LAPORAN AKHIR PENELITIAN TERAPAN DANA RISTEK ...

LOG BO

LAPORAN AKHIR

PENELITIAN TERAPAN

DANA RISTEK-BRIN 2020

UNLOCKING THE POTENTIAL OF PRECAST IN SUSTAINABLE URBAN DEVELOPMENT (UPP-SUD)

Tim Peneliti: Prof. Ir. Priyo Suprobo, M.S., Ph.D. (Departemen Teknik Sipil/FTSPK/ITS)

Ir. Faimun, MSc, PhD (Departemen Teknik Sipil/FTSPK/ITS) Benny Suryanto B.Eng. M.Eng. Ph.D. FHEA (Civil Engineering Dept./Heriot-Watt University)

Sesuai Surat Keputusan No. 1308/PKS/ITS/2020 dan Perjanjian/Kontrak No. 3/AMD/EI/KP.PTNBH/2020

DIREKTORAT RISET DAN PENGABDIAN KEPADA MASYARAKAT INSTITUT TEKNOLOGI SEPULUH NOPEMBER

SURABAYA 2020

Pengisian poin C sampai dengan poin H mengikuti template berikut dan tidak dibatasi jumlah kata atau halaman namun disarankan seringkas mungkin. Dilarang

menghapus/memodifikasi template ataupun menghapus penjelasan di setiap poin.

In the second year of project basis, centre of research have been mainly directed toward series

of experimental and finite element analyses to support findings. Due to Coronavirus ramping

up globally, however, the main large-scale experiment have been postponed and it was anticipated to be re-carried out in September to December 2020 together with industrial

partnership, PT. WIKA Beton Tbk.

The first work package of the project undertaken is the finite element modelling. The motive

behind this work relies primarily on gaining improved insights of the new material used and

the mechanics of the precast beam-column joint. The majority of the work was focused on the development of appropriate constitutive model for concrete and engineered cementitious

composite (ECC), nonlinear finite element simulations of reinforced concrete members

subjected critically to shear and beam-column joint, and development of master curve rapid

ECC calculator. Thorough experimental analysis of small ECC members was also undertaken as a means to corroborate findings of the ECC calculator being developed.

1. Development of Constitutive models for concrete and ECC 1.1. Compression and tension models

The nonlinear constitutive law of concrete can be modelled in ATENA using either the

SBETA or the fracture-plastic model [1]. In the latter, the behaviour of concrete in tension is treated following the principle of fracture mechanics, whereas the behaviour of concrete

in compression is formulated following the theory of plasticity [1]. Two fracture-plastic

models are available in the software library: 3DNonlinearCementitious2 and 3DNonlinearCementitiousUser. In the former model, the only input required is the cube

compressive strength of concrete; this is then used to determine other parameters

required for analysis. Should it be necessary to input/modify other parameters, the

second model (3DNonlinearCementitiousUser) can be selected – it allows users to input appropriate constitutive laws. The second model is employed in this study.

Figure 1 presents the user compression model employed in this study, with an elliptical shape for the ascending part and a linear shape for the descending (softening) part. In

hardening branch, the ratio of normal compressive stress 𝜎𝑐 (MPa) to the cylinder

compressive strength 𝑓𝑐′ (MPa) is determined based on the computed strains and is related

to the compressive stress post-elastic point 𝑓𝑐𝑜 (MPa); concrete strain at corresponding

stress 휀𝑐 (mm/mm), and plastic strain at the peak point 휀𝑐𝑝 (mm/mm) in the following

manner [1, 2],

𝜎𝑐𝑓𝑐′= 𝑓𝑐𝑜 + (𝑓𝑐

′ − 𝑓𝑐𝑜)√1 − (휀𝑐 − 휀𝑐

𝑝

휀𝑐)

2

(1)

𝑓𝑐𝑜 = 2𝑓𝑡 (2)

휀𝑐𝑝=𝑓𝑐′

𝐸𝑐 (3)

𝐸𝑐 = (6000 − 15.5𝑓𝑐𝑢)√𝑓𝑐𝑢 (4)

C. HASIL PELAKSANAAN PENELITIAN: Tuliskan secara ringkas hasil pelaksanaan

penelitian yang telah dicapai sesuai tahun pelaksanaan penelitian. Penyajian meliputi

data, hasil analisis, dan capaian luaran (wajib dan atau tambahan). Seluruh hasil atau capaian yang dilaporkan harus berkaitan dengan tahapan pelaksanaan penelitian

sebagaimana direncanakan pada proposal. Penyajian data dapat berupa gambar, tabel,

grafik, dan sejenisnya, serta analisis didukung dengan sumber pustaka primer yang relevan dan terkini.

𝑓𝑐𝑢 =𝑓𝑐′

0.85 (5)

The Young’s modulus of concrete 𝐸𝑐 (MPa) is calculated based on the cube compressive

strength 𝑓𝑐𝑢 (MPa), whereas 𝑓𝑐𝑜 is defined from the tensile strength of the concrete 𝑓𝑡 (MPa).

Figure 1 Compression Model. (a) Constitutive Relations of Concrete and ECC; (b) Model

Verification.

Whilst the ascending branch of the compression model is computed based on the strains,

the descending (softening) branch (the linear curve) is computed based on the displacements to ensure mesh objectivity [3]. It is assumed that the post-peak

compressive displacement and energy dissipation are localised in a plane normal to the

direction of principal stress. The displacement value of 𝑤𝑑 = 0.05 mm is found to be

appropriate for normal concrete [3, 4].

In the tension (fracturing) model, Rankine failure criterion is used for defining concrete

cracking. In the fixed crack representation, stresses and strains are computed in a local

coordinate system in which the orientation is determined by the orientation of the principal stresses at the onset of cracking. In general, the user tension model of concrete

consists of two parts: linear (before cracking) and nonlinear (after cracking) (see Figure

2(a)). For the latter, the softening law is adopted following the formulation of fictitious crack model which is based on a crack-opening law and fracture energy. This is

determined based on experimentally derived empirical functions, as given by [1, 2]:

𝜎𝑡𝑓𝑡= (1 + (𝑐1

𝑤

𝑤𝑐)3

) exp (−𝑐2𝑤

𝑤𝑐) −

𝑤

𝑤𝑐(1 + 𝑐1

3)exp(−𝑐2) (6)

𝑓𝑡 = 0.24𝑓𝑐𝑢23 (7)

𝑤 = 휀𝑡𝐿𝑡 (8)

𝑤𝑐 = 5.14𝐺𝑓𝑓𝑡

(9)

𝐺𝑓 = 𝐺𝑓0 (𝑓𝑐′

10)

0.7

(10)

where 𝜎𝑡 is the normal tensile stress (MPa); w is the crack opening (mm); 𝑤𝑐 is the crack

opening at the complete release of stress which is normally at zero tensile stress (mm); 𝐿𝑡 is the characteristic length obtained from the finite element mesh size (mm); 𝐺𝑓 is the

fracture energy required to create a unit area of stress-free crack (N/mm); and 𝐺𝑓0 = 0.03

N/mm is the base value of fracture energy based on the maximum size of aggregate of 16

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

=

− + − −

s

( ) = −

+

mm [40]. The values of 𝑐1 = 3 and 𝑐2 = 6.93 are considered.

The tension model of ECC differs to considerable extent with concrete as the properties

provide tensile strain hardening (in the order of a few percent which is typically 300 higher

than that of concrete. Given this distinctive characteristic, the tension model was

specifically developed and has been the subject of interest of researchers. In this study, Petr Kabele’s model [5] was used as it has been included in the library of ATENA Science

(see Figure 2(b) and (c)).

Figure 2 Tension Model. (a) Basic Model of Concrete; (b) Multiple Cracking Regime ECC;

(c) Localised Cracking Regime ECC.

1.2. Shear model

The shear modulus of concrete and ECC decreases after cracking and this can be

represented by a shear retention factor following the expression proposed by Kolmar [6] and Kabele [5, 7] respectively (see Figure 3).

Figure 3 Shear Retention Model for Concrete and ECC.

=

s

( ) + −

=

s

( ) + −

b

b =

2. Proof-of-concept of user-defined constitutive models 2.1. Details of Vecchio and Shim beams

In order to ensure that the above constitutive models of concrete and ECC recently being

developed and used in ATENA Science software are capable of presenting accurate prediction of behavioural response of structural elements, first phase of finite element

studies was undertaken by modelling shear-critical reinforced concrete beams. Vecchio

and Shim beams [8] were selected their work have been a major subject of finite element

validation.

In 2004, Vecchio and Shim [8] undertook an experimental programme on twelve shear-

critical reinforced concrete beams which were essentially identical to the beams tested by Bresler–Scordelis (BS) four decades earlier [9] (hereinafter referred to as VS and BS

beams, respectively). The test programme aimed to testify the repeatability of the original

experiment, particularly with respect to failure modes and load capacities, and investigate the post-peak response which was not explored in the original experiment.

Figure 4 Geometric and reinforcement details of VS beams [8].

The schematic diagram of the beam geometry and reinforcement layout is displayed in

Figure 4, with beam cross-section details presented in Figure 5 and Table 1 for clarity.

Four series of three beams were tested: OA series with no transverse reinforcement; and A, B, and C series all having transverse reinforcement. In each series, the beam was

labelled with a numeral suffix to indicate the overall span: 1 representing the short span

(3.7 m); 2 representing the intermediate span (4.6 m); and 3 representing the long span (6.4 m). As summarized in Table 1, all beams were of rectangular cross-section and had

the same overall depth of 552 mm, whereas the width, amount of transverse

reinforcement and concrete strength in each series were varied.

