Two-hinged Arch Research Articles

Safety assessment of masonry undamaged and damaged arches subjected to gravitational loads and horizontal forces. A numeric procedure to identify the optimal thrust line

In 2019 the authors formulated a numerical procedure for assessing the safety of masonry arches based on their geometry and the shape of the thrust line. The thrust line is calculated to be nearest to the geometric axis of the arch, because it is that corresponding to the optimal inner stress state. The original procedure, which focused on the safety analysis of undamaged fixed arches subject to gravitational loads, is reformulated here to also consider arches on pinned supports as well as damaged arches, i.e. one- and two-hinged arches. The procedure is further extended to also assess safety against horizontal actions, such as those resulting from an earthquake. Finally, safety is evaluated by identifying the domain of admissible thrust lines within the thickness of the arch and by computing the degree of safety in terms of the capacity of the thrust line to be moved vertically within the domain. The reformulation and extension of the procedure exploits the technique of partitioned matrices to enable automation and easy implementation in structural calculation software.

Study on key parameters of buckling deformation instability and fracture of rock beams and asymmetric distribution law of stope stress.

The moving deformation of the strata and the redistribution of stope stress after mining show asymmetrical characteristics, which do not conform to the symmetrical structural characteristics of the original rock beam fracture. To further analyze the deformation of rock beams and the asymmetry law of stope pressure distribution after strata caving, the detailed process of instability and deformation of composite rock beams before failure was revealed through similar material simulation, theoretical analysis, and numerical simulation. Through similar simulation experiments, the structural characteristics of strata caving were observed. After excavation, the caving angle near the open-off cut side of the model is greater than that on the stop-mining line side. The maximum bending moment of the rock beam is located at the open-off cut side. The rock beam fracture is located on the partial open-off cut side in the middle of the rock beam. The rock beam on the open-off cut side is easy to shear slip and not easy to hinge. The rock beam in front of the advancing direction of the working face is easily hinged. Based on the structural characteristics of strata caving, considering the thickness of the composite rock beam, the two-hinged arch mechanical model for rock beam fracture is established. On this basis, the key parameters of rock beam instability and fracture such as limit load, additional horizontal stress, limit break distance, and break position are analyzed. Based on the deformation characteristics of two hinged arches, the caving structure and the asymmetric distribution mechanism of stress redistribution during the deformation of overburden in stope are explained. Finally, the deformation of rock beam and the asymmetry of stress distribution in stope are verified by numerical calculation. The results show that the concentrated stress value of the coal pillar at the open-off cut side is greater than that in front of the working face. There is a pressure relief area behind the working face, and the pressure relief area has a certain range. The range of stress concentration area, pressure relief area, and stress value tend to be stable, and only the range of the original rock stress zone expands when the working face is advanced to a certain distance. The asymmetric distribution of compaction stress in goaf is related to the buckling deformation of strata.

Approximate closed-form solutions for free vibration of circular arches with discrete lateral braces

Discrete lateral braces are commonly employed to enhance the out-of-plane stability of arches. However, these braces generate coupling effects among vibration modes, which significantly impact the vibration characteristics of the arches. This paper presents an analytical solution for the free vibration analysis of two-hinged arches with equally-spaced lateral translational and/or rotational braces. A simplified method of evaluating the fundamental frequency for the out-of-plane vibration of arches with equally-spaced lateral braces is introduced. The method relies on the conventional approach of representing arch braces through elastic springs, but here the out-of-plane deflection of the braced arch is constructed by adding related coupled sinusoidal functions to that of the unbraced arch, satisfying both the boundary and kinematic conditions. Subsequently, the fundamental frequency and threshold bracing stiffness or stiffness requirement are derived using the Rayleigh–Ritz method. Finite element analysis (FEA) is applied to investigate the flexural-torsional vibration mode and fundamental frequency of arches with discrete braces, and the results from FEA closely match the theoretical predictions. The effects of number of lateral translational and/or rotational brace, out-of-plane slenderness, included angle, bracing stiffness and bracing position on the fundamental frequency are comprehensively analyzed. It is found that when the fundamental frequency of the braced arch increases due to changes in bracing stiffness, the mode shape displays more intricate behavior, rather than following a straightforward low-to-high mode growth pattern. Furthermore, it is observed that in some cases, the addition of rotational bracing stiffness can markedly enhance the maximum fundamental frequency of the arch with both translational and rotational braces.

