Beam Segments Research Articles

Natural frequencies analysis of a composite beam consisting of Euler-Bernoulli and Timoshenko beam segments alternately

Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections. For the special geometry characteristic, the beam was modelled as the combination of long equal-length uniform Euler-Bernoulli beam segments and short equal-length uniform Timoshenko beam segments alternately. By using continuity conditions, the hybrid beam unit (ETE-B) consisting of Euler-Bernoulli beam, Timoshenko beam and Euler-Bernoulli beam in sequence was developed. Classical boundary conditions of pinned-pinned, clamped-clamped and clamped-free were considered to obtain the natural frequencies. Numerical examples of the equal-length composite beam with 1, 2 and 3 ETE-B units were presented and compared with the equal-length and equal-cross-section Euler-Bernoulli beam, respectively. The work demonstrates that natural frequencies of the composite beam are larger than those of the Euler-Bernoulli beam, which in practice, is the interpretation that the inner-welded plate can strengthen a hollow beam. In this work, comparisons with the finite element calculation were presented to validate the ETE-B model.

Displacement-based finite layer element analysis on rotational behavior of reinforced concrete beam segments containing hinges

Rotation capacity of reinforced concrete (RC) beams is a vital property for its relationships with moment redistribution, energy absorbability, and so on. Evaluation of the rotation capacity has been one of the classic and intractable problems in structural engineering over the past decades. The precise prediction about rotational behavior of a RC beam is the primary basis of quantifying its rotation capacity. In this paper a displacement-based finite layer element method considering the factors of flexural cracks, concrete crushing, and pre-and postyield behavior of bond is presented to predict the rotational behavior. In conclusion, it shows good agreement between simulation results, implemented by the proposed method, and the test results in the literature.

A Half-Arc Multiple Deep-Inspiration Breath-Hold Volumetric Modulated Arc Therapy for a Lung Tumor with 10 MV Flattening-Filter-Free Beams and an Image Sensor Measuring a Distance Map to Thorax Surface: An Initial Clinical Experience

A technique for multiple deep-inspiration breath-hold (DIBH) volumetric modulated arc therapy (VMAT) for a lung tumor has been proposed with 10 MV flattening-filter-free beams and an image sensor measuring a distance map to thorax surface. Planning CT images were acquired under a DIBH condition and a clinical target volume (CTV) was contoured. This procedure was repeated five times and an internal target volume (ITV) among the multiple DIBHs was created by integrating the five CTVs. A planning target volume (PTV) was defined by adding an isotropic margin of 5 mm to the ITV. Immediately before treatment, a 30-second half-arc cone-beam computer tomography (CBCT) imaging was performed under another DIBH condition, and the couch was repositioned so that tumor may be located inside the PTV contours. An infrared distance measurement device having laser diodes and an image sensor was attached to the couch, and a distance map to the patient thorax surface was recorded as a reference during still another DIBH condition. A half-arc segmented VMAT beams with two beam interrupts were delivered to the patient under multiple DIBHs, where the delivery time of each of the three segmented beams was 30 seconds. During the beam delivery, the distance map was monitored in real time to confirm that the distance to the thorax surface remained unchanged. In-treatment CBCT images suggested that the tumor position at the time of tumor registration was accurately reproduced during the DIBH VMAT delivery.

Dental measurements and Bolton index reliability and accuracy obtained from 2D digital, 3D segmented CBCT, and 3d intraoral laser scanner.

BackgroundTo compare the reliability and accuracy of direct and indirect dental measurements derived from two types of 3D virtual models: generated by intraoral laser scanning (ILS) and segmented cone beam computed tomography (CBCT), comparing these with a 2D digital model.Material and MethodsOne hundred patients were selected. All patients’ records included initial plaster models, an intraoral scan and a CBCT. Patients´ dental arches were scanned with the iTero® intraoral scanner while the CBCTs were segmented to create three-dimensional models. To obtain 2D digital models, plaster models were scanned using a conventional 2D scanner. When digital models had been obtained using these three methods, direct dental measurements were measured and indirect measurements were calculated. Differences between methods were assessed by means of paired t-tests and regression models. Intra and inter-observer error were analyzed using Dahlberg´s d and coefficients of variation.ResultsIntraobserver and interobserver error for the ILS model was less than 0.44 mm while for segmented CBCT models, the error was less than 0.97 mm. ILS models provided statistically and clinically acceptable accuracy for all dental measurements, while CBCT models showed a tendency to underestimate measurements in the lower arch, although within the limits of clinical acceptability.ConclusionsILS and CBCT segmented models are both reliable and accurate for dental measurements. Integration of ILS with CBCT scans would get dental and skeletal information altogether. Key words:CBCT, intraoral laser scanner, 2D digital models, 3D models, dental measurements, reliability.