552

220 2203660

D5@210*

D5@210**

4570

6400

552

552

220

220 220

220

D4@168***

Notes:*D5@190 for B1**D5@190 for B2***D4@152 for B3

Figure 5 Cross-section details of VS beams [8].

Table 2 lists the steel reinforcement used in the beam tests. It was not clear whether the

M25 longitudinal reinforcement in Beams C2 and C3 was type M25a or M25b. In this

study, it is assumed that M25a is the correct bar type and used throughout. Table 3 summarises the concrete compressive and tensile strength along with Young's modulus

for each series of beams. Steel plates with dimensions of 15035020 mm and 15030058 mm were used at both the support and loading points, respectively. This is in addition to 25 mm thick end plates which were welded to the bottom reinforcement at

both ends of each beam to provide adequate anchorage length. The length of these plates

was estimated from the finite element mesh size reported in the work.

M25

M30

M25

M30

M25

M30

M30

M30

M25

M30

M25

M30

M25

M30

M25

M30

M10 M10 M10

M10 M10 M10

D5 D5 D4

D5 D5 D4

D5 D5 D4

M10 M10 M10

M25

M30

M25

M30

M25

M30

M25

M30

183

183

178

178

132

128

91.5

89

66

91.5

89

64

64

64

64

64

64

64

64

64

64

50

50

50

OA1 OA2 OA3

A1 A2 A3

B1 B2 B3

C1 C2 C3

Table 1 Cross-section details of VS beams [8]

Beam

Label

b h d L Span Bottom Steel

Top

Steel Stirrup

(mm) (mm) (mm) (m) (m)

OA1 305 552 457 4.10 3.66 2M30; 2M25 - -

OA2 305 552 457 5.01 4.57 3M30; 2M25 - -

OA3 305 552 457 6.84 6.40 4M30; 2M25 - - A1 305 552 457 4.10 3.66 2M30; 2M25 3M10 D5-210 A2 305 552 457 5.01 4.57 3M30; 2M25 3M10 D5-210

A3 305 552 457 6.84 6.40 4M30; 2M25 3M10 D4-168 B1 229 552 457 4.10 3.66 2M30; 2M25 3M10 D5-190

B2 229 552 457 5.01 4.57 2M30; 2M25 3M10 D5-190

B3 229 552 457 6.84 6.40 3M30; 2M25 3M10 D4-152 C1 152 552 457 4.10 3.66 2M30 3M10 D5-210 C2 152 552 457 5.01 4.57 2M30; 2M25 3M10 D5-210

C3 152 552 457 6.84 6.40 2M30; 2M25 3M10 D4-168

Table 2 Material properties of steel bars reproduction of VS beams [8]

Bar Size Diameter fy fu Es

(mm) (MPa) (MPa) (GPa)

M10 11.3 315 460 200

M25a 25.2 440 615 210

M25b 25.2 445 680 220

M30 29.9 436 700 200

D4 3.7 600 651 200

D5 6.4 600 649 200

Note: aSeries 2; bSeries 2 and 3

Table 3 Material properties of concrete [8]

Beam Label

Suffix

f'c 0 Ec ft

(MPa) (%) (GPa) (MPa)

1 22.6 0.16 36.5 2.37

2 25.9 0.21 32.9 3.37

3 43.5 0.19 34.3 3.13

Note: The suffix is designated for VS-OA, A, B, C-series

2.2. Finite element mesh and boundary conditions

All beams were modelled using an 8-node hexahedral (brick) linear element, with each

node having x-, y- and z-translation. A typical mesh size of 0.05 m was used. The plates

at the loading, support, and anchor points were modelled using a tetrahedral linear

element to prevent localised yielding. The geometry and dimensions of these plates were

in accordance with those used in the experiment. Each beam was simply supported at

the bottom as in the experiment. An example of the finite element mesh used in the

analysis is presented in Figure 6. The bottom longitudinal bars were extended past both

ends of each beam and connected to a steel element representing the anchor plates as in

the experiment.

Figure 6 Mesh and boundary conditions.

The analysis for each beam was run under a monotonically increasing displacement at a

rate of 0.5 mm per step until failure. At each displacement increment, the displacement

applied at the centre point of the loading plate, the beam deflection at the bottom of the

beam at midspan, the load acting on the top plate were all monitored. The computed load

and midspan deflection were then compared with the experimental data reported in [8,

9].

2.3. Response of beam B1

To demonstrate the suitability of the models in predicting the nonlinear behaviour of

concrete in a shear-critical beam, Figure 7(a) presents the predicted load-deflection response of Beam B1. This beam was chosen as it displays three different behavioural

responses (flexure, shear and compression), which, whilst making it more difficult to

predict with accuracy, will provide a more comprehensive measure of the accuracy of the models employed in this work. To describe the different behavioural responses, six stages

of loading are highlighted in Figure 7(a) with data marker and discussed below. For clarity,

Figures 7(b)-(g) display the corresponding maximum principal strains and crack patterns in the deformed state with displacements magnified 5 times. In general, the response of

the beam can be characterised as shear-compression in nature.

With reference to Figure 7(b), the early stage of loading (50 kN) is shown to result in the formation of flexural cracks at the bottom (tension zone) of the beam and a consequent

increase in principal strain. As the load increases to 135 kN, new and pre-existing flexural

cracks propagate upwards, thereby increasing the prominence of the strain bands which are also extending upwards (Figure 7(c)). As the load further increases to 205 kN (Figure

7(d)), existing cracks propagate further upwards alongside with the strain bands,

resulting in a fan-shaped pattern which radiates from the point load at the centre span. A highly localised strain is evident in the web region when the load reaches 280 kN (Figure

7(e)) which is indicative of the onset of shear crack formation. This continues up to the

peak load (417 kN; see Figure 7(f)), although by comparing Figures 7(e) and (f), it is clear that throughout this stage, the flexural cracks stop progressing and damage is

concentrated mainly at the web region indicating that the beam behaviour changes from

being flexural to shear critical. As demonstrated in Figure 7(g), failure is predicted to occur

due to crushing of the concrete at the top (compression zone) of the beam next to the loading plate which is in a good agreement with the shear-compression failure observed

from the test (see Figure 7(h)). Only limited ductility is evident beyond the peak load

highlighting the brittle and dangerous nature of the response.

Monitoring point for

applied load (P)

Monitoring point for

midspan deflection (d)ux,uy,uz = 0 uy,uz = 0

Hexahedral

Tetrahedralx

y

z

Figure 7 (a) Load-deflection response of Beam B1; (b)-(g) predicted principal strain and

crack pattern; (h) failure crack pattern [8].

2.62.42.32.10 1.91.81.

6

1.5

x10-4

1.10.90.80.70 0.50.40.

3

0.2

x10-3

1.61.41.21.00 0.80.

6

0.

4

0.2

x10-3

2.32.01.71.50 1.20.90.

6

0.

3 x10-3

2.52.21.91.60 1.20.90.

6

0.3

x10-2

1.61.41.21.00 0.80.

6

0.

4

0.2

x10-2

(b)

onset of cracking

crack propagation

inclined cracks

shear cracks

peak load

failure

(c)

(d)

(e)

(f)

(g)

(h)

0

100

200

300

400

500

0 10 20 30 40 50Deflection (mm)

Lo

ad

(kN

)50

135

205

280

417

265

Vecchio-Shim Bresler-Scordelis

ATENA-3D

(a)

2.4. Comparison of load-deflection response To further check the accuracy of the models presented in this work, Figures 8(a)-(l)

compares the predicted and observed load-deflection responses for all beams, together

with predictions of ACI 318M-14 shear design code equations [10]. Each row presents the response of each series of beams with notionally identical cross-section, but with different

span lengths and reinforcement arrangements. The first and second row display the

results of notionally identical beams with and without transverse reinforcement, whereas

the rest displays the results of companion beams with smaller widths (B and C series). The beam span increases from left-to-right, from 3.7 m; 4.6 m; and 6.4 m. A summary of

the predicted and observed load capacity and beam deflection for the twelve VS beams

(and their BS duplicates) is presented in Table 4.

Table 4 Summary of observed and predicted load capacities and deflections

Ultimate Load Midspan Deflection

Beam

Label

Pu-Test Pu-Calc

Pu-Test/Pu-Calc

u-Test u-Calc

u-Test/u-Calc (kN) (kN) (kN) (kN)

VS-OA1 331 308 1.07 9.10 7.0 1.30

VS-OA2 320 298 1.07 13.2 10.0 1.32

VS-OA3 385 419 0.92 32.4 34.0 0.95

VS-A1 459 451 1.02 18.8 14.0 1.34

VS-A2 439 448 0.98 29.1 17.0 1.71

VS-A3 420 454 0.93 51.0 46.0 1.11

VS-B1 434 417 1.04 22.0 13.5 1.63

VS-B2 365 388 0.94 31.6 23.0 1.37

VS-B3 342 326 1.05 59.6 44.0 1.35

VS-C1 282 273 1.03 21.0 16.5 1.27

VS-C2 290 292 0.99 25.7 19.0 1.35

VS-C3 265 275 0.96 44.3 43.0 1.03

Mean 1.00 Mean 1.31

COV (%) 5.32 COV (%) 20.82

BS-OA1 334 308 1.08 6.6 7.0 0.94

BS-OA2 356 298 1.19 11.7 10.0 1.17

BS-OA3 378 419 0.90 27.9 34.0 0.82

BS-A1 468 451 1.04 14.2 14.0 1.01

BS-A2 490 448 1.09 22.9 17.0 1.35

BS-A3 468 454 1.03 35.8 46.0 0.78

BS-B1 446 417 1.07 13.7 13.5 1.01

BS-B2 400 388 1.03 20.8 23.0 0.90

BS-B3 356 326 1.09 35.3 44.0 0.80

BS-C1 312 273 1.14 17.8 16.5 1.08

BS-C2 324 292 1.11 20.1 19.0 1.06

BS-C3 270 275 0.98 36.8 43.0 0.86

Mean 1.06 Mean 0.98

COV (%) 7.26 COV (%) 16.05

With reference to Figures 8(a)-(l), it is evident that the predicted load-deflection responses

closely replicate the observed responses and display a reasonably accurate agreement

with the experimental data, considering the natural variations exhibited by the BS and VS beams. As before, each beam is predicted to display a linear response, followed by a

transitional nonlinear response up to the peak. The extent of the nonlinearity varies

depending on the beam span, the load resisting mechanism developed within each

individual beam, and the extent of damage that develops locally.

