scholarly journals THE DESIGN BENDING MOMENT ON THE BOUNDARIES OF A FIXED END TRIANGULAR SLAB AND A FIXED END TANGENTIAL QUADRILATERAL SLAB SUBJECTED TO UNIFORM LOAD

2013 ◽  
Vol 78 (690) ◽  
pp. 1423-1428
Author(s):  
Keisuke NOMURA ◽  
Shigehiro MOROOKA ◽  
Taiichi TSUJII ◽  
Yuuki IMAI
Keyword(s):  
Bending Moment ◽  
Uniform Load ◽  
Fixed End

Estimation of the severity of damage produced by a transverse crack

2020 ◽  
Vol 65 (1) ◽  
pp. 137-144
Author(s):  
Marius-Vasile Pop
Keyword(s):  
Transverse Crack ◽  
Bending Moment ◽  
Cantilever Beams ◽  
Trend Line ◽  
The Real ◽  
Symmetrical Deformation ◽  
Frequency Drop ◽  
Equidistant Points ◽  
Fixed End ◽  
Crack Position

This paper presents a method to find the severity of a crack for cantilever beams that can be used to estimate the frequency drop due to the crack. The severity is found for the crack located at the location where the biggest curvature (or bending moment) is achieved. Because the fixing condition does not permit a symmetrical deformation around the crack, the apparent severity is smaller as the real one. The latter is found by the estimated value of the trend-line at the fixed end, it being constructed on points that consider the crack position (equidistant points in the proximity of the fixed end) and the resulted deflections.

scholarly journals Analytical Method for Geometric Nonlinear Problems Based on Offshore Derricks

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 610
Author(s):  
Chunbao Li ◽  
Hui Cao ◽  
Mengxin Han ◽  
Pengju Qin ◽  
Xiaohui Liu
Keyword(s):  
Analytical Method ◽  
Bending Moment ◽  
Nonlinear Problems ◽  
Weather Conditions ◽  
Order Effect ◽  
Practical Calculation ◽  
Geometrically Nonlinear ◽  
Uniform Load ◽  
Safety Research ◽  
Calculation Results

The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the local stability of marine derrick and propose an analytical method for geometrically nonlinear problems. The rod in the derrick is simplified as a compression rod with simply supported ends, which is subjected to transverse uniform load. Considering the second-order effect, the differential equations were used to establish the deflection, rotation angle, and bending moment equations of the derrick rod under the lateral uniform load. This method was defined as a geometrically nonlinear analytical method. Moreover, the deflection deformation and stability of the derrick members were analyzed, and the practical calculation formula was obtained. The Ansys analysis results were compared with the calculation results in this paper.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

Elastic Analysis of Beam-Support Impact

1985 ◽  
Vol 107 (1) ◽  
pp. 64-67 ◽  
Author(s):  
M. A. Salmon ◽  
V. K. Verma ◽  
T. G. Youtsos
Keyword(s):  
Analytical Solutions ◽  
Beam Theory ◽  
Bending Moment ◽  
General Purpose ◽  
Euler Beam ◽  
Piping Systems ◽  
Euler Beam Theory ◽  
Impact Problems ◽  
Fixed End ◽  
Spring Support

The effect of gaps present in the seismic supports of nuclear piping systems has been studied with the use of such large general-purpose analysis codes as ANSYS. Exact analytical solutions to two simple beam-impact problems are obtained to serve as benchmarks for the evaluation of the ability of such codes to model impact between beam elements and their supports. Bernoulli-Euler beam theory and modal analysis are used to obtain analytical solutions for the motion of simply supported and fixed-end beams after impact with a spring support at midspan. The solutions are valid up to the time the beam loses contact with the spring support. Numerical results are obtained which show that convergence for both contact force and bending moment at the point of impact is slower as spring stiffness is increased. Finite element solutions obtained with ANSYS are compared to analytical results and good agreement is obtained.

