# Derivation and Verification of Laminated Composite T-Beam Theory
###### Abstract
Detailed literature is available on the mechanical properties of the beam, such as warpage, deflection, torsion, and extension when the composite beam is subjected to external forces. Furthermore, various theories and experiments have been proposed to verify whether the beam is subjected to shear force. High-end composite beams are widely used in wing rib structures, four-axis fixed-wing unmanned aerial vehicles (UAVs), and vehicle protective structures. [PERSON] et al. [21] analyzed the bending moment and torsional stiffness of a wing during flight using a finite element at a high aspect ratio. The analyzed wing comprised a composite I-beam, rib, and skin structure. A method was proposed to effectively reduce the bending deformation of airfoils at a high aspect ratio. [PERSON] and [PERSON] [22] optimized the rib of a symmetric laminate using a topology model. The deformation of the material was successfully reduced by 20% through the optimization of different fiber orientations. [PERSON] et al. [23] investigated the strength and rigidity of the carbon fiber composite wings of ultralight UAVs. The static response of the wing was estimated using the proposed geometrically nonlinear finite element model. The data were in good agreement with the experimental results. [PERSON] et al. [24] proposed a multiobjective function surrogate model to optimize the structural design of an unmanned helicopter composite rotor blade. Carbon nanotubes were incorporated as a design variable in the composite material to increase the stiffness of the composite blade. Recently, pollution caused by automobile exhaust emissions has garnered considerable attention. Reducing the use of fuel and weight of vehicles to reduce exhaust emissions has become a global necessity. The use of composite materials in automobiles is increasing because of their higher specific strength than that of steel and the same safety performances of both composite materials based- and conventional automobiles. [PERSON] [25] used CFRP as a side-impact beam and compared the impact energy absorption characteristics of steel and composite beams. The results showed that the composite beam could absorb deformation energy better than the steel beam, and the weight could be reduced by 65%. In addition, the combination of carbon nanotubes and CFRP smart beams has been preliminarily suggested to have better longitudinal, transverse, and shear properties than those of traditional composite materials [26]. This composite smart beam was reported suitable for sensor structures in micro-electro-mechanical systems. In conventional theoretical analysis, the basic assumptions of the beam and laminated plate theories [27; 28] and the effects of shear force, torsion, warpage, and extension are ignored regardless of the length of the beam to simplify the formula and calculation process. Moreover, the cross-sectional nonsymmetric structures of the T-beams have not been explored yet. In this study, the bending stress and deflection analyses of laminated composite T-beams were carried out based on the beam and composite laminate theories. The formula was derived by considering the one-dimensional (1D) and two-dimensional (2D) theories for analysis. The sequence of the composite laminate T-beam was divided into symmetrical and non-symmetrical to identify the center position of the structure. The effective stiffness of the beam was derived by dividing the flange into wide and narrow flanges, according to the beam theory. Subsequently, the maximum deflection and bending stress of the beam were calculated under a uniformly distributed force. Furthermore, the results were compared with that of the FEM to verify the accuracy of the analytical solution. The difference between the analytical and finite element solutions was used to define the applicable range of the proposed laminated composite T-beam theory. This study presents a reliable and fast method to analyze the stress and deflection of composite beams.