Regarding the response of beams with no transverse reinforcement (Beams OA1, OA2,

and OA3) displayed in Figures 8(a)-(c), it is apparent that the predicted curves exhibit stiffer post-peak responses than VS beams, replicating more closely the overall stiffness

of BS beams. In terms of the peak load and maximum deflection, a good agreement

between predicted and observed values is noted, with a slight underestimation in case of Beams OA1 and OA2 and a slight overestimation in case of Beam OA3. The mean ratios

of experimental-to-predicted load capacity for the OA beam series are 1.02/1.06 (based

on VS/BS beams) with coefficient of variations (COV) of 7.3%/12.1% (VS/BS). It is noteworthy that, due to absence of transverse reinforcement, a significant drop in load is

apparent immediately after the peak load, highlighting the dangerous and brittle mode of

failure a beam without transverse reinforcement can exhibit.

Figure 8 Computed and observed load-deflection responses for all beams.

From the comparison of predicted and observed responses of beams with transverse

reinforcement (Beams A1-A3, B1-B3, and C1-C3) presented in Figures 8(d)-(l), a similar

trend in terms of the initial stiffness, peak load and maximum deflection can be observed as in the series of beams with no transverse reinforcement discussed above. Slight

variations are apparent in terms of peak load and maximum deflection predictions, but

0

100

200

300

400

500

0 10 20 30 40

0

100

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500

0 10 20 30

0

100

200

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0 20 40 60 80

0

100

200

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500

0 10 20 30 40 50

0

100

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0 20 40 60 80 100

0

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0 10 20 30 40 50

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0 20 40 60 80

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0 5 10 15

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0 10 20 30 40

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0 10 20 30 40 50 60

0

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0 10 20 30 40

Deflection (mm)

Lo

ad

(kN

)L

oad

(kN

)L

oad

(kN

)L

oad

(kN

)

Deflection (mm) Deflection (mm)

OA1 OA2 OA3

A1 A2 A3

B1 B2 B3

C1 C2 C3

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

Vecchio and Shim Bresler and Scordelis ATENA-3D ACI 318

all are within a reasonable agreement. Of interest is the ability of the models to reproduce the more ductile response for the longer beam series (i.e. Beams A3, B3, and C3). The

mean ratios of experimental-to-predicted load capacity for the beams with transverse

reinforcement are 0.99/1.07 (VS/BS) with a COV of 4.2%/4.7% (VS/BS) highlighting once again the accuracy of the numerical predictions.

Table 4 presents the mean ratios of experimental-to-predicted load capacity and

maximum deflection. Overall, based on the comparisons with the twelve BS beams and their duplicates (VS beams), the models presented in this studyproduce a mean load

capacity ratio of 1.00/1.06 (VS/BS) and a COV of only 5.3%/7.3% (VS/BS), which is

better than the ACI predictions with a mean of 1.06/1.13 (VS/BS) and a COV of 18.6%/18.5% (BS/VS). The beam deflection is less accurately predicted, producing a

mean ratio of 1.31/0.98 (VS/BS) and a COV of 20.8%/16.1% (VS/BS). Considering the

natural variations across the tests, however, the models presented in this study could be regarded as sufficiently accurate. The tendency to underestimate beam deflection in

beams with shorter spans could be attributed to difficulties inherent in performing such

tests due to increasing influence of several factors with decreasing span–including but not limited to the effect of boundary conditions, plate dimensions and the stiffness of test

rig.

2.5. Comparison of crack patterns To provide further evidence of the accuracy of the models employed in this study, Figures

9 to 12 compare the observed crack patterns at failure with the predicted maximum

principal strains beyond the peak load overlaid by the predicted crack patterns. In general, there is a reasonably good agreement between the predicted and experimentally

observed failure crack patterns, including the overall crack pattern, location of failure,

and extent of damage. This indicates accurate predictions of internal load carrying mechanisms and modes of failure. The method of presentation of maximum principal

strains in combination with crack pattern is, therefore, recommended to provide full

appreciation of the location and extent of damage in the concrete.

Based on the predicted crack patterns of the first three beams with no transverse

reinforcement (OA series) presented in Figure 9, it is shown that final failure occurs due

to sudden formation of diagonal tension cracking which then continues as a horizontal splitting crack to the end of the beam, and in case of Beam OA3, passing the support.

This is consistent with the observed failure crack patterns and explains the brittle nature

of the overall response. In beams with transverse reinforcement, the predicted mode of failure of beams of short and intermediate spans (Beams A1, A2, B1, B2, C1 and C2) can

be described mainly as shear-compression in nature (see Figures 10 and 12). On the

contrary, the predicted mode of failure of the longest spanning beams (Beams A3, B3 and C3) can be characterised as flexural-compression failure, with evidence of local

crushing/splitting of the concrete in the compression zone adjacent to and under the

point of load application. This highlights the successful modelling of concrete under a complex stress condition. It is also interesting to note, although Beams A, B, and C series

were specifically designed to promote shear failure, the predictions show that the extent

of the diagonal cracking is only minor, particularly in beams with a long span (Beams A3, B3, and C3). In beams with short and intermediate spans (Beams A1, A2, B1, B2, C1 and

C2), it is predicted that severe diagonal cracking only develops in the later stages of

loading, although failure is ultimately triggered by crushing of the concrete in the flexural

compression zone, which is consistent with experimental findings.

Figure 9 Computed and observed crack patterns and maximum principal strains for

OA-series beams with no shear reinforcement.

Figure 10 Computed and observed crack patterns and maximum principal strains for

A-series beams with no shear reinforcement.

5.85.04.33.60 2.92.21.40.7

x10-2

5.64.94.23.50 2.82.11.40.7

x10-2

5.14.43.83.20 2.51.91.30.6

x10-2

OA1

OA2

OA3

A1

6.45.64.84.00 3.22.41.60.8

x10-2

A2

5.44.74.03.40 2.72.01.40.7

x10-2

A3

2.32.01.71.40 1.20.90.60.3

x10-2

Figure 11 Computed and observed crack patterns and maximum principal strains for

B-series beams with no shear reinforcement.

Figure 12 Computed and observed crack patterns and maximum principal strains for

C-series beams with no shear reinforcement.

3. Beam-column joint simulations

In this work package, the practical value and application of three-dimensional nonlinear

finite element analysis is demonstrated through accurate simulations of the cyclic hysteretic responses of beam-column joints along with crack patterns. The beam-column

joints tested by Shiohara and Kusuhara [11] were selected as a benchmark to testify the

2.52.21.91.60 1.20.90.60.3

x10-2

B1

B2

7.46.55.54.60 3.72.81.80.9

x10-2

B3

2.62.32.01.70 1.31.00.70.3

x10-2

C1

3.32.92.52.10 1.61.20.80.4

x10-2

C2

2.82.52.11.80 1.41.10.70.4

x10-2

2.21.91.71.40 1.10.80.60.3

x10-2

C3

accuracy of the finite element analyses. A combination of plasticity and fracture model in conjunction with a smeared fixed crack approach and crack band model was adopted to

this end.

3.1. Details of Shiohara and Kusuhara beam-column joints

In 2006, Shiohara and Kusuhara [11] undertook a detailed experimental programme on

six half-scale beam-column joints (hereinafter referred to as the SK beam-column joints).

The primary objective of the test programme was to provide benchmark test data for the validation of their in-house mathematical models. Due to the high quality and

comprehensive documentation of test results, their test data have been referred to by

many researchers and used to support the corroboration in many software developments [12, 13].

In this study, only one series (series A) of the three series of SK beam-column joints was analysed. In this series, there were three specimens (labelled A1, A2 and A3), each of

which was tested under different loading patterns to cover possible types of beam-column

joint in moment-resisting frame buildings. All specimens in this series are of critical form and were designed as per AIJ guidelines [14]. Loading type I was intended to simulate an

interior joint and this was applied to specimen A1 to address significant joint core

distress. Loading types II and III were intended to simulate an exterior and corner joint,

respectively, and applied to specimens A2 and A3 (these are the specimens that sustained the least joint core distress). The joint shear capacity of specimen A1 was designed to be

10% higher than the joint shear demand. The strong column-weak beam concept was

considered, with an overstrength factor of 1.25 to allow the beams to achieve their full flexural capacities prior to the columns.

Table 5 Material properties of reinforcing bars in series A specimen [11].