Analytic Solution of Single Span Beam under Non Uniform Load

2012 ◽  
Vol 166-169 ◽  
pp. 3035-3038
Author(s):  
Qing Xing Feng ◽  
Chen Qu
Keyword(s):  
Analytic Solution ◽  
Bending Moment ◽  
Structure Design ◽  
Uniform Load ◽  
Symmetric Load

During the process of structure design, non uniform load on beam usually is considered as similar uniform load. Some analytic solution formulas of bending moment about beams acted on symmetric load are deduced. Table of equivalent uniform load coefficient according to the principle of bending moment equivalency is listed. The feasibility and beware are also discussed.

scholarly journals Simplified Design Equations for a Class of Rhombic Auxetic Plates

2018 ◽  
Vol 206 ◽  
pp. 01009 ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Bending Moment ◽  
Empirical Models ◽  
Simplified Model ◽  
Bending Moments ◽  
Uniform Load ◽  
Load Curve ◽  
Simply Supported ◽  
Exact Data ◽  
Second Derivatives ◽  
Auxetic Materials

Equations for solving the deflection and bending moments of rhombic plates by exact method are known to be highly tedious. A set of simplified equations is developed for design purposes of such simply supported plates under uniform load. Curve-fitting from exact data allows the deflection and its second derivatives, evaluated at the plate centre, to be expressed in greatly simplified and yet sufficiently accurate empirical models for thin rhombic plates. Using the simplified model, it is shown that the maximum bending moment can be reduced by using auxetic materials. By including the effects of shear deformation for thick rhombic plates, it is demonstrated that the ratio of shear-to-bending deformation decreases as the rhombic plate approaches a square shape and as the plate’s Poisson’s ratio becomes more negative.

Buckling Analysis of Two-Span Continuous Beams with Lateral Elastic Brace under Uniform Load

2010 ◽  
Vol 163-167 ◽  
pp. 641-645 ◽  
Author(s):  
Wen Fu Zhang ◽  
Hai Yan Sui ◽  
Zong Wang ◽  
Jing Ji
Keyword(s):  
Potential Energy ◽  
Mathematical Optimization ◽  
Bending Moment ◽  
Variation Method ◽  
Uniform Load ◽  
Optimization Analysis ◽  
Total Potential ◽  
Minimum Potential ◽  
Energy Variation Method ◽  
The Relationship

Both total potential energy and buckling equation of two-span continuous beam with lateral elastic brace under uniform load are deduced, based on energy variation method and the principle of minimum potential energy. Buckling of H-beams is simulated by ANSYS software, then compared to theoretical value, validated its rationality. High precision buckling moment formula is regressed using 1stOpt which is a famous mathematical optimization analysis software in China. The relationship between lateral brace stiffness and buckling moment is obtained. Results: with lateral brace stiffness increases, critical bending moment of beam increases within up-limit, e.g. when lateral brace stiffness increases to certain extent, buckling moment no longer increases.

Bending of an Annularly Loaded Square Plate With a Central Circular Hole

1982 ◽  
Vol 104 (3) ◽  
pp. 544-550
Author(s):  
L. K. Oja ◽  
G. L. Kinzel ◽  
A. W. Leissa
Keyword(s):  
Circular Hole ◽  
Systematic Approach ◽  
Bending Moment ◽  
Outer Edge ◽  
Loading Conditions ◽  
Uniform Load ◽  
Approximate Methods ◽  
Point Matching ◽  
Plate Size ◽  
Plate Bending Problem

Although uniformly loaded square plates with round holes are analyzed in several references, a systematic approach to the analysis for a ring load does not appear to have been presented before. As in the case of the uniform load, the exact solution to the plate bending problem for an annular load about a central circular hole cannot be developed in closed form; however, accurate approximate methods can be developed. The method employed in this paper uses least-squares point-matching for the boundary conditions along the straight edges and the singularity-function approach for the radially discontinuous loading conditions. Deflection and bending-moment results in the form of curves are presented for selected ratios of hole diameter to plate size and for different annular loading conditions. Both simply supported and clamped boundaries at the outer edge are considered while the inner edge is assumed to be free.

Sign in / Sign up

Export Citation Format

Share Document