Analiza slobodnih ravanskih oscilacija struktura sastavljenih od krutih tela i elastičnih grednih segmenata

This article presents free vibration analysis of structures composed of rigid bodies connected with elastic beam segments. It is assumed that the mass centers of rigid bodies are not located on the neutral axes of undeformed elastic beam segments as well as rigid bodies perform planar motion in the same plane and their mass centers are located in that plane. For determination of natural frequencies of the system, modification of the conventional continuous-mass transfer matrix method has been performed. The elastic beam segments are treated as Euler-Bernoulli beams. Numerical example is presented.

Linear and angular momenta in tightly focused vortex segmented beams of light (Invited Paper)

We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.

Dynamic analysis of a cable-stayed bridge subjected to a continuous sequence of moving forces

In this work, an eigenfunction expansion approach is used to study the dynamic response of a cable-stayed bridge excited by a continuous sequence of identical, equally spaced moving forces. The nonlinear dynamic response of the cable-stayed bridge is obtained by simultaneously solving nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality conditions of exact mode shapes of the linearized cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is numerically solved. Convergence of the dynamic response from the Galerkin method is investigated. Effects of close natural frequencies, mode localization, the distance between any two neighboring forces, and geometric nonlinearities of stay cables on the forced dynamic response of the cable-stayed bridge are captured using a convergent modal truncation.

Deformation analysis of a non-prismatic beam with corrugated steel webs in the elastic stage

Based on the concept of isoparametric mapping, a generic approach for investigating the bending and shear deformation in a non-prismatic elastic beam with corrugated steel webs (CSWs) was presented in this study. The strain field of an actual element (namely, the non-prismatic beam segments) is expressed as a function of the local coordinates in the parent element. Continually, the solution of the bending and shear deformation of the non-prismatic beam segment can be transformed into the integration of strain in the parent element under local coordinates. Since it is usually laborious to solve the displacement field by direct integration of strain in a non-prismatic beam segment using global coordinates. In addition, this study found that shear deformation cannot be ignored in the actual design of this type of structure because the thin-walled section has a small shear stiffness. In contrast, for a composite beam with CSWs, shear deformation occurs beyond bending deformation and becomes a major contributor of total deformation in some critical sections. Finally, experimental study of the mechanical properties of a non-prismatic beam with CSWs is conducted for the first time. The experimental results further demonstrate the validity of the proposed theoretical analysis methods.

Multiple breath-hold segmented volumetric modulated arc therapy under real-time fluoroscopic image guidance with implanted fiducial markers: preliminary clinical experience

A technique for multiple breath-hold segmented volumetric modulated arc therapy (VMAT) has been proposed under real-time fluoroscopic image guidance with implanted fiducial markers. Fiducial markers were embedded as close as possible to a tumour and the patient was asked to breathe in slowly under fluoroscopy. Immediately after the marker positions on the fluoroscopic image moved inside the planned marker contours transferred from a digitally reconstructed radiographic image at each gantry start angle, the patient was asked to hold their breath and a segmented VMAT beam was delivered. During beam delivery, the breath-hold status was continuously monitored by viewing a pointer in a breath monitoring system, Abches (Apex Medical, Tokyo, Japan), with the aid of a video camera installed in the treatment room. As long as the pointer stayed still, the segmented VMAT delivery continued for a preset period of 15–30 s, depending on the breath-hold capability of each patient. As soon as each segmented delivery was completed, the beam interrupt button was pushed; subsequently, the patient was asked to breathe freely. Because the preset breath-hold period was determined in order for each patient to hold their breath without fail, an intermediate beam interrupt due to breath-hold failure during the segmented beam delivery was not observed. This procedure was repeated until all the segmented VMAT beams were delivered. A case of pancreatic cancer is reported here as a preliminary study. The proposed technique may be clinically advantageous for treating tumours that move with respiration, including pancreatic cancer, lung tumour and other abdominal cancers.

