Finite element analysis on steel–concrete–steel sandwich beams

ORIGINAL ARTICLE

Finite element analysis on steel–concrete–steel sandwichbeams

Jia-Bao Yan

Received: 25 September 2013 / Accepted: 28 January 2014

� RILEM 2014

Abstract Steel–concrete–steel (SCS) sandwich

composite structure with J-hook connectors has been

developed and exhibited versatile potential applica-

tions in the building and offshore constructions. In this

structure, J-hook connectors were used to bond the

steel face plates and concrete as integrity. In this

paper, finite element model (FEM) by general finite

element program ABAQUS was developed to analyze

the nonlinear structural behavior of the developed SCS

sandwich beam structures with J-hook connectors

under quasi-static loading. In this FEM, the novel

J-hook connectors were simplified and simulated by

cylindrical studs linked by the nonlinear spring

element. The validations of the FEM cover from the

component to structure level. Firstly, the simulations

of the FEM on the longitudinal shear-slip and axial

tension–elongation behaviors of the J-hook connectors

were firstly validated against the push- and pull- out

tests. Then, the FE analysis (FEA) on the structural

behaviors of the SCS sandwich beams was validated

against those from the beam in the references.

Through these verifications, the accuracy of the FEA

on the nonlinear structural behaviors of the SCS

sandwich beam with J-hook connectors was

confirmed.

Keywords Finite element � Steel–concrete–

steel � Sandwich beam � Push-out � Ultimate

strength � Ultra-lightweight concrete � J-hook

1 Introduction

Steel–concrete–steel (SCS) sandwich composite struc-

tures consisting of two steel face plates and a

sandwiched concrete core becomes popular in recent

three decades due to their excellent cost to strength

performance. In SCS sandwich composite structures,

cohesive material e.g. epoxy or mechanical shear

connectors were common measures to bond the steel

and concrete together. Compared with the cohesive

materials, mechanical shear connectors exhibited

advantage in provision of transverse shear resistance

[1]. Many types of connectors have been developed for

SCS sandwich composite structures e.g. angle connec-

tors, C channel connectors, friction welded connectors

in ‘bi-steel’ structure, overlapped headed studs in

‘double skin’ structure, corrugated strip connectors,

and J-hook connectors as shown in Fig. 1 [2]. SCS

sandwich composite structures with J-hook connectors

(see Fig. 2) have advantages of no limitation on the

thickness of the structure, allowing prefabrication in the

factory, easy fabrication, saving site construction time

and formwork of concrete casting, relative high strength

under static, impact and fatigue loadings [3–5]. This

type of SCS sandwich composite structure exhibited

J.-B. Yan (&)

Department of Civil and Environmental Engineering,

National University of Singapore, E1A-07-03,

1 Engineering Drive 2, Singapore 117576, Singapore

e-mail: [email protected]

Materials and Structures

DOI 10.1617/s11527-014-0261-3

versatile potential applications as the submerged tun-

nels, shear walls and floors in the high rise building,

bridge and offshore deck, protection structures, oil

storage tank, ship hulls, nuclear plant towers, and ice

walls in the arctic offshore structure [6].

Since the SCS sandwich composite structures with

J-hook connectors was developed, experimental studies

and analysis on this type of structures have been carried

out to obtain more information on their structural

performances [3–5]. Among the analysis methods,

numerical method especially the finite element (FE)

method is a very useful mean. Though there was less

information on FE analysis (FEA) on J-hook connec-

tors, there were still some related works on other forms

of SCS sandwich structure. A two-dimensional FE

model was developed for bi-steel beams [7]. However,

this FE model was two-dimensional that limited the

simulation of the connector–concrete interaction that

usually was three-dimensional (3D) and significantly

influenced the shear strength of the connector. Another

simplified FE model was developed for the ‘double

skin’ structure with overlapped headed shear studs [8].

In this model, the concrete core with headed shear studs

was simplified to a homogeneous anisotropic material

(a) Angle connector (b) C channel connector (c) overlapped headed stud

(d) Friction welded connector (e) Corrugated-strip connector (f) J-hook connector

Fig. 1 Sandwich composite structure with different shear connectors

(a) SCS sandwich beam with J-hook connector

(b) Curved SCS sandwich structure with J-hook

Fig. 2 SCS sandwich

structure with J-hook

connectors


with enhanced shear strength contributed by the

connectors. This simplification significantly reduces

the difficulty of modeling the overlapped shear con-

nectors in the concrete core and reduces the total

amounts of the elements. However, this simplified FE

model cannot simulate the structural behavior of the

connectors in the SCS sandwich beam structure.

Nonlinear spring elements were also used in the FE

model to replace the headed stud connectors and

connect the concrete slab and I-beam in steel–concrete

composite structure [9]. However, this simplification

could not reflect the interaction between the connector

and the concrete, and underestimates the transverse

shear strength of the structure. In SCS sandwich

composite structure with J-hook connectors, the con-

nectors that work in pairs and interlock each other are

used to transfer longitudinal shear force, resist trans-

verse shear force, and prevent local buckling of the steel

face plates. Since their roles in SCS sandwich structures

are such important, it is of importance to capture their

structural behaviors in the FEA. From the above

literature review, all these developed FE models have

limitations on properly simulate the concrete–connector

interactions [7–9]. Moreover, the complex geometry of

the J-hook connectors also brings challenges to the FEA

of the SCS sandwich beams.

In this paper, a 3D FE model by general commercial

FE program ABAQUS was developed to simulate the

structural behavior of the SCS sandwich beam under

quasi-static loading. In this FE model, as the basic

component of the SCS sandwich structure, structural

behaviors of one pair of interlocked J-hook connectors

were firstly simulated. FE simulations on these basic

structural behaviors of the J-hook connectors i.e. the

longitudinal shear-slip and axial tension–elongation

behaviors were first evaluated by the push-out tests and

tensile tests on a pair of J-hook connectors. Followed,

from the structure level, the accuracy of the FE model

was checked through validations against twenty beam

tests. Through these validations, the accuracy of the FEA

was confirmed. These works in this report extend the

studies and provide useful analysis method on the SCS

sandwich composite beams with J-hook connectors.

2 Finite element model

This finite element model includes (1) modeling the

basic component of the SCS sandwich structure with

J-hook connectors that will be validated by the push-

out tests and tensile tests on a pair of J-hook

connectors, and (2) modeling the SCS sandwich beam

with J-hook connectors.

The ABAQUS CAE and standard type of implicit

solver were used for model building and FEA solution.

2.1 Description on the basic behaviors

of the J-hook connector

J-hook connectors in the SCS sandwich structure play

essential roles such as transferring longitudinal shear

force at the steel–concrete interface, providing trans-

verse shear force through linking the shear cracks in

the concrete, and preventing uplifting and local

buckling of the steel face plates (see Fig. 3). There-

fore, the FE model should properly capture these

structural behaviors. The first characteristic structural

behavior is the longitudinal shear behavior. Generally,

push-out tests are used to obtain the ultimate shear

strength and shear-slip behaviors of the J-hook con-

nectors [6]. The second structural characteristic of the

J-hook connectors is the axial tension behavior. This

behavior can be obtained through direct tensile test. In

this study, the push-out tests and tensile tests carried

out by the authors were used to validate the FE model.

