scholarly journals Limit analysis of beams under combined stresses

2008 ◽  
Vol 6 (1) ◽  
pp. 75-88 ◽  
Author(s):  
Marina Mijalkovic ◽  
Marina Trajkovic ◽  
Bojan Milosevic
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Shear Force ◽  
Pure Shear ◽  
Bending Moment ◽  
Beam Cross Section ◽  
Combined Stress ◽  
Pure Bending ◽  
Combined Stresses

The problem of the determination of limit bearing capacity of beam cross section under pure bending, eccentric tension, pure shear, as well as combined stress is considered in this paper. The influence functions of the bending moment and axial force, as well as the bending moment, axial and shear force on the cross section limit bearing capacity in case of rectangular and I beam cross section are derived.

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.

THE ANALYSIS OF SHEAR STRENGTH OF FLEXURAL RC ELEMENTS ACCORDING TO EC2 AND STR / LENKIAMŲJŲ GELŽBETONINIŲ ELEMENTŲ ĮSTRIŽOJO PJŪVIO STIPRUMO PAGAL STR IR EC2 ANALIZĖ

2013 ◽  
Vol 4 (4) ◽  
pp. 133-144 ◽  
Author(s):  
Šarūnas Kelpša ◽  
Mindaugas Augonis
Keyword(s):  
Shear Strength ◽  
Reinforced Concrete ◽  
Cross Section ◽  
Shear Force ◽  
Bending Moment ◽  
Intersection Point ◽  
Shear Reinforcement ◽  
Truss Model ◽  
Calculation Results ◽  
The Difference

When the various reinforced concrete structures are designed according to EC2 and STR, the difference of calculation results, is quite significant. In this article the calculations of shear strength of bending reinforced concrete elements are investigated according to these standards. The comparison of such calculations is also significant in the sense that the shear strength calculations are carried out according to different principles. The STR regulations are based on work of the shear reinforcement crossing the oblique section and the compressed concrete at the end of the section. In this case, at the supporting zone, the external bending moment and shear force should be in equilibrium with the internal forces in reinforcement and compressed concrete, i.e., the cross section must be checked not only from the external shear force, but also from bending moment. In EC2 standard, the shear strengths are calculated according to simplified truss model, which consists of the tension shear reinforcement bars and compressed concrete struts. The bending moment is not estimated. After calculation analysis of these two methods the relationships between shear strength and various element parameters are presented. The elements reinforced with stirrups and bends are investigated additionally because in EC2 this case is not presented. According to EC2 the simplified truss model solution depends on the compression strut angle value θ, which is limited in certain interval. Since the component of tension reinforcement bar directly depends on the angle θ and the component of compression strut depends on it conversely, then exists some value θ when the both components are equal. So the angle θ can be found when such two components will be equated. However, such calculation of angle θ became complicated if the load is uniform, because then the components of tension bar are estimated not in support cross section but in cross section that are displaced by distance d. So, the cube equation should be solved. For simplification of such solution the graphical method to find out the angle θ and the shear strength are presented. In these graphics the intersection point of two components (shear reinforcement and concrete) curves describes the shear strength of element. Santrauka Straipsnyje apžvelgtos ir palygintos STR ir EC2 įstrižojo pjūvio stiprumo skaičiavimo metodikos stačiakampio skerspjūvio elementams. Normatyve neapibrėžtas EC2 metodikos santvaros modelio spyrių posvyrio kampo skaičiavimas, lemiantis galutinį įstrižojo pjūvio stiprumą. Straipsnyje pateikiamos kampo θ apskaičiavimo lygtys, atsižvelgiant į apkrovimo pobūdį. Norint supaprastinti pateiktų lygčių sprendimą siūlomas grafoanalitinis sprendimo būdas, pritaikant papildomus koeficientus. EC2 neapibrėžia skaičiavimo išraiškų, kai skersinis armavimas yra apkabos ir atlankos. Minėtos išraiškos suformuluotos ir pateiktos straipsnyje. Nustačius EC2 metodikos dėsningumus siūlomas alternatyvus apytikslis skaičiavimo būdas atlankomis ir apkabomis armuotiems elementams. Straipsnyje apžvelgtos abi – STR ir EC2 – metodikos, išskiriant pagrindinius skirtumus ir dėsningumus.

