Beam Segments Research Articles

Three-level experimental approach for creep and shrinkage of high-strength high-performance concrete

Most of the existing prediction models for creep and shrinkage are established based on the statistical regression analysis of test data drawn mostly from experiments performed on normal-strength concrete, and they might not be as applicable to high-strength high-performance concrete. The prediction precision can be improved by carrying out on the given concrete short-term creep and shrinkage measurements. A three-level experimental approach for creep and shrinkage is proposed in this study. Take the high-strength high-performance concrete used in the auxiliary shipping channel bridge of Sutong Bridge for example, the detailed three-level experimental process and results were presented. The specimens were grouped on three levels: “Material level”, “Component level” and “Structural level”. On the first level, plain concrete specimens were experimented in a constant temperature and constant humidity room. On the second level, creep and shrinkage of reinforced concrete specimens with different reinforcement ratio were experimented. On the third level, the long-term behavior of a segmental concrete cantilever beam, 12.8m long, under natural environment which was close to that of the actual bridge was studied. This experimental approach can provide a new train of thought to improve the predicted precision of the creep and shrinkage effects of the long-span concrete structures.

A software tool to automatically assure and report daily treatment deliveries by a cobalt-60 radiation therapy device.

The aims of this study were to develop a method for automatic and immediate verification of treatment delivery after each treatment fraction in order to detect and correct errors, and to develop a comprehensive daily report which includes delivery verification results, daily image‐guided radiation therapy (IGRT) review, and information for weekly physics reviews. After systematically analyzing the requirements for treatment delivery verification and understanding the available information from a commercial MRI‐guided radiotherapy treatment machine, we designed a procedure to use 1) treatment plan files, 2) delivery log files, and 3) beam output information to verify the accuracy and completeness of each daily treatment delivery. The procedure verifies the correctness of delivered treatment plan parameters including beams, beam segments and, for each segment, the beam‐on time and MLC leaf positions. For each beam, composite primary fluence maps are calculated from the MLC leaf positions and segment beam‐on time. Error statistics are calculated on the fluence difference maps between the plan and the delivery. A daily treatment delivery report is designed to include all required information for IGRT and weekly physics reviews including the plan and treatment fraction information, daily beam output information, and the treatment delivery verification results. A computer program was developed to implement the proposed procedure of the automatic delivery verification and daily report generation for an MRI guided radiation therapy system. The program was clinically commissioned. Sensitivity was measured with simulated errors. The final version has been integrated into the commercial version of the treatment delivery system. The method automatically verifies the EBRT treatment deliveries and generates the daily treatment reports. Already in clinical use for over one year, it is useful to facilitate delivery error detection, and to expedite physician daily IGRT review and physicist weekly chart review.PACS number(s): 87.55.km

Vibration Analysis of a Cracked Beam on an Elastic Foundation

The transverse vibrations of cracked beams with rectangular cross sections resting on Pasternak and generalized elastic foundations are considered. Both the Euler–Bernoulli (EB) and Timoshenko beam (TB) theories are used. The open edge crack is represented as a rotational spring whose compliance is obtained by the fracture mechanics. By applying the compatibility conditions between the beam segments at the crack location and the boundary conditions, the characteristic equations are derived, from which the nondimensional natural frequencies are solved as the roots. Sample numerical results showing the effects of crack depth, crack location, foundation type and foundation parameters on the natural frequencies of the beam are presented. It is observed that the existence of crack reduces the natural frequencies, whereas the elasticity of the foundation increases the stiffness of the system and thus the natural frequencies. It is also observed that the type of elastic foundation has a significant effect on the natural frequencies of the cracked beam.

Calculation of the piezoelectric and flexoelectric effects in nanowires using a decoupled finite element analysis method

A simple and effective decoupled finite element analysis method was developed for simulating both the piezoelectric and flexoelectric effects of zinc oxide (ZnO) and barium titanate (BTO) nanowires (NWs). The piezoelectric potential distribution on a ZnO NW was calculated under three deformation conditions (cantilever, three-point, and four-point bending) and compared to the conventional fully coupled method. The discrepancies of the electric potential maximums from these two methods were found very small, validating the accuracy and effectiveness of the decoupled method. Both ZnO and BTO NWs yielded very similar potential distributions. Comparing the potential distributions induced by the piezoelectric and flexoelectric effects, we identified that the middle segment of a four-point bending NW beam is the ideal place for measuring the flexoelectric coefficient, because the uniform parallel plate capacitor-like potential distribution in this region is exclusively induced by the flexoelectric effect. This decoupled method could provide a valuable guideline for experimental measurements of the piezoelectric effects and flexoelectric effects in the nanometer scale.