Damage Identification Method of Tied-Arch Bridges Based on the Equivalent Thrust-Influenced Line

Early tied-arch bridges cannot satisfy the current traffic load demand due to their load grades and maintenance levels. Also, these tied-arch bridges have accumulated structural damage with increasingly prominent safety risks. In order to accurately evaluate the characteristics of tied-arch bridges’ structural-influenced lines and identify damage of their arch ribs and suspenders, two analytical solutions are derived and established in this paper for the thrust-influenced lines of parabola and catenary two-hinged arches with a tie beam. A new method and an index for identifying damage of arch ribs and suspenders of tied-arch bridges are proposed. The results of numerical simulation in this paper verified that the proposed analytical solution has good analytical accuracy in practice on those two-hinged nonflat arches. With the use of equivalent thrust-influenced line difference curvature, the effectiveness of damage identification and the verification method were verified on the tie beam, suspender, and arch rib of plane tie arch structure as well as the suspender and arch rib of tied-arch bridges in this research. Furthermore, combining with grey relation analysis, the noise immunity of the proposed index method can be verified. Also, thrust-influenced line recognition based on VMD (variational mode decomposition) is introduced, and a practical process of bridge health assessment based on the quasistatic-influenced line loading of three-axle heavy vehicles is established. Theoretical analysis and numerical verification show that the calculated error of the analytic solution of two-hinged arches with a rise-span ratio greater than 1/8 is less than 9.57%, and the error decreases with the increase of the rise-span ratio. Therefore, it can be applied to the calculation and analysis of tied-arch bridges with a rise-span ratio range between 1/4 and 1/5. With the equivalent thrust-influenced line index proposed in this paper, the damage of suspenders and arch ribs of tied-arch bridges can be accurately located. It has been found that the proposed method is more effective to identify the damage of suspenders than the damage of arch ribs does, showing good noise immunity. In summary, this research has provided theoretical support for arch bridge design and evaluation. Combining with existing bridge-monitoring methods, the new bridge damage identification method proposed in this paper has the prospect of realizing the normal health status assessment of existing tied-arch bridges.

Study on Mechanical Calculation Model of Arch Ring in Freestanding Stone Cave-Dwelling

The freestanding stone cave-dwelling is a kind of arched and sheltered house built with stones in the Loess Plateau region of northwest China. Amazingly, before construction, this kind of cave-dwelling was not formally calculated and designed in theory, but only built on the experience passed down by predecessors. The arch ring is the main load-bearing component of the freestanding stone cave-dwelling, through which the upper loads are transmitted to the legs on the left and right sides of the cave-dwelling and then to the foundations. Therefore, it is a prerequisite to ensure the safety of cave dwellings by adopting a reasonable and accurate mechanical calculation model for the arch ring of a stone cave-dwelling to reveal the distribution of internal forces in the arch ring and scientifically design the arch ring accordingly. Three mechanical calculation models (structural calculation diagrams) are adopted for the arch ring of stone cave-dwelling, namely, hingeless arch, two-hinged arch, and three-hinged arch. Based on the force equilibrium and the force method from the structure mechanics, the formulae for calculating the internal force of the stone arch ring under these three different mechanical calculation models are derived respectively. The mechanical calculation results of three calculation models are compared and analyzed to clarify the difference and rationality of the stress results of the arch ring under the three mechanical calculation models and the degree of influence on the force of the lower cave-dwelling leg members. Lastly, in accordance with the internal force calculation results, the calculation formulae for the design of the arch ring thickness are proposed. The study shows that the hingeless arch and two-hinged arch models are more consistent with the actual failure characteristics, two-hinged arch calculation model is safer, more accu-rate, and more reliable than the hingeless arch calculation model when it is used in the mechanical analysis of circular arc arch ring. The findings are intended to serve as theoretical references for the design and construction, protection and reinforcement, and sustainable development and inheritance of cave dwellings in the future.

