The Effect of Shear and Normal Forces on the Fully Plastic Moment of a Beam of Rectangular Cross Section

1961 ◽  
Vol 28 (2) ◽  
pp. 269-274 ◽  
Author(s):  
B. G. Neal
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Lower Bounds ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Shear Forces ◽  
Normal Forces ◽  
Interaction Relations

The value of the fully plastic moment of a beam is known to be reduced by both normal and shear forces, and their separate effects have been studied in some detail, but little attention has been paid to the reduction caused by normal and shear forces acting simultaneously. This problem is discussed with reference to a cantilever beam of rectangular cross section subjected to both shear and normal forces at the free end. Upper and lower bounds to the collapse load are determined, and the results are presented in the form of interaction relations between the shear and normal forces and the bending moment at the clamped end of the cantilever at collapse.

On the Determination of Stresses and Deflections for Anisotropic Homogeneous Cantilever Beams

1976 ◽  
Vol 43 (1) ◽  
pp. 75-80 ◽  
Author(s):  
S. Nair ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Lower Bounds ◽  
Basic Assumption ◽  
Rectangular Cross Section ◽  
Upper And Lower Bounds ◽  
Cantilever Beams ◽  
Normal Stresses ◽  
Complementary Energy ◽  
Minimum Potential

We analyze the effect of anisotropy on beam flexibility by the derivation of upper and lower bounds, through use of the principles of minimum potential and complementary energy, for the load-deflection ratios of narrow rectangular cross-section cantilever beams. The basic assumption is a class of stress-strain relations of such nature that normal strains are caused not only by normal stresses but also by shearing stresses, and shearing strains are caused not only by shearing stresses but also by normal stresses.

Nonlinear Creep Deformations of Columns of Rectangular Cross Section

1959 ◽  
Vol 26 (4) ◽  
pp. 517-525
Author(s):  
H. H. Bleich ◽  
O. W. Dillon
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Critical Time ◽  
Bending Moment ◽  
Qualitative Reasoning ◽  
Upper And Lower Bounds ◽  
Nonlinear Creep ◽  
Essential Point ◽  
History Of ◽  
Creep Deformations

Abstract Creep deformations of columns of rectangular cross section are studied for the case of materials following the nonlinear law ϵ̇ = (1/E) σ̇ + λσk. The essential point of the paper is the following: The time rate of the curvature κ̇ of an element of a bar loaded by a constant force P and an increasing bending moment M(t) has bounds, which depend on P and on the instantaneous values of M and Ṁ, but not on the history of M. In combination with the collocation method, this permits the formulation of ordinary differential equations for upper and lower bounds on the deformations. Closed solutions for the critical time are obtained for one bound, while the other requires numerical integration. The bounds which are a function of the initial eccentricity are reasonably close and are presented in tables and graphs. By qualitative reasoning it is further shown that the location of the actual critical time with respect to the two bounds is governed by the ratio of the column load P and the nominal Euler buckling load PE of the column if it were elastic.

Bearing Capacity of Structures Made of Materials with Different Tensile and Compression Strengths

2019 ◽  
Vol 968 ◽  
pp. 200-208
Author(s):  
Mykola Soroka
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Limit State ◽  
Analytical Calculation ◽  
Bending Moment ◽  
Maximum Load ◽  
Longitudinal Force ◽  
Plastic State ◽  
Limiting State ◽  
Tension And Compression

The paper considers the problem of the ultimate load finding for structures made of a material with different limits of tensile strength and compression. The modulus of elasticity under tension and compression is the same. It is assumed that upon reaching the ultimate strength, the material is deformed indefinitely. The calculations use a simplified material deformation diagram — Prandtl diagrams. The limiting state of a solid rectangular section under the action of a longitudinal force and a bending moment is considered. The dependences describing the boundary of the strength of a rectangular cross section are obtained. Formulas allowing the calculation of the values of the limit forces and under the action of which the cross section passes into the plastic state are derived. Examples of the analytical calculation of the maximum load for the frame and two-hinged arch are given. An algorithm is proposed and a program for calculating arbitrary flat rod systems according to the limit state using the finite element method is compiled. The proposed algorithm does not involve the use of iterative processes, which leads to an exact calculation of the maximum load within the accepted assumptions.

