Reliability Calculation of RC Monopod Structures Under Extreme Wave Loading

2006 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Bending Moment ◽  
Wave Loading ◽  
Compression Zone ◽  
Reliability Calculation ◽  
Eurocode 2 ◽  
Strain Stress ◽  
The Cross ◽  
Stress Relation

In this paper, a general formulation of section-capacities of a circular RC tubular cross-section is first presented. It is assumed that the strain-stress relation of the concrete in the compression zone is simply modelled as bilinear function with ultimate values given in Eurocode 2, and the concrete works only in the compression zone. Tension stresses of the cross-section are carried by the reinforcement. Having presented a general formulation of extreme bending moment and axial force of a RC monopod offshore tower under wave loading, uncertainties in both section capacities and loading terms are presented. Then, a reliability calculation of the cross-section is performed. In this calculation, the balance of the axial force is used to determine concrete compression zone during the reliability iteration and the failure function is defined on the basis of the section capacity- and applied bending moments. Variation of the reliability index with various parameters is investigated and most sensitive uncertainty variables are identified.

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 INTERACTION DIAGRAMS AXIAL FORCE-BENDING MOMENT FOR FIRE EXPOSED STEEL-CONCRETE COMPOSITE SECTIONS

2016 ◽  
Author(s):  
Milivoje Milanovic ◽  
Meri Cvetkovska
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Axial Force ◽  
Bending Moment ◽  
Cross Sectional ◽  
Load Bearing ◽  
Composite Columns ◽  
Interaction Diagram ◽  
Steel Sections ◽  
The Cross

The bearing capacity of the column cross section can be determined from the interaction diagram moment-axial force (M–N). Fire induced temperatures cause reduction of the load-bearing characteristics of the constitutive materials, steel and concrete, and this effect directly reflects on the reduction of the axial force and the bending moment that could be accepted by the column cross section, respectively the interaction diagram of the column cross section is changed. The load bearing capacity of the steel-concrete composite columns exposed to fire from all four sides and loaded by axial force and uni-axial or bi-axial bending moments, was estimated on the basis of the changes in the interaction diagrams moment-axial force amd the results are presented in this paper. Different types of composite columns made of totally or partially encased steel sections, or concrete filled hollow sections were analyzed and a detailed discussion on the effects of the shape of the cross section and the cross sectional dimensions are presented.

scholarly journals Rational Choice of Reinforcement of Reinforced Concrete Frame Corners Subjected to Opening Bending Moment

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3438
Author(s):  
Michał Szczecina ◽  
Andrzej Winnicki
Keyword(s):  
Cross Section ◽  
Bending Moment ◽  
Plasticity Model ◽  
Reinforced Concrete Frame ◽  
Moment Frame ◽  
Concrete Frame ◽  
Rational Reinforcement ◽  
Eurocode 2 ◽  
Analysis Of Results

This paper discusses a choice of the most rational reinforcement details for frame corners subjected to opening bending moment. Frame corners formed from elements of both the same and different cross section heights are considered. The case of corners formed of elements of different cross section is not considered in Eurocode 2 and is very rarely described in handbooks. Several reinforcement details with both the same and different cross section heights are presented. The authors introduce a new reinforcement detail for the different cross section heights. The considered details are comprised of the primary reinforcement in the form of straight bars and loops and the additional reinforcement in the form of diagonal bars or stirrups or a combination of both diagonal stirrups and bars. Two methods of static analysis, strut-and-tie method (S&T) and finite element method (FEM), are used in the research. FEM calculations are performed with Abaqus software using the Concrete Damaged Plasticity model (CDP) for concrete and the classical metal plasticity model for reinforcing steel. The crucial CDP parameters, relaxation time and dilatation angle, were calibrated in numerical tests in Abaqus. The analysis of results from the S&T and FE methods allowed for the determination of the most rational reinforcement details.