Research on Mechanical Characteristics of Slope Reinforcement by Spatial Arc Crown Beam Composite Supporting Structure

To effectively optimize the mechanical behavior of a traditional anti-slide pile and reduce environmental destruction, a new method for slope reinforcement by a spatial arc crown beam composite supporting structure was proposed. First, a numerical model was validated through lab-scale model test data obtained herein, and then a full-scale numerical model was created for an in-depth understanding of the distribution regularity of displacement along the pile, the soil pressure, the crown beam stiffness, and so on. The results demonstrated that: (1) The spatial arc crown beam is simplified to a two-hinged arch, and the maximum value of the bending moment in the arc crown beam is about one-third of the straight crown beam through theoretical calculation. (2) The spatial arc crown beam redistributes the load sharing among different piles, and the extreme bending moment of other piles varies within 10% along the downhill direction except for the piles at the slope foot. (3) Bending moments are close to zero at the pile end, and the anti-slide pile can be simplified as a vertical beam with one end fixed and the other end hinged. (4) The axial force in the spatial arc crown beam is always presented as pressure, so the crown beam can make full utilization of the compression resistance of concrete. (5) The distribution characteristic of soil pressure in front of the pile at the arch foot is different from that in other positions, and the stable soil at the slope foot provides greater soil resistance for anti-piles. (6) As the crown beam stiffness is above five times the reference value, the axial force of the crown beam tends to be stable, and as the crown beam stiffness increases continually, the maximum value of My is −1013.13 kN·m, and the constraining effect of the crown beam is gradually weakened.

Design method of compression-bending arches with web openings considering local buckling of web

This paper studies the in-plane stability design method of two-hinged steel arches with web openings I-shaped cross sections when local web buckling is allowed. The paper compares two types of failure mechanisms, namely, global buckling and local buckling. Based on the analogy of calculation formula of beam bending, the author proposes a formula for calculating the bearing capacity when web buckling is taken into consideration.

New in Old: Simplified Equations for Linear-elastic Symmetric Arches and Insights on Their Behavior

Closed-form equations for determination of reactions and internal forces of linear-elastic symmetric arches with constant cross-sections are derived. The derivation of the equations was initially made for segmental, threehinged, two-hinged, and hingeless arches. Not all derived equations are simple, but still not excessively complex to apply, and they reveal several new insights into the structural behavior of arches. The first is an extremely simple approximate equation for horizontal reactions of a hingeless arch under self-weight, which could be also applied with excellent accuracy to catenary and parabolic arches, and with a desirable level of accuracy to two- and three-hinged arches with a relatively wide range of geometries. The second insight is an approximately linear relationship between reactions and between internal forces of arches with different structural systems, which helps understand the global structural behavior of arches in a new way and enables inference of some other insights presented in the paper. The third insight reflects the relationships between normal force distribution and its eccentricity in different types of arches. Finally, the fourth insight regards the comparison of behavior of arches under the self-weight with those loaded with uniformly distributed load along their span.

A pseudo-modal structural damage index based on orthogonal empirical mode decomposition

A structural damage identification technique hinged on the combination of orthogonal empirical mode decomposition and modal analysis is proposed. The output-only technique is based on the comparison between pre- and post-damage free structural vibrations signals. The latter are either kinematic (displacements, velocities or accelerations) or deformation measures (strains or curvatures). The response data are decomposed by means of the orthogonal empirical mode decomposition to derive a finite set of orthogonal intrinsic mode functions; the latter are used as a multi-frequency and data-driven basis to build pseudo-modal shapes. A new damage index, the so-called pseudo-mode index, is introduced to compare the response obtained for the two states of the structural system and detect potential damages. The performance of the devised index in detecting a localised damage is shown through numerical and experimental tests on two structural models, namely a 4-degrees-of-freedom system and a two-hinged parabolic arch.

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

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.

Mechanical behavior of Chinese woven timber arch bridges

Chinese woven timber arch bridge is an important part of the precious cultural heritage handed down from ancient times. Its construction technology has been inscribed on the List of Intangible Cultural Heritage in Need of Urgent Protection by UNESCO in 2009, and twenty-two bridges of this kind have been listed in the tentative list of the Chinese World Cultural Heritage since 2012. Made by longitudinal and transverse straight logs woven together with mortises and tenon joints, the main arch is not a planar structure nor a general three-dimensional spatial one, and its mechanical behavior cannot be computed by the traditional structural analysis method. In this study, loading tests and FE analyses on the woven arch, and field tests and FE analyses on a really bridge are carried out. For the woven arch, two joint types, rigid and hinged joints are considered in the tests and analyses. The results show that: (1) the deflection shapes of woven arch models with rigid joints and hinged joints are similar; (2) the deflection of a hinged woven arch is larger than that of a rigid one; (3) the two systems of a woven arch can work together simply by the contact between them, but in some loading cases, some portions of them will separate and no force is transferred between them; (4) the mechanical behavior of the woven arch is similar to that of the two-hinged arch. In other words, it is also subjected to horizontal thrusts under vertical loads, but the compression force is the dominant one; and (5) the modeling method of the woven arch is applicable to Chinese timber arch bridges.