2.2 Modeling of J-hook connector

For a pair of interlocked J-hook connectors, it is very

difficult to make a full geometry simulation due to

their complex geometry. A full geometry simulation

will lead to mesh and contact simulation difficulties

that probably terminate the FEA prematurely devel-

oped. Moreover, it will also lead to a great deal of

elements that proves to be time costing and reduce the

computing efficiency. In this paper, a pair of J-hook

connectors was simplified to two cylindrical stud

connectors linked by a nonlinear spring element as

shown in Fig. 4. A small gap of 5 mm is reserved

between these two cylindrical studs for facilitating the

modeling of spring element. The tension–elongation

behavior of the J-hook connectors obtained from the

tensile tests was used to define tension–elongation

behavior of the nonlinear spring element. The defini-

tion of the tension–elongation relationship of spring

cannot be realized through editing the Unicode in the

input program with the values of the tension–elonga-

tion relationship.


In the longitudinal direction, the cylindrical studs

were built with the same diameter and similar

embedding depth as the real J-hook connectors in the

SCS sandwich beams. From the Eurocode 4 [10], it

can be well known that the shear strength of the

connectors are determined by the following

PJ ¼ min 0:8fu

pd2

4cv

; 0:29ad2ffiffiffiffiffiffiffiffiffiffi

fckEc

p

=cv

� �

; ð1Þ

where d is the diameter of the stud shank, fu is the

ultimate tensile strength of the stud (B500 MPa), fck is

the characteristic cylinder strength of concrete, Ec is

the secant modulus of concrete, a = 0.2(hs/d ? 1) for

3 B hs/d B 4 or a = 1.0 for hs/d C 4; hs = overall

height of the stud. The recommended value for the

partial safety factor cv is 1.25.

From Eq. 1, it can be seen that the shear strength of

the connectors were determined by both material

properties and geometry that include the diameter and

height of the stud. Therefore, in many FE models as

aforementioned [7–9], the simplifications may not

properly capture this structural behavior and cannot

correctly estimate the connector’s shear strength. In

this paper, the simplified method can simulate the

(a)

T

M

J-

T

M

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C

C=

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C

=Co

con

L

omp

J

nne

Loca

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J-ho

cto

al B

ssiv

ook

ors t

(b)

Buck

ve fo

con

tran

J-

T

T

klin

orce

nnec

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-hoo

T

ng

e; T

ctor

er in

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T=T

r

nter

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T

T

P

Tens

rfac

nne

T

P

sile

cial

cto

for

l sh

ors p

T

Trce;

ear

prev

T

M

r an

ven

M=be

nd p

nt lo

end

prov

oca

ding

vide

l bu

g mo

e tra

uck

C

ome

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ans

kling

ent

caluckl

sver

g

T

M

ing

rse she

T

T

T

ear res

C

C

istaance

T

T

T

e

Fig. 3 Functions of the J-hook connectors in SCS sandwich structure


closest geometry to shear connectors in terms of height

and diameter compared with other developed FE

models.

In the axial direction of the connector, the axial

tension–elongation behaviors from the direct tensile

tests were used to define the nonlinear spring element.

Thus, this characteristic of the J-hook connectors was

simulated.

2.3 Description of finite element model

In order to simulate the SCS sandwich beam structure

with J-hook connectors from the component to

structure level, the FE model includes the simulation

on the push-out and tensile tests, and the simulation on

the SCS sandwich beam.

2.3.1 FE model for the push-out test

In the push-out test, the main components were steel

face plates, shear connector, concrete core, and load

cell as shown in Fig. 5. All these components were

modeled by the 3D eight-node continuum element

(C3D8R). For a pair of interlocked J-hook connectors,

nonlinear spring element is used to simplify its

complex geometry as shown in Fig. 5. Considering

the symmetry of the structure and loading, only half of

the specimen was built in the FE model. At the

conjunction between the connectors and the steel face

plates and contacting locations between the connector

and concrete core, fine mesh sizes were used to make a

better simulation as shown in Fig. 5.

2.3.2 Finite element model for the SCS sandwich

beams

Different components of the SCS sandwich beams were

built in the developed FE model, which include steel face

plates, shear connectors attached to the steel plates,

support, load cells, and concrete core (as shown in

Fig. 6). Considering the symmetry of the geometry and

loading patterns, one quarter of the full specimen was

modeled. Three-dimensional eight-node linear contin-

uum element with hourglass control was used for steel

face plates, connectors, and concrete core. Nonlinear

spring elements were also used to simulate the axial

tension–elongation behavior of the interlocked J-hook

connectors in the SCS sandwich beam as shown in Fig. 4.

In order to balance the computing accuracy and

efficiency, different mesh sizes were used for the SCS

sandwich beams at different locations. Considering

the interaction between the steel connectors and

concrete core, fine mesh size was used at the

contacting locations between the connectors and

concrete. Typical mesh sizes for the SCS sandwich

beam were shown in Fig. 6.

2.4 Material modeling of concrete and steel

There are mainly two types of materials were involved

in this FEA i.e. steel and concrete.

NelNonlem

lineent

ear t

sprringg

Fig. 4 Simulation of a pair of interlocked J-hook connectors in

FE model

Steel face plate

Steel face plate

Connector

Load cell

Symmetrical surface

Movement restraint Ux=Uy=Uz=0

Displacement loading

Fig. 5 Finite element model for the push-out test


2.4.1 Concrete

In ABAQUS material library, the concrete damage

plasticity model was used for the concrete core

materials in the SCS sandwich composite beams.

The concrete damage model is a continuum, plasticity-

based, damage model. In this model, the assumed two

main failure mechanisms are compressive crushing

and tensile cracking of the concrete. The yield

function proposed by Lubliner et al. [11] and modified

by Lee and Fenves [12] was adopted to account

different evolution of strength under tension and

compression. The isotropic damage and non-associ-

ated potential flow rule was assumed in this model

[13]. Considering the concrete damage material model

with softening behavior and stiffness degradation

often lead to severe convergence difficulties in

implicit analysis programs, in Abaqus/Standard type

of program, the viscoplastic regularization of the

constitutive equations is used to improve the conver-

gence rate in the softening regime.

For concrete damage plasticity model, two failure

mechanisms including tensile cracking and axial

compressive crushing were needed to be defined. In

this FEA, different types of concretes were used i.e.

normal weight concrete (NWC), lightweight concrete

(LWC), and ultra-lightweight cement composite

(ULCC). For the LWC and ULCC, the compression

and tension behaviors of the concrete materials were

obtained through compression and splitting tests on

the concrete cylinders according to ASTM [14, 15].