Flexural behavior of precast concrete segmental beams with hybrid tendons and dry joints

Precast concrete segmental bridges (PCSBs) with hybrid tendons and dry joints might be the most competitive solution for achieving the advantages of rapid construction and favorable structural performance. A series of tests were carried out to investigate the flexural behavior of PCSBs with hybrid tendons and dry joints. Influences of hybrid tendons, load locations and joint numbers were studied. For comparison purpose, a monolithic beam with hybrid tendons was also tested. The deflections, ultimate loads, stresses of prestressing strands and failure modes were investigated. At the ultimate stage, the stresses of all tendons are greater than 1500MPa. The flexural strength of fully segmental beams with hybrid tendons of S-4 is 30% less than that of the monolithic beam with hybrid tendons of M-1. Due to a high concentration of rotation and deflection at individual joints, the flexural strength of the partially segmental beam with hybrid tendons of S-2 is 12.8% less than that of the fully segmental beam with hybrid tendons of S-4. The segmental beam with hybrid tendons can achieve satisfied flexural capacity and better ductility. The research outcome will help in understanding the roles of types of prestressing tendons and joints numbers on the flexural performance of the segmental bridges.

Leakage-Penumbra effect in intensity modulated radiation therapy step-and-shoot dose delivery.

To study the leakage-penumbra (LP) effect with a proposed correction method for the step-and-shoot intensity modulated radiation therapy (IMRT). Leakage-penumbra dose profiles from 10 randomly selected prostate IMRT plans were studied. The IMRT plans were delivered by a Varian 21 EX linear accelerator equipped with a 120-leaf multileaf collimator (MLC). For each treatment plan created by the Pinnacle(3) treatment planning system, a 3-dimensional LP dose distribution generated by 5 coplanar photon beams, starting from 0(o) with equal separation of 72(o), was investigated. For each photon beam used in the step-and-shoot IMRT plans, the first beam segment was set to have the largest area in the MLC leaf-sequencing, and was equal to the planning target volume (PTV). The overshoot effect (OSE) and the segment positional errors were measured using a solid water phantom with Kodak (TL and X-OMAT V) radiographic films. Film dosimetric analysis and calibration were carried out using a film scanner (Vidar VXR-16). The LP dose profiles were determined by eliminating the OSE and segment positional errors with specific individual irradiations. A non-uniformly distributed leaf LP dose ranging from 3% to 5% of the beam dose was measured in clinical IMRT beams. An overdose at the gap between neighboring segments, represented as dose peaks of up to 10% of the total BP, was measured. The LP effect increased the dose to the PTV and surrounding critical tissues. In addition, the effect depends on the number of beams and segments for each beam. Segment positional error was less than the maximum tolerance of 1 mm under a dose rate of 600 monitor units per minute in the treatment plans. The OSE varying with the dose rate was observed in all photon beams, and the effect increased from 1 to 1.3 Gy per treatment of the rectal intersection. As the dosimetric impacts from the LP effect and OSE may increase the rectal post-radiation effects, a correction of LP was proposed and demonstrated for the central beam profile for one of the planned beams. We concluded that the measured dosimetric impact of the LP dose inaccuracy from photon beam segment in step-and-shoot IMRT can be corrected.

On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through-width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature.

The new proposed details for moment resisting connections of steel beam to continuous concrete column

Six new details for composite steel–concrete connections are proposed for a continuous concrete column and a steel beam segment. A steel sleeve is used to connect the steel beam to the concrete column. Connection components are either steel studs or U-channels used in two different types of joints to connect the sleeve to the concrete column. Attachment of beam to the sleeve is in three different ways including direct connection, using steel plates at beam flange levels, and utilizing apron plates all around the column at beam flanges. The behavior of the connections is evaluated, and stiffness, strength, and ductility of the suggested connections are compared with the conventional steel and concrete joints. Effects of axial load, beam size, steel sleeve thickness, and height of steel sleeve are investigated. Based on the results of this study, appropriate ranges for the thickness and height of the steel sleeves are determined. In addition, some optimized design parameters are proposed in order to improve the behavior of the connections. The proposed connections are categorized based on their strength and ductility for use in ordinary, moderate, and special frames.

