Interaction Curves for Shear and Bending of Plastic Beams

1957 ◽  
Vol 24 (3) ◽  
pp. 453-456
Author(s):  
P. G. Hodge
Keyword(s):  
General Formula ◽  
Plane Stress ◽  
Elementary Theory ◽  
Beam Theory ◽  
Present Theory ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Interaction Curves

Abstract Interaction curves are presented for plastic beams subject to combined shear and bending. A general formula is obtained and specific curves are drawn for rectangular and I-sections. A simply supported beam with a concentrated load is considered as an example. The results are compared with those of simple beam theory and with available plane-stress solutions. It is concluded that the elementary theory is adequate for height-to-length ratios of less than 0.1, while the present theory is useful in the range from 0.1 to 1.0.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

scholarly journals Analysis of simply supported wood beams at ambient and high temperatures

2018 ◽  
Vol 7 (2.23) ◽  
pp. 180 ◽  
Author(s):  
Elza M M Fonseca ◽  
Pedro J V Gouveia
Keyword(s):  
High Temperatures ◽  
Cross Sections ◽  
Beam Theory ◽  
Sufficient Accuracy ◽  
Load Bearing Capacity ◽  
Concentrated Load ◽  
Standard Methods ◽  
Simply Supported ◽  
Wood Beams ◽  
Safe Load

The main objective of this work is to present a methodology for safety analysis of simply supported wood beams at ambient and high temperatures with a concentrated load at mid-span. Sixteen different beam configurations will be studied. All calculations were conducted according the Eurocode 5, part 1-1 and part 1-2. During this study will be analyzed the safe load bearing capacity according standards and compared with the elastic and plastic load from beam theory. The beam theory can provide sufficient accuracy up to the point of instability. The standard methods are generally conservative and they are suitable to be used for design purposes with safety. The studied beam cross sections will be in glued laminated wood, as yellow birch, with characteristics equals to a Glulam GL28H. 

Solution for the Shear Lag Problem of U-Shaped Beam by Three Bar Stimulation Method

2013 ◽  
Vol 405-408 ◽  
pp. 1161-1165
Author(s):  
Ya Wen An ◽  
Qi Zhen Zheng ◽  
Ya Min Bao
Keyword(s):  
Differential Equation ◽  
Beam Theory ◽  
Shear Lag ◽  
Uniform Load ◽  
Concentrated Load ◽  
Simply Supported ◽  
Shaped Beam ◽  
Relative Stress ◽  
Stimulation Method ◽  
Theoretical Results

three bar stimulation method was adopted to build a differential equation about shear stress for U-shaped beam slab. Relative stress formula for simply supported beam which is subject to uniform load and concentrated load was obtained by solving and deducing differential equation.In order to compare with general beam theory simply,this paper introduced a concept of shear lag coefficient. Finally,combined with a actual example,after compared with measured value and other theoretical results,final result was satisfactory.

scholarly journals Cause Analysis and Countermeasures of Through Shakes in Foamed Concrete Subgrade

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Xianbin Huang ◽  
Chenyang Liu ◽  
Yahong Wangren ◽  
Mingxing Wang ◽  
Yujiao Mei ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Underground Water ◽  
Groundwater Table ◽  
Maximum Displacement ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Load Effect ◽  
The Maximum Principle ◽  
Simply Supported ◽  
Foamed Concrete

The paper presents a new type of material—foamed concrete—adopted for expansion subgrade of the expressway. Intriguingly, the irregular through shakes appear on its top. The method combining the engineering case, theoretical analysis, and numerical simulation is employed to analyze its T-shaped and tree-shaped through shake. The research indicates that when the underground water table is high, cracks are easily seen on the top of step-shape foamed concrete due to buoyancy force. Under the concentrated load effect, the maximum displacement of 27.09 mm is observed on the top of the simply supported beam when elastic modulus is 200 MPa. The maximum principle tensile stress of 0.34 MPa also occurs on the top of the simply supported beam when elastic modulus is 200 MPa and 400 MPa, which is greater than tensile strength of foamed concrete of 0.31 MPa and 0.26 MPa at 7 d and 28 d, respectively. Thus, the adoption of a simply supported beam structure fits site through crack. To avert cracks on the top of foamed concrete in high groundwater table, the antibuoyancy measures should be adopted prior to construction of the upper bearing stratum. The study has expanded the application scope of subgrade and enriched theory of foamed concrete filled in high groundwater table, providing a significant reference to similar projects.

scholarly journals On the deformation of laminated composite and sandwich curved beams

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Pravin V. Avhad ◽  
Atteshamuddin S. Sayyad
Keyword(s):  
Boundary Conditions ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Deformation Analysis ◽  
Solution Technique ◽  
Curved Beams ◽  
Simply Supported ◽  
Fifth Order

Abstract Plenty of research articles are available on the static deformation analysis of laminated straight beams using refined shear deformation theories. However, research on the deformation of laminated curved beams with simply supported boundary conditions is limited and needs more attention nowadays. With this objective, the present study deals with the static analysis of laminated composite and sandwich beams curved in elevation using a new quasi-3D polynomial type beam theory. The theory considers the effects of both transverse shear and normal strains, i.e. thickness stretching effects. In the present theory, axial displacement has expanded up to the fifth-order polynomial in terms of thickness coordinates to effectively account for the effects of curvature and deformations. The present theory satisfies the zero traction boundary condition on the top and bottom surfaces of the beam. Governing differential equations and associated boundary conditions are established by using the Principal of virtual work. Navier’s solution technique is used to obtain displacements and stresses for simply supported beams curved in elevation and subjected to uniformly distributed load. The present results can be benefited to the upcoming researchers.

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