Cyclic Behavior of Replaceable Steel Coupling Beams

For improving the seismic resiliency of coupled shear wall systems, a type of replaceable steel coupling beam was developed, which consists of a central “fuse” shear link connecting to steel beam segments at its two ends. Inelastic deformation is concentrated in the shear link during a severe earthquake, and the damaged links can be replaced easily as specialized link-to-beam connections are adopted. This paper presents a series of quasi-static tests conducted to examine the seismic behavior and replaceability of the replaceable coupling beams. A total of four large-scale specimens were designed and tested, where different types of beam-to-link connections were adopted, including end plate, splice plate, bolted web, and adhesive web. All specimens fully developed the shear strength of the fuse links and showed large inelastic rotation capacity of no less than 0.06 rad, except for the specimen with the adhesive web connection, which failed at an early stage. The specimen with the end plate connection had inelastic deformation concentrated in the shear link, showing very stable hysteresis behavior. Slippage of high-strength bolts was observed at the splice plate and bolted web connections, which led to increased deformation and “pinching” in hysteresis loops of coupling beams. Interestingly, at a coupling beam rotation exceeding 0.01 rad, a large axial force developed in the steel coupling beams, the maximum value of which reached approximately a quarter to half of the axial yield strength of the shear link. In addition, on-site replacement of shear links was demonstrated after the coupling beam specimens experienced 0.02-rad rotation. The end plate connection was replaced within the shortest time, whereas the bolted web connection was able to accommodate the largest residual deformation.

A pulse-front-tilt-compensated streaked optical spectrometer with high throughput and picosecond time resolution.

A high-throughput, broadband optical spectrometer coupled to the Rochester optical streak system equipped with a Photonis P820 streak tube was designed to record time-resolved spectra with 1-ps time resolution. Spectral resolution of 0.8 nm is achieved over a wavelength coverage range of 480 to 580 nm, using a 300-groove/mm diffraction grating in conjunction with a pair of 225-mm-focal-length doublets operating at an f/2.9 aperture. Overall pulse-front tilt across the beam diameter generated by the diffraction grating is reduced by preferentially delaying discrete segments of the collimated input beam using a 34-element reflective echelon optic. The introduced delay temporally aligns the beam segments and the net pulse-front tilt is limited to the accumulation across an individual sub-element. The resulting spectrometer design balances resolving power and pulse-front tilt while maintaining high throughput.

Local coordinate systems-based method to analyze high-order modes of n-step Timoshenko beam

High-frequency transverse vibration of stepped beams has attracted increasing attention in various industrial areas. For an n-step Timoshenko beam, the governing differential equations of transverse vibration have been well established in the literature on the basis of assembling classic Timoshenko beam equations for uniform beam segments. However, solving the governing differential equation has not been resolved well to date, manifested by a computational bottleneck: only the first k modes (k ≤ 12) are solvable for i-step (i ≥ 0) Timoshenko beams. This bottleneck diminishes the completeness of stepped Timoshenko beam theory. To address this problem, this study first reveals the root cause of the bottleneck in solving the governing differential equations for high-order modes, and then creates a sophisticated method, based on local coordinate systems, that can overcome the bottleneck to accomplish high-order mode shapes of an n-step Timoshenko beam. The proposed method uses a set of local coordinate systems in place of the conventional global coordinate system to characterize the transverse vibration of an n-step Timoshenko beam. With the method, the local coordinate systems can simplify the frequency equation for the vibration of an n-step Timoshenko beam, making it possible to obtain high-order modes of the beam. The accuracy, capacity, and efficiency of the method based on local coordinate systems in acquiring high-order modes are corroborated using the well-known exact dynamic stiffness method underpinned by the Wittrick-Williams algorithm as a reference. Removal of the bottlenecks in solving the governing differential equations for high-order modes contributes usefully to the completeness of stepped Timoshenko beam theory.

Laminated connections for structural glass components: a full-scale experimental study

The use of glass material for structural components has drastically increased in the last decade. Among others, a laminated connection is a type of adhesive joint that makes use of foil interlayer adhesive to transfer forces between glass and metal parts. In this work, the use of embedded laminated connections is studied as connection between glass beams. In particular, it is experimentally investigated the use of embedded connections laminated to make a moment joint between laminated glass beam segments. The mechanical behaviour of such glass beams with embedded laminated connections is studied under different loading scenario. Tests are performed under monotonic, creep and damage protocol. Different geometry and location of the embedded laminated connections are compared. The results of this work showed that embedded laminated connections represent an efficient means of load transfer between glass beams. It is observed that the choice of an appropriate geometry and location of the embedded connections can provide a substantial enhancement to the mechanical behaviour of the beam. In particular, a redundant and ductile structural behaviour of the moment connection can be achieved. Furthermore, results also showed that beams with embedded laminated connections are able to resist to severe damage scenarios and to sustain the applied load over time, even in the case of breakage of all glass panels.

