Magdi Mohareb

Mobilization of Fully Plastic Moment Capacity for Pressurized Pipes

An analytical expression is derived for the prediction of fully plastic moment capacity of pipes subjected to axial loading and internal pressure. The expression is based on the von Mises yield criterion. The expression predicts pipe moment capacities that are in good agreement with full-scale experimental results. A universal nondimensional moment versus effective axial force-pressure interaction diagram is developed for the design of elevated pipe lines.

Exact yield hyper-surface for thin pipes

A yield hyper-surface for pipe sections subjected to combinations of normal forces, internal and external pressure, twisting moments, biaxial bending moments and biaxial shearing forces is developed. The formulation is based on the fully plastic capacity of the pipe as determined by the maximum distorsional energy density yield criterion. The solution is obtained by maximizing a lower bound analysis and yields a yield hyper-surface that is exact within the limitations of the formulation. The developments are expressed as universal non-dimensional relationships suitable for limit states design of elevated pipes, submerged pipes, offshore platforms and structural tubular steel members. Previously established interaction relations for bending moments, axial forces and internal pressure are recovered as a special case of the general solution. The merits of using the yield hyper-surface to characterize generalized plastic hinge behavior in elasto-plastic pipe stress analysis are presented.

Nonsway Model for Lateral Torsional Buckling of Wooden Beams under Wind Uplift

AbstractSimply supported wooden beams nailed to deck boards subjected to wind uplift forces are subjected to compressive stresses at their bottom fibers. Because the restraining action provided by decking is at the top fibers, it is unclear to what extent such restraints are effective in controlling lateral torsional buckling as a possible mode of failure under wind uplift. Present design standards do not have provisions for such cases. Thus, the present study aims to quantify the effect of restraints provided by the deck boards on the lateral torsional buckling capacity of twin-beam-deck systems under wind uplift. Toward this goal, a series of analytical and numerical models were formulated. All models capture the continuous rigid lateral restraint and partial twisting restraint provided by the deck boards. The effects of load type and load position were investigated. The bending stiffness of deck boards was observed to have a significant influence on the lateral torsional buckling capacity of twin-beam-...

Complementary Energy Based Formulation for Torsional Buckling of Columns

A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural b...

Finite-Element Formulation for the Linear Steady-State Response of Asymmetric Thin-Walled Members under Harmonic Forces

AbstractA closed-form solution and finite-element formulation are developed for the dynamic analysis of thin-walled members with asymmetric open sections subjected to harmonic forces. The dynamic equations of motion and associated boundary conditions are derived from Hamilton’s principle. The formulation is based on a generalized Vlasov-Timoshenko beam theory and accounts for the effects of shear deformation caused by bending and warping and translational and rotary inertia effects. It also captures the effects of flexural-torsional coupling caused by cross-sectional asymmetry. From this a general closed-form solution is obtained. A family of shape functions is then developed based on the exact solution of the coupled field equations and is used to formulate a beam finite element. The new element has two nodes with six degrees of freedom per node and successfully captures the coupled bending-torsional static and steady-state responses of asymmetric thin-walled members under harmonic forces. Results based ...

Finite-Element Formulation for the Lateral Torsional Buckling of Plane Frames

AbstractA finite-element formulation is developed for the lateral torsional buckling analysis of plane frames with moment connections consisting of two pairs of welded plate stiffeners. The finite element provides a realistic representation of the partial warping restraint provided by the joint to the adjoining members. The element consists of two nodes with four generalized buckling degrees of freedom per node and is thus devised to interface with two classical beam buckling elements connected at right angles. The new finite element extends the functionality of the classical beam finite element to predict the lateral buckling load for noncollinear structures, such as portal frames. A comparison with results based on shell finite-element analysis demonstrates the ability of the new formulation to reliably predict the lateral buckling resistance of plane frames at a fraction of the computational and modeling cost of shell-based finite-element solutions.

Nonshear Deformable Theory for Analysis of Steel Beams Reinforced with GFRP Plate Closed-Form Solution

AbstractThe present study complements recent published work by developing a general closed-form solution for the analysis of steel beams reinforced with glass-fiber-reinforced plastic (GFRP) plates under general loading and boundary conditions. Comparisons against three-dimensional (3D) finite-element (FE) solutions indicate that the solution accurately captures the transverse-longitudinal and predominantly lateral responses. For predominantly torsional responses, the solution is shown to provide good predictions when the shear modulus of the adhesive layer is weak. For cases where the shear modulus is stiff, the present theory is found to lead to an overly stiff response. Careful examination of strain profiles as predicted by the 3D FE analyses provides valuable insight on the reason for the overly stiff behavior in such cases and shows the necessity of incorporating transverse shear deformation effects into the formulation.

Effect of Eccentric Lateral Bracing Stiffness on Lateral Torsional Buckling Resistance of Wooden Beams

An energy-based solution is developed for the lateral torsional buckling (LTB) analysis of wooden beams with flexible mid-span lateral bracing offset from section mid-height and subjected to uniformly distributed or mid-span point load. The study shows that such beams are prone to two potential buckling modes; symmetric or anti-symmetric. The symmetric mode is shown to govern the capacity of the beam for low bracing stiffness while the anti-symmetric mode governs the capacity when the bracing stiffness exceeds a threshold value. Using the present formulation, the threshold bracing stiffness required to suppress the symmetric mode and maximize the critical moments is directly obtained by solving a special eigenvalue problem in the unknown bracing stiffness. The technique thus eliminates the need for trial and error in standard solutions. A parametric study is conducted to investigate the effect of bracing height, load height, and bracing stiffness on the critical moments. A large database of runs is genera...

Lateral Torsional Buckling of Wooden Beams with Midspan Lateral Bracing Offset from Section Midheight

AbstractAn energy-based solution is developed for the lateral torsional buckling analysis of wooden beams with a midspan lateral brace subjected to uniformly distributed loads or midspan point load...

Finite-Element Formulations for the Distortional Analysis of Wide Flange Steel Beams

AbstractTwo finite-element formulations are developed for the general distortional analysis of beams with monosymmetric sections. In the first formulation, cubic and linear Hermitian polynomials are adopted to interpolate the nodal displacements; whereas in the second formulation, shape functions that exactly satisfy the governing field equations were used. Because the distortional lateral-torsional and the longitudinal-transverse responses are fully uncoupled, separate finite elements were developed for both types of behaviors. A comparison with other finite-element solutions and a recently developed distortional theory established the validity of the present formulations. A study was then performed on the stability and convergence characteristics of both elements. The new elements were then adopted to solve linearly static analysis of simple beams and beams with overhangs. The formulation is shown to reliably capture the difference in behavior between stiffened and unstiffened beams.