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the cross-section. In the very location, the plane of cross-section
(y–z plane) could be approximated as a plane of isotropy. Thus,
the material at the corner location of a CFRP box beam was mod-
elled as a transversely isotropic material with five independent
constants. Details of fibre orientation, fibre volume fraction and
rigorous calculations are necessary for obtaining the exact
strengths. However, this study made simplified assumptions. Prop-
erties in either y and z directions of the corner elements were as-
sumed similar to the CFRP properties in the y direction at the
web (or the z direction at the flange). Also due to transverse isot-
ropy, Gyz = Ey/2(1+l yz), where Gyz is shear modulus in the y–z
plane, Ey is extensional modulus in the y-direction and lyz is Pois-
son’s ratio in the y–z plane.3.3. Concrete
Material properties for concrete are shown in Table 3. Elastic
modulus, Poisson’s ratio and compressive strength (fwhere fc, ec are the compressive stress and strain of concrete, respec-
tively; Ec, E2 are the first and second slopes of a bilinear model,
respectively; n is the curve-shaped parameter (=1.5) and f0 is the ref-
erence plastic stress. E2 and f0, inMPa unit, are respectively given as:where fr is the confinement pressure given as follows:
fr ¼ 2f j
tj
D : ð5Þ
Here, Ej, tj, D, and fj are respectively the hoop-directional exten-
sional modulus of CFRP, thickness of a CFRP box, inside dimension
of the box, and hoop strength of the CFRP. Once these parameters
are known, confined strength of concrete f
and corresponding
ultimate strain (ecu) can be obtained as:
Mirmiran et al. [21] have shown that this model, though proposed
initially for circular sections, can be used for rectangular cross-sec-
tions if the modified confinement ratio (MCR) exceeds 0.15. The
MCR for a box beam with internal corner radius (R) is given as:
Samaan et al.’s confinementmodel was utilized for concrete in com-
pression. Constitutive relation for concrete is shown in Fig. 3. Addi-
tionally, stress–strain relation up to half of the unconfined
compressive strength ð0:5f
cÞ was assumed to be linearly elastic.
4. Finite element analysis (FEA)
FEA was performed for the five beams as tested in the experi-
ment. A general purpose FEA software Marc was utilized in this
study for the analysis of the empty and the concrete-filled CFRP
box beams. A graphical user interface, Mentat, was employed for
mesh generation, graphics, and post processing.
Only one quarter of each beam was modelled taking advantage
of symmetry in two mutually perpendicular vertical planes (Fig. 4).
Symmetric boundary conditions were applied at the two vertical
planes of symmetry. 8-Node 3D solid elements with tri-linear
interpolation were utilized both for concrete and CFRP. Five milli-
metres thick steel plates (width 10 mm) were used both at the
tained from a test. Tensile strength (ft) was adopted based on ACI
code 318-95 [17]:
Concrete behaviour in tension was assumed as linearly elastic. After
principal stress in tension reaches ft, concrete cracks, and softens
linearly until a strain of 5000 l [18] where it completely loses its
tensile load carrying capacity. Tensile softening modulus (Es) was
calculated based on this assumption.
3.4. Concrete confinement model
The behaviour of concrete inside a box structure is different
from that of unconfined concrete. Confinement provided by the
casing structure can significantly enhance both strength and duc-
tility of the concrete. Samaan et al. [19] proposed a concrete con-
finement model for FRP tube confined concrete. Even though this