The compressive stress–strain curves of the LWC and

ULCC obtained from the compression tests on the

cylinders are shown in Fig. 7. The stress–strain curve

suggested by Carreira and Chu [16] was used to model

the elastic–plastic characteristics of the NWC with

strain softening as the following:

rc ¼fckb ec=eckð Þ

b� 1þ ec=eckð Þb; ð2Þ

where rc is the compressive stress of the concrete, ec is

the compressive strain of the concrete, fck is the

compressive strength of the concrete cylinder, eck is the

compressive strain at fck is the b is a function of secant

modulus of elasticity Ec that can be determined by

b ¼ 1 ec=eckð Þ1� fck= eckEcð Þ : ð3Þ

Other plasticity parameters including dilation angle

of 36�, flow potential eccentricity of 0.6, and ratio of

Steel face plate

Load cell

Support

Concrete core

Holes cut for connector

Support

Connector Steel face plate

Load cell

Steel face plate Symmetrical surface Uz=0

Symmetrical surface Ux=0

Movement Restrained

Displacement Loading

Fig. 6 Finite element model for SCS sandwich beam


the biaxial/uniaxial compressive strength ratio of 1.16

were set for this plastic damage model according to the

ABAQUS user manual [13].

For the tension capacity of the core material, linear

elastic tensile behavior is assumed before the cracking

in the concrete develops. The cracked concrete can be

simulated by the nonlinear stress–strain behavior or

fracture energy cracking model. The ultimate tensile

strength of the ULCC was obtained through the

splitting tensile tests on the cylinders. For the fracture

energy parameter, it can be determined by the

following equation in CEB-FIP [17]

Gf ¼ Gf0

fck

10

� �0:7

; ð4Þ

where Gf is the fracture energy, Nmm/mm2, Gf0 varies as

the coarse aggregate of the concrete changes,

Gf0 = 0.025 Nmm/mm2 for the d = 8 mm coarse aggre-

gate, Gf0 = 0.030 Nmm/mm2 for the d = 16 mm,

Gf0 = 0.058 Nmm/mm2 for the d = 32 mm; d is the

diameter of the coarse aggregate in the concrete, mm, fck

is the compressive strength of the concrete cylinder, MPa.

Since ULCC is a new material and there is no test data

available on the fracture energy, a smallest value

Gf0 = 0.0025 Nmm/mm2 is used for ULCC consider-

ing there is no coarse aggregate in it, and Gf =

0.088 Nmm/mm2 is used in the tensile behavior of the

plastic material model for the ULCC. For the NWC used

in the SCS sandwich beams, Gf0 = 0.060 Nmm/mm2

was used for the d = 18 mm coarse aggregate, and

Gf = 0.18 Nmm/mm2 was used. For LWC used in the

sandwich composite beam, Gf = 0.060 Nmm/mm2

was used in the FEA.

2.4.2 Steel

A nonlinear isotropic/kinematic hardening model with

Mises yield surface for the definition of isotropic

yielding in ABAQUS material library was used for

steel material [13]. This stress–strain behavior defined

in this model was bi-linear with strain hardening as

shown in Fig. 8. For the elastic behavior of the steel

material, the elastic Young’s modulus Es and Pois-

son’s ratio were needs to be defined. For the plastic

behavior, the yield strength, ultimate strength and the

corresponding strains were needs to be defined.

For these material properties including the elastic

Young’s modulus, yield strength, ultimate strength

and the corresponding strains were obtained from the

tensile tests on the steel coupons.

The elastic Young’s modulus of 205 GPa and yield

strength 275 MPa were used for the sandwich beams

in the Group A and beam J1 in Group B as shown in

Table 1. For the steel plates in the SCS sandwich beam

in Group B, elastic Young’s modulus of 205 GPa and

yield strength 310 MPa were used for the beams in

Group B except J1 in Table 1. For the J-hook

connectors, the same material properties were used

as the steel plates as listed above.

2.5 Boundary, loading, interactions, and solutions

In the push-out tests, the bottom end of the steel face

plates were restrained against moving in the any

directions as shown in Fig. 5. From this figure, it can

be seen than the rotation restrained in the Y and

Z directions and movements in the X direction were

applied to the symmetrical surface. In the LOAD

menu of the ABAQUS CAE modeling, displacement

controlled type of loading was applied to the load cell.

0

10

20

30St

ress

(M

Pa)

Strain

LWC C300

25

50

75

0 0.001 0.002 0.003 0 0.003 0.006 0.009

Stre

ss (

MP

a)Strain

ULCC C60

Fig. 7 Compressive stress–strain curves of LWC and ULCC

Fig. 8 Stress–strain model for the steel material


For the beam tests, symmetrical restraints were

applied to the cross section as shown in Fig. 6. The

support was restrained from moving but free in

rotation. Displacement controlled type of loading

was applied to the SCS sandwich beam through the

load cell by setting the Load Menu in the ABAQUS

library.

The contact between the concrete and steel face

plates in push-out and beam tests is simulated by the

general contact with ‘‘hard formulation’’ in the normal

direction and ‘‘penalty friction formulation’’ in the

tangential direction. The hard formulation in the

‘‘Interaction’’ menu of ABAQUS library means that

the pressure will be transferred once two interacting

surfaces contact whilst no pressure will be transferred

when they are separated. The penalty friction formu-

lation permits relative slip between the two contacting

surfaces and the interacting friction force is

proportional to the defined friction coefficient. This

contact permits the two contacting surface separating

but not allows penetrating each other. Friction coef-

ficient is taken as 0.4 as in the previous FE studies

carried out by Yan [2]. For the push-out tests, the

‘‘hard contact’’ formulation and ‘‘penalty friction

formulation’’ were also used to define the interactions

in normal and tangential directions respectively at the

steel face plate and concrete interface, interface of

concrete and load cell in the push-out tests. ‘‘Hard

contact’’ formulation was used in the normal direction

to the interface between the connectors and the

concrete core and in the tangential direction along

this interface no contact was defined for both push-out

tests and beam tests. For the beam tests, ‘‘hard

contact’’ formulation and ‘‘penalty friction formula-

tion’’ were also used to define the interactions in

normal and tangential directions respectively at the

Table 1 Details of the SCS sandwich beam

Beam tc and tt(mm)

hc

(mm)

B

(mm)

D

(mm)

S

(mm)

Core Vf

(%)

w (kg/

m3)

fck

(MPa)

fy(MPa)

ru

(MPa)