Diameter

(mm)

Grade Young’s

Modulus

(GPa)

Yield

Strength

(MPa)

Ultimate

Strength

(MPa)

13a SD390 176 456 582

13b SD390 176 357 493

6 SD295 151 326 488

Notes: a: steel bar used for beams; b: steel bar used for columns

Table 6 Details of SK beam-column joint specimens [11].

Description A1 A2 A3

Model Interior Exterior Corner

Loading type I II II

Compressive strength of concrete 28.3 MPa

Beams Cross-section 300 × 300 mm

Span 2700 mm

Longitudinal bar 8D13 (top) and 8D13 (bottom)

Transverse bar D6 at 50 mm

Columns Cross-section 300 × 300 mm

Height 1470 mm Longitudinal bar 16D13

Transverse bar D6 at 50 mm

Joint Transverse bar D6 at 50 mm (3 NoS)

The typical schematic representations of all beam-column joints geometry and reinforcement layout are displayed in Figure 13(a), together with the schematic of the test

setup in figures 13(b)-(d). All beam-column joints had a similar square section of 300 by

300 mm and were reinforced with steel bars of identical arrangement and properties (see Table 5). The concrete used to cast these specimens had the mean compressive and tensile

splitting strengths of 28.3 MPa and 2.67 MPa, respectively. The specimen details are

summarised in Table 6.

Figure 13 Schematic of series A of SK beam-column joints: (a) cross-section and bar

arrangement; (b) loading type I; (c) loading type II; and (d) loading type III [11].

Figure 14 (a) Finite element mesh and (b) bar arrangement in ATENA Science.

3.2. FE model of beam-column joints

Three-dimensional nonlinear finite element analyses were performed using a specialist

finite element software package ATENA Science developed exclusively by Červenka

Consulting [15] for simulations of reinforced concrete structures [16, 17]. In this study, the accuracy of a smeared fixed crack approach to model the highly nonlinear cracked

concrete behaviours experiencing bi-directional cracking [18, 19] resulting from reversed

cyclic loads is tested. Figures 14(a) and (b) display the typical finite element meshes and bar arrangements used to represent SK beam-column joints, which was prepared in a

pre-processor finite element software GiD. The concrete was modelled using 8-node

hexahedral (brick) linear elements with a typical size of 25 mm (in columns, beams and

300

50 5066 6668

3535

3535

16

0

30

0

grooved bars

4D134D13

4D134D13

Stirrup D6@50

50

50

Stirrup D6@50

(a) (b)

(c) (d)

(a) (b)

joint region), thereby giving 12 elements across the overall depth or width. All plates were modelled using tetrahedral linear elements with larger unstructured mesh size as a

means to expedite the runtime of analysis. Although different mesh sizes were used for

the concrete and steel (end) plates, this would not affect the accuracy as there is a full compatibility between two mesh surfaces.

Figure 15 Concrete constitutive model: (a) compression and (b) tension.

0 2 4 6 8 10 12 14 16 18

-4

-2

0

2

4

6

88

43

21

0.50.25

0.125

Dri

ft R

ati

o (

%)

Number of Cycles

0.0625

Figure 16 Loading history for reversed cyclic loading.

The nonlinear concrete used in this study was the “Cementitious2” model which was

formulated based on the CEB-FIP Model Code 1990 [20]. In this model, the response in compression is treated following the theory of plasticity, whereas the response in tension

is formulated following the Rankine fracturing model for concrete cracking [15]. In the

shear model, a constant shear factor coefficient (SF), which defines a relationship between normal and shear (both modes II and III) crack stiffnesses, was used. Figures 15(a) and

(b) show a summary of the constitutive laws adopted in this study. To model concrete

behaviour under cyclic loading, the unloading factor parameter was activated to control the crack closure stiffness. In ATENA, this parameter can be set between 0 and 1, with 0

for unloading to the origin (default value for backward compatibility) and 1 for unloading

parallel to the initial elastic stiffness. In this work, this factor was set to 0.2 and found to simulate residual displacement during unloading reasonably. Apart from this, the plastic

flow was modified to a value of 0.5 to account for dilatancy resulting from the concrete

volumetric expansion when undergoing compression failure.

All embedded steel bars were modelled in discrete representation using one-dimensional

2-noded linear truss elements. Elasto-plastic Manegotto-Pinto model [21] was used to

accurately capture the cyclic behaviour of steel bars as it takes into account the Bauschinger's effect during unloading and reloading sequences. Bond-slip with memory

bond was also considered following the nonlinear bond-slip formulation in the CEB-FIP

Model Code 1990 [20].

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

(tensile cracking

strength)

sof tening f unction

Crack Width, w

=

ft,cr

Ten

sil

e S

tress

, s

crack closing

(a) (b)

=

− + − −

Comp. Strain,

Co

mp

Str

es

s,

s

Lc

unloading

linear sof tening

( ) = −elastic limit

ecu 0.2% +

In all models, the lower column was supported by a pin-joint. In the first loading interval,

each beam-column joint was loaded with a constant axial load of 216 kN at the top of the

upper column. In the second and subsequent intervals, cyclic lateral loads were then applied in the form of displacement increments, with a rate of 1.0 mm per step until

reaching the drift ratio of 8% (see Figure 16). For loading type I (specimen A1), the interior

beam-column joint was supported at both sides of beam ends (with a pin and a roller

support respectively) and the cyclic lateral loads were then applied at the top of the upper column. For loading type II (specimen A2 or an exterior beam-column joint), the lateral

loads were applied in the same manner to that applied in loading type I – however, only

one side of the beams was supported by a roller; accordingly, no internal stresses would develop in the other (dummy) beam. For loading type III (specimen A3 or a corner beam-

column joint), the analysis was done by applying cyclic lateral loads at one of the beam

ends. The support conditions were similar to that of loading type II.

Table 7 Summary of material and finite element input parameters in ATENA.

No Parameter Value/Reference

Concrete constitutive model

1. Elastic modulus CEB-FIP Model Code [27] 2. Tensile strength CEB-FIP Model Code [27]

3. Smeared crack model 1 (fixed crack)

4. Aggregate size 20 mm

5. Unloading factor for cyclic loading 0.2

6. Critical compressive displacement 0.5 mm 7. Limit of comp. strength reduction due to cracking 0.8

8. Eccentricity (defining the shape of failure surface) 0.52

9. Plastic flow (defining dilatancy of plastic factor) 0.5

Reinforcement bar model

10. Stress-strain relationship Bilinear with strain hardening

11. Bond-slip model for cyclic (bar with memory bond) CEB-FIP Model Code [27] 12. Cyclic behaviour (Menegotto-Pinto) R = 10; C1 = 0.925; and C2 = 0.15 [28]

Loading procedure and solution parameter

13. Loading procedure for axial load Static (force-controlled)

14. Loading procedure for cyclic load reversal Quasi-static(displacement-controlled)

15. Iteration method for cyclic Modified Newton-Raphson

16. Stiffness type Elastic predictor with conditional break criteria

17. Iteration limit 300

18. Solver Pardiso

In this study, the modified Newton-Raphson iterative solution parameter with elastic

predictor was used to allow for consistent convergence at each of load steps. Input parameters in conditional break criteria were set higher than that of default values,

typically ten times higher to provide more space when convergence difficulties are

encountered. The convergence tolerance was set constant throughout intervals with a value of 1.0% for displacement, residual, and absolute residual error, whilst energy error

was set at 0.1%. High iteration limits (e.g. 200-300) were found to be beneficial. The key

input parameters used in the analyses are summarised in Table 7.

3.3. Hysteretic response

Figures 17(a)-(c) display the load-drift responses for specimens A1 to A3, with a summary of the measured and predicted load capacities presented in Table 8. As shown in the

figures, the overall behaviours of the beam-column joints can be predicted reasonably

well. The finite element models successfully exhibit comparable hysteretic shapes,

particularly for specimens A2 and A3 which display similar response as observed in the experiment.

-4 -2 0 2 4 6-150

-100

-50

0

50

100

150

measured

calculated

Late

ral

Lo

ad

(kN

)

Drift Ratio (%)

(a)

-4 -2 0 2 4 6-100

-50

0

50

100

(b) measured

calculated

Late

ral

Lo

ad

(kN

)

Drift Ratio (%)

-4 -2 0 2 4 6-200

-100

0

100

200

(c) measured

calculated

La

tera

l L

oa

d (

kN

)

Drift Ratio (%) Figure 17 Loading history under reversed cyclic loading. Test data were taken from [11].

Table 8 Summary of experimental [17] and predicted load capacities.

Joint

Specimen

Positive Loading Direction Negative Loading Direction

Pu-Test Pu-Calc Pu-Test /Pu-Calc Pu-Test Pu-Calc Pu-Test /Pu-Calc

(kN) (kN) (-) (kN) (-)

A1 126.6 117 1.08 -122.8 -106 1.16

A2 77.9 82 0.95 -77.1 -79 0.98

A3 176.4 182 0.97 -124.5 -129 0.97

Mean 1.00 Mean 1.03

CoV (%) 5.82 CoV (%) 9.46

With regard to the response of interior beam-column joint (specimen A1), it is apparent

from figure 5(a) that at low drift levels, the predicted hysteretic response displays accurate representation of strength and stiffness degradation. As the drift is increased further,

however, the analysis starts to slightly underestimate the load capacity (particularly from

the 5th cycle), but the agreement is still reasonable. Of interest to note is the overly high total energy dissipation in the analysis due to the more rounded shape of hysteretic loops

during load cycles (compared to the highly pinched response). This could also be

attributed to high complexity of joint distress incurred by the specimen, thereby making it difficult to predict with accuracy. As shown in table 4, the ratios of experimental-to-

predicted load capacity for specimen A1 in the positive and negative loading direction are

1.08 and 1.16 respectively.

