereas a finer mesh yielded

similar predictions with a undesired increases in run-time.

Thus, 22 elements were used through the depth of the beam, with an average size of 25

mm in the x- and y-direction; the longitudinal reinforcing bar was modeled as a truss

bar centered at 50 mm below the bottom of the beam.

Support conditions were represented with a vertical roller located under a steel plate

with the dimension of 22.5 mm long the y-direction and of 90 mm in the x-direction,

and horizontal rollers throughout the depth along the right edge.

For these models, a displacement control was used, as a monotonically increasing

vertical displacement applied directly to the top right corner of the specimen

(representing centre point loading). This was increased in load step of 0.1 mm until the

shear failure was reached: load plate were also used to avoid local failures at the vertical

roller (as previously described) and under the applied displacement. 249

6. FINITE ELEMENT MODELING

Figure 6.9: FormWork model for beams.

(element size: 25 x 25 mm; 22 elements through the depth of the beam)

Predictions obtained by VecTor2 were accurate: the failure mode and the cracking load

were correctly captured as diagonal tension splitting in the web of the members,

following by longitudinal bond splitting along the reinforcement bars.

Following pictures shows the crack patterns of this experimental test studied with

VecTor2, starting from a displacement of 0.00 to the failure:

Figure 6.10: Crack patterns at displacement factor of 0.00.

Figure 6.11: Crack patterns at displacement factor of 1.00. 250

6. FINITE ELEMENT MODELING

Figure 6.12: Crack patterns at displacement factor of 3.50.

Figure 6.13: Crack patterns at displacement factor of 5.00.

Figure 6.14: Crack patterns at displacement factor of 6.50.

Figure 6.15: Crack patterns at displacement factor of 8.00. 251

6. FINITE ELEMENT MODELING

Figure 6.16: Crack patterns at failure displacement factor of 9.10.

6.5.2 Macro-synthetic Fiber Reinforced Concrete Beams

The document ”Shear Behavior of Macro-Synthetic Fiber-Reinforced Concrete Beams

without Stirrups” by Altoubat, Yazdanbakhsh and Rieder, was analyzed and

represented with the FE Program to understand if it was possible to capture the behavior

of these MSNFRC element using the “fiber steel option” offered by the program;

discussions about Susetyo’s panel will be done in the following paragraph to interpolate

the data with the panels analysis of this experimental program.

These beams were constructed with no stirrups and smooth polypropylene macro-

synthetic fibers.

Variables used in this experimental program includes longitudinal reinforcement ratio,

effective depth and shear span-to-depth ratio. The findings of these tests showed that

shear strength sufficiently close to the FRC minimum limit of 0.3= could be attained

using at least 0.75% by MSN Fiber Reinforced Concrete.

Multiple diagonal shear cracks were exhibited in the web of the beams and the crack

widths were well controlled, leading to improvements in deformation capacity over

plain concrete (as theory declaims).

Following Figure 6.17 shows the experimental configurations and dimensions executed

by Altoubat et al. (2009). 252

6. FINITE ELEMENT MODELING

Figure 6.17: Schematic outline of experimental beam configuration (Altoubat et al.,

2009).

The beams were named according to the shear span-to-depth ratio (“Sh” for short beams

⁄

> = 3.5), the experimental series (“2” for the second series with d = 330 mm and

with

?

( = 3.18%), and the fiber volume fraction (“0.0”, “0.5”, “0.75” and “1.0”).

In addition each beam test was duplicated, denotes as “a” for the first beam and “b” for

the second; for the purpose of this experimental study, the first series of beams were

modeled using the Fiber Reinforcement Type 6 with the original VecTor2 version (Steel

– Straight Fibers).

Taking advantage of symmetry, half-beams of the shorter one was modeled, with an

overall outside dimension of 390 mm x 950 mm; thickness of beam was 230 mm and it

was modeled with in-plane rectangular elements: the mesh depicted was deemed to be

the most efficient (a finer one yielded similar predictions with undesired increases in

run-time.

So, 26 elements were used through the depth of the beams, with an average size of 15

mm in the y-direction and 20 mm in the x-direction. Longitudinal reinforcing bars were

modeled as truss bar centered at 330 mm below the top of the beam.

