Bending of Shear Deformable Plates Resting on Winkler Foundations According to Trigonometric Plate Theory

A trigonometric plate theory is assessed for the static bending analysis of plates resting on Winkler elastic foundation. The theory considers the effects of transverse shear and normal strains. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the traction free conditions at the top and bottom surfaces of the plate without using shear correction factors. The governing equations of equilibrium and the associated boundary conditions of the theory are obtained using the principle of virtual work. A closed-form solution is obtained using double trigonometric series. The numerical results are obtained for flexure of simply supported plates subjected to various static loadings. The displacements and stresses are obtained for three different values of foundation modulus. The numerical results are also generated using higher order shear deformation theory of Reddy, first order shear deformation theory of Mindlin, and classical plate theory for the comparison of the present results

ANALYSIS AND DESIGN OF THREE LEGGED 400KV DOUBLE CIRCUIT STEEL TRANSMISSION LINE TOWERS

ABSTRACT Transmission line towers constitute about 28 to 42 percent of the cost of the transmission line. The increasing demand for electrical energy can be met more economically by developing different light weight configurations of transmission line towers. The present work describes the analysis and design of three legged self-supporting 400 kV double circuit steel transmission line towers models with an angle and tube sections. In this study constant loading parameters including wind forces as per IS: 802 (1995) are taken into account in both models. The efforts have been made to do 3D analysis of tower considering all the members of the space truss as primary members. STAAD. Pro program has been used to analysis and design the members of 400 kV double circuit tower have deviation angle 2 degree. The maximum sag and tension calculations of conductor and ground wire as per IS: 5613 (Part 3/ Sec 1) 1989. The comparative study is presented here with respective to axial forces, deflections, maximum sectional properties, critical loading conditions between both models of towers. The study shows that tower with tube sections are efficient and have better forceweight ratio including 20.6% saving in weight of steel with tubes against steel with angles in three legged transmission line tower

Buckling analysis of thick isotropic plates by using exponential shear deformation theory

In this paper, an exponential shear deformation theory is presented for the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane forces. The theory accounts for a parabolic distribution of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations and associated boundary conditions of the theory are obtained using the principle of virtual work. The simply supported thick isotropic square plates are considered for the detailed numerical studies. A closed form solutions for buckling analysis of square plates are obtained. Comparison studies are performed to verify the validity of the present results. The effects of aspect ratio on the critical buckling load of isotropic plates is investigated and discussed

A refined shear deformation theory for flexure of thick beams

A Hyperbolic Shear Deformation Theory (HPSDT) taking into account transverse shear deformation effects, is used for the static flexure analysis of thick isotropic beams. The displacement field of the theory contains two variables. The hyperbolic sine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the shear stress-free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. General solutions of thick isotropic simply supported, cantilever and fixed beams subjected to uniformly distributed and concentrated loads are obtained. Expressions for transverse displacement of beams are obtained and contribution due to shear deformation to the maximum transverse displacement is investigated. The results of the present theory are compared with those of other refined shear deformation theories of beam to verify the accuracy of the theory

Bending Analysis of Thick Isotropic Plates by Using 5th Order Shear Deformation Theory

A 5th order shear deformation theory considering transverse shear deformation effect as well as transverse normal strain deformation effect is presented for static flexure   analysis of simply supported isotropic plate. The assumed displacement field accounts for non-linear variation of in-plane displacements as well as transverse displacement through the plate thickness. The condition of zero transverse shear stresses on the upper and lower surface of plate is satisfied. Hence the present formulation does not require the shear correction factor generally associated with the first order shear deformable theory. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Closed-form analytical solutions for simply supported square isotropic thick plates subjected to single sinusoidal distributed loads are obtained. Numerical results for static flexure analysis include the effects of side to thickness ratio and plate aspect ratio for simply supported isotropic plates. Numerical results are obtained using MATLAB programming. The results of present theory are in close agreement with those of higher order shear deformation theories and exact 3D elasticity solutions

Buckling analysis of thick isotropic plates by using exponential shear deformation theory

In this paper, an exponential shear deformation theory is presented for the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane forces. The theory accounts for a parabolic distribution of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations and associated boundary conditions of the theory are obtained using the principle of virtual work. The simply supported thick isotropic square plates are considered for the detailed numerical studies. A closed form solutions for buckling analysis of square plates are obtained. Comparison studies are performed to verify the validity of the present results. The effects of aspect ratio on the critical buckling load of isotropic plates is investigated and discussed

Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory

This paper presents a variationally consistent an exponential shear deformation theory for the bi-directional bending and free vibration analysis of thick plates. The theory presented herein is built upon the classical plate theory. In this displacement-based, refined shear deformation theory, an exponential functions are used in terms of thickness co-ordinate to include the effect of transverse shear deformation and rotary inertia. The number of unknown displacement variables in the proposed theory are same as that in first order shear deformation theory. The transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate, hence the theory does not require shear correction factor. Governing equations and boundary conditions of the theory are obtained using the dynamic version of principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of proposed theory. Results obtained by using proposed theory are found to be agree well with the exact elasticity results. The objective of the paper is to investigate the bending and dynamic response of thick isotropic square and rectangular plates using an exponential shear deformation theory

Flexural analysis of deep beam subjected to parabolic load using refined shear deformation theory

A trigonometric shear deformation theory for flexure of thick or deep beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy 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 free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick isotropic beams are considered for the numerical studies to demonstrate the efficiency of the theory. It has been shown that the theory is capable of predicting the local effect of stress concentration due to fixity of support. The fixed isotropic beams subjected to parabolic loads are examined using the present theory. Results obtained are discussed critically with those of other theories

Single variable refined beam theories for the bending, buckling and free vibration of homogenous beams

In this paper, single variable beam theories taking into account effect of transverse shear deformation are developed and applied for the bending, buckling and free vibration analysis of thick isotropic beams. The most important feature of the present beam theories is that unlike any other higher order theory, the proposed class of theories contains only one unknown variable and does not require shear correction factor. The displacement field of the present theories is built upon the classical beam theory. The theories account for parabolic distribution of transverse shear stress using constitutive relations, satisfying the traction free conditions at top and bottom surfaces of the beam. Governing differential equation and boundary conditions of these theories are obtained using the principle of virtual work. Results obtained for the displacements, stresses, fundamental frequencies and critical buckling loads of simply supported isotropic solid beams are compared with those obtained by other theories to validate the accuracy of the present theories