Large Bending Moment Research Articles

An analytical study on the bending moment acting on the girder of a long-span cable-supported bridge suffering from cable failure

In this study, the structural behavior of a long-span cable-supported bridge after the sudden rupture of one of its axial cables is of concern. Cable failure produces large bending moments on the girder of the bridge. Henceforth, the focus of this study is to find the “maximum bending moment” on the girder due to the cable failure. For this purpose, an analytical approach based on differential equations of the system will be used. Then, an approximation function for a simplified bridge model in a cable-loss scenario will be derived. The use of the least squares method is also applied to minimize the error of the approximation function. The proposed approximation function has been checked by numerical models, and its good accuracy has been proven. The results show that by increasing the ratio of the bending stiffness of the girder to the axial stiffness of the cables, cable failure produces a larger bending moment on the girder.

Study on mechanical behaviors of large diameter shield tunnel during assembling

In order to study the mechanical behavior of shield tunnel segments during assembly stage, the in-situ tests and FDM numerical simulation were conducted based on the Foguan Shiziyang Tunnel with large cross-section. Analysis for the load state of the assembling segments in different assembly steps as well as the investigation for the changing of inner forces and longitudinal stress of segments with assembling steps were carried out in this paper. By comparing the tested results with the simulated results, the conclusions and suggestions could be drawn as follows: (1) It is the most significant for the effects on axial force and bending moment caused by the assembly of adjacent segment, followed by the insertion of key segment while the effects in the other assembly steps are relative smaller. With the increasing value of axial force, the negative bending moment turns into positive and remains increasing in most monitored sections, while the bending moment of segment B1and B6 are negative and keeping increasing; (2) The closer the monitored section to the adjacent segments or the key segment, the more significant the internal forces response, and the monitored effects of key segment insertion are more obvious than that of calculation; (3) The axial forces are all in compression during assembling and the monitored values are about 1.5~1.75 times larger than the calculated values, and the monitored values of bending moment are about 2 times the numerical calculation. The bending moment is more sensitive to the segments assembly process compared with axial force, and it will result in the large bending moment of segments during assembling when the construction parameters are not suitable or the assembly error is too large. However, the internal forces in assembly stage are less than those in normal service stage; (4) The distribution of longitudinal stress has strong influence on the changing of the internal forces. The segment side surface and intrados in the middle of two adjacent jacks are the crack-sensitive positions in the early assembly stage, and subsequently segment corners far away from the jacks become the crack-sensitive parts either.

Testing of jacket pile sleeve grouted connections exposed to shear forces and bending moments

Modern offshore jacket structures are designed with piles that are carrying large shear forces and bending moments. Even if the geometry of the grouted connection is quite simple the load transfer mechanism is complex. It involves friction, contact stresses, brittle material, abrasion, cyclic degradation etc. In order to improve our understanding of the behaviour and load-carrying capacity of grouted connections a laboratory test program involving 12 test specimens was executed. The specimens were full scale representation of a segment of a part of a pile sleeve connection close to the lower end. The tests are carefully planned to represent the real load and deformation conditions of the connection under cyclic loads. Two design geometries “Retracted” and “Extended” were tested. Four of the tests included reinforcement bars. The effect of the grout seal keeper plate was also investigated.The load-carrying capacity under cyclic loading was found. There were significant differences in the behaviour of the two different geometries.