Figures 5(b) and (c) compare the measured and predicted hysteretic responses for

specimens A2 and A3 respectively. An excellent agreement is observed in terms of initial

stiffness, load capacity, and the overall shape of the hysteretic loops. The strength and stiffness degradation can also be predicted with accuracy, although there is a slight

variation of strength degradation during the 8th cycle which corresponds to the drift ratio of 4%. It is noteworthy that the models can better replicate the hysteretic shapes for

specimens with less joint core distress. The ratios of experimental-to-predicted load

capacity for specimens A2 and A3 in the positive and negative loading direction are 0.95/0.98 (A2) and 0.97/0.97 (A3) respectively which is indicative of marginal differences

(consistently less than 5%), highlighting the excellent accuracy of finite element

predictions.

3.4. Comparison of crack patterns

To facilitate further evidence of the accuracy of finite element models used in this study,

Figures 18-20 compare the observed and predicted crack patterns at selected drift ratio levels of 0.5%, 2%, and 4%. It is evident that, in general, the overall predicted crack

patterns are in excellent agreement with the observed crack patterns in terms of the

extent of accuracy of crack-alike development, location of crack, and mode of failure. The successful representation of crack angle (also principal strain profile) in all specimens

under increasing loads is also appealing, highlighting once again successful appreciation

of the highly nonlinear behaviours of the concrete by the finite element models.

With reference to the cracking behaviour of specimen A1, it is apparent that under load

reversals, flexural cracks initially develop at the beam corners at the joint and then

propagate diagonally within the joint core which is indicative of shear cracks. These existing shear cracks, during the increasing load levels, progress significantly within the

joint, replicating more to a typical concrete strut action. The reason for this relates to the

low overstrength factor of joint shear capacity (10%) as reported by Shiohara and Kusuhara [11]. At a drift ratio of 4%, shear cracks start to develop within the plastic hinge

regions of both lower and upper columns. This is attributed to the marginal value of the

overstrength factor in the strong column-weak beam design (i.e. 1.25). Therefore, it is not surprising that joint core exhibits heavy shear distress followed by diagonal concrete

crushing, while the columns also experience significant damage. Furthermore, the

analysis clearly shows that the longitudinal bars in the beams have reached their yield capacities, as evidenced by considerable flexural cracks formation along the beam length.

Figure 18 Computed and observed crack patterns and maximum principal strains of

specimen A1.

`

Drift Ratio 0.5% Drift Ratio 2% Drift Ratio 4%

Figure 19 Computed and observed crack patterns and maximum principal strains of

specimen A2.

Figure 19 Computed and observed crack patterns and maximum principal strains of

specimen A3.

Drift Ratio 0.5% Drift Ratio 2% Drift Ratio 4%

Drift Ratio 0.5% Drift Ratio 2% Drift Ratio 4%

With respect to specimens A2 and A3, the failure modes are predicted to be flexure-shear in nature which is consistent with experimental observation. Significant flexural cracks

manifest vastly in one side of the beam, following the formation of shear cracks in the

joint core. In this specimen, damage is dominated primarily by flexural cracks with no existence of concrete crushing. It is interesting to note that in specimen A2 (exterior beam-

column joint), concrete cracking is shown to develop primarily in the beam and within

the joint core, whereas in specimen A3 (a corner or knee joint), concrete cracking is shown

to also manifest in the lower column at locations within the plastic hinge region.

4. Development of master curves for flexural testing of ECC

4.1. Details of ITS test plates The ECC plates tested in the Concrete and Building Materials Laboratory of the

Department of Civil Engineering at the Institute of Technology Sepuluh Nopember (ITS)

comprise three types which differ only in overall thickness (15 mm, 30 mm and 45 mm). All plates are of rectangular cross-section and have the same overall length of 300 mm

and width of 75 mm. Figure 20 displays the overall dimensions of the plates, labelled

Plates P15, P30 and P45, respectively.

Each plate is supported on two circular supports over a distance of 270 mm and subjected

to two equal concentrated loads over three equal spans (90 mm each), as displayed in

Figure 20. Loading is undertaken under a constant displacement increment. The applied load and the load-point deflections are recorded directly from the testing machine using

an automated data acquisition system. Since the load-point deflection is generally more

sensitive to errors as it may include the deformation of the test rig and bedding errors at both load and support points, it is desirable to use the mid-span deflection in place of the

load-point deflection. This measurement is undertaken using an additional linear variable

displacement transducer (LVDT) placed under the centreline of the plate.

Plate P15

Plate P30

Plate P45

Figure 20 Longitudinal and cross-section details of ITS plates.

9090 90

15

75

P/2P/2

P/2 P/2LVDT

30

9090 90 75

P/2 P/2LVDT

P/2P/2

9090 90 75

P/2 P/2LVDT

45

P/2P/2

4.2. Structural model and constitutive relations The structural model used to predict the full load-deflection response of an ECC plate is

presented in Figure 21; due to symmetry only half of the plate is modelled. The plate is

divided into 11 elements, with shorter elements provided close to the point-load over the shear span in order to accurately capture the highly nonlinear response (i.e. curvature)

at this location due to crack formation. The plate cross-section is further divided into fine

layers, each having similar width b (= 75 mm) and depth d. At multiple locations along

the plate (Nodal points 2–12), section analysis was done based on the assumption that the cross-sections under deformation remain plane (section compatibility). Accordingly,

the longitudinal strain in each layer 휀ican be related to the strain at the centroid of the

bottom layer 휀tb through the relationship,

휀i =(𝑦i − 𝑥)

(ℎ − 𝑥 − 0.5𝑑)휀tb (11)

where 𝑦i is the position of the centroid of layer 𝑖 from the top of the plate (mm); 𝑥 is the

neutral axis depth (mm); ℎ is the overall depth (mm); 𝑑 is the layer thickness (mm). The

longitudinal stress in each layer can be determined directly from the computed longitudinal strain using predefined stress-strain relations displayed in Figure 22.

Structural model for half plate length

Plate cross-section Longitudinal Strain Longitudinal Stress

Figure 21 Layered approach used in the analysis.

ECC in compression ECC in tension

Figure 22 Average stress-strain relations for ECC.

81

0.5P

2 3 4 5 6 7

9

10 11 12

CL

휀t 휀

𝑓 ′

휀 ′

𝑓 = 𝐸 휀i − 휀

𝐸

휀t

𝐸

𝐸

𝑓t 𝑓t

𝑓

휀

𝑓

e

The compressive stress in the ECC 𝑓 is related to the fracture parameter 0, initial

stiffness 𝐸0, plastic strain 휀 , and compressive strength 𝑓 ′ in the following manner [22,

23],

𝑓 = 0𝐸0(휀i − 휀 ) (12a)

0 = 𝑒𝑥𝑝 [−0.73휀i휀𝑐′[1 − 𝑒𝑥𝑝 (−1.25

휀i휀𝑐′)]] (12b)

𝐸0 = 2𝑓𝑐′

휀𝑐′ (12c)

휀 = 𝛽 [휀i휀𝑐′−20

7[1 − 𝑒𝑥𝑝 (−0.35

휀i휀𝑐′)]] 휀𝑐

′ (12d)

The strain at the peak stress 휀 ′ can be taken as 0.5%, while the strain rate 𝛽 as 1.0. Prior

to cracking, the tensile stress in the ECC 𝑓t is related to the initial stiffness 𝐸0 as given by

[24]

𝑓t = 𝐸 휀i ( f 휀i ≤ 휀t ) (13a)

After cracking, the tensile stress in the ECC is assumed to vary linearly with strain [24,

25], as given by,

𝑓t = 𝐸 휀t + 𝐸 (휀i − 휀t ) ( f 휀i > 휀t ) (13b)

The use Equations (13a) and (13b) will result in a bilinear stress-strain response, as

displayed in Figure 2(b). Failure is assumed to take place when the strain at the centroid

of the bottom layer tb at the most critical section (Nodal points 10-12) reaches the tensile

strain capacity of the ECC (i.e. 휀tb = 휀t ). Having evaluated the tensile strain capacity, it is

then possible to determine the longitudinal stresses (and, hence, the longitudinal forces).

The resultant forces are then checked to ensure that they are in equilibrium with the

applied sectional moment. If this condition is not satisfied, the strain at bottom fibre is adjusted and the whole analysis is repeated until equilibrium is achieved. For more

detailed explanations on the iteration procedures, the reader is referred to [22].

4.3. Load-deflection response

The analytical models presented in the previous section was used to determine the

theoretical response of the three plates displayed earlier in Figure 20. The following

material data were assumed in the analysis (see Figure 23(f)): 𝐸 = 18 GPa; 𝑓t = 3.6 MPa;

𝑓t = 4.5 MPa; 휀t = 5%; 𝑓 ′= 45 MPa; and 휀

′ = 0.5%. Figures 23(a)-(f) display the full

response of Plate P30, including the load-deflection, curvature profile, moment-curvature and longitudinal stresses at the critical section. For comparative purposes, Figures 23(a)-

(f) also present the results of another series of analysis which was performed using an

elastic-plastic (EP) stress-strain relation (𝑓t = 𝑓t = 4.5 MP ) considering its frequent use

in previous studies. In both cases, the analysis was performed in nine steps and each response was highlighted on the figures with numbers 1–9.