Following Table 6.4 list the experimental beams configuration used in the experimental

program: 253

6. FINITE ELEMENT MODELING

@ G

@ A 6

a h d b ⁄

2 F

Beam DE [%]

[MPa] [MPa] [mm] [mm]

[mm] [xBC ]

Sh2-0.0 1,900 1,500 750 390 330 230 2.3 3.18

Sh2-0.5 1,900 1,500 750 390 330 230 2.3 3.18

Sh2-0.75 1,900 1,500 750 390 330 230 2.3 3.18

L2-0.0 2,700 2,300 1,150 390 330 230 2.3 3.18

L2-0.5 2,700 2,300 1,150 390 330 230 2.3 3.18

L2-0.75 2,700 2,300 1,150 390 330 230 2.3 3.18

L2-1.0 2,700 2,300 1,150 390 330 230 2.3 3.18

Table 6.4: Altoubat et al. (2009) – Beam dimension.

Support conditions were represented with a vertical roller at 200 mm from the bottom

left corner of the beam and horizontal rollers throughout the depth along the right edge.

For this model, displacement control was used, with a monotonically increasing vertical

displacement applied directly to the top right corner of the specimen (representing

centre point loading): this was increased in load steps of 0.1 mm until the shear failure

was reached.

No plates were used in the experimental setup, so also here no plates were used. Only in

the first attempt, as shown, plates were needed since results without plates crashed at

the beginning into local failure.

Following picture shows the FormWorks models for this beam with steel loading plate:

254

6. FINITE ELEMENT MODELING

Figure 6.18: FormWork model for short beams with loading plates.

(Element size: 20 x 15 mm; 26 elements through the depth of the beam)

8

13 H F

@ 4

2

4 4 4

4 I4

123

5 Fiber Type

8

19

Beam [mm]

[mm]

[MPa] [%] [mm]

[mm] [MPa]

[mm]

Sh2-0.0 40.9 20 297 - - - - -

Sh2-0.5 41.9 20 297 Polypropylene 0.5 40 0.433 620

Sh2-0.75 41.9 20 297 Polypropylene 0.75 40 0.433 620

L2-0.0 40.9 20 297 - - - - -

L2-0.5 419 20 297 Polypropylene 0.5 40 0.433 620

L2-0.75 41.9 20 297 Polypropylene 0.75 40 0.433 620

L2-1.0 35.6 20 297 Polypropylene 1.0 40 0.433 620

Table 6.5: Altoubat et al. (2009) – Concrete and Fiber Properties.

As will be with the panels, the concrete strength and aggregate size were provided. In

addition it was deemed necessary to set the maximum crack spacing in the x- and y-

/ /

JK JL

directions, and , to (where is the effective shear depth, taken as 0.9d in

accordance with the shear provision of the Canadian Concrete Design Code (CAN/CSA

Standard A23.3-04, 2004)). This was used in lieu of the default maximum crack spacing

of 1000 mm included in VecTor2. 255

6. FINITE ELEMENT MODELING

The default maximum crack spacing was unrealistic (a crack spacing of roughly three

times the depth of the beam is not attainable) and led to large crack widths and

premature analytical failure.

Default parameters were used for all other concrete properties.

Following Table 6.6 shows the reinforcement properties of the beams tested in this

experimental program: 4 P P

M F 4 O

9 8Q I

8 N I 8

Beam Bars BC BC

DE DE

[mm²] [mm] [MPa [MPa]

[MPa]

Sh2-0.0 3 - 32 mm 2413 32.0 400 600 200,000 10 100

Sh2-0.5 3 - 32 mm 2413 32.0 400 600 200,000 10 100

Sh2-0.75 3 - 32 mm 2413 32.0 400 600 200,000 10 100

L2-0.0 3 - 32 mm 2413 32.0 400 600 200,000 10 100

L2-0.5 3 - 32 mm 2413 32.0 400 600 200,000 10 100

L2-0.75 3 - 32 mm 2413 32.0 400 600 200,000 10 100

L2-1.0 3 - 32 mm 2413 32.0 400 600 200,000 10 100

Table 6.6: Altoubat et al. (2009) – Reinforcement Properties.

Many attempts were done, to understand the behavior of the beam, and to verify if the

program can currently represent the experimental program done: changing in the fiber

percentage and modifying the dimension of the mesh that subdivide the all structure the

best option was found.

Some of the attempts of the different fiber percentage and of the different mesh

structure is here showed: 256

6. FINITE ELEMENT MODELING

Figure 6.19:

: FormWork attempt model for short beams (0.0% fibers).

fibers)

: F