Beam Loading Conditions Research Articles

Utilization of Short Span Web-Tapered Beams Using Flexible Nodal Bracing

For many years member with varying cross-sectional dimensions along the length have been widely used in steel structures. The use of nodal braces to enhance the load-carrying capacity and stability of these elements is prevalent. These supports ensure structural stability by regulating the distribution of loads within the structural system while also enhancing the structure's resistance to lateral loads. Presently, the design of these nodal braces are carried out according to requirements outlined in Design Guide 25 and AISC Specification (2022). However, these standards offer a general framework for elements with fixed brace conditions and prismatic cross-section. This study aims to be a pioneering investigation into the variation of brace force values in short-span and compact web-tapered beams under different loading conditions. The article seeks to comprehensively examine the requirements and limits of brace force in short-span web-tapered compact beams. To achieve this goal, parametric finite element analyses is utilized to explore how brace force changes concerning beam geometry, material properties, and loading conditions. The beam used was considered as doubly symmetric and divided into 100 nodes and supported by a nodal brace at the middle node. The beam is 50 inches long, tapering from 42 inches to 36.40 inches over its span of 100 nodes. In terms of finite element analysis, the software utilized significantly influences the accuracy and reliability of results, particularly in scenarios involving inelastic nonlinear analysis. In this study, the Abaqus program was employed specifically to conduct parametric finite element analyses, considering the complexities of inelastic material behavior. The findings of this research are intended to contribute to the development of a new design method for determining the requirements and limits of brace force in short-span and variable cross-sectional dimension compact beams. Consequently, the aim is to enable the safe and economical design of such beams, providing engineers with ideas to consider and data to utilize in their designs.

Experimental investigation of the shear force capacity of prismatic cross laminated timber beams

Experimental tests of Cross Laminated Timber (CLT) under in-plane beam loading conditions are presented. The influence of the element layup, the individual lamination width, and the beam overhang at the supports on the shear force capacity was investigated. All the CLT beams had the same gross cross section, and a 4-point-bending test setup was used. The experimentally determined load-bearing capacities are compared with the load-bearing capacities resulting from analytical methods proposed for structural design, focusing on shear failure in the crossing areas of flatwise bonded laminations (shear failure mode III). The test results indicate no or very small influence of the element layup and the lamination width on the shear force capacity. These results partly contradict the predictions of the proposed design methods. Of the three studied beam geometry parameters, the beam overhang at the support had the greatest influence on the load-bearing capacity.

Structural behaviour of air-inflated beams

Inflatable structures have been proposed for many applications because they are constructed of lightweight fabric skins that enclose a volume of pressurised air and are easy for transportation and construction. This structure differs fundamentally from the conventional structures made of construction materials, and thus, the structural behaviour cannot be solved by a general theory of structures. This paper is the first to address the influence of air pressure on the structural behaviour of an air-inflated beam. The effects of beam length and loading conditions were also considered. The experiments, with several measurement sensors including an air pressure sensor and displacement sensors, were rigorously performed. After loading, the air pressure increases slightly with a continuous load increase. We found that different loading conditions created a similar deformed shape of the air-inflated beam, as the loads transformed into the fixed end moment, which was then plotted against beam deformation. According to the analytical solutions derived in this study, the pressure change significantly affected the structural behaviour of the air-inflated beam. This was demonstrated by the results of rigorous experiments that agreed well with the derived analytical solutions. Interestingly, wrinkling was observed when it reached the nonlinear stage. The beam returned to its original length after unloading with no permanent deformation, but with wrinkles, completely different from other construction materials. Therefore, in this paper, we propose a novel analytical solution to predict the deformation of air-inflated beams.

