Analysis of Equivalent Flexural Stiffness of Steel–Concrete Composite Beams in Frame Structures

Vertical deflection of a frame beam is an important indicator in the limit-state analysis of frame structures, particularly for steel–concrete composite beams, which are usually designed with large spans and heavy loads. In this study, the equivalent flexural stiffness of composite frame beams is analysed to evaluate their vertical deflection. A theoretical beam model with a spring constraint boundary and varied stiffness segments is established to consider the influence of both the rotation restraint stiffness at the beam ends and the cracked section in the negative moment region, such that the inelastic bending deformation of the composite beams can be elaborately described. By an extensive parametric analysis, a fitting formula for evaluating the equivalent flexural stiffness of the composite beams, including the effects of the rotational constraint and the concrete cracking, is obtained. The validity of the proposed formula is demonstrated by comparing its calculation accuracy with those of existing design formulas for analysing the equivalent flexural stiffness of the composite beam members. Moreover, its utility is further verified by conducting non-linear finite element simulations of structural systems to examine the serviceability limit state and the entire process evolution of beam deflections under vertical loading. Finally, to facilitate the practical application of the proposed formula in engineering design, a simplified method to calculate the deflection of composite beams, which utilises the internal force distribution of elastic analysis, is presented based on the concept of equivalent flexural stiffness.

Simulation of Soil Compaction by a Tractor Passing

Several methods for agricultural soil compaction evaluation are known. However, there is a lack of knowledge about a soil elasticity, which could be an important factor for final level of compaction. The paper deals with a possibility of evaluation of soil elasticity using automatic computerized oedometer. A simulation of tractor passing was performed as a part of research focused on the monitoring of soil conditions in vineyards. Cyclic loading test of five loading cycles (loading 300 kPa and un-loading 5 kPa) was performed and vertical deflection was observed, which changed in dependency on change of vertical stress. Course of vertical deformation indicates the ability of soil to relax when the load subsides. The paper presents pilot results, that show good potential of using oedometer for soil elasticity evaluating. Information on the elastic behaviour of soil will make it possible to design and apply means for improving soil elasticity and thus help to mitigate the effects of soil compaction.

Study on Coupled Vertical Vehicle-Bridge Dynamic Performance of Medium and Low-Speed Maglev Train

The levitation stability of maglev trains is determined by the interaction of vehicle-bridge dynamic characteristics. The state change of vehicle and track beam will affect the dynamic performance of maglev trains. In order to study the levitation characteristics of maglev trains, a coupled vehicle-bridge dynamic model based on an elastic beam was established to study the influence of beam stiffness and vehicle load on the dynamic performance of the maglev system. In the form of numerical simulation, the time-domain characteristics of key characteristic variables, such as levitation gap and vertical deflection of track beam, under different working conditions of stiffness and load were analyzed. The simulation shows that the levitation system can smoothly converge to the stable value under each working condition, which indicates the rationality of the field test. Based on the Shanghai Lingang medium-and-low-speed maglev test line, the maglev test was carried out, and the time-domain and frequency-domain characteristics of the above key variables were analyzed based on the measured data. The results show that the fluctuation of the levitation gap was affected by load and stiffness, and the law was consistent with the simulation results. The increase in load or the decrease in beam stiffness would lead to an increase in vertical deflection and vibration of the track beam. However, the train could still maintain good levitation performance under the above extreme conditions, which verified the reliability of the levitation system and the correctness of the simulation model. The conclusion of this paper can provide a reference for the design of the levitation system and track line of medium-and-low-speed maglev train.

Modified Reed Equation of Blast Load on Plate with Stiffener

The purpose of this study is to analyze numerically the effect of explosions on orthotropic slabs which have partial fixity placement and stiffeners in the x direction, namely in the short span direction. The modified blast load dynamic behavior is from Reed’s equation with 4th order polynomial on orthotropic plates with x-direction stiffener. The localized blast load centered in the middle of the strain, and the effects of thickness and stiffening on the vertical deflection of the plates are solved numerically using two auxiliary equations in the x and y-directions. It is found that there is vertical deflection with related to time.