Residual Strength Analysis of a Damaged WWII T2 Tanker

The S.S. Ohio, the T2 tanker that replenished Malta during the Second World War in 1942 saved the Islands from capitulation. En route, the tanker was bombarded and heavily damaged but remained afloat. This historic event provided a research opportunity to analyze the tanker's residual strength and how she survived. A strength assessment of the damaged hull indicated that the S.S. Ohio was at risk of collapse. However, simple beam theory indicated that when least damaged, large bending moments were exerted on the ship's midship but diminished with further damage, providing evidence on how the S.S. Ohio survived, shedding light on this 75-year-old mystery. 1. Introduction The T2 tanker, S.S. Ohio, is enshrined in the Maltese history as the saver of the islands during the Second World War (WWII). On the 15th of August 1942, the S.S. Ohio was towed into the Grand Harbour of Valletta, Malta, carrying vital oil replenishments essential to continue the fight against the enemy. Had it not been for the cargo the T2 tanker was carrying, the island fortress of Malta would have capitulated to the Axis Powers within 3 weeks (Caruana 1992; Holland 2003; Pearson 2004). En route to Malta, knowing how important the oil tanker was to the survival of the Maltese, the Axis Powers attacked her relentlessly, inflicting heavy damage. Yet the tanker remained afloat, but on the brink of sinking. Those living and witnessing the event were mesmerized on how the S.S. Ohio survived. The historians hypothesize that the tanker survived without breaking in half, thanks to her adequately strengthened and fully welded hull which was capable to withstand such an onslaught (Shankland & Hunter 1983). Thus, through this historic event, a research opportunity was identified. A residual strength analysis was conducted to assess the damage sustained, with the main aim to confirm or disprove the historical hypothesis.

Responses of retaining wall and surrounding ground to pre-excavation dewatering in an alternated multi-aquifer-aquitard system

Pre-excavation dewatering (PED) is an important construction stage in deep excavation. Field measurements show that retaining walls can develop obvious deflections during PED, which has been rarely considered in the past. The characteristics of PED-induced wall deflection, and the relationship of this deflection to surrounding ground deformation are still unclear. In this study, a PED test is simulated by a numerical model. The model is verified by field observations and used to investigate the responses of retaining wall and surrounding ground to PED. Results indicate that the maximum wall defection (δhm) and surface settlement (δvm) can all reach centimeter level under common conditions of PED. The ratio of δvm to δhm varies at the range of 0.45–0.67. Wall and soil deformations will be more obvious if the soils within the dewatering depth (Hd) have better permeability. The relative positions between Hd and strata (i.e., aquifer or aquitard) have great influence on the PED-induced deformations. If an aquifer appears below Hd, further increasing Hd can induce a rapid growth of wall and soil deformations. If thick aquitard appears below Hd, the deformation increments by further increasing Hd are not apparent. However, once Hd exceeds the center of the thick aquitard and reaches a thick confined aquifer, the wall deflections and soil deformation zones behind the wall will enlarge significantly. Meanwhile, a large bending moment in the retaining wall will arise around the bottom of the confined aquifer. The designers should consider this condition and allocate enough steel rebars there, preventing the appearance of wall cracks in the confined aquifer.

Numerical investigation of the influence of the yield stress of the yielding element on the behaviour of the shotcrete liner for yielding support

When tunneling in squeezing rock, the use of yielding support is recommended. In the yielding supports, the shotcrete liner is often divided into several segments with the yielding elements installed between them. The deformation ability of the yielding element is considerably greater than that of the shotcrete, and the yield stress of the yielding element can be adjusted as the support requirements. To investigate the influence of the yield stress of the yielding element on the behaviours of the shotcrete liner, a number of numerical analyses were conducted. In all of these numerical analyses, a connector element that can simulate the large deformation ability of the yielding element was used. According to the numerical results, the yield stress of the yielding element has a significant influences on the internal forces and failure behaviours of the liner. With the decrease of the yield stress, the axial force of the liner clearly decreases, while the bending moment concentration of the liner obviously increases. When the yield stress is extremely low, obvious tensile failure of the liner will occur because of the large bending moment of the liner, whereas when the yield stress is extremely high, clear shear failure of the liner will occur due to high axial forces of the liner. According to the total failure zone of the shotcrete liner, the optimum yield stress of the yielding element for the Xiakou tunnel is determined.

Testing of jacket pile sleeve grouted connections exposed to variable axial loads

Modern offshore jacket structures are designed with piles that are carrying variable axial loads, large shear forces and bending moments. Even if the geometry of the grouted connection is quite simple the load transfer mechanism is complex. It involves friction, contact stresses, brittle material, abrasion, cyclic degradation, etc.Current design recommendations were developed based on relatively small scale test and with only a few tests performed with cyclic loads that include change of load direction. In order to study the capacity of grouted connections with shear keys for alternating axial load, four (4) segment specimens were tested. The specimens were full scale representation of a segment of a part of the annulus of an axially loaded pile sleeve connection.The load-carrying axial capacity under cyclic loading was found.