Group A

SCS 80 4.0 80 240 10 80 NWC – 2,350 48.3 275 405

SLSC80 4.0 80 240 10 80 LWC – 1,445 28.5 275 405

SCS 100 4.0 80 200 10 100 NWC – 2,350 48.3 275 405

SLCS100 4.0 80 200 10 100 LWC – 1,445 28.5 275 405

SLFCS100 4.0 80 200 10 100 LWC 1S? 1,450 28.1 275 405

SCS150 4.0 80 300 10 150 NWC – 2,350 48.3 275 405

SLCS150 4.0 80 300 10 150 LWC – 1,445 28.5 275 405

SLCS200 3.9 80 200 16 200 LWC – 1,445 27.4 275 405

SLF200-1 3.9 80 200 16 200 LWC 1P? 1,450 28.7 275 405

SLF200-2 3.9 80 300 16 200 LWC 2P? 1,450 28.2 275 405

SLF300-1 3.9 80 200 16 300 LWC 1P? 1,450 28.0 275 405

Group B

J1 4.0 100 200 12 100 ULCC 0.5 P? 1,441 60.0 275 460

J2-1 6.0 100 200 12 100 ULCC 0.5 P? 1,450 60.0 310 460

J2-2 6.0 100 200 12 100 LWC – 1,324 24.0 310 460

J2-3 6.0 100 200 12 100 HPC – 2,672 160 310 460

J3 12.0 100 200 12 100 ULCC 0.5 P? 1,481 60 310 460

J4 6.0 100 200 12 150 ULCC 0.5 P? 1,521 60 310 460

J5 6.0 100 200 12 200 ULCC 0.5 P? 1,440 60 310 460

J6 6.0 100 200 12 100 ULCC 0.5 P? 1,481 60 310 460

J7 6.0 100 200 12 100 ULCC 0.5 P? 1,482 60 310 460

tc thickness of the steel plate under compression, tt thickness of the steel plate under tension, B width of the beam cross section,

D diameter of the J-hook, S spacing of the connector, w density of the concrete, Vf volume fraction of the fibre in the concrete, fy yield

strength of the steel plate, fck compressive strength of the concrete cylinder, ru ultimate strength of J-hook connector, S? denotes steel

fiber, P? denotes polyvinyl alcohol fiber


interface between concrete and steel plate, interface

between load cell and top steel face plate, and interface

between bottom steel face plate and support; ‘‘hard

contact’’ formulation was used in the normal direction

between the connectors and the concrete core and in

the tangential direction no contact was defined.

Abaqus Standard type of implicit solver was used for

the solution. Numerous control parameters are associ-

ated with the convergence criteria in Abaqus/Standard

for the solutions. Usually there are default values set to

optimize the accuracy and efficiency of the solution for

a wide spectrum of nonlinear problems. For the

convergence criteria, solution control parameters can

be used to define tolerances for field equations such as

force and moment. For the contact, the contact stresses

and contact displacements were selected for the field

equations of convergence criteria.

3 Push-out tests, tensile tests and SCS sandwich

beam tests

The push-out tests and SCS sandwich beams tests

carried out by the authors were used in this study for

the validation of the FE model.

3.1 Push-out tests

Twelve push-out tests were used to validate the FE

model. The setup of the push-out tests and the geometry

illustration are shown in Fig. 9. The details of the

specimens are listed in Table 2. In the push-out test, a

pair of interlocked J-hook connectors embedded in the

concrete block was pushed off under the quasi-static

interfacial shear forces as shown in Fig. 9. As shown in

this figure, the displacement controlled type of loading

was applied to the concrete core through the load cell,

and then this load will be taken by a pair of J-hook

connectors. The load obtained from the test will be

equal to two times the shear strength of single J-hook

connectors. Linear varying displacement transducers

(LVDTs) were used record the interfacial slip between

the concrete and the steel face plate. Finally, the shear

force versus slip of each specimen was recorded.

3.2 Tensile tests

Tensile tests on the J-hook connectors were also

carried out to obtain the axial tension–elongation

behavior of the J-hook connectors in different concrete

mixtures. The test setup is shown in Fig. 10. As shown

in this figure, a pair of the interlocked J-hook

connectors was embedded in the concrete that was

confined by a steel tube. This steel tube was used to

simulate the confinement of the neighbor concrete in

the structure. The tensile forces was applied to the

specimen and transferred to the J-hook connectors.

The tensile strength as well as the tension–elongation

behaviors of the J-hook connectors can be obtained

that can be used for the validation of the FE mdoel.

3.3 Quasi-static tests on SCS sandwich beams

The SCS sandwich beams with J-hook connectors

subjected to one- or two- point loading were used in

this paper to check the accuracy of the FEA [14, 15].

The beams in Ref. [15] were designed with a span of

1,000 mm under one-point loading. The geometry and

setup of the beam test is shown in Fig. 11a. LWC that

was made of both coarse and fine aggregates was used as

the main core material. NWC was also used in three

specimens. Steel or polyvinyl alcohol (PVA) fibers were

used in four specimens. The details of these SCS

sandwich beams are illustrated in Table 1 (Group A

beams).

The sandwich beams in Ref. [4] were tested under

one- or two- point loading. SCS sandwich beam J1–J5

were set a span of 500 mm and subjected to one-point

loading at the mid-span; beam J6 and J7 that were tested

under two-point loading were designed with spans of

1,100 and 1,600 mm, respectively (see Fig. 11). All the

beams were designed with the same cross section (with

height of core = 100 mm and width 200 mm). The

ULCC was used as the main core materials. LWC and

high performance concrete were used in beam J2-2 and

J2-3, respectively. The test setup and geometry of the

SCS sandwich beams were shown in Fig. 11. The

material properties and details of the SCS sandwich

beams were listed in Table 1 (Group B beams).

4 Validation of the FE model

4.1 Validation of the FE model against push-out

and tensile test

By the recommended FE model, FE analyses (FEA) on

push-out tests were carried out. The validations of the


FEA consist of validation of shear force-slip curves of

the J-hook connectors, ultimate shear strength, and

failure mode.

4.1.1 Shear force-slip curves of push-out test

The shear force-slip curves obtained from FEA were

compared with the experimental ones in Fig. 12. From

these figures, it can be seen that the load-slip curves by

the FEA show good agreements with the experimental

curves in terms of initial elastic stiffness, threshold of

the plastic behavior initializing, and nonlinear load-

slip behaviors. In some specimens, there is still some

mismatch of load-slip curves between the FEA and the

experimental ones at the nonlinear part e.g. load-slip

curves of PU2 and PU3. These discrepancies may be

caused by the splitting of the concrete that cannot well

be simulated in the FE model. For PU2, splitting

failure occurred to the concrete core which prevented

the specimen continuing taking more loads. However,

in the FEA, the specimen failed in the shear off of the

connector, and no splitting failure was observed.