A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

As one of major failure modes of mechanical structures subjected to periodic loads, embedded cracks due to fatigue can cause catastrophic failure of machineries. Understanding the dynamic characteristics of a structure with an embedded crack is helpful for early crack detection and diagnosis. In this work, a new three-segment beam model with local flexibilities at crack tips is developed to investigate the vibration of a cantilever beam with a closed, fully embedded horizontal crack, which is assumed to be not located at its clamped or free end or distributed near its top or bottom side. The three-segment beam model is assumed to be a linear elastic system, and it does not account for the nonlinear crack closure effect; the top and bottom segments always stay in contact at their interface during the beam vibration. It can model the effects of local deformations in the vicinity of the crack tips, which cannot be captured by previous methods in the literature. The middle segment of the beam containing the crack is modeled by a mechanically consistent, reduced bending moment. Each beam segment is assumed to be an Euler–Bernoulli beam, and the compliances at the crack tips are analytically determined using a J-integral approach and verified using commercial finite element software. Using compatibility conditions at the crack tips and the transfer matrix method, the nature frequencies and mode shapes of the cracked cantilever beam are obtained. The three-segment beam model is used to investigate the effects of local flexibilities at crack tips on the first three natural frequencies and mode shapes of the cracked cantilever beam. A stationary wavelet transform (SWT) method is used to process the mode shapes of the cracked cantilever beam; jumps in single-level SWT decomposition detail coefficients can be used to identify the length and location of an embedded horizontal crack.

An Edge-integrated Connection for Segmented Glass Beams

There are different options to obtain a structural glass beam with a span of more than 6 meters. One option is segmentation, which has many advantages compared with the other options. However, the choice for segmentation is often avoided, because of aesthetic reasons. Existing connections, even the most slender ones, result in a reduction of the transparency of the beam. While transparency is the key reason to use glass beams. In this paper a connection is presented that should improve the transparency of segmented glass beam. The connection is integrated in the least transparent part of a glass segment, the edge. It has a twofold effect; the transparency of the beam will decrease less, and by following the contours of the segment the connection is less noticeable. Since such a connection seems to be highly compatible with edge-integrated steel reinforcement, which can be applied to reach safe failure behavior, it is investigated how reinforced beam segments can be connected in an edge-integrated way. A connection is designed and its performance is determined by finite element analysis and physical testing of prototypes.

SU‐F‐T‐527: A Novel Dynamic Multileaf Collimator Leaf‐Sequencing Algorithm in Radiation Therapy

Purpose:A novel leaf‐sequencing algorithm is developed for generating arbitrary beam intensity profiles in discrete levels using dynamic multileaf collimator (MLC). The efficiency of this dynamic MLC leaf‐sequencing method was evaluated using external beam treatment plans delivered by intensity modulated radiation therapy technique.Methods:To qualify and validate this algorithm, integral test for the beam segment of MLC generated by the CORVUS treatment planning system was performed with clinical intensity map experiments. The treatment plans were optimized and the fluence maps for all photon beams were determined. This algorithm started with the algebraic expression for the area under the beam profile. The coefficients in the expression can be transformed into the specifications for the leaf‐setting sequence. The leaf optimization procedure was then applied and analyzed for clinical relevant intensity profiles in cancer treatment.Results:The macrophysical effect of this method can be described by volumetric plan evaluation tools such as dose‐volume histograms (DVHs). The DVH results are in good agreement compared to those from the CORVUS treatment planning system.Conclusion:We developed a dynamic MLC method to examine the stability of leaf speed including effects of acceleration and deceleration of leaf motion in order to make sure the stability of leaf speed did not affect the intensity profile generated. It was found that the mechanical requirements were better satisfied using this method.The Project is sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

SU-G-BRB-06: Commissioning and Evaluation of EPID-Based in Vivo Dosimetry Software Using a Tissue-Maximum Ratio Approach