Mechanical Behavior of a Partially Encased Composite Girder with Corrugated Steel Web: Interaction of Shear and Bending

Abstract The synergistic use of partially encased concrete and composite girders with corrugated steel webs (CGCSWs) has been proposed to avoid the buckling of corrugated steel webs and compression steel flanges under large combined shear force and bending moment in the hogging area. First, model tests were carried out on two specimens with different shear spans to investigate the mechanical behavior, including the load-carrying capacity, failure modes, flexural and shear stress distribution, and development of concrete cracking. Experimental results show that the interaction of shear force and bending moment causes the failure of specimens. The bending-to-shear ratio does not affect the shear stiffness of a composite girder in the elastic stage when concrete cracking does not exist, but significantly influences the shear stiffness after concrete cracking. In addition, composite sections in the elastic stage satisfy the assumption of the plane section under combined shear force and bending moment. However, after concrete cracking in the tension field, the normal stresses of a corrugated web in the tension area become small due to the “accordion effect,” with almost zero stress at the flat panels but recognizable stress at the inclined panels. Second, three-dimensional finite-element (FE) models considering material and geometric nonlinearity were built and validated by experiments, and parametric analyses were conducted on composite girders with different lengths and heights to determine their load-carrying capacity when subjected to combined loads. Finally, an interaction formula with respect to shear and flexural strength is offered on the basis of experimental and numerical results in order to evaluate the load-carrying capacity of such composite structures, thereby providing a reference for the design of partially encased composite girders with corrugated steel webs (PECGCSWs) under combined flexural and shear loads.

Fracture behavior of clad pipeline containing a canoe shape surface crack subjected to large bending moment

This paper concerns the fracture assessment of a clad pipeline subjected to large bending moment, and identifies different parameters influencing the fracture behaviors. The evolution of Crack Tip Opening Displacement (CTOD) of a pipeline containing a canoe shape crack on the external surface of the girth weld is studied under pure bending and combined pure bending and internal pressure through 3D elastic-plastic Finite Element (FE) simulations. Various parameters affecting the evolution of CTOD like crack depth, crack length to perimeter diameter ratio, internal pressure and the weld geometrical configurations have been investigated. It is observed that only the average width of the weld has a significant influence on the fracture response under pure bending, while the weld reinforcement height and fusion line slope have a moderate influence on the fracture behavior under biaxial loading. The crack at the interface between the weld and back steel has a similar fracture response to that of a crack located in the weld with equivalent effective crack depth. Finally, a strain based Failure Assessment Diagram (FAD) is proposed and compared with the fracture assessments produced by BS7910:2013, and 3D elastic-plastic FE simulations suggest that the British Standard is more conservative especially for deep cracks.

RATIONAL PLANNING OF PILE FOUNDATIONS

The existing methods (design directory) recommend using nomograms depending on the eccentricity of bending moment and numbers of piles while acting only vertical loads. These methods have a number of shortcomings and are inconvenient, because of lack of adequate alternatives and they do not provide the greatest efficiency. The convenient method of pile foundation designing (grillages and fields), depending on the load values, is the foundation proposed by the authors in this article. The results of numerical investigations determined the optimal grillages dimensions and numbers of pile in "bush" of pile, showed that this method gives optimal options for pile foundation under single column with large bending moments and minimum material expenditures and also provides its bearing capacity

Static and seismic behaviours of innovative hybrid steel reinforced concrete bridge