Non-Linear Analysis of Rheological Effects in Slender Composite Columns

2014 ◽  
Vol 578-579 ◽  
pp. 389-395
Author(s):  
E. Fenollosa ◽  
Ivan Cabrera ◽  
Ana Almerich-Chulia
Keyword(s):  
Axial Force ◽  
Bending Moment ◽  
Order Effects ◽  
Analysis Software ◽  
Composite Columns ◽  
Long Run ◽  
Eurocode 2 ◽  
Lateral Displacements ◽  
Slender Columns ◽  
Effects Assessment

A thorough analysis of slender columns under axial force and bending moment requires second order effects assessment. Concrete’s creep is one of the factors that increase lateral displacements of the bar in the long run. This phenomenon propitiates the instability and reduces its bearing capacity. This paper shows a procedure for assessing rheological effects based on Eurocode 2 method. This procedure will be added to structural analysis software which takes into consideration geometrical and mechanical non-linearity. As an example interaction diagrams for concrete-encased composite columns with different slenderness values are obtained. These diagrams will demonstrate that rheological effects have a greater influence as axial force eccentricity and slenderness values increase.

scholarly journals VII.—Rupture Stresses in Beams and Crane Hooks.

1914 ◽  
Vol 50 (1) ◽  
pp. 211-223
Author(s):  
Angus R. Fulton
Keyword(s):  
Compressive Stress ◽  
Cross Section ◽  
Bending Moment ◽  
Neutral Axis ◽  
Sectional Area ◽  
Inverse Proportion ◽  
Direct Loading ◽  
The Cross ◽  
External Forces ◽  
Distribution Of Stress

CONCLUSIONS1. It may be taken as conclusive that the final distribution of stress at rupture point in a member subjected to an external bending moment is a rectangular one, unless where the cohesion of adjacent layers is not sufficient to withstand the shear induced by the resisting moment of the section.2. That, provided shear does not take place, the neutral axis moves always to the position which reduces the summation of the tensile and compressive stress areas, across a section, to the equilibrant of the external forces. (In the case of a beam this reduces to zero; in that of a hook, at the principal section to the suspended weight.)3. That the total resisting moment of these stresses must be equal to the external bending moment as measured to the neutral axis at rupture point, but that these balancing moments do not differ materially from those measured to an axis obtained by dividing the sectional area into tensile and compressive stress areas which are in inverse proportion to the magnitude of their respective ultimate direct stresses.The advantage of these formulæ are important. It is possible to indicate with certainty the magnitude of the load which will cause rupture in a beam or a hook provided there is known the point of application or the effective arm of the load, the cross-section of the beam or hook, and the breaking strengths of the material when subjected to the different forms of direct loading.

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 PLASTIC DEFORMATIONS OF STEEL FRAME: STATICS AND DYNAMICS

2010 ◽  
Vol 2 (3) ◽  
pp. 101-105 ◽  
Author(s):  
Vytautas Kargaudas ◽  
Nerijus Adamukaitis
Keyword(s):  
Dynamic Analysis ◽  
Cross Section ◽  
Axial Force ◽  
Bending Moment ◽  
Transverse Force ◽  
Steel Frame ◽  
Plastic State ◽  
Strain Diagram ◽  
Plastic Deformations ◽  
Elastic Plastic

