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model is reported to overestimate the ductility and strength of
concrete, the model is found good to predict the shape of stress–
strain curve [20]. This model, unlikemany other confinementmod-
els, considers the hoop stiffness of FRP and proposes a bilinear con-
finement model as:support and at the transverse load application location to reduce
stress concentration. A vertical constraint was applied at the bot-
tom of the support plate along its centre line. Transverse load
was distributed to all the nodes on top of the loading plate, with
nodes at symmetry plane getting half of the load at rest of the
nodes. Axial load was given as a uniform pressure load at the beam
end. It was applied in such a way that its ratio with mid-span
bending moment was always maintained constant, which was
the case in the experiment too. For instance, axial load in F-04
beam would be increased with an increase in transverse load to
constantly maintain mid-span moment (kN m) to axial force (kN)
ratio of 0.04.
P-delta effect was considered in this study with the help of large
displacement option in the software. Follower force condition was
assumed such that axial force in the form of pressure at the beam
end was treated based on the deformed geometry.
4.1. Contact analysis
Analysis was performed for both perfect bond condition and
slip condition to investigate the interface interaction between con-
crete and CFRP. A contact analysis possesses a provision for slip,
and can be utilized to simulate the slip between concrete and CFRP.
Separate nodes were assigned for concrete and CFRP at the same
location. Friction was also considered in the contact analysis for
studying the interface interaction between concrete and CFRP.
Coulomb friction model [22] was utilized which is given as:
rfr 6 lrn t ð9Þ
where rfr is the tangential (friction) stress, rn is the normal stress
vector, l is the friction coefficient, and t is the unit tangential vector
in the direction of relative sliding velocity. Notations in bold face in
Eq. (9) indicate vectors while a dot is used to indicate the scalar
product of two vectors.
5. Results
This section presents the results of CFRP box beams obtained
from the finite element analysis. Comparison is made between
the experiment and the analysis. Fig. 5 shows the load–deflection
curve for an empty beam. Good correlation is noted, with beam
stiffness from the analysis being within a 10% margin of error of
the experimental stiffness. Fig. 6 shows the comparison of longitu-
dinal strain from the analysis and the experiment in relation to the
transverse load. Both tensile and compressive strains assure a per-
fect agreement with the experiment.复合材料结构
1．介绍
复合材料已成为一个在土木工程的重要建筑材料，每单位重量纤文增强复合材料（FRP）具有非常高的强度和弹性模量。其中一个最早的研究由Fardis和哈利利开展，作为一个具体的梁装与FRP表。随后，不同的研究人员研究了使用FRP约束混凝土[2,3]。这些FRP结构作为膜结构中的工程。在除了这些应用程序外，使用FRP弯曲的应用已逐渐被接受为一种为减少重量和横截面可行的替代钢或钢筋混凝土的结构。
一些研究已经进行了特别束应用的玻璃纤文增强复合材料（GFRP）复合材料[4,5]。最近的一项研究由Hayes和Lesko[6]讨论了一个空的玻璃钢箱组合梁组成的混合故障分析。碳纤文束组成的玻璃纤文的增强层的一些聚合物（CFRP）附着在凸缘。这项研究是有限故障分析，也没有澄清的弯曲和剪切的行为。
梁和柱应用的FRP材料已被认为是混凝土填充的FRP管或箱式结构的形式。由于FRP材料的各向异性的性质，大部分的经典理论的假设的基础上的材料各向同性不能应用于为分析的FRP制的箱形梁。此外，接口相和混凝土互作用的FRP壳体结构内的响应是必不可少的机制，以澄清一个具体的FRP组合梁。