Bridges using rolled steel H-section seem to be economical compared with plate girder bridges due to lower material and fabrication cost in the short-span length. The rolled steel H-section is a compact section and no stiffener is necessary. However, as the maximum available web height of the rolled H-sections is 900mm, the applicable span-length is 20–25m. A new composite girder bridge was proposed using rolled steel H-section to extend the span-length. The superstructure consists of continuous rolled steel H-girders composite with the RC slab, and the substructure is RC piers. The girder and the pier are rigidly connected by concrete and reinforcements to resist large negative bending moment at the joints. Experiments were conducted with the partial SRC bridge model, which showed that the proposed structure with a rolled H-girder had high ultimate strength with good ductile property, and attained the full plastic moment. A FE model was established considering material non-linearity and shear transfer between steel and concrete and compared with the experiments, which showed good agreement and clarified the load transfer mechanism. A trial design with the SRC highway bridge was carried out, confirmed that the applicable span length can be extended to 50m. Seismic performance of the SRC system was verified by dynamic analysis, showed sufficient strength and ductility for strong earthquake with peak acceleration of 810m/s2. Cross beams were eliminated in the new SRC bridge because the girder height was low, which was verified by FEM analysis with the full bridge model.

Numerical Investigation on the excavation methods for Large Span Dome in Deep Buried Railway Station

Badaling Great Wall Station, excavated with drilling and blasting method, is the first underground railway station in China. The domeshaped distribution hall is of the maximum span within the entire station and is rare in underground transit projects. To find out an optimal excavation method, the sector method and the ring method are proposed and compared by threedimensional numerical simulation in this paper. The results are as follows: (1) Dome excavated by the modified ring method is of better shape with small and uniform convergence, when compared to the sector method. (2) For the modified ring method, the primary support can be closed in time under the protection of the reserved core rock. Hence, the structure performs well in restraining the surrounding rock from loosening, with larger bending moment and more uniform corresponding axial force response than that induced by the sector method. (3) The modified ring method is recommended for the large span dome. And the reserved core rock plays a beneficial role to support the surrounding rock, which helps to guarantee safety during construction. This research can make guidance for similar projects.

Failure mechanism of hollow tree trunks due to cross-sectional flattening.

Failure of hollow trees in urban areas is a worldwide concern, and it can be caused by different mechanisms, i.e. bending stresses or flattening-related failures. Here we derive a new analytical expression for predicting the bending moment for tangential cracking, and compare the breaking moment of various failure modes, including Brazier buckling, tangential cracking, shear failure and conventional bending failure, as a function of t/R ratio, where t and R are the trunk wall thickness and trunk radius, respectively, of a hollow tree. We use Taiwan red cypress as an example and show that its failure modes and the corresponding t/R ratios are: Brazier buckling (Mode I), tangential cracking followed by longitudinal splitting (Mode II) and conventional bending failure (Mode III) for 0 < t/R < 0.06, 0.06 < t/R < 0.27 and 0.27 < t/R < 1, respectively. The exact values of those ratios may vary within and among species, but the variation is much smaller than individual mechanical properties. Also, shear failure, another type of cracking due to maximum shear stress near the neutral axis of the tree trunk, is unlikely to occur since it requires much larger bending moments. Hence, we conclude that tangential cracking due to cross-sectional flattening, followed by longitudinal splitting, is dominant for hollow trunks. Our equations are applicable to analyse straight hollow tree trunks and plant stems, but are not applicable to those with side openings or those with only heart decay. Our findings provide insights for those managing trees in urban situations and those managing for conservation of hollow-dependent fauna in both urban and rural settings.

Maximum Load Carrying Capacity Estimation of The Ship and Offshore Structures by Progressive Collapse Approach

Abstract The aim of the paper is to represent step by step progressive collapse analysis for maximum load carrying capacity estimation of a hull girder by using variant of Smith Method, named HULT by authors, with different element separation including single plates, stiffeners, hard corners and stiffened panels. The structural elements that form the ships and offshore structures are exposed to large vertical bending moments and especially compression or tension forces in the longitudinal axis in case of hogging and sagging under bad sea conditions. In recent years, it becomes very important and valuable to practically, fast and nearly correct estimation of the maximum vertical bending moment just before breaks in two (collapse) under the worst conditions. The optimum (accuracy, time, practicality) estimation of these values depend on how accurate the stress-strain relation of the structural elements are established. In this first part of study, the ultimate strength behaviour of the stiffened panels in decks, bottoms and sides is estimated by developed semi-analytical method with updated orthotropic panel calculation approach under uniaxial (only longitudinal axis) compression loads. The second part of calculation is focused on the progressive collapse analysis of hull girders under longitudinal uniaxial compression with Smith Method but with different element discretization in contrast to the conventional beam-column elements. Also some benchmark studies of such methods on ultimate limit state assessment of stiffened panels and nine benchmark hull girders of ships are conducted, using some candidate methods such as IACS Common Structural Rules (CSR), FEA with Ansys v13 and HULT prepared by authors. The results from the tests, FEM analysis and different computational approaches are compared to determine performance of the method.