Analysis of Pure Bending Vertical Deflection of Improved Composite Box Girders with Corrugated Steel Webs

Steel bottom plates are applied as replacements for the concrete bottom plates in order to reduce the dead weight of the composite box girders with corrugated steel webs and steel bottom plates (CSWSB). Due to the change in the material, the previous analytical calculation methods of vertical deflection of composite box girders with corrugated steel webs (CSWs) cannot be directly applied to the improved composite box girders. The shear lag warpage displacement function was derived based on the shear deformation laws of the upper flange and the bottom plates of the improved composite box girders. The equations for the calculation of the shear deformation and the additional deflection due to the shear lag of continuous and simply supported composite box girders with CSWSB under concentrated and uniformly distribution loads were derived by considering the double effects of the shear lag and the shear deformations of the top and the bottom plates with different elastic moduli. The analytical solutions of the vertical deflection of the improved composite box girders include the theory of the bending deflection of elementary beams, shear deformation of CSWs, and the additional deflection caused by the shear lag. Based on the theoretical derivation, an analytical solution method was established and the obtained vertical deflection analytical solutions were compared with the finite element method (FEM) calculation results and the experimental values. The analytical equations of vertical deflection under the two supporting conditions and the two load cases have verified the analyses and the comparisons. Further, the additional deflections due to the shear lag and the shear deformation are found to be less than 2% and 34% of the total deflection values, respectively. Moreover, under uniform distributed load conditions, the deflection value was found to be higher than that of the under concentrated load condition. It was also found that the ratio of the deflection caused by the shear lag or the shear deformation to the total deflection decreased gradually with the increase in the span width ratio. When the value of the span width ratio of a single box and single chamber composite box girder with CSWSB was equal to or greater than 8, the deflections caused by the shear lag and the shear deformation could be ignored.

The Deflection of the Vertical, from Bouguer to Vening-Meinesz, and Beyond – the unsung hero of geodesy and geophysics

<p>When thinking of gravity in geodesy and geophysics, one usually thinks of its magnitude, often referred to a reference field, the normal gravity.  It is, after all, the free-air gravity anomaly that plays the significant role in terrestrial data bases that lead to Earth Gravitational Models (such as EGM96 or EGM2008) for a multitude of geodetic and geophysical applications.  It is the Bouguer anomaly that geologists and exploration geophysicists use to infer deep crustal density anomalies.  Yet, it was also Pierre Bouguer (1698-1758) who, using the measured direction of gravity, was the first to endeavor a determination of Earth’s mean density (to “weigh the Earth”), that is, by observing the deflection of the vertical due to Mount Chimborazo in Ecuador.  Bouguer’s results, moreover, sowed initial seeds for the theories of isostasy.  With these auspicious beginnings, the deflection of the vertical has been an important, if not illustrious, player in geodetic history that continues to the present day.  Neglecting the vertical deflection in fundamental surveying campaigns in the mid to late 18<sup>th</sup> century (e.g., Lacaille in South Africa and Méchain and Delambre in France) led to errors in the perceived shape of the Earth, as well as its scale that influenced the definition of the length of a meter.  The vertical deflection, though generally excluded from modern EGM developments, nevertheless forms a valuable resource to validate such models.  It is also the vertical deflection that is indispensable for precision autonomous navigation (i.e., without external aids such as GPS) using inertial measurement units.  It is the deflection of the vertical that, measured solely along horizontal lines, would readily provide geoid undulation profiles, essential for the modernization of height systems (i.e., vertical geodetic control) without the laborious and traditional methods of spirit leveling.  But, measuring the deflection of the vertical is itself an arduous undertaking and this has essentially contributed to its neglect and/or underusage.  Even Vening-Meinesz’s formulas of convolution with gravity anomalies do not greatly facilitate its determination.  This presentation offers a review of the many roles the vertical deflection has, or could have, played over the centuries, how it has been measured or computed, and how gravity gradiometry might eventually awaken its full potential.</p>

NUMERICAL CALCULATION OF STRENGTH AND SHEAR RESISTANCE OF NON-RIGID ROAD PAVEMENT BY THE FINITE ELEMENT METHOD

The paper presents 2D mathematical simulation results for a T–90 tank interacting with the III-type road in a plane-strain formulation. The purpose of the work is to determine the vertical deflection of an asphalt-concrete road, as well as the load factor of the two-layer road pavement (dense-graded asphalt concrete, open-graded asphalt concrete) and two-layer roadbed (gravel roadbed, ground roadbed – silt sandy loam). To calculate the load factor of the road pavement, the ratio of the von Mises stress to the ultimate compression stress is used. To analyze the shear resistance of the roadbed, the modified Drucker-Prager strength criterion is utilized. The computed results reveal the maximum vertical deflection in the contact area of the tracks. In the same area, the load factor of the road pavement is 3–12, which indicates the high bearing capacity of the dense-graded asphalt concrete. Analysis of the shear resistance of the roadbed shows that irreversible deformations occur in the gravel base in the contact area of the tracks, which can lead to the subsidence of the coating, while the load factor for sandy loam is 3–10.