LVDT

Steel face plate

Steel face plate

Load cell

J-

Co

hook

ncrete core

Fig. 9 Push-out test on

specimens with J-hook

connectors

Table 2 Details of push-out test on sandwich specimens with J-hook

Item t (mm) d (mm) hc (mm) hs (mm) B (mm) ru (MPa) fck (MPa) Ec (GPa) w (kg/m3) hc

d

PN1 6 9.9 40 49.9 300 405 48.3 32.5 2,400 4.04

PN2 6 11.8 75 90.5 250 480 47.7 24.0 2,343 6.36

PN3 6 11.7 75 90.5 250 450 34.1 19.5 2,329 6.41

PL1 6 9.9 40 49.9 300 405 28.5 12.7 1,450 4.04

PL2 6 11.7 75 90.5 250 450 51.2 18.0 1,874 6.41

PL3 6 11.7 75 90.5 250 450 51.2 18.0 1,874 6.41

PL4 6 11.7 100 120 250 480 51.2 18.0 1,874 7.50

PLF1 6 9.9 40 49.9 300 405 28.1 12.6 1,460 4.04

PU1 4 11.8 50 61.8 250 464 60.0 16.5 1,490 4.24

PU2 6 11.8 50 61.8 250 464 60.0 16.5 1,440 4.24

PU3 8 11.8 50 61.8 250 464 60.0 16.5 1,440 4.24

PU4 12 11.8 50 61.8 250 464 60.0 16.5 1,440 4.24

PU5 6 11.8 75 86.8 250 464 60.0 16.5 1,440 6.36

PU6 6 11.8 100 111.8 250 464 60.0 16.5 1,440 8.47


4.1.2 Ultimate shear strength and failure mode

of push-out test

The ultimate shear strengths of the J-hook connectors

obtained from the FEA are compared with the shear

strengths obtained from the push-out tests in Table 3.

From this table, it can be observed that the average

test-to-prediction ratio of the ultimate shear strength

for the fourteen push-out tests is 1.00 with a coefficient

of variance (COV) of 0.05. This implies ultimate shear

strengths of the J-hook connectors attained from the

FEA agree well with the experimental results. In

Eurocode 4, Eq. 1 was used to predict the shear

strength of the connectors. The predictions by Eq. 1

In-filled concrete

Steel plate

J-hook

T

T

Steel plate

Steel tube

e

T

T

Fig. 10 Tensile test on a pair of interlocked J-hook connectors

(a) Test setup and details of sandwich beams in group A

(b) Test setup and details of sandwich beams in group B

P

A

A

A-A

t t

tc

P

P

B

B

B-B

B

B

CL

P

B

B

J1-5 J6

t t

tc

Fig. 11 Test setup and details of the SCS sandwich beams


are given in Table 3. From this table, it can be also

seen that the Eq. 1 offers about 20 % average

underestimations on shear strength of the J-hook

connectors. Both Eq. 1 and FEA exhibit close COV of

the predictions on these fourteen push-out tests.

Unfortunately, FEA method shows advantages of

describing both the linear and nonlinear shear-slip

behaviors over the analytical model.

There were two types of failure modes that were

observed from the push-out test i.e. shank shear failure

(SS) and concrete cracking failure (CC) [6]. The

predicted failure modes by the FE model were

compared with the failure modes observed from the

push-out tests in Table 3. From this table, it can be

found that the FEA predicts about 80 % correct failure

modes compared with the observed failure modes

during the test. The 20 % error predictions on failure

mode may be caused due to the concrete splitting of

the specimens that might be caused by the even

distribution of the shear loads on the concrete core

(c)(b)(a)

0

20

40

60

80

Loa

d (k

N)

Slip (mm)

PN1 TestPN1 FE

0

30

60

90

120

Loa

d (k

N)

Slip (mm)

PN2 TestPN2 FE

0

20

40

60

0 2 4 6 8 10 0 2 4 6 8 0 2 4 6 8

Loa

d (k

N)

Slip (mm)

PL1 TestPL1 FE

(f)(e)(d)

(i)(h)(g)

(l)(k)(j)

0

40

80

120

Loa

d (k

N)

Slip (mm)

PL2 TestPL3 TestPL2-3 FE

0

40

80

120

Loa

d (k

N)

Slip (mm)

PL4 TestPL4 FE

0

20

40

60

Loa

d (k

N)

Slip (mm)

PLF1 TestPLF1 FE

0

25

50

75

100

Loa

d (k

N)

Slip (mm)

PU1 Test

PU1 FE0

25

50

75

100

Loa

d (k

N)

Slip (mm)

PU2 TestPU2 FE

0

25

50

75

100

Loa

d (k

N)

Slip (mm)

PU3 TestPU3 FE

25

50

75

100

Loa

d (k

N)

Slip (mm)

PU4 Test

PU4 FE0

30

60

90

120

Loa

d (k

N)

Slip (mm)

PU5 Test

PU5 FE0

30

60

90

120

0 2 4 6 8 0 3 6 9 12 0 4 8 12

0 2 4 6 8 0 2 4 6 0 2 4 6

00 2 4 6 0 3 6 9 0 4 8 12

Loa

d (k

N)

Slip (mm)

PU6 TestPU6 FE

Fig. 12 Comparisons of

shear-slip curve between the

tests and FEA


material during the tests. Figure 13 shows the com-

parisons of the SS and CC failure modes between the

FEA and the experimental failure mode. The principle

plastic strain contours of the FEA were used to assist

judging of the failure in these two materials. Once the

lower limit of the cracking strain for the steel or

concrete were set, the cracking developed in the

elements can be judged if the strains in these elements

exceed this limit. For the limit of the steel cracking

strain herein is set as 0.30, and this value for the

concrete is set as 0.035. From Fig. 13, it can be seen

that these two failure modes can be well simulated by

the FE model.

4.1.3 Tension–elongation behavior of the tensile test

The other important characteristic behavior of the

J-hook connector is the axial tension versus elongation

behavior. The experimental tension–elongation behav-

iors of the J-hook connectors are compared with the

FEA in Fig. 14 (The details of the tensile tests are listed

in Table 4). From this figure, it can be seen that the

introduced spring element can capture the tension–

elongation behavior of the J-hook connectors in the

sandwich structure.

4.2 Validation of the FE model against SCS

sandwich beam test

By the recommended FE model, FE analyses were

carried out on the SCS sandwich beams under quasi-

static loading.

4.2.1 Deformed shape

The deformed shape of the SCS sandwich beams

under one- or two- point loading obtained from the

tests were compared with the deformed shape of the

sandwich beam obtained from the FEA at the same

loading levels in Fig. 15. From these figures, it can be

seen that developed FE model is capable of describing

the deformations of the sandwich beam with J-hook

connectors though there are some mismatches. These

differences may be caused by the soft support

problem.

