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.

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.

Stresses Due to Diametral Forces on a Circular Disk With an Eccentric Hole

1955 ◽  
Vol 22 (2) ◽  
pp. 263-266
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Circular Hole ◽  
Normal Force ◽  
Infinite Plate ◽  
Circular Disk ◽  
Outer Edge

Abstract In this paper stresses in a circular disk with an eccentric circular hole have been determined when the disk is compressed along the line of centers by two equal and opposite forces acting on its outer edge, the inner edge being unstressed. From the results obtained, the solution of the problem of a semi-infinite plate acted on by a concentrated normal force on its straight boundary and containing an unstressed circular hole has been deduced.

An Analysis of Flexural Systems under Arbitrary Distortion and End Loading

1957 ◽  
Vol 61 (559) ◽  
pp. 475-484
Author(s):  
P. J. Midgley
Keyword(s):  
Bending Moment ◽  
Beam Equation ◽  
Loading Conditions

SummaryThe effects of end loading on an arbitrarily distorted flexing beam are investigated, with particular reference to bending moment distributions along the span of the beam, and the effects of lengthwise strains. Cross-spring and “ spider ” type flexural systems are treated in detail. Curves are presented which enable the stiffness and stressing of any flexural system to be calculated for any loading conditions, subject only to the restriction that deflections are small, so that the linearised beam equation may be applied.

Stress Analysis and the Characteristics of T-Shape Bolted Joints Under Tensile Loadings

2005 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Seiichi Hamamoto
Keyword(s):  
Bending Moment ◽  
Theory Of Elasticity ◽  
Bolted Joints ◽  
Load Factor ◽  
Two Dimensional ◽  
Bolted Joint ◽  
Dimensional Theory ◽  
Matching Method ◽  
Point Matching ◽  
Bolt Stress

In designing a bolted joint, it is important to examine the interface stress distribution (clamping effect) and to estimate the load factor, that is the ratio of an additional axial bolt force to a load. In order to improve the clamping effect raised faces of the interface have been used. But these interfaces in bolted joints have been designed empirically and the theoretical grounds are not made clear. In the present paper, in the case of T-shaped flanges with raised faces the clamping effect is analyzed by a two-dimensional theory of elasticity and the point matching method. Then, the load factor is analyzed. Moreover, with the application of the load a bending moment is occurred in bolts and the stress is added due to this bending moment. The bending moment in the bolt is also analyzed. In order to verify these analyses experiments to measure the load factor and the maximum bolt stress were carried out. The values of the load factor and the load when interface start to separate are compared with those of the joints with flat-faces. The analytical results are in fairly good agreements with the experimental ones.

Time History Analysis of Steel Tall Buildings

2014 ◽  
Vol 1025-1026 ◽  
pp. 918-921 ◽  
Author(s):  
Yong Chul Kim ◽  
Sung Won Yoon
Keyword(s):  
Wind Direction ◽  
Time History ◽  
Tall Buildings ◽  
Bending Moment ◽  
Ground Level ◽  
Structural Systems ◽  
Loading Conditions ◽  
Normal Stresses ◽  
History Analysis ◽  
Principal Axes

The results of wind tunnel experiments were used to conduct time history analyses of three conventional square cross-section tall buildings with different structural systems. The primary purpose of the study was the direct comparison of the effects of the wind loads on the steel tall buildings. Time history analyses were conducted by applying local wind forces to the center of each floor. The results showed that, although the bending moments in the ground-level column on the two principal axes were different, the peak normal stresses were almost the same regardless of the structural systems. Similar observations were made regarding the tip displacements. Furthermore, analyses for the various loading conditions revealed that the contribution of the bending moment in the across-wind direction was the largest, followed by that in the along-wind direction. The ratio of the peak normal stresses for different loading conditions were observed to be almost the same regardless of the structural systems.

Characterisation of a Simplified Aeroengine Casing Subjected to a Radial Loading Condition Using FE and Approximate Methods

2006 ◽  
Author(s):  
Sabesan Rajaratnam ◽  
Tom H. Hyde ◽  
Sean B. Leen
Keyword(s):  
High Reliability ◽  
High Stress ◽  
Bending Moment ◽  
Local Stress ◽  
Load Path ◽  
Approximate Methods ◽  
Loading Mode ◽  
Structure Changes ◽  
Extreme Load ◽  
Radial Loading

In general, aeroegine casings may experience an axial force, a bending-moment and radial loading. Under these loads, the high stress regions of these complex aerongine casings will experience local stress and strain concentrations, with various load combinations. The stiffness will also depend on the loading mode. Hence, careful design is required to avoid the various types of failure such as buckling, crack initiation and propagation must be taken into account when designing an aeroengine casing structure. In addition, aerongine casings require extremely high reliability in service and adequate strength under extreme load conditions, i.e. Fan-Blade-Off (FBO) condition, must be demonstrated. Under radial loading of aeroengine casings, which have spoke to shell connections, these are the most likely sites for plastic deformation to occur and cracks to initiate. Also, the load path for each spoke to shell connection within the casing structure changes during loading. Based on these observations, this paper concentrates on the behavior which occurs in spoke to shell connections, referred to as local joints. The intention is first to characterize the local joint behavior and then to incorporate this into a global casing model. The work reported in this paper includes studies of mesh sensitivity, predictions of load path at each local joint under radial load, FE failure loci, upper bound techniques for predicting limit loads and stresses-strains predictions at local casing notches under elastic-plastic and creep situations using approximate notch methods. Hence, the global responses of a casing structure were predicted by utilizing a “repeated local joint” technique in conjunction with simplified global models.

scholarly journals Stress Intensity Factors for a Non-Circular Hole with Inclusion Layer Embedded in a Cracked Matrix

Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Chenchun Chiu ◽  
Shaochen Tseng ◽  
Chingkong Chao ◽  
Jheyuan Guo
Keyword(s):  
Stress Intensity ◽  
Circular Hole ◽  
Composite Structures ◽  
Failure Behavior ◽  
Uniform Load ◽  
Intensity Factors ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
The Matrix ◽  
Stress Functions

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.

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