Case Study of the Effect of Combined Axial and Lateral Loadings on the Critical Buckling Capacity of Piping Supports

Snubbers are used in industry to restrain piping in dynamic events which can see significant axial loading as well as lateral acceleration. Snubbers are often employed with an extension when required to bridge gaps between the piping and building structure. As a result, they are susceptible to buckling instability issues. The pipe support and restraint design by analysis buckling criteria for supports given within the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 1, Subsection NF is investigated to determine the behavior of snubber assemblies under combined axial and lateral loadings. Four types of analyses are performed on the assemblies under the action of axial loading to demonstrate finite element and closed form solutions. These include the following: linear Eigen buckling, nonlinear second order large deformation method, energy method and Euler Bernoulli beam theory. In addition, a variety of snubber assembly sizes are subjected to combined axial and lateral loading in the form of multiple magnitudes of lateral acceleration. The behavior was analyzed by the Euler Bernoulli beam theory and nonlinear second order large deformation method. The techniques of each method are compared providing explanations of the assumptions taken, relevant limitations and recommended applications.

Uplift Deformation of the Bottom Plate of the Cylindrical Shell Tanks Under Steady-State Response of Tank Rocking Motion

The uplift phenomenon of a flat-bottom cylindrical shell tank is a long-term unsolved problem. In this study, uplift deformation of a tank bottom plate calculated by an explicit finite element analysis (refer to PVP2016-63916) is observed, and a hand calculating model based on Euler–Bernoulli beam theory is examined by comparing with the results of the numerical analysis. First, this study analyzes the results of uplift displacement and uplift width calculated by the FE analysis. Then, the results of the relationship between the uplift displacement and the uplift width are observed. Moreover, comparing the results of the maximum uplift width of a thick bottom plate case and a thin bottom plate case, trends of the maximum uplift width that depends on the thickness of the tank bottom plate are obtained. Seconds, this study tries to verify the hand calculating model based on Euler–Bernoulli beam theory. Compering the results of the deformation of the tank bottom plate calculated by the hand calculation and the FE analysis, accuracy of the hand calculating model is examined. The comparison implies that the hand calculating model may be able to estimate uplift deformation of the tank bottom plate until the uplift displacement of the juncture reaches some height even though the geometrical nonlinearity is not considered.

Estimation of damping in riveted short cantilever beams

In layered and riveted structures, vibration damping happens because of a micro slip that occurs because of a relative motion at the common interfaces of the respective jointed layers. Other parameters that influence the damping mechanism in layered and riveted beams are the amplitude of initial excitation, overall length of the beam, rivet diameter, overall beam thickness, and many layers. In this investigation, using the analytical models such as the Euler–Bernoulli beam theory and Timoshenko beam theory and half-power bandwidth method, the free transverse vibration analysis of layered and riveted short cantilever beams is carried out for observing the damping mechanism by estimating the damping ratio, and the obtained results from the Euler–Bernoulli beam theory and Timoshenko beam theory analytical models are validated by the half-power bandwidth method. Although the Euler–Bernoulli beam model overestimates the damping ratio value by a very less fraction, both the models can be used to evaluate damping for short riveted cantilever beams along with the half-power bandwidth method.

Rail Joint Model Based on the Euler-Bernoulli Beam Theory

In this paper, a rail joint model consisting of three Euler-Bernoulli beams connected via a Winkler foundation is proposed in order to point out the influence of the joint gap length upon the stiffness of the rail joint. Starting from the experimental results aiming the stiffness of the rail joint, the Winkler foundation stiffness of the model has been calculated. Using the proposed model, it is shown that the stiffness of the rail joint of the 49 rail can decreases up to 10 % when the joint gap length increases from 0 to 20 mm.