4.2.2 Ultimate strength and failure mode

The ultimate strength and failure modes by the FEA

were compared with those by experimental results in

Table 5. From this table, it can be seen that the

Table 3 Comparisons of the ultimate shear strength of the J-hook connectors

No. Item PTest (kN) Test failure mode PFE (kN) FE failure mode PTest

PFEPa by Eq. 1 (kN) PTest/Pa

1 PN1 31.0 SS 31.6 SS 0.98 24.9 1.24

2 PN2 47.2 SS 50.4 SS 0.94 42.0 1.12

3 PN3 36.4 CC 37.5 CC 0.97 32.4 1.12

4 PL1 20.9 CC 21.1 CC 0.99 17.1 1.22

5 PL2 41.4 CC 42.3 SS 0.98 38.1 1.09

6 PL3 45.5 SS 42.3 SS 1.08 38.1 1.19

7 PL4 48.3 SS 49.1 SS 0.98 38.1 1.27

8 PLF1 22.6 SS 23.0 SS 0.98 16.9 1.34

9 PU1 46.8 SS 45.7 SS 0.98 40.2 1.16

10 PU2 42.1 CC 45.6 SS 1.09 40.2 1.05

11 PU3 44.2 CC 46.7 SS 1.06 40.2 1.10

12 PU4 48.6 SS 48.2 SS 0.99 40.2 1.21

13 PU5 51.2 SS 53.8 SS 1.05 40.2 1.27

14 PU6 51.7 SS 50.6 SS 0.98 40.2 1.29

Mean 1.00 1.19

Cov 0.05 0.07

SS shank shear failure, CC concrete cracking


predicted ultimate strength by FEA agree well with the

experimental ultimate strengths with an average test-

to-prediction ratio 0.99 and a COV 0.06. With regards

to the failure mode, it can be seen that the FE model

can offer 95 % correct predictions except on beam

SCS100. Nevertheless, the FE model shows advanta-

ges on observing the connector shear failure (CSF)

that was usually difficult to observe due to the

connectors were invisible in the embedded concrete.

It can be also found that the connectors failed in

vertical shear (VSF) for most of the beam tests as listed

in Table 5. Because, for the beams failed in VSF, the

connectors were under the most critical working state

i.e. under combined shear and tensile loads. It is thus

can be concluded from the comparisons of the ultimate

strengths and failure modes that the developed FE

Test SS failure mode

Back viewFE SS failure mode

(a) Shank shear failure of the connector (SS)

Splitting crack of the FE

Splitting crack observed in the test

(b) Concrete cracking failure mode (CC)

Back View

Fig. 13 Comparison of failure mode between the test and FEA

0

10

20

30

Ten

sion

(kN

)

Elongation (mm)

FE TU1TU2 TU3TU4 TU5

0

10

20

30

0 10 20 30 0 10 20 30

Ten

sion

(kN

)

Elongation (mm)

TN1 TestTN1 FETL1 TestTL1 FE

Fig. 14 Validation of the tension–elongation behavior of the

J-hook connector


model is capable of predicting the ultimate load

carrying capacities as well as failure modes of the SCS

sandwich beams with J-hook connectors.

4.2.3 Load–central deflection curves

The load versus central deflection curves of the SCS

sandwich beam by the FEA were compared with the

experimental curves in Fig. 16. From these figures, it

can be seen that most of the predicted load–central

deflection curves resembles well with the test curves in

terms of linear and nonlinear behaviors. However, it

was also observed that the elastic stiffness of the load–

deflection curves by the FEA was somehow smaller

compared with the test curves. These differences in the

elastic stiffness of sandwich beams may be caused by

the soft support of the beam test. Except these

differences of the elastic stiffness, the FEA provides

good agreements on the ultimate strength and nonlin-

ear load–deflection behaviors of the beam.

Table 4 Details of the tensile test specimens

Specimen t (mm) hs (mm) hc (mm) d (mm) Fiber by volume ry (MPa) ru (MPa) fck (MPa) Material type

TN1 6 58.8 100 11.8 – 310 480 47.7

TL1 6 56.3 95 11.8 – 310 465 30.0 LWC

TU1 6 56.3 95 11.8 310 465 65.2

TU2 6 71.3 125 11.8 310 465 65.2

TU3 4 57.3 95 11.8 310 465 65.2

TU4 8 55.3 95 11.8 0.50 % 310 465 65.2 ULCC

TU5 12 53.3 95 11.8 310 465 65.2

TU6 6 60.5 95 16.0 280 405 65.2

NWC denotes normal weight concrete, NWFC denotes normal weight concrete with fibers, LWC denotes light weight concrete, LWFC

denotes light weight concrete with fibers, ULCC denotes ultra-lightweight cement composite

(a) Beam J2-3

0

1

2

3

0 100 200 300 400 500

Def

lect

ion

(mm

)

Distance (mm)

150 kN FE 150 kN Test220 kN FE 220 kN Test270 kN FE 270 kN Test

J2-3

(b) Beam J4 (c) Beam J5

0

2

4

6

8

0 100 200 300 400 500

Def

lect

ion

(mm

)

Distance (mm)

115 kN FE 115 kN Test150 kN FE 150kN Test200 kN FE 200 kN Test

J4

0

0.5

1

1.5D

efle

ctio

n (m

m)

Distance (mm)


J5

0 100 200 300 400 500

(d) Beam J6

0

4

8

12

0 200 400 600 800 1000

Def

lect

ion

(mm

)

Distance (mm)


J6

(e) Beam J7

0

4

8

12

0 400 800 1200 1600

Def

lect

ion

(mm

)

Distance (mm)

30 kN Test 30 kN FE60 kN Test 60 kN FE80 kN Test 80 kN FE

J7

Fig. 15 Validation of the deformed shapes of the FE model against test results


4.2.4 Cracks in the concrete core

The contours of the cracking in the concrete core by

the FEA were exhibited by plotting the principle strain

contour of the concrete elements. Once achieving the

limit of the cracking strain, the cracks are assumed to

be developed in the concrete. All the elements

exceeded the cracking strain were highlighted and

compared with the cracks that were observed from the

tests in Fig. 17. Through the comparisons of the cracks

developed in the SCS sandwich beam between the

observations in the test and FEA, it can be seen that the

developed FE model can be capable of predicting most

of the cracks developed in the concrete that were

observed in the tests.

4.2.5 Load-end slip behaviors between steel face

plate and concrete core

The load-slip behaviors between the concrete core and

bottom steel face plate given by the FEA were

compared with the corresponding experimental load-

slip curves in Fig. 18. From these figures, it can be

seen that the developed FE model offers reasonable

predictions of the load-slip behavior between the steel

face plate and the concrete core during the working

state with acceptable differences. It was also observed

from the test that sometimes the slip was very difficult

to measure due to the small values especially at the

elastic working stage of the SCS sandwich beam. This

might be one reason that caused the differences of the

load-slip curves between the predictions and the test

results.