On the Stress Intensity Factors of Cracked Beams for Structural Analysis

2011 ◽  
Vol 488-489 ◽  
pp. 379-382 ◽  
Author(s):  
Erasmo Viola ◽  
Yong Li ◽  
Nicholas Fantuzzi
Keyword(s):  
Stress Intensity ◽  
Structural Analysis ◽  
Cross Section ◽  
Stress Intensity Factors ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Intensity Factors ◽  
Close Approximation ◽  
Shear Forces ◽  
Cracked Beams

In this paper simple engineering methods for a fast and close approximation of stress intensity factors of cracked beams and bars, subjected to bending moment, normal and shear forces, as well as torque, are examined. As far as the circular cross section is concerned, comparisons are made on the base of numerical calculations. The agreement between the present results and those previously published is discussed. New formulae for calculating the stress intensity factors are proposed.

scholarly journals NUMERICAL INVESTIGATION OF THE ELASTIC-PLASTIC LINEAR HARDENING STRESS-STRAIN STATE OF THE FRAME ELEMENT CROSS-SECTION

2016 ◽  
Vol 8 (3) ◽  
pp. 94-100
Author(s):  
Andrius Grigusevičius ◽  
Gediminas Blaževičius
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Software Environment ◽  
Stress Strain ◽  
Hardening Material ◽  
Frame Element ◽  
Nonlinear Stress

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments.

scholarly journals Cross-Sectional Analysis of the Resistance of Rc Members Subjected to Bending With/without Axial Force

2021 ◽  
Author(s):  
Marek Lechman
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Nonlinear Stress ◽  
The Cross ◽  
Sectional Analysis

The paper presents section models for analysis of the resistance of RC members subjected to bending moment with or without axial force. To determine the section resistance the nonlinear stress-strain relationship for concrete in compression is assumed, taking into account the concrete softening. It adequately describes the behavior of RC members up to failure. For the reinforcing steel linear elastic-ideal plastic model is applied. For the ring cross-section subjected to bending with axial force the normalized resistances are derived in the analytical form by integrating the cross-sectional equilibrium equations. They are presented in the form of interaction diagrams and compared with the results obtained by testing conducted on RC columns under eccentric compression. Furthermore, the ultimate normalized bending moment has been derived for the rectangular cross-section subjected to bending without axial force. It was applied in the cross-sectional analysis of steel and concrete composite beams, named BH beams, consisting of the RC rectangular core placed inside a reversed TT welded profile. The comparisons made indicated good agreements between the proposed section models and experimental results.

scholarly journals Bounds for the Collapse Load of a Beam Compressed by Three Dies

1956 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
W Freiberger
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Plastic Yielding ◽  
Plane Plastic

This paper deals with the problem of the plastic deformation of a beam under the action of three perfectly rough rigid dies, two dies applied to one side, one die to the other side of the beam, the single die being situated between the two others. It is treated as a problem of plane plastic flow. Discontinuous stress and velocity fields are assumed and upper and lower bounds for the pressure sufficient to cause pronounced plastic yielding determined by limit analysis.

The Limit Design of a Transversely Loaded Square Grid

1952 ◽  
Vol 19 (2) ◽  
pp. 153-158
Author(s):  
Jacques Heyman
Keyword(s):  
Exact Solutions ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Transverse Loading ◽  
Square Grid ◽  
Modes Of Failure ◽  
Combined Actions

Abstract An earlier paper discussed the derivation of a breakdown criterion for beams subjected to combined bending and torsion. The present paper deals with the limit design of grids, formed by two sets of parallel beams intersecting at right angles, subjected to transverse loading at the joints. This form of loading introduces both bending and twisting moments in the beams, and modes of failure under these combined actions are investigated. Exact solutions are determined for some simple grids, but general methods are demonstrated which lead to upper and lower bounds on the collapse load.

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