Soil-pile-structure kinematic and inertial interaction observed in geotechnical centrifuge experiments

This paper reports the results of a series of centrifuge tests examining dynamic responses of single and 3×3 grouped piles embedded in sand and supporting SDOF and 2DOF structures. A total of 7 model tests were conducted with the centrifugal acceleration of 40g. Each model was subjected to 12 sinusoidal waves with constant acceleration amplitude and varying frequencies. The results of the tests indicate that pile-head motion is dominated by two sequential frequencies: a lower frequency (fSSI) where pile-head motion is substantially maximized and a higher one (fpSSI) where the response is minimized with respect to free field surface motion. These results confirm recent published numerical results on single piles supporting SDOF structures and generalize their findings to grouped piles supporting SDOF and 2DOF structures. The results show also strong mobilized kinematic interaction effect generating significant pile bending when the ground is excited at its resonant frequency. On the other hand, structural vibrations tend to impose large bending moments as the excitation frequency approaches the natural frequency of the coupled soil-pile-structure system. Distribution of pile bending moments in the group is found to be a function of the pile position and the excitation frequency. In contrast to inner piles having the greatest kinematic bending moments, outer piles have a more pronounced inertial ones.

On the Mechanism of Drop Self-Shaping in Cooled Emulsions.

Two recent studies (Denkov et al., Nature 2015, 528, 392 and Guttman et al. Proc. Natl. Acad. Sci. U.S.A.2016, 113, 493) demonstrated that micrometer-sized n-alkane drops, dispersed in aqueous surfactant solutions, can break their spherical symmetry upon cooling and self-shape into a variety of regular shapes, such as fluid polyhedra, platelet-shaped hexagons, triangles, rhomboids, toroids, and submicrometer-diameter fibers. In the first study, the observed phenomenon was explained by a mechanism involving the formation of interfacial multilayer of self-assembled alkane molecules in the so-called rotator phases, templated by the frozen surfactant adsorption layer. Such phases are known to form in alkane droplets under similar conditions and are sufficiently strong to deform the droplets against the capillary pressure of a finite interfacial tension of several mN/m. The authors of the second study proposed a different explanation, namely, that the oil-water interfacial tension becomes ultralow upon cooling, which allows for surface extension and drop deformation at negligible energy penalty. To reveal which of these mechanisms is operative, we measure in the current study the temperature dependence of the interfacial tensions of several systems undergoing such drop-shape transitions. Our results unambiguously show that drop self-shaping is not related to ultralow oil-water interfacial tension, as proposed by Guttmann et al. These results support the mechanism proposed by Denkov et al., which implies that the large bending moment, required to deform an oil-water interface with an interfacial tension of 5 to 10 mN/m, is generated by an interfacial multilayer of self-assembled alkane molecules.

In-site experiments on the swelling characteristics of a shield tunnel in expansive clay: A case study

Expansive soil swells, softens, and disintegrates when absorbing water, whereas it shrinks when losing water. Understanding the swelling characteristics of a shield tunnel in expansive soil is important. However, most in-site experiences on the swelling characteristics of a tunnel are obtained from the NATM tunnels constructed in swelling rock using drill and blast method; most laboratory experiments or theoretical analyses on the swelling characteristics of a shield tunnel in expansive soil are under certain hypotheses which have not been verified in actual situation. To solve the problems, the Slender West Lake tunnel was selected as the background, laboratory and in-site experiments were performed to understand the swelling characteristics of a shield tunnel in expansive clay. Four experimental sections were constructed in the actual tunnel. The measuring gauges were pre-installed in the segments in factory and the segments were installed in-site to observe the actual earth pressure and temperature during construction. The influences of expansive soil to the distributions and variations of earth pressure, bending moment, and temperature were analyzed. The increasing earth pressure was divided into three stages. Large earth pressure was detected at the top, bottom, left, and right sides of the tunnel. The earth pressure at the left and right sides was larger than that at the top and bottom. Large negative bending moment was detected at the top and bottom of the tunnel, whereas large positive bending moment was detected at the left and right sides of the tunnel. The minimum bending moment appeared at 45° oblique. The largest negative bending moment was larger than the largest positive bending moment. Based on the observations, a load mode of swelling pressure for a beam-spring model was suggested. It can be referred by the similar tunnels.