Purpose: To commission and evaluate an in vivo EPID-based transit dosimetry software (EPIgray, DOSIsoft, Cachan, France) using simple fields and TG119-based IMRT treatment plans. Methods: EPIgray was commissioned on a Truebeam based on finite tissue-maximum ratio (fTMR) measurements with solid water blocks of thicknesses between 0 and 37 cm. Field sizes varied from 2×2 to 20×20 cm2. Subsequently, treatment plans of single and opposed beams with field sizes between 4×4 and 15×15 cm2 as well as IMRT plans were measured to evaluate the dose reconstruction accuracy. Single field dose predictions were made for anterior-posterior and lateral beams. IMRT plans were created based on TG119 recommendations. The reconstructed dose was compared to the planned dose for selected points at isocenter and away from isocenter. Results: For single square fields, the dose in EPIgray was reconstructed within 3% accuracy at isocenter relative to the planned dose. Similarly, the relative deviation of the total dose was accurately reconstructed within 3% for all IMRT plans with points placed inside a high dose region near the isocenter. Predictions became less accurate than 5% when the evaluation point was outside the majority of IMRT beam segments. Additionally, points 5 cm or more away from the isocenter or within an avoidance structure were predicted less reliably. Conclusion: EPIgray formalism accuracy is adequate for an efficient error detection system. It provides immediate intra-fractional feedback on the delivery of treatment plans without affecting the treatment beam. Besides the EPID, no additional hardware is required, which makes it accessible to all clinics. The software evaluates point dose measurements to verify treatment plan delivery and patient positioning within 5% accuracy, depending on the placement of evaluation points. EPIgray is not intended to replace patient-specific quality assurance but should be utilized as an additional layer of safety for continuous patient treatment verification. This research is supported by DOSIsoft.

Dynamic response of a cable-stayed bridge subjected to a moving vehicle load

In this work, the dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a moving vehicle load, is studied. The vehicle is modeled as a mass–spring–damper system moving at a constant velocity, which is assumed to keep contact with the deck beam at all times. Convective velocity and acceleration terms associated with the moving vehicle as it traverses along the vibrating deck beam are taken into consideration, as well as geometric nonlinearities of stay cables. The nonlinear response of the cable-stayed bridge is obtained by solving nonlinear and linear partial differential equations which govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality relations of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear cable-stayed bridge model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is calculated using the Runge–Kutta–Fehlberg method in MATLAB. Convergence of the dynamic response from the Galerkin method is investigated for two cases in which the velocities or masses of the moving vehicle are different. Results show that an accurate calculation of the dynamic response of the cable-stayed bridge needs use of a large number of modes of the linearized undamped cable-stayed bridge model, and needs many more modes for the deck beam than stay cables. Moreover, effects of the velocity and mass of the moving vehicle and the convective terms on the dynamic response of the cable-stayed bridge are studied with convergent Galerkin truncation.

Design of PC beam-column joint applied X-braced bars in the segmented structural system

This study suggests a joint design using an X-brace bar to identify the stability and structural performance of a precast concrete (PC) beam-column joint design, which may cause problems when used in a segmented PC beam system for a long-span structure. For this, an experimental PC beam-column model at half scale was designed and veri­fied for applicability of X-braced bars in a panel zone. While previous studies suggested the development of a long-span structural system using precast concrete (PC) and described the problems with PC beam-column joints, this study proposes a solution to improve the structural stability and performance of a PC beam-column joint design and conducts analytical verification.

Analysis of Elastic Flexural Waves in Non-Uniform Beams Based on Measurement of Strains and Accelerations

Elastic flexural waves in an unloaded and unsupported segment of a non-uniform beam were considered. A method based on Timoshenko’s model was established for evaluation of shear force, transverse velocity, bending moment and angular velocity at an arbitrary section from four independent measurements of such quantities at one to four sections. From the evaluated quantities, shear stress, power transmission, etc. can be obtained. Experimental tests were carried out with an aluminium beam which had an abrupt change in height from 15 to 20 mm and was equipped with strain gauges and accelerometers at four uniformly distributed measurement sections and at three evaluation sections. The distance between the two outermost measurement sections was 600 mm, corresponding to 1.12 wave lengths at the upper end of the frequency interval 2500 Hz considered. Bending moments and transverse velocities evaluated from four measurements of any one of these quantities agreed well with those measured at evaluation sections located (i) centrally among the measurement sections and (ii) at a distance of 100 mm, or 0.17 wave lengths, outside. When it was located (iii) at a distance of 500 mm, or 0.83 wave lengths, outside, there was relatively large disagreement as expected from error analysis.