A Corotational Formulation for Large Displacement Analysis of Functionally Graded Sandwich Beam and Frame Structures

A corotational finite element formulation for large displacement analysis of planar functionally graded sandwich (FGSW) beam and frame structures is presented. The beams and frames are assumed to be formed from a metallic soft core and two symmetric functionally graded skin layers. The Euler-Bernoulli beam theory and von Kármán nonlinear strain-displacement relationship are adopted for the local strain. Exact solution of nonlinear equilibrium equations for a beam segment is employed to interpolate the displacement field for avoiding the membrane locking. An incremental-iterative procedure is used in combination with the arc-length control method to compute the equilibrium paths. Numerical examples show that the proposed formulation is capable of evaluating accurately the large displacement response with just several elements. A parametric study is carried out to highlight the effect of the material distribution, the core thickness to height ratio on the large displacement behaviour of the FGSW beam, and frame structures.

Dosimetric quality, accuracy, and deliverability of modulated radiotherapy treatments for spinal metastases

Cancer often metastasizes to the vertebra, and such metastases can be treated successfully using simple, static posterior or opposed-pair radiation fields. However, in some cases, including when re-irradiation is required, spinal cord avoidance becomes necessary and more complex treatment plans must be used. This study evaluated 16 sample intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) treatment plans designed to treat 6 typical vertebral and paraspinal volumes using a standard prescription, with the aim of investigating the advantages and limitations of these treatment techniques and providing recommendations for their optimal use in vertebral treatments. Treatment plan quality and beam complexity metrics were evaluated using the Treatment And Dose Assessor (TADA) code. A portal-imaging–based quality assurance (QA) system was used to evaluate treatment delivery accuracy, and radiochromic film measurements were used to provide high-resolution verification of treatment plan dose accuracy, especially in the steep dose gradient regions between each vertebral target and spinal cord. All treatment modalities delivered approximately the same doses and the same levels of dose heterogeneity to each planning target volume (PTV), although the minimum PTV doses in the vertebral plans were substantially lower than the prescription, because of the requirement that the plans meet a strict constraint on the dose to the spinal cord and cord planning risk volume (PRV). All plans met required dose constraints on all organs at risk, and all measured PTV-cord dose gradients were steeper than planned. Beam complexity analysis suggested that the IMRT treatment plans were more deliverable (less complex, leading to greater QA success) than the VMAT treatment plans, although the IMRT plans also took more time to deliver. The accuracy and deliverability of VMAT treatment plans were found to be substantially increased by limiting the number of monitor units (MU) per beam at the optimization stage, and thereby limiting beam modulation complexity. The VMAT arcs that were optimized with MU limitation had higher QA pass rates as well as higher modulation complexity scores (less complexity), lower modulation indices (less modulation), lower MU per beam, larger beam segments, and fewer small apertures than the VMAT arcs that were optimized without MU limitation. It is recommended that VMAT treatments for vertebral volumes, where the PTV abuts or surrounds the spinal cord, should be optimized with MU limitation. IMRT treatments may be preferable to the VMAT treatments, for dosimetry and deliverability reasons, but may be inappropriate for some patients because of their increased treatment delivery time.

New Method for a Beam Resting on a Tensionless and Elastic-Plastic Foundation Subjected to Arbitrarily Complex Loads

AbstractMany soil-structure interaction problems can be idealized as foundation beam problems. In the present work, the tensionless contact problem of an Euler-Bernoulli beam of finite length resting on an elastic-plastic foundation and carrying arbitrarily complex static loads was investigated. Fourth-order difference equations dealing with the vertical displacement of a beam under three different soil support conditions were presented for each beam segment. On the basis of the continuity conditions at the junctions of two adjacent segments, the response of the whole beam was expressed through the response of the initial beam segment in a matrix form. A comparison with the results from the transfer displacement function method (TDFM) showed the expected complete agreement. A simple case was used to illustrate the influence of the foundation models (elastic model, tensionless-elastic model, and tensionless and elastic-plastic model), and the tensionless and nonlinear behavior of the soil on the beam respon...

Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam

AbstractA mechanically-based nonlocal Timoshenko beam model, recently proposed by the authors, hinges on the assumption that nonlocal effects can be modeled as elastic long-range volume forces and moments mutually exerted by nonadjacent beam segments, which contribute to the equilibrium of any beam segment along with the classical local stress resultants. Long-range volume forces/moments linearly depend on the product of the volumes of the interacting beam segments, and on pure deformation modes of the beam, through attenuation functions governing the space decay of nonlocal effects. This paper investigates the response of this nonlocal beam model when viscoelastic long-range interactions are included, modeled by Caputo’s fractional derivatives. The finite-element method is used to discretize the pertinent fractional-order equations of motion. Closed-form solutions are obtained for creep tests by typical tools of fractional calculus. Numerical results are presented for various nonlocal parameters.