When all deformations of a column are elastic, transverse deflections of the column depend on transverse force and axial displacements depend on axial force only. These classical dependences are unsuitable for elastic-plastic deformations. Plastic deformations develop in columns when steel frame is influenced by extreme action. When a steel column is in the elastic-plastic state, the distribution of elastic and plastic deformations in the cross-section depends on both the bending moment and compressing force. The ideal elastic-plastic material is assumed in this investigation (Prandtl stress – strain diagram). If the shape of the column section is double tee, flange width is neglected with respect to web height, but the area of the flange cross-section is assumed a constant. Single-sided or double-sided yield depends on the moment and force, and therefore curvature and the axial strain of the column can be calculated when yielding dependences are determined. Transverse and axial displacements of the highest point of the column are deduced by integration and depend on two arguments: bending force and axial force. These dependences are essentially non-linear, so linear approximations can be assessed for some vicinity of axial force and bending moment values. When axial force is a constant and transverse force increases, both axial and transverse displacements tend to increase. If transverse force is a constant and axial force increases, both displacements increases but dependence lines remain different and depend on cross-section shape parameter equal to the ratio of the flange area and the area of the whole cross-section. A distinguished feature of plastic deformations is dependence on the history of loading a frame of which can be selected in an arbitrary way by an investigator if a quasi-static solution is under examination. The loading of a frame and inertia forces have to be deduced if dynamic analysis is studied. Not only the ultimate result but also the way of approaching a plastic piston – plastic hinge is important. The bended and compressed column is the structure when inelastic dynamic analysis is really important.

scholarly journals Non-linear Analysis of Slender High Strength Concrete Column

2019 ◽  
Vol 5 (7) ◽  
pp. 1440-1451
Author(s):  
Ernesto Fenollosa ◽  
Iván Cabrera ◽  
Verónica Llopis ◽  
Adolfo Alonso
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Axial Force ◽  
High Strength Concrete ◽  
Bending Moment ◽  
High Strength ◽  
Concrete Columns ◽  
Strength Concrete ◽  
The Moment ◽  
High Strength Concrete Columns

This article shows the influence of axial force eccentricity on high strength concrete columns design. The behavior of columns made of normal, middle and high strength concrete with slenderness values between 20 and 60 under an eccentric axial force has been studied. Structural analysis has been developed by means of software which considers both geometrical and mechanical non-linearity. The sequence of points defined by increasing values of axial force and bending moment produced by eccentricity has been represented on the cross-section interaction diagram until failure for each tested column. Then, diagrams depicting the relationship between failure axial force and column's slenderness have been drawn. The loss of bearing capacity of the member for normal and middle strength columns when compared with the bearing capacity of their cross-section is more noticeable as axial force eccentricity assumes higher values. However, this situation reverses for high strength columns with high slenderness values. On the basis of results obtained, the accuracy level for the moment magnifier method was checked. Despite the good concordance in most of the cases, it was verified that the moment magnifier method leads to excessively tight results for high strength concrete columns with high slenderness values. In these specific cases, a coefficient which amends the column rigidity is proposed so as to obtain safer values.

scholarly journals The Ovalisation of Steel Circular Hollow Sections under Bending

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Manahel Sh. Khalaf ◽  
Amer M. Ibrahim
Keyword(s):  
Cross Section ◽  
Local Buckling ◽  
Bending Moment ◽  
Thickness Ratio ◽  
Experimental Results ◽  
Experimental Program ◽  
Specimen Length ◽  
Specimen Cross Section ◽  
The Cross

This paper investigates the ovalisation behavior of the Steel Circular Hollow Sections (CHSs) when subjected to bending moment. The experimental program included testing of ten specimens in four groups in order to examine the influence of changing the diameter, thickness, length and the presence of openings on the ovalisation phenomenon of these specimens.The experimental results showed that the ovalisation of the specimen cross-section appears clearly when the diameter to thickness ratio (D/t) is ranging from 17 to 50, while the ovalisation of the specimens that have D/t ratio greater than 50 is very little or unclear because the instability of these specimens are controlled by the local buckling. In addition, the change of the specimen length and the presence of openings didn’t cause the cross-section ovalisation

Part II. The Flattening of Monocoque Cylinders

1938 ◽  
Vol 42 (328) ◽  
pp. 302-319
Keyword(s):  
Variational Method ◽  
Potential Energy ◽  
Cross Section ◽  
Radial Displacement ◽  
Bending Moment ◽  
Experimental Investigations ◽  
Pure Bending ◽  
Centre Line ◽  
Thin Walled ◽  
The Cross

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

Sign in / Sign up

Export Citation Format

Share Document