5 Recommended finite element analysis

procedures

To carry out the FEA on the SCS sandwich beam with

J-hook connectors, it is essential to offer proper

simulations of the J-hook connectors at the working

state. This requires the FE model can capture the

longitudinal shear behavior and axial tensile behav-

iors. The longitudinal shear behaviors can be simu-

lated by cylindrical stud with the same diameter and

Table 5 Ultimate strengths

and failure modes of SCS

sandwich beam

BSY bottom steel plate yield,

VSF vertical shear failure in the

concrete core, CF connector

failure, CF connector fail

Beam Pt (kN) Experimental

failure mode

PFE (kN) Predicted

failure mode

PFE/Pt

SCS 80 119.1 BSY 114.8 BSY 0.96

SLSC80 95.6 BSY 84.7 BSY 0.89

SCS 100 86.2 BSY 80.3 VSF 0.93

SLCS100 55.2 VSF 54.9 CF/VSF 0.99

SLFCS100 68.7 VSF 65.1 CF/VSF 0.95

SCS150 66. 7 VSF 62.5 CF/VSF 0.94

SLCS150 45.4 VSF 42.2 CF/VSF 0.93

SLCS200 40.1 VSF 39.2 CF/VSF 0.98

SLF200-1 45.6 VSF 47.1 CF/VSF 1.03

SLF200-2 48.9 VSF 46.4 CF/VSF 0.95

SLF300-1 30.3 VSF 30.4 CF/VSF 1.01

J1 174.7 BSY/VSF 182.7 CF/VSF 1.05

J2-1 221.2 VSF 228.2 CF/VSF 1.03

J2-2 137.2 VSF 135.8 CF/VSF 0.99

J2-3 352.4 VSF 380.1 CF/VSF 1.08

J3 368.3 BSY/VSF 396.4 CF/VSF 1.08

J4 230.4 VSF 201.3 CF/VSF 0.87

J5 146.0 VSF 154.8 CF/VSF 1.06

J6 164.5 BSY/VSF 166.7 BSY/VSF 1.01

J7 121.8 BSY/TSY 122.2 BSY/TSY 1.00

Mean 0.99

Cov 0.06


(c)(b)(a)

(f)(e)(d)

(i)(h)(g)

0

25

50

75

100

125

Loa

d (k

N)

Deflection (mm)

SCS80 Test

SCS80 FE0

25

50

75

100

Loa

d (k

N)

Deflection (mm)

SLCS80 TestSLCS80 FE

0

20

40

60

80

100

Loa

d (k

N)

Deflection (mm)

SCS100 TestSCS100 FE

0

20

40

60L

oad

(kN

)

Deflection (mm)

SLF200-2 Test

SLF200-2 FE0

15

30

45

Loa

d (k

N)

Deflection (mm)


0

20

40

60

Loa

d (k

N)

Deflection (mm)


0

20

40

60

Loa

d (k

N)

Deflection (mm)

SLCS100 Test

SLCS100 FE0

20

40

60

80L

oad

(kN

)

Deflection (mm)

SLFCS100 TestSLFCS100 FE

0

50

100

150

200

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40 0 5 10 15

Loa

d (k

N)

Deflection (mm)

J1 TestJ1 FE

(l)(k)(j)

(o)(n)(m)

0

100

200

300

Loa

d (k

N)

Deflection (mm)

J2-1 TestJ2-1 FE

0

50

100

150

Loa

d (k

N)

Deflection (mm)

J2-2 TestJ2-2 FE

0

100

200

300

400

Loa

d (k

N)

Deflection (mm)

J2-3 TestJ2-3 FE

0

50

100

150

200

250

Loa

d (k

N)

Deflection (mm)

J4 TestJ4 FE

0

50

100

150

200

Loa

d (k

N)

Deflection (mm)

J6 TestJ6 FE

0

50

100

150

0 5 10 15 20 0 5 10 15 20 0 10 20 30 40

0 5 10 15 0 10 20 30 40 0 20 40 60 80

Loa

d (k

N)

Deflection (mm)

J7 TestJ7 FE

Fig. 16 Validation of the

load–central deflection

curves of the FE model

against test results


(b) FE of J2-2(a) Test of J2-2

(d) FE of J4(c) Test of J4

(f) FE of J5(e) Test of J5

(g) Test of J6

(h) FE of J6

(i) Test of J7

(j) FE of J7 Fig. 17 Validations of the cracks in the concrete of the FE mode


height of the J-hook connector. Regarding the axial

tension–elongation behaviors, it needs to be carefully

calibrated through the tensile tests. Thus, tensile tests

on the J-hook connectors in the sandwich specimen

become quite important to this FE model. The

recommended FEA procedure were summarized as

the following.

(1) Carrying out tensile tests on a pair of interlocked

J-hook connectors to obtain the tension–elonga-

tion behaviors. These tension–elongation behav-

iors will be assigned to the spring element that

was used to connect two cylindrical stud con-

nectors in the FE model.

(2) Modeling the steel face plates with the same

geometry and materials as used in the beam tests.

(3) Modeling the cylinder shear stud pairs with the

same diameter, effective height, and materials as

the J-hook connectors that work in pairs. All

these modeled shear stud will share nodes with

the steel face plates.

(4) Using the 3D spring element to link a pair of

shear studs that were attached to the top and

bottom steel face plates. The tension–elongation

behaviors of the J-hook connectors obtained

from the tensile tests in step (1) are assigned to

the spring elements.

(5) Building the concrete cores and defining the

interactions among different interacting parts.

(6) Solutions

6 Discussions of the finite element model

The finite element model developed in this paper not

only can be used for the analysis of SCS sandwich

beams with J-hook connectors, but also can be applied

to the SCS sandwich beams with overlapped headed

shear studs and other forms of interacted connectors.

The key elements in this model are the simulations of

the longitudinal shear-slip behavior and axial tension–

elongation behavior of a pair of interacting connectors

in the SCS sandwich composite beams.

6.1 Validation of the finite element model against

SCS sandwich beams with overlapped headed

shear stud

Another nine SCS sandwich beams with overlapped

headed shear studs in Ref. [2] were also used to

validate this FE model. The details of the specimens

were given in the Table 6.

Following the recommended finite element analysis

procedures in Sect. 5, the FEA were carried out on the

(a) (b) (c)

(d) (e) (f)

0

100

200

300

Loa

d (k

N)

Slip (mm)

J2-1 FE

J2-1 Test0

50

100

150

Loa

d (k

N)

Slip (mm)

J2-3 FE

J2-3 Test0

100

200

300

Loa

d (k

N)

Slip (mm)

J4 FE

J4 Test

0

50

100

150

200

Loa

d (k

N)

Slip (mm)

J6 Test

J6 FE0

50

100

150

Loa

d (k

N)

Slip (mm)

J7 FE

J7 Test0

20

40

60

0 1 2 3 0 0.2 0.4 0.6 0 1 2 3

0 2 4 6 0 1 2 3 0 3 6 9

Loa

d (k

N)

Slip (mm)

SLCS150 Test

SLCS150 FE

Fig. 18 Validations of the

load-slip behaviors of the FE

model


SCS sandwich beams with overlapped headed shear

studs.

6.1.1 Simulation of the overlapped headed shear stud

As recommended in step (1) of Sect. 5, three direct

tensile tests on a pair of overlapped headed shear studs

were carried out to obtain the tension–elongation

behavior of the basic component of the SCS sandwich

composite beams with overlapped headed shear stud

(see Fig. 19). From Fig. 19, it can be seen that the FE

model simulates well the tension–elongation behavior

of the basic component of the SCS sandwich beam.

6.1.2 Finite element model of the SCS sandwich beam

with headed shear studs

Following the recommended FEA procedure in Sect.