It is evident from Figure 23(a) that the tensile stress-strain relations of the ECC have a significant influence on the post-cracking response of Plate P30. The bilinear (BL) model

is shown to result in a more gradual increase in load-deflection and moment-curvature

responses than the EP model. It is also shown that the BL model predicts lower load and

moment capacities than the EP model. This is attributed to the lower first cracking stress

assumed in the BL model (= 0.8𝑓t ), although it would be difficult to identify this aspect from the stress-strain profiles displayed in Figure 4(e) due to their close resemblance.

Figure 23 Theoretical response of Plate PL30 with 𝐸 = 18 GPa; 𝑓t = 3.6 MPa; 𝑓t = 4.5

MPa; 휀t = 5%; 𝑓 ′= 45 MPa; and 휀

′ = 0.5%.

With regard to the curvature profile displayed in Figures 23(c) and (d), it is noteworthy

that both models predict a highly nonlinear curvature profile over the shear span,

although the BL model produces a slightly more spread out and gradual increase in curvature as we move toward the centre span, which is indicative of a more widespread

crack formation over the shear span. Although the BL model predicts a lower curvature

over the centre span, it produces a larger cumulative curvature over the whole span and, hence, a larger predicted deflection value at the peak load.

To study the influence of plate thickness, Figure 24(a) displays the load-deflection response for the three different plate depths using the bilinear model and other properties

used in the previous analysis. It is evident that as the plate thickness is increased from

15 mm to 45 mm (by threefold), this results in a ninefold increase in the peak load (from

0 2 4 6 8 10 120

1

2

3

4

Bilinear (BL)

Elastic-plastic (EP)

Loa

d (

kN

)

Mid-point deflection (mm)

(a)

1

23

4 56

78

9

0.0 0.4 0.8 1.2 1.6 2.00.00

0.05

0.10

0.15

0.20

Bilinear (BL)

Elastic-plastic (EP)

Mom

ent (k

Nm

)

Curvature (1/m)

(b)

1

23

4 5 67

89

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.4

0.8

1.2

1.6

2.0

BL model

Load step

9

8

7

6

5

4

3

2

1

Cu

rva

ture

(/m

)

Normalised position

(c)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.4

0.8

1.2

1.6

2.0

Load step

9

8

7

6

5

4

3

2

1C

urv

atu

re (

/m)

Normalised position

(d)

EP model

-40 -20 00.0

0.2

0.4

0.6

0.8

1.0

-40 -20 0

EP modelBL model

Norm

alis

ed d

epth

Longitudinal stress (MPa)

(e)

Load step

9

8

7

6

5

4

3

2

1

0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

BL model

EP model

Tensile

str

ess (

MP

a)

Tensile strain(%)

(f)

0.7 kN to 6.4 kN, or a quadratic increase) and a threefold reduction in the deflection at the peak load (from 22 mm to 7.3 mm). To generalise the above finding, the computed

load of the plates is converted to the equivalent flexural stress through the relationship,

𝑓t q =3𝑃𝑎

𝑏ℎ2 (14)

where P being the applied load (N); a being the shear span (=90 mm); b being the plate

width (=75 mm) and h being the plate thickness (= 15 mm or 30 mm or 45 mm). In

addition, the term normalised deflection is introduced which is equal to the mid-span

deflection of the plate at any load stage (mm), normalised by the corresponding mid-span deflection of the plate at the peak load (mm). The resulting equivalent flexural stress is

plotted against the normalised deflection in Figure 24(b). It is interesting to note that by

presenting the response of the plates in this manner, the three curves collapse onto a single master-curve despite the highly nonlinear response exhibited by each individual

plate. This method of presentation could, therefore, have considerable value in the

development of a simplified testing protocol for ECC and hence is exploited in the following

section.

Figure 24 (a) Predicted load-deflection and (b) corresponding equivalent stress-

deflection responses for all plates. 𝐸 = 18 GPa; 𝑓t = 3.6 MPa; 𝑓t = 4.5 MPa; 휀t = 5%; 𝑓 ′

= 45 MPa; and 휀 ′ = 0.5%.

4.4. Development of master curves

Three series of analyses were performed for the three plate thicknesses based on the

material properties presented in Table 9. The predicted mid- and load-point deflections at

the peak load for the three plate thicknesses are presented in Figure 25(a). Each value

was plotted against each value of tensile strain capacity presented in Table 1; all were

highlighted with data marker and connected with a dashed line for clarity. It is evident

that the two parameters are highly correlated and lie on a narrow band of straight lines;

the slope of which increases with increasing plate thickness due to the increase in overall

stiffness. Furthermore, the load-point deflection is consistently smaller than the mid-

point deflection, as would be expected.

To investigate the relationship between the peak load and tensile strength, the tensile strength inputted in the analysis is plotted against the peak load in Figure 6(b). In this

plot, the peak load was multiplied with an empirical constant, 75/𝑏ℎ2, following the denominator in Equation (4). By presenting the tensile strength and the peak load in this

format, a considerably simple expression could be derived and further used to produce

estimates of tensile strength without the need to perform the full flexural analysis.

0 4 8 12 16 20 240

1

2

3

4

5

6

7

PL45

PL30

PL15

Loa

d (

kN

)

Mid-point deflection (mm)

(a)

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

PL45

PL30

PL15Equ

ivale

nt flexu

ral str

ess (

MP

a)

Normalised deflection

(b)

Table 9 Summary of key parameters used in the analysis. 𝐸 ≅ 18 GPa.

Series Compression 𝑓t (MPa)

–

𝑓 ′

(MPa) 휀 ′

(%) 𝑓t

(MPa) 휀t

0.5%

휀t 1%

휀t 2%

휀t 3%

휀t

4%

휀t 5%

휀t 6%

1 30 0.5 3.2 3.28 3.36 3.52 3.68 3.84 4.00 4.16

2 45 0.5 3.6 3.69 3.78 3.96 4.14 4.32 4.50 4.68

3 60 0.5 4.0 4.10 4.20 4.40 4.60 4.80 5.00 5.20

Figure 25 ((a) Predicted deflection at peak load plotted against tensile strain capacity.

(b) Comparison of values for tensile strength given by a simple empirical equation with

values determined from the full analysis

Having obtained these relationships, it is now possible to determine master-curves for

quick calculation of the tensile strain capacity and tensile strength of ECC using the

results of four-point bending tests; the results of which are presented in Figures 26(a) and (b). It is noteworthy that the master-curves presented in these Figures are easy to

read and require minimal calculations for use in a frequent/regular testing regime. The

steps to use the curves are as follows:

Step 1–Multiply the recorded load- or mid-point deflection at peak load (in mm) with n,

with n being the ratio of the plate thickness (mm) to the reference plate thickness

(=15 mm). The use of mid-point deflection is highly recommended due to the inherent errors normally encountered in load-point deflection measurements.

Step 2–Read Figure 26(a) to obtain the tensile strain capacity, tu , (in %) or use either of

the following equations:

휀t = 0.23𝑛𝛿m − 0.1 (15)

휀t = 0.28𝑛𝛿l − 0.1 (16)

Step 3–Multiply the peak load recorded with 1/h2 and then either read Figure 26(b) or

use the following equation to determine the tensile strength (in MPa):

𝑓𝑡 = 1.26𝑃

ℎ2+ 0.46 (17)

with being the peak load (N) and h the plate thickness (mm).

To evaluate the accuracy of Equations (15)–(17), let us consider the peak load and

corresponding deflection values for Plates PL15, PL30 and PL45 presented earlier in Figure 24, assuming that they were obtained from a physical laboratory testing; the

0 5 10 15 20 25 300

1

2

3

4

5

6

7

Load-point

Mid-point

Te

nsile

str

ain

ca

pa

city (

%)

Deflection (mm)

(a) PL15PL30PL45

2.0 2.5 3.0 3.5 4.03

4

5

6

f 'c values

30 MPa

45 MPa

60 MPa

Te

nsile

str

en

gth

(M

Pa

)

Peak load x 75/(bh2)

(b)

ft = 1.26 + 0.46P

h2

summary of which are presented in Table 10. Note that when analysing these plates, the tensile strength and tensile strain capacity were taken as 4.5 MPa and 0.5%, respectively.

By substituting the peak load and deflection values into either Equations (5) or (6), and

(7), the tensile strength and tensile strain capacity can be evaluated, which, in this case, are 4.46 MPa and 4.95%, respectively, highlighting clearly the accuracy of the master-

curve approach.

Table 10 Comparison of full analysis and master-curve (𝑓 ′= 45 MPa; 휀

′ = 0.5%).