A Leaf Sequencing Algorithm for Multileaf Collimator in Intensity Modulated Radiotherapy

Background: In intensity modulated radiotherapy (IMRT), leaf sequencing algorithm is used to control the multileaf collimator (MLC) to produce beam segments resulting in a beam intensity map for highly conformal dose coverage. Objectives: A novel leaf sequencing algorithm based on the Langer’s integer programming method is proposed. Methods: Our algorithm selected the horizontal or orthogonal leaf direction of beam intensity maps as per Xia and Verhey’s algorithm with a new constraint to optimize the MLC leaf travel distance (LTD). Results: Comparison among the leaf sequencing algorithms from Xia and Verhey, Langer et al. and ours, both Langer’s and our algorithms have lower monitor units (8 and 10) compared to 15 of Xia’s algorithm. For the number of segment and LTD, our new algorithm has the smallest number and distance (5 and 7 cm) compared to both the Xia’s and Langer’s algorithm (7 and 24 cm and 6 and 20 cm). This revealed that model modifications could yield better results according to three criteria namely, total number of monitor unit, number of segment and LTD. Conclusions: In conclusion of experimental comparison performed, our algorithm can generate photon beam in IMRT dose delivery with lower monitor unit, number of segment and LTD compared to the Xia’s and Langer’s algorithm.

Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton’s principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.

Natural frequency analyses of segmented Timoshenko–Euler beams using the Rayleigh–Ritz method

This paper proposes part by part usage of Timoshenko and Euler–Bernoulli beam theories for obtaining natural frequencies of the non-uniform beam that has partially thick and thin beam vibration characteristics. The paper also presents convergence tests to determine proper function among the simple admissible shape functions taken into consideration. By doing so, closer approximation of the Rayleigh–Ritz method is achieved. The method is applied using a simple computation technique. In the analyses of the Timoshenko beams, an additional function is employed to identify shear deformation and rotational inertia effects. Modified angular displacement functions are defined to improve convergence capability of the method. Furthermore, optimal numbers of lateral and angular displacement terms are investigated for suggested function couple of the Timoshenko beams. Efficiencies of part by part modelling and advantages of novel approaches suggested for the Rayleigh–Ritz approximation are introduced by the comparative studies performed on tapered, stepped and continuously segmented beams under some classical end conditions. All of the computational outcomes for the beams with rectangular cross-section are validated by the results given in current literature and also those obtained by the finite element analyses.

Hencky Bar-Chain Model for Buckling and Vibration of Beams with Elastic End Restraints

This paper presents the Hencky bar-chain model (HBM) for buckling and vibration analyses of Euler–Bernoulli beams with elastic end restraints. The Hencky bar-chain comprises rigid beam segments (of length a = L/n where L is the total length of beam and n the number of beam segments) connected by frictionless hinges with elastic rotational springs of stiffness EI/a where EI is the flexural rigidity of the beam. The elasticity and the mass of the beam are concentrated at the hinges with rotational springs. The key contribution of this paper lies in the modeling of the elastic end restraints of the Hencky bar-chain that will simulate the same buckling and vibration results as that furnished by the first-order central finite difference beam model (FDM) which was earlier shown to be analogous to the HBM. The establishment of such a physical discrete beam model allows one to obtain solutions for beam-like structure with repetitive cells (or elements) as well as to calibrate the Eringen's coefficient e0 in the nonlocal beam theory that captures the small length scale effect.

Application of Chebyshev-tau method to the free vibration analysis of stepped beams

A Chebyshev-tau method based on Euler–Bernoulli beam theory and Timoshenko beam theory is applied to the free vibration analyses of stepped beams. The lateral deflection and the rotation of each segment of stepped beam are approximated by partial sums of Chebyshev expansions. The number of expansions per segment is larger by four than the number of intended degrees of freedom, and the surplus expansions accommodate the continuity conditions and the boundary conditions. The governing equation and test function are integrated to result in inner products and the orthogonality property of Chebyshev polynomials is utilized. Numerical examples are provided for a various number of steps and boundary conditions. The results of the present method coincide with those of theoretical results for both of lower modes and high-order modes. It is demonstrated that the present method computes the natural frequencies of stepped beams accurately when compared with experimental measurements.