Vibration Analysis of Multi-Disk Multi-Profiled Shaft-Rotor Systems

2014 ◽  
Vol 612 ◽  
pp. 17-22 ◽  
Author(s):  
P.M.G. Bashir Asdaque ◽  
R.K. Behera ◽  
Jakeer Hussain Shaik
Keyword(s):  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Shear Force ◽  
Bending Moment ◽  
Rotor System ◽  
Step Response ◽  
Rotor Systems

Cantilevered shaft-rotor systems consisting of multi disks and multi profiled shafts are considered. In this paper the procedures for the determination of the deflection, slope, shear force and bending moment at the extremities of the shaft are employed. Critical speeds or whirling frequency conditions are computed using transfer matrix method (TMM). For particular shaft-lengths, rotating speeds and shaft-profiles, the response of the system is determined for the establishment of the dynamic characteristics. A built-in shaft-rotor system consisting of two disks and two different profiled shafts is investigated for illustration purposes. Step response of the multi profiled shaft-rotor system is also found out.

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 Influence of the percentage of reinforcement by unstressed rebar on the deformability of pre-stressed RC beams

2021 ◽  
Vol 27 (3) ◽  
pp. 212-216
Author(s):  
Yaroslav Blikharskyy ◽  
Jacek Selejdak ◽  
Taras Bobalo ◽  
Roman Khmil ◽  
Mykhailo Volynets
Keyword(s):  
Reinforced Concrete ◽  
Concrete Beams ◽  
Bending Moment ◽  
Reinforced Concrete Beams ◽  
Practical Significance ◽  
Pure Bending ◽  
Static Loads ◽  
Steel Bars ◽  
Periodic Profile

Abstract This article presents the materials of deformability studies of pre-stressed steel-concrete beams reinforced with a package of reinforcement with different ratio of tape and rebar in the pure bending moment zone. The aim of the research was determination of the reinforcement percentage influence, for pre-stressed reinforced concrete beams reinforced with a package of reinforcement on their deformability. Also, the aim was to evaluate the effectiveness of using pre-stressed rebar in combined reinforcement. The practical significance of the experimental research is to study the deformability in pre-stressed bending elements with external tape and rebar reinforcement, taking into account the influence of different ratios of reinforcement areas within the combined reinforcement and development of proposals for such structures` calculation and design. The scientific novelty of the research is in obtaining the deformability characteristics of reinforced concrete beams reinforced with a package of reinforcement (tape and steel bars with periodic profile) with different ratios in the case of static loads` action.

Singularity functions revisited: Clarifications and extensions for construction of shear–moment diagrams in beams

2019 ◽  
Vol 48 (4) ◽  
pp. 351-370
Author(s):  
Stephen Boedo
Keyword(s):  
Shear Force ◽  
Function Method ◽  
Mathematical Formulation ◽  
Bending Moment ◽  
Distributed Load ◽  
Subsequent Determination ◽  
Main Emphasis ◽  
Load Function ◽  
Points Of Discontinuity

This paper provides clarification and extension of singularity functions for the construction of shear–moment diagrams in beams and the subsequent determination of beam deflections. The mathematical formulation for impulse, polynomial, and general-form singularity functions and their integral properties is reviewed, clarified, and provided graphically in tabular form. Several examples of various complexity are presented to assist the student at evaluating the constants of integration and properly interpreting the values of shear force and bending moment in the limit of approach to points of discontinuity. The main emphasis of the paper is to demonstrate the applicability of the singularity function method for any specified distributed load function.

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.