Virtual estimation of the Griffith’s modulus and cohesive strength of ultra-high performance concrete

This investigation presents a computational methodology to estimate the unit fracture energy (Griffith’s modulus) and the cohesive strength of ultra-high performance concrete (UHPC). The hydration of plain UHPC mixtures is simulated using the National Institute of Standards and Technology (NIST) Virtual Cement and Concrete Testing Laboratory (VCCTL) hydration simulator. The Young’s modulus of elasticity of the hardened concrete is obtained via finite-element analysis of a sample cube of its micro-structure. Applying the Extended Finite Element modeling capabilities of ABAQUS to previously grooved simple structural elements under gradually-increasing load, the results of computational simulations of the start of crack growth are linked to the corresponding predictions by regressions on experimental observations in classical linear elastic fracture mechanics physical tests. A procedure is developed to estimate both the Griffith’s modulus and the cohesive strength of the UHPC, which are difficult to assess experimentally. As an application, the effect on the horizontal thrust at the abutments of a two-hinged symmetric arch with a crown crack and uniformly loaded is analyzed using the data provided by the pure-bending test on a pre-grooved simply supported beam.

Adjustable module for variable depth steel arch bridges

This paper presents a new strategy for modular steel construction: an adjustable module. Existing rapidly erectable, steel panelized bridge systems (e.g., Bailey, Acrow, Mabey-Johnson) have limited material efficiency (span squared per weight) as they are comprised of rigid modules in a girder-type configuration. This paper addresses this limitation by developing a new adjustable, steel module comprised of a four-bar linkage which can form more efficient variable depth arch bridges. The objectives of this study are to (1) present methodologies for the development of rational variable depth three- and two-hinged arch forms, (2) evaluate the geometry of the adjustable module to scribe these rational forms, and (3) demonstrate the promise of the adjustable module through three-dimensional finite element analyses. Results show that a lightweight, adjustable module can form variable depth three- and two-hinged arches which increase the material efficiency by a factor of approximately 3 compared to existing systems. The module and other arch components can be comprised of American Institute of Steel Construction Steel Construction Manual standard rolled section sizes, thereby forming a versatile, kit-of-parts systems. The module weighs 1.41 times less than a conventional module, suggesting significant advancement compared to existing practice.

The real static behaviour of historic bridge in town Krásno nad Kysucou in Slovakia

The paper is focused on real static behaviour of the oldest reinforced concrete arch bridge in middle Europe, which is located in the town Krasno nad Kysucou over the river Bystrica. This bridge was diagnosed and the task was to determine the load-carrying capacity of the bridge. Documentation of the object has not been available, so, it was not clear what the static schema of the bridge is – whether it is fixed arch or two-hinged arch and whether the spandrel walls located on the both sides in the longitudinal direction are cooperating with the arch. The paper is focused on the static calculation and the load-carrying capacity calculation in order to compare various static schemas.

Assessment of damaged timber structures using proof load test – Experience from case studies

In this paper assessment of damaged timber structures using proof load test is given, which is mandatory according to Macedonian standards. Two types of structures were analyzed in the paper: Glued laminated timber structure, Cambered beam span of L=24.00m and Glued Laminated pedestrian timber bridge, two-hinged arch, span of L=26.00m plus two simple supported beams span of L=12.5m each.The results were also used for reliability verification to define partial safety factor for material for ultimate limit state and serviceability limit state, according to Eurocodes EN1990 and EN1995.