5, the FE models were built to simulate the different

components of the SCS sandwich beam as shown in

Fig. 20. Similar to the SCS sandwich beam with the

J-hook connectors, the steel face plates, studs, con-

crete core, support and load cell were modeled as

shown in Fig. 21.‘

6.1.3 Validation of the finite element model

The validation of the finite element model was carried

out by comparing the load–central deflection of the

SCS sandwich beams with the experimental load–

central deflection curves in Fig. 22. From these

figures, it can be concluded that the load–central

deflection curves by the FEA agree well with exper-

imental curves. The ultimate strengths and failure

modes of the nine SCS sandwich beams were

compared with the FE predictions in Table 6. From

Fig. 22 and Table 6, it can be concluded that the

developed FE model is capable of describing the

structural performance of the SCS sandwich beam

with overlapped headed shear studs in terms of load–

central deflection curves, ultimate strength and failure

modes of the specimens.

Table 6 Ultimate strength and failure mode of the beam B1–

B9

Beam Test Finite element

analysis

Ratio of

PE/Pu

Failure

mode

Pu

(kN)

Failure

mode

PE

(kN)

B1 VSF,

BSY

212.3 CF, VSF 221.8 1.04

B2 VSF 236.0 CF, VSF 241.0 1.02

B3 VSF,

BSY

378.0 VSF 403.2 1.07

B4 VSF 133.6 VSF 135.1 1.01

B5 VSF 451.3 VSF 462.2 1.02

B6 CF, VSF 233.1 CF, VSF 233.7 1.00

B7 CF, VSF 165.4 CF, VSY 162.6 0.98

B8 VSF,

BSY

174.3 VSF,

BSY

171.7 0.99

B9 FF, BSY 127.8 FF, BSY 121.9 0.95

Mean 1.01

Cov 0.03

BSY bottom steel plate yield, VSF concrete core shear failure,

CF connector shear failure, FF flexural failure, Pu ultimate

strength of the test, PE ultimate strength by finite element

analysis (FEA), Cov coefficient of variance

(a) Tension test on overlapped headed studs (b) Tension-elongation curve

0

10

20

30

40

0 4 8 12

Ten

sion

For

ce (

kN)

Elongation (mm)

T1T2T3FE model

T

T

Concrete

Headed

stud

200 mm

200 mm

100 mm

Fig. 19 Tension–

elongation behavior of

overlapped headed studs


Non-linear spring element

Fig. 20 Simulation of the

overlapped headed shear

stud by the spring element

Load cell

Support Steel plate

Steel plate

Stud Concrete core

Fig. 21 FE model for the SCS sandwich beam with overlapped headed shear stud

(a) (b) (c)

(d) (e) (f)

0

100

200

300

P (

kN)

Deflection (mm)

B2 Test

B2 FE0

150

300

450

P (

kN)

Deflection (mm)

B3 TestB3 FE

0

50

100

150

P (

kN)

Deflection (mm)

B4 Test

B4 FE

0

200

400

600

P (

kN)

Deflection (mm)

B5 Test

B5 FE0

50

100

150

200

P (

kN)

Deflection (mm)

B8 FE

B8 Test0

50

100

150

0 5 10 15 20 0 10 20 30 40 0 10 20 30 40

0 5 10 15 20 0 10 20 30 40 0 25 50 75

P (

kN)

Deflection (mm)

B9 Test

B9 FE

Fig. 22 Validation of the

load–deflection curves of FE

model


6.2 Discussions

The validations of the FE model on nine SCS

sandwich beams with the overlapped headed shear

studs further confirmed the accuracy of the FE

simulation and the fact that this model can be used

in analysis on SCS sandwich beams with other

interacted shear connectors. One key issue addressed

herein is the proper simulations on the structural

behaviors of the basic component in the structure.

From this point of view, the tensile tests on the

connectors become necessary and important. More-

over, so far there are no design codes that can be

followed to describe the tension–elongation behaviors

of the connectors. This should be further investigated,

and included in the design codes.

Another point needs to be pointed out is that the

spring model also has limitations on modeling the

interaction between the tensile and shear resistance of

the connectors. In the proposed spring model, the

tensile force in the spring can reduce the shear strength

of the connectors. Conversely, the shear resistance

also affects the tensile resistance of the two connectors

by the linking spring. If the steel shank that the spring

was linked to is under high shear, the tensile capacity

of the shank was also reduced even though the tensile

capacity of the spring was not decreased. Therefore,

the model can partially reflect the interaction between

the shear and tension of the connector, but the model

could not completely simulate this interaction.

7 Conclusions

This study presents a three dimensional nonlinear finite

element model for SCS sandwich composite beams with

the J-hook shear connectors and overlapped headed

shear studs. In the FE model, a pair of interlocked J-hook

connectors were simplified by two cylindrical stud

linked by 3D nonlinear spring elements. Through the

validations against the push-out and tensile tests on the

J-hook connectors, the simplified connectors in the FE

model were capable of simulating the shear-slip behav-

ior and axial tension–elongation behavior of the basic

component i.e. a pair of interlocked J-hook connectors

in the SCS sandwich beams. Nevertheless, this simpli-

fication of the interlocked J-hook shear connectors

significantly reduced the total amounts of the elements,

simplified the simulating of the interaction between the

connectors and the concrete core, and avoided the

singular elements used in the FEA. All these advantages

resulted in improving the efficiency of the FEA,

improving the convergence and avoiding the pre-mature

termination of the nonlinear FEA.

Extensive experimental data (20 beam tests) on the

quasi-static tests on the SCS sandwich beams with

J-hook connectors was used to validate the FE model.

Through the validations, it indicates that the developed

FE model was capable of simulating the structural

behavior of the SCS sandwich beams with the J-hook

connectors in terms of ultimate load carrying capacity,

load–central deflection curves, deformed shapes at

different loading levels, relative slip between the steel

face plate the concrete core, and cracks in the concrete

core materials. The errors of the FEA might be caused

by the simulation errors of shear-slip behavior and

tension–elongation behaviors for J-hook connectors,

limited information on the tensile fracture energy of

the ULCC, and ignoring the confining effect of the

concrete to the tensile and shear strength of the J-hook

connectors. The tensile fracture tests on the ULCC

needs to be carried out to provide more information on

the tensile fracture energy of this material.

This developed FE model is not only applied to the

SCS sandwich beams with the J-hook connectors, but

also can be extended to SCS sandwich beams with

other types of interacted connectors. In this paper, nine

SCS sandwich beam with overlapped headed shear

studs were used to confirm the applicability of the FE

model. Through the validation, the FEA agrees well

with the test results. Standard FEA procedures were

recommended. One point needs to be addressed is that

tensile tests are commonly necessary and important for

the new types of connectors used in the SCS sandwich

beam. This is because the necessary information on the

tensile behaviors of them is needed for the FEA.

The FEA extends the studies and offers alternative

nonlinear analysis method on the SCS sandwich

composite beams with J-hook connectors and other

types of interacted connectors.

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Finite element analysis on steel–concrete–steel sandwich beams

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