Plate Input material

properties Results of full analysis Prediction results

𝑓t (MPa)

𝑓t (MPa)

휀t (%)

𝛿l

(mm)

𝛿m

(mm)

𝑃

(kN)

휀t ,Eq.15

(%)

휀t ,Eq.16

(%)

𝑓t ,Eq.17

(MPa)

PL15 3.6 4.5 5.0 18.19 21.98 0.71 4.95 4.95 4.46

PL30 3.6 4.5 5.0 9.10 10.99 2.86 4.95 4.95 4.46

PL45 3.6 4.5 5.0 6.06 7.33 6.43 4.95 4.95 4.46

Figure 26 Master curves for determining (a) tensile strain capacity and (b) tensile

strength of ECC

0 5 10 15 20 25 30

0

1

2

3

4

5

6

7

Load-point

Mid-pointTe

nsile

str

ain

ca

pa

city (

%)

Deflection at peak load (mm) x n

(a) t = 0.28nlp−0.1

t = 0.23nmp−0.1

n =15

Plate thickness

2.0 2.5 3.0 3.5 4.0

3

4

5

6

Tensile

str

ength

(M

Pa)

Peak load (N) / h2

(b)

ft = 1.26 + 0.46P

h2

4.5. Development of ECC calculator The above equations have been implemented in an HTML document using the JavaScript

programming language. The equations and related diagrams have been generated using

the JavaScript to allow the intermediate calculations to be performed in the background based on the user input. Apart from the JavaScript development, the layout and style of

the webpage has been designed using the Cascading Style Sheets (CSS) to offer a positive

user experience. The developed webpage can be saved from the HTML page to a user local

device (i.e. desktop PC, laptop, tablet or mobile phone) and used on a day-to-day basis without internet connection– should access to the internet be limited. If required, a user

could also modify the coefficients in the equations to suit the preferred test configuration

as they see fit. As feedback is received from the user community, new features will be incorporated to the prototype virtual environment in the future.

Figure 27 Main page of the ECC calculator (https://ecc-calculator.netlify.app/)

Figure 27 presents the developed webpage when opened, displaying two main areas as

marked by the light grey and red colours. In the grey (left-hand side) box, the three test

configurations are displayed, each preceded by a radio button, and four input boxes for user input. Once a test configuration is selected, the corresponding schematic diagram is

displayed in the right-hand side. At the same time, the default values are shown in the

input boxes displayed in the left-hand side to indicate the range of reasonable values.

Real test data from an actual flexural test can be inputted to replace the default values.

Once the user has provided the necessary input values (or decided to use the default

values), the Calculate button can be pressed to trigger the calculations in the background. The computed results are then displayed inside the white boxes displayed around the

tensile stress-strain diagram in the right-hand side, including the first cracking stress

(MPa); tensile strength (MPa); strain at first cracking (%); and tensile strain capacity (%). To maximise the benefits of this development, the webpage has been tailored using Media

Queries during the CSS implementation to enable the page to be displayed to various user

devices including desktops, laptops, tablets and mobile phones.

5. Fabrication of Large-Scale Precast Beam-Column Joints

5.1. Concrete and ECC Mixing

3000 litre tilting drum mixer and 250 litre pan mixer were used to cast normal concrete and ECC respectively. To mix each of beam-column joint specimen with the overall volume

of 3500 litre, concrete mixing was done in two batches, whereas ECC casting was done

in four batches. In normal concrete, dry materials were first mixed following the addition of water and HRWR. In ECC, however, a special treatment was devoted with care to ensure

the successful mixing and uniform fibres dispersion. At the first stage of mixing, all dry

materials (i.e. fly ash, cement and silica sand) were inserted into the bucket and were manually mixed using a wooden scoop. The mixing was done gently to prevent the release

(loss) of fly ash particles and hence trap them under the cement and silica sand particles. 100% of water was then added and mixed manually with these dry materials. After the

water was roughly mixed, the bucket was then moved to mixer machine and a single-

speed mixing was applied to create a uniform smooth paste. Mixing was continued at similar speed for approximately 25 minutes following the insertion of high range water

reducer (i.e. viscocrete). The gradual inspection was performed to ensure that the bottom

deposit disappeared and had mixed up consistently. It was also of importance to ensure

that the viscosity level was achieved. Upon this stage, fibres were poured into the fresh matrix slowly. Mixing was continued for another 15 minutes to let the fibres dispersed

uniformly. The final inspection was done by griping the fresh ECC with a hand for several

times as a means of ensuring that there was no fibre ball occurred. The documentation of ECC mixing can be viewed from the link below:

https://itsacid-

my.sharepoint.com/:v:/g/personal/1990201911077_staff_integra_its_ac_id/Ef9bu-DpCaZInmHPFXls7v0BZ5I6qPDse-_Q496IlOqYLQ?e=SOeRqR

5.2. Concrete and ECC Casting All test specimens were fabricated using water-resistant plywood moulds specifically

designed to follow the desired geometry of the interior beam-column joint. Additional

fabrication for materials test were also undertaken on standard size cylinder for

compression test, dog-bone shaped for direct tensile test, and plate for flexural test. These there were intentionally cast to obtain the mechanical properties of concrete and ECC

which could be useful for the input parameters in computational modelling. The

schematic drawing of the specimen and proof of physical work on the casting are accessible through the links below.

a) https://itsacid-my.sharepoint.com/:p:/g/personal/1990201911077_staff_integra_its_ac_id/EXNO2

2hf4ytLsQXh1WIfsBEBrldvsZ9uc1MYB4qD3F8uGg?e=7C1M9I

b) https://itsacid-

my.sharepoint.com/:v:/g/personal/1990201911077_staff_integra_its_ac_id/EQyPyi

_VTh1Er-Y30Z0-5h0BxlJ6374nxA6-PRziYkAKCw?e=kgpQcX

c) https://itsacid-

my.sharepoint.com/:v:/g/personal/1990201911077_staff_integra_its_ac_id/EYcu2

MBaKD9BhJh6ZQUoW2UBIAmV9oKotpQOt-9OEjOarQ?e=7Lxtk3

D. STATUS LUARAN: Tuliskan jenis, identitas dan status ketercapaian setiap luaran

wajib dan luaran tambahan (jika ada) yang dijanjikan. Jenis luaran dapat berupa

publikasi, perolehan kekayaan intelektual, hasil pengujian atau luaran lainnya yang telah dijanjikan pada proposal. Uraian status luaran harus didukung dengan bukti

kemajuan ketercapaian luaran sesuai dengan luaran yang dijanjikan. Lengkapi isian

jenis luaran yang dijanjikan serta mengunggah bukti dokumen ketercapaian luaran wajib dan luaran tambahan melalui Simlitabmas.

1. International Journal Publications

No Article Title Name of Journal Progress Status *)

1. Digital Image Correlation for Cement-

based Materials and Structural Concrete

Testing

Civil Engineering

Dimension Published

2.

Predicting the Flexural Response of a

Reinforced Concrete Beam using the

Fracture-Plastic Model

Journal of Civil Engineering

Published

3.

Application of Nonlinear Finite Element

Analysis on Shear-Critical Reinforced

Concrete Beams

Journal of Engineering

and Technological

Sciences

Revision Required

4. Development of Master Curves for

Flexural Testing of Engineered

Cementitious Composite Plates

MDPI Materials Draft

2. Conference Proceeding

No Article Title Conference Details Progress

Status *)

1.

Influence of Link Spacing

on Concrete Shear

Capacity: Experimental

Investigations and Finite Element Studies

The Fourth of International Conference

on Civil Engineering Research,

Department of Civil Engineering,

Institut Teknologi Sepuluh Nopember, 22-23 July 2020

Published in IOP

Conference

Series:

Materials Science and

Engineering

2.

Nonlinear Finite Element

Analysis of Reinforced Concrete Beam-Column

Joints under Reversed

Cyclic Loading

The Fourth of International Conference

on Civil Engineering Research, Department of Civil Engineering,

Institut Teknologi Sepuluh Nopember,

22-23 July 2020

Published in

IOP

Conference Series:

Materials

Science and Engineering

E. PERAN MITRA: Tuliskan realisasi kerjasama dan kontribusi Mitra baik in-kind

maupun in-cash (untuk Penelitian Terapan, Penelitian Pengembangan, PTUPT, PPUPT

serta KRUPT). Bukti pendukung realisasi kerjasama dan realisasi kontribusi mitra

dilaporkan sesuai dengan kondisi yang sebenarnya. Bukti dokumen realisasi kerjasama dengan Mitra diunggah melalui Simlitabmas.

The collaboration has launched both institutions, HWU and ITS, at the forefront in the

structural applications of damage-cement concrete. Through the funding and the successful partnership, the project has now developed the first mix composition of damage tolerant

concrete in Indonesia, utilising materials locally available in the country. The partnership

has also the first of its kind to apply the material in a full-scale structural component in an

earthquake active region such as in Indonesia. This was achieved through precast technology, allowing for common site problems such as poor workmanship and non-compliance

construction to be eliminated.

The damage tolerant feature provides critical and timely technology for buildings and

structures in general to remain within the serviceability limit whilst dissipating forces under

major earthquakes. Not only has the potential to save hundreds of thousands of lives, but also benefits building owners and operators in terms of cost and time. The partnership has

also provided other researchers and practising engineers with a fuller understanding of the

nonlinear mechanics of reinforced concrete, via computer simulations. A knowledge which can provide a more informed assessment of the response of new or deteriorated reinforced

concrete members by researchers and structural engineers alike in the future.

As for wider and larger application, both institutions have also established excellence partnership with PT. Wijaya Karya Beton Tbk. which is famous to being the largest state-

owned enterprise for concrete and precast manufacturer in Indonesia. This partnership has

allowed both institutions to fabricate and cast the large-scale damage-tolerant beam-column joint structures which is indicative of actual size of structural members in high-rise building.

The industrial partner have also provided great in-kind support including facilities for casting

and fabrication, raw materials, curing facilities, specimen transport to the testing facilities (i.e. at PUSKIM).

F. KENDALA PELAKSANAAN PENELITIAN: Tuliskan kesulitan atau hambatan yang

dihadapi selama melakukan penelitian dan mencapai luaran yang dijanjikan, termasuk penjelasan jika pelaksanaan penelitian dan luaran penelitian tidak sesuai dengan yang

direncanakan atau dijanjikan.