CALCULATION OF BENDING ELEMENTS OF WOOD AFTER THE ACTION OF LOW-CYCLE REPEATED LOADS ON THE CRITERION OF DEFORMATION DESTRUCTION

2020 ◽  
pp. 106-117
Author(s):  
E M Babich ◽  
S S Gomon
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Strain State ◽  
Repeated Loading ◽  
Building Structures ◽  
Deformation Method ◽  
Stress Strain ◽  
Stress Strain State ◽  
Layer Deformation

Existing norms of design for wooden constructions valid in different countries including Ukraine entirely disregard the effect of low-cycle repeated loadings during the operation of buildings and structures. The article deals with development of the bearing capacity computation of the bending elements manufactured from solid and glue-laminated wood exposed to repeated loadings in accordance with the deformation model.Equilibrium equations for computing the bending element made of wood after being exposed to repeated loadings are presented in the article. The deformation method is proposed for the computation of the rectangular wooden beams manufactured from solid and glued laminated wood with allowance for the occurrence of folds in the compression zone.The results of the research allow designing the solid and glue-laminated wooden constructions taking into consideration the possibilities of the material and peculiar features of the performance of the element, which in turn will allow choosing the cross-section of the elements of building structures more economically.On the basis of the study of the process of layer deformation by section height and the determination of the characteristics of the stress-strain state of these layers under the effect of repeated loading, it is possible to fulfill more accurate computation of the elements manufactured from wood at different stages of the stress-strain state through destruction.

ACCURATE DETERMINATION OF TORSION AND PURE BENDING MOMENT FOR VISCOELASTIC MEASUREMENTS

2013 ◽  
Vol 24 ◽  
pp. 1360016
Author(s):  
YUN-CHE WANG ◽  
CHIH-CHIN KO ◽  
LI-MING SHIAU
Keyword(s):  
Material Properties ◽  
Complex Modulus ◽  
Accurate Determination ◽  
Low Frequency ◽  
Bending Moment ◽  
Magnetic Interactions ◽  
Torque Measurement ◽  
Pure Bending ◽  
Creep Tests

Measurements of time-dependent material properties in the context of linear viscoelasticity, at a given frequency and temperature, require accurate determination of both loading and deformation that are subjected to the testing materials. A pendulum-type viscoelastic spectroscopy is developed to experimentally measure loss tangent and the magnitude of dynamic modulus of solid materials. The mechanical system of the device is based on the behavior of the cantilever beam, and torsion and pure bending moment are generated from the interaction between a permanent magnet and the Helmholtz coils. The strength of the magnetic interactions may be determined with a material with known mechanical properties, such as aluminum 6061T4 alloy. The sensitivity of the torque measurement is on the order of one micro N-m level. With the high accurate torque measurement and deformation detection from a laser-based displacement measurement system, viscoelastic properties of materials can be experimentally measured in different frequency regimes. Sinusoidal driving signals are adopted for measuring complex modulus in the sub-resonant regime, and dc bias driving for creep tests in the low frequency limit. At structural resonant frequencies, the full-width-at-half-maximum (FWHM) method or Lorentzian curve fitting method is adopted to extract material properties. The completion of determining material properties in the wide frequency spectrum may help to identify the deformation mechanisms of the material and to create better models for simulation work.

scholarly journals Determination of the load-bearing capacity of «steel-wood» connections of LVL structures under tension

2021 ◽  
Vol 18 (1) ◽  
pp. 60-69
Author(s):  
Quoc Phong Tran ◽  
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Steel Plate ◽  
Experimental Studies ◽  
Steel Plates ◽  
Load Bearing Capacity ◽  
Load Bearing ◽  
Dowel Connections ◽  
Wooden Structures

The article presents the results of calculation of the load-bearing capacity of connections of LVL structures under tension using cylindrical dowels in trusses and frames. The description of calculation schemes for determining the load-bearing capacity of connections with different location and sizes of steel plates in the connection is given. The influence of steel plate placement on the distribution of forces in the cross-section of samples is investigated. Based on the results of analytical and experimental studies, the load-bearing capacity of dowels during bending is considered, as well as the mechanism of wooden structures` fracture during chipping. A comparative analysis of the effectiveness of different schemes of dowel connections with three steel plates under tension is carried out.

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