Deep water drilling riser mechanical behavior analysis considering actual riser string configuration

A dynamic analysis model considering the actual riser string configuration is established to analyze the mechanical behavior of a drilling riser. The riser in this model is regarded as a simply supported beam located in the vertical plane and is subjected to axial and lateral ocean environment loadings. The model is solved using the finite element method. The validity of the analysis model has been proved by a similar experiment conducted in a deep water basin and ANSYS. Riser lateral displacement, bending moment, and deflection of the deep water well considering actual riser string configuration in South China Sea are simulated. The effects of top tension, drilling platform drift distance, surface current speed, wave height, wave period, wave length, wind speed and damping coefficient on riser lateral displacement, bending moment, and deflection are also discussed. Results indicate that riser string configuration has a significant effect on riser mechanical behavior, particularly in the distribution of bending moment. Riser string configuration designing according to concrete ocean environment can significantly improve the riser’s mechanical behavior. The distribution of riser lateral displacement, bending moment, and deflection increases with the increase in surface current speed and drilling platform drift distance, whereas decreases with the increasing top tension and damping coefficient. The distribution of riser lateral displacement, bending moment, and deflection significantly increases with the increase in surface current speed and large current speed may lead to large lateral displacement, bending moment, and deflection. Increasing top tension can significantly decrease riser mechanical behavior parameters and avoid large lateral displacement, bending moment, and deflection when suffering extreme ocean environment conditions in deepwater drilling field. Drilling platform should avoid a large drift distance, which may result in the deflection over the flex joint working range and the enlargement of the riser bend moment.

Impact of Vertical Ground Excitation on a Bridge with Footing Uplift

Ground motions recorded in the epicentral region of an earthquake often have a strong vertical component with dominant high frequencies. Damage to bridges in near-source regions due to strong vertical ground motion has been reported. The beneficial effects of footing uplift on structural performance in form of reduction of seismic response of structural members have been confirmed in previous research. The uplift of bridge piers has been utilised in a very limited number of bridge structures, e.g., the South Rangitikei railway bridge in New Zealand. However, the near-fault seismic behaviour of bridges with footing uplift has been even less addressed. In this study shake table investigations were carried out on the response of a single-span bridge model with footing uplift subjected to simultaneous vertical and horizontal excitations. Near-fault ground motions recorded in the Canterbury earthquake sequences of 2010 and 2011 were used. The experimental results show that inclusion of vertical ground motions produce stronger axial force in the pier and larger bending moment in the deck. Concurrent horizontal and vertical excitations may also cause more frequent footing uplift than the solely horizontal excitations.

A method for modeling and analyzing the rotor dynamics of a locomotive turbocharger

The rotor of the locomotive turbocharger is prone to malfunction of the turbocharger, and it is also the most important part of the turbocharger. The reasonable establishment of rotor dynamics model is very important in the study. It determines the accuracy of analysis. The influence of the shaft quality on the turbine and impeller was not considered in the process of analyzing the dynamic model in the passed research. But the quality of locomotive turbocharger rotor shaft is relatively large, it cannot be ignored because it will have a large bending moment in the model simplified. So the rotor dynamic equation was deduced in the case of considered the quality of the rotor axis. The rotor of the turbocharger rotor was simplified firstly, the various parts of the simplified rotor were analyzed, and the dynamic model of the rotor was established. And the dynamic model was verified by the hammer experiment. The factors considered in the dynamic model were more comprehensive, so the model would be more practical for the future research.