With recent Coronavirus outbreak ramping up globally since January 2020, the proper

delivery of the project has been hindered – if not on hiatus – due to major restriction during lockdown. As a result, the delay of the project was pronounced considerably and it affected

the completion WP4 of this project (i.e. fabrication and experimental testing of large-scale

beam-column joint specimens). This was consistent until July 2020 and there was no way to combat the regulation. Another point worth noting is the difficulties to start over the

fabrication and testing as the former and the latter would require the involvement from

research partners (i.e. PT. Wijaya Karya Beton Tbk. and Puskim, respectively). The fabrication was postponed until August 2020 as it was not possible to do this (due to the delay of material

delievery from some suppliers and partial lockdown from the company), whilst the testing

was also on-hold and would not be availabe until the end of the year as Puskim was not and would also not be available.

Upon August 2020, all peers (Heriot-Watt Universities, Institute of Technology Sepuluh

Nopember, and PT. Wijaya Karya Beton Tbk.) were doing their best to continue the physical work. This has resulted in the completion of specimen fabrications both in Indonesia and

Scotland. In Indonesia, five large-scale interior beam column joints have been fabricated with

concrete and L-ECC and they are now under curing in the Workshop of PT. Wijaya Karya Beton Tbk. Bogor. Aside from this, small-scale specimens to define the mechanical properties

of the beam-column joints have also been fabricated and they will be tested in December

2020. The latter is important to help PI and Co-I(s) to establish the constitutve model and hence support good prediction and parametric studies for further advanced analysis. The

testing, however, is on hold as Puskim is still not availble until next year. In Scotland, four

half-scale exterior beam-column joint specimens have also been fabricated and they are expected for testing in December 2020 since the testing equipments are available in the

Structures Laboratory at Heriot-Watt University.

Apart from this delay, however, most of the work packages have been completed and these include the success of small and large batch production of low-carbon ECC (or L-ECC) which

the latter will be included in the upcoming publication, development of advanced constitutive

models for concrete and L-ECC to support the accurate prediction using the concept of computational modelling. One article of this work has been in correspondence with the editor

of the journal and decision has been made (i.e revision required). The revised version of the

manuscript have also been reverted by submission and it is anticipated to be considered for publication in Scopus-indexed journal.

G. RENCANA TAHAPAN SELANJUTNYA: Tuliskan dan uraikan rencana penelitian di

tahun berikutnya berdasarkan indikator luaran yang telah dicapai, rencana realisasi

luaran wajib yang dijanjikan dan tambahan (jika ada) di tahun berikutnya serta roadmap penelitian keseluruhan. Pada bagian ini diperbolehkan untuk melengkapi

penjelasan dari setiap tahapan dalam metoda yang akan direncanakan termasuk jadwal

berkaitan dengan strategi untuk mencapai luaran seperti yang telah dijanjikan dalam proposal. Jika diperlukan, penjelasan dapat juga dilengkapi dengan gambar, tabel,

diagram, serta pustaka yang relevan. Jika laporan kemajuan merupakan laporan

pelaksanaan tahun terakhir, pada bagian ini dapat dituliskan rencana penyelesaian

target yang belum tercapai.

Of the four work packages (WPs) we proposed, we have now fully completed WPs 1 and 2 on

mix developments and automated damage assessment (100%). In the UK, WPs 3 and 4 are

currently running in parallel with WP3 at approximately 85% from the completion and WP4 at approximately 90%. Both of these remaining WPs will be fully completed by the third week

of December 2020. In Indonesia, however, continuation of this project on WP 3 will be

undertaken in the following year with centre of work focusing on the delivery of laboratory

testing of five large-scale beam-column joint specimens. International publications on Q1 journal(s) will be prepared in the year of 2021 and they will be anticipated to be submitted at

the same year (preferrably in the third quarter of the year as per the completion of

experimental testings). Furthermore, patents will be sought after all the test data are acquired to ensure that the hypothesis adopted in this research is truthful.

In terms of number of Scopus-indexed journals, it is expected by the PI and Co-I(s) to have

more than one manucript submitted as the scope of the project is wide enough and it is adequate to be adressed in a number of publications which will include all the analysis of

test data, computational modelling, and material testing. Accordingly, all publications

referred to this project will be acknowledged and it will be included in details in the acknowledgement body of the article as in case of the preceeding published conference paper

in IOP Conference Series: Materials Science and Engineering (i.e.

https://iopscience.iop.org/article/10.1088/1757-899X/930/1/012055/pdf).

H. DAFTAR PUSTAKA: Penyusunan Daftar Pustaka berdasarkan sistem nomor sesuai

dengan urutan pengutipan. Hanya pustaka yang disitasi pada laporan kemajuan yang

dicantumkan dalam Daftar Pustaka.

1. Cervenka, V., Jendele, L., & Cervenka, J., ATENA Program Documentation-Part 1: Theory, Cervenka Consulting, Prague, December 3, 2018.

2. Menétrey, P. & Willam, K.J., Triaxial Failure Criterion for Concrete and Its

Generalization, ACI Structural Journal, 95(3), pp. 311-318. 1995. 3. Cervenka, J., Hajkova, K., Jendele, L., Sajdlova, T., & Smilaucr, V., Durability

Assessment of Reinforced Concrete Structures Assisted by Numerical Simulation, 71st RILEM Annual Week & ICACMS 2017, Chennai, India, Sept. 2017, pp. 567-576.

4. Cervenka, V., Cervenka, J., Pukl, R., & Sajdlova, T., Prediction of Shear Failure of Large Beam Based on Fracture Mechanics, 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-9). 2016.

5. Kabele, P., Equivalent Continuum Model of Multiple Cracking, Engineering Mechanics, 9(1), pp. 75-90. 2002.

6. Kolmar, W., Beschreibung der Kraftuebertragung Über Risse in Nichtlinearen Finite-

Element-Berechnungen von Stahlbetontragwerken, PhD Thesis, Darmstadt University

of Technology, Germany. 1986. 7. Kabele, P., New Developments in Analytical Modelling of Mechanical Behavior of ECC,

Journal of Advanced Concrete Technology, 1(3), pp. 253-264. 2003.

8. Vecchio, F.J. & Shim, W., Experimental and Analytical Reexamination of Classic Concrete Beam Tests, Journal of Structural Engineering, 130(3), pp. 460-469. 2004.

9. Bresler, B. & Scordelis, A., Shear Strength of Reinforced Concrete Beams, Journal of American Concrete Institute, 60(1), pp. 51-72. 1963.

10. ACI 318M-14, Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute. 2014.

11. Shiohara H and Kusuhara F 2006 Benchmark test for validation of mathematical

models for non-linear and cyclic behavior of R/C beam-column joints The University of Tokyo (Tokyo: Japan).

12. Guner S and Vecchio F J 2010 Analysis of shear-critical reinforced concrete plane frame

elements under cyclic loading J. Struc. Eng. 137 8 834-43. 13. Pan Z, Guner S and Vecchio F J 2017 Modeling of interior beam-column joints for

nonlinear analysis of reinforced concrete frames Eng. Struc. 142 182-91.

14. AIJ 1999 Design guidelines for earthquake resistant reinforced concrete building based

on inelastic displacement concept Architectural Institute of Japan (Tokyo: Japan). 15. Cervenka V, Jendele L and Cervenka J 2018 Program documentation ATENA theory

Czech Republic, Cervenka Consulting.

16. Tambusay A and Suprobo P 2019 Predicting the flexural response of a reinforced concrete beam using the fracture-plastic model J. Civ. Eng. 34 2 61-7.

17. Cervenka J, Cervenka V and Laserna S 2018 On crack band model in finite element

analysis of concrete fracture in engineering practice Eng. Fract. Mech.197 27-47. 18. Suryanto B, Nagai K and Maekawa S 2010 Modeling and analysis of shear-critical ECC

members with anisotropy stress and strain fields J. Adv. Conc. Techn. 8 2 239-58. 19. Suryanto B, Nagai K and Maekawa S 2010 Smeared-crack modeling of R/ECC

membranes incorporating an explicit shear transfer model J. Adv. Conc. Techn. 8 3

315-26. 20. CEB-FIP Model Code 1990 Comité Euro-International du Béton Inf. Bullet. 195.

21. Menegotto M and Pinto P E 1973 Method of analysis of cyclically loaded RC plane frames

including changes in geometry and non-elastic behavior of elements under combined

normal force and bending IABSE Symp. (Lisbon: Portugal) pp 15-22. 22. Suryanto, B., Reynaud, R., & Cockburn, B., Sectional Analysis of Engineered

Cementitious Composite Beams, Magazine of Concrete Research, 70(22), pp. 1135-

1148. 2018. 23. Maekawa, K., Okamura, H., & Pimanmas, A., Nonlinear Mechanics of Reinforced

Concrete, Spon press, London, UK, Chapter 2. 2003.

24. Suryanto, B., Nagai, K., & Maekawa, K., Smeared-Crack Modeling of R/ECC Membranes Incorporating an Explicit Shear Transfer Model, Journal of Advanced Concrete Technology, 8(3), pp. 315-326. 2010.

25. Tambusay, A., Suprobo, P., Faimun, F., & Amiruddin, A., Finite Element Analysis on

the Behavior of Slab-Column Connections using PVA-ECC Material, Jurnal Teknologi (Sciences & Engineering), 79(5), pp. 23-32. 2017.