SU‐E‐T‐814: Whole Breast Irradiation with Two Different Intensity Modulation Radiotherapy Techniques

Purpose:Breast cancer now mainly received forward intensity modulation radiotherapy (f‐IMRT) and inverse IMRT (i‐IMRT). The purpose of this study was to observe the differences of two treatment methods.Methods:10 patients after left breast‐conserving surgery were selected to receive radiotherapy. For each patient, two treatment plans (f‐IMRT and i‐IMRT) were designed. For f‐IMRT plans, two tangent beams were designed to the target, and in each tangent orientation two or three segment beams were designed to reduced high dose region in the target and the dose of lung received. For i‐IMRT plans, two tangent beams were designed to the target and the treatment planning system optimize the dose according to the optimization parameters. For each plan 50Gy was prescribed.Results:In f‐IMRT and i‐IMRT plans, the average target conformal index (CI) were (0.67±0.06) and (0.66±0.06), (P>0.05); average homogeneity index (HI) were (28.2±6.0)% and (26.1±6.8)%, (P>0.05); volume of left lung received 20Gy (V20) were (18.7±3.3)% and (17.0±2.8)%, (P<0.05), V30 were (15.5±3.0)% and (14.0±2.6)%, (P<0.05); V30 of heart were (4.1±3.1)% and (3.5±2.5)%, (P>0.05); Monitor Unit (MU) were (262±5)MU and (308±14)MU.Conclusion:Compared with i‐IMRT plan, for breast cancer, the differences of CI and HI were not significant. Because of fewer MU, f‐IMRT plan could reduce the machine abrasion and treatment time, but dose of normal tissue received were higher significantly than i‐IMRT plan.

SU‐E‐T‐356: Efficient Segmentation of Flattening Filter Free Photon Beamsfor 3D‐Conformal SBRT Treatment Planning

Purpose:It has been argued that a 3D‐conformal technique (3DCRT) is suitable for SBRT due to its simplicity for non‐coplanar planning and delivery. It has also been hypothesized that a high dose delivered in a short time can enhance indirect cell death due to vascular damage as well as limiting intrafraction motion. Flattening Filter Free (FFF) photon beams are ideal for high dose rate treatment but their conical profiles are not ideal for 3DCRT. The purpose of our work is to present a method to efficiently segment an FFF beam for standard 3DCRT planning.Methods:A 10×10 cm Varian True Beam 6X FFF beam profile was analyzed using segmentation theory to determine the optimum segmentation intensity required to create an 8 cm uniform dose profile. Two segments were automatically created in sequence with a Varian Eclipse treatment planning system by converting isodoses corresponding to the calculated segmentation intensity to contours and applying the “fit and shield” tool. All segments were then added to the FFF beam to create a single merged field. Field blocking can be incorporated but was not used for clarity.Results:Calculation of the segmentation intensity using an algorithm originally proposed by Xia and Verhey indicated that each segment should extend to the 92% isodose. The original FFF beam with 100% at the isocenter at a depth of 10 cm was reduced to 80% at 4cm from the isocenter; the segmented beam had +/−2.5 % uniformity up to 4.4cm from the isocenter. An additional benefit of our method is a 50% decrease in the 80%‐20% penumbra of 0.6cm compared to 1.2cm in the original FFF beam.Conclusion:Creation of two optimum segments can flatten a FFF beam and also reduce its penumbra for clinical 3DCRT SBRT treatment.

SU‐E‐T‐605: Performance Evaluation of MLC Leaf‐Sequencing Algorithms in Head‐And‐Neck IMRT

Purpose:To investigate the efficiency of three multileaf collimator (MLC) leaf‐sequencing algorithms proposed by Galvin et al, Chen et al and Siochi et al using external beam treatment plans for head‐and‐neck intensity modulated radiation therapy (IMRT).Methods:IMRT plans for head‐and‐neck were created using the CORVUS treatment planning system. The plans were optimized and the fluence maps for all photon beams determined. Three different MLC leaf‐sequencing algorithms based on Galvin et al, Chen et al and Siochi et al were used to calculate the final photon segmental fields and their monitor units in delivery. For comparison purpose, the maximum intensity of fluence map was kept constant in different plans. The number of beam segments and total number of monitor units were calculated for the three algorithms.Results:From results of number of beam segments and total number of monitor units, we found that algorithm of Galvin et al had the largest number of monitor unit which was about 70% larger than the other two algorithms. Moreover, both algorithms of Galvin et al and Siochi et al have relatively lower number of beam segment compared to Chen et al. Although values of number of beam segment and total number of monitor unit calculated by different algorithms varied with the head‐and‐neck plans, it can be seen that algorithms of Galvin et al and Siochi et al performed well with a lower number of beam segment, though algorithm of Galvin et al had a larger total number of monitor units than Siochi et al.Conclusion:Although performance of the leaf‐sequencing algorithm varied with different IMRT plans having different fluence maps, an evaluation is possible based on the calculated number of beam segment and monitor unit. In this study, algorithm by Siochi et al was found to be more efficient in the head‐and‐neck IMRT.The Project Sponsored by the Fundamental Research Funds for the Central Universities (J2014HGXJ0094) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.