‘Structural Performance of Two-Hinged Islamic Arches’

‘Structural Performance of Two-Hinged Islamic Arches’ Shehdeh Ghannam, Husam Najm Abstract This paper presents an investigation of Islamic arch forms and structural performance based on its geometrical formation. Arch form depends on several interrelated variables such arc angles, the ratio of arc radius to arc span, and the height of the arch. These variables are controlled in Islamic architecture by the geometry. This paper provides insights for the geometric design of Islamic arches and outlines its structural analysis under different load cases. A parametric study of the buckling behavior of arches for several load cases, horizontal thrust, and bending moment will be analyzed. This paper aims to provide an understanding of the structural concepts of the arch form in Islamic architecture based on the significance of geometry in construction of Islamic arches. Arches described by geometry and proportions, plays a crucial role in the composition and structure of the arch form. Typically design parameters are based on estimating force vectors to determine arch shape, assuming that they represent the architecture properly and are constant. To describe arch architecture in more detail and compare geometrical and non-geometrical states, geometric approach was validated. Arch forms are constructed from historical sections, based on geometric language, as well as the shape of the arch. The proposed approach may help to identify functional structural concepts within the arch, with homogeneous architectural geometric properties. The related results are discussed regarding the parameters essential for structural arch modeling and challenge aesthetic parameters of the arch-model. Full Text: PDF DOI: 10.15640/jea.v3n1a5

Out-of-Plane Elastic Stability Analysis of Parabolic and Circular Arches

Effects of different load modes, rise-span ratios and support conditions on out-of-plane buckling and differences between parabolic and circular arches were studied. With the increase of rise-span ratio, buckling loads of arches under vertical load uniformly distributed along the horizontal line get bigger and bigger compared with those of vertical load uniformly distributed along the axis. With increase of rise-span ratio, the buckling loads of hingeless and two-hinged arch increase after decrease, then decrease. The buckling load of three-hinged arch decreases after increases. When rise-span ratio is small, support condition has a great influence on out-of-plane buckling. The parabolic arch is better than circular arch in out-of-plane stability and economy. But circular arch is better than parabolic arch in manufacture.

Parametric study of the structural and in-plane buckling analysis of ogee arches

As part of a pilot project an ogee arch is being studied as a self-supporting skin skylight for the Housing and Building National Research Center’s (HBRC) patio. The ogee arch consists of a pair of two tangential circular arcs making an arch shape. The geometry of the arch depends on several interrelated variables including the angles subtended by the arcs, the ratio of the radii of the two arcs, and the height of the arch. This paper provides curves for designing the geometry of ogee arches. The structural analysis of two-hinged ogee arches under different cases of loading is outlined deriving expressions for the horizontal base thrust and plotting their graphs. A parametric study of the antisymmetric in-plane buckling behavior of ogee arches is presented using a finite element eigenvalue buckling analysis for several cases of loading. The finite element models consist of beam elements and have varying geometrical dimensions representing different shapes of ogee arches. The structural response of the arches is verified through a linear finite element analysis. The results of the buckling analysis are verified through a nonlinear finite element analysis with initial imperfections. It is found that the buckling load is a function of the ratio of the height-to-base radius of the arch and expressions for the lower bound buckling load are derived as a function of this height-to-base radius ratio.

Analytical Solution of Sidewise Buckling of Two-Hinged Circular Arch under Concentrated Force

By the setting torsional and lateral displacement function of sidewise buckling of two-hinged circular arch under concentrated force, the single-arch structure's bending, torsional deformation and external force potential can be constructed. An analytical solution for the lateral critical buckling load of two-hinged arch is first deduced by using the energy method; the results are also compared and analyzed by the finite element method. The results show that the analytical solution of single arch’s lateral critical buckling load is in good agreement with the finite element numerical solution, and the validity of the formula is proven.

Studies on In-Plane Stability Behavior of Arches with Web Openings

As a new type structural member, the steel arch with web openings combines the features of both arches and members with web openings and its applications has been found. Studies on in-plane stability behavior of two-hinged arches with web hexagonal openings are made using Eigen buckling model of the finite element software ANSYS. The buckling load and buckling mode are obtained and the in-plane buckling mode is antisymmetrical. It is shown that buckling load decreases gradually as the circumcircle radius of openings increases and it increases as the gap between openings increases through analysis of buckling load with different parameters such as r/h, g/h, f/l. It can be found that the structural efficiency is the highest when the radius of openings is 0.3h with the aid of optimized function.