Flexural Analysis of Deep Aluminum Beam

Abstract

Many parts of spacecrafts, airplane are made up of aluminum, which are thick or deep in section. For the analysis of deep or thick beams, a trigonometric shear deformation theory is used, taking into account transverse shear deformation effects, is developed. To represent the shear deformation effects, a sinusoidal function is used in displacement field in terms of thickness coordinate. The important feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress conditions on the end surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Using the principle of virtual work governing differential equations and boundary conditions are obtained. The thick aluminum beam is considered for the numerical study to show the accuracy of the theory. The cantilever beam subjected to cosine loads is examined using the present theory. Results obtained are discussed with those of other theories.