Chromatic transverse dynamics in a nonlinear plasma accelerator

We present a theoretical investigation of the chromatic dynamics of the witness beam within a plasma based accelerator. We derive the single particle motion of an electron in an ion column within a nonlinear, blowout wake including adiabatic dampening and adiabatic variations in plasma density. Using this, we calculate the evolution of the beam moments and emittance for an electron beam. Our model can handle near arbitrary longitudinal phase space distributions. We include the effects of energy change in the beam, imperfect wake loading, initial transverse offsets of the beam, and mismatch between the beam and plasma. We use our model to derive analytic saturation lengths for the projected, longitudinal slice, and energy slice emittance under different beam loading conditions. Further, we show that the centroid oscillations and spot sizes vary between the slices and the variation depends strongly on the beam loading. Next, we show how a beam evolves in a full plasma source with density ramps and show that the integral of the plasma density along the ramp determines the impact on the beam. Finally, we derive several simple scaling laws that show how to design a plasma based injector to produce a target beam energy and energy spread.

Advanced Theoretical Models for Broadband Klystron Development

Broadband klystrons (BBKs) offer the potential of both high power and broad-bandwidth performance as microwave amplifiers. Staggered tuned bunching circuit and filter-loaded output cavity are the mainstream techniques adopted for developing such devices. However, in the design and optimization stage, the accurate and fast theoretical models are still missing before final particle-in-cell (PIC) simulations are conducted. In this article, the small-signal theory of klystron has been derived from accurate large-signal models used in KlyC, where complex mode field distribution, relativistic effects, mode coupling, and precise space charge model are fully considered in the final analytic formulas compared with existing simplified models. Furthermore, mode coupling theory with partially beam-loading conditions has been developed in KlyC to analyze the filter-loaded output cavity and overall klystron performance in the large-signal domain. An example of the retrofit design of 100-kW five-cavity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> -band klystron is then presented to demonstrate the advanced design methodology based on the above fast theoretical models. The 3-D PIC simulation finally verifies this BBK design, showing −1-dB bandwidth of 200 MHz is attainable with output power over 100 kW, where the maximum discrepancy between theoretical models and PIC is within 2% in the whole bandwidth.

A unified design proposal for shear stress prediction in crossing areas for cross laminated timber at in-plane shear and beam loading conditions

Environmental and urbanization challenges during the last few decades encouraged steady growth of mass timber construction where attention is drawn to cross laminated timber (CLT) as one of the most interesting products in terms of mechanical properties, versatility, efficient prefabrication and sustainability. Standardisation and codification regarding testing and design of CLT elements are hence pointed out as one of the main issues within the ongoing revision procedure of Eurocode 5. A consistent and unified design approach for CLT at pure in-plane shear loading conditions (shear walls) and at in-plane beam loading conditions is however still missing. This paper deals with analytical models for the determination of stress components related to predictions of load bearing capacity of CLT with respect to shear failure mode III – shear failure in the crossing areas constituted by the flatwise bonded areas between laminations of adjacent layers. This failure mode is relevant for both pure in-plane shear loading and in-plane beam loading conditions. The paper presents a review of previously proposed models for the prediction of shear stresses in crossing areas of CLT, for both loading conditions. Comparisons between FE-results and model predictions are reviewed indicating significant differences between them concerning the predicted influence of the CLT element lay-up and values of maximum shear stresses. Based on simplifications of models previously presented, a unified design proposal that is based on a rational and consistent mechanical background for both loading situations and that shows overall good agreement with FE-results is presented.

Experimental Investigation of Cross Laminated Timber Elements with Holes or Notches at In-Plane Beam Loading Conditions

Environmental and urbanisation challenges have encouraged steady growth of mass timber structures where cross laminated timber (CLT) stands out in applications as full-size wall, floor, or beam elements. Beam elements are used mainly in situations where cross layers have a reinforcing effect on the tensile stress perpendicular to the beam axis, such as when introducing holes or notches, which is common practice in beams, due to engineering, installation, or architectural requirements. This paper presents experimental investigations of CLT beams with holes or notches for comparison and validation of an analytical model provided in the literature. Different sizes of holes and notches as well as different placements of the holes were considered in the experiments. All relevant failure modes were analysed and discussed in detail. Two predominant failure modes were indicated, i.e., bending failure and shear failure in crossing areas (mode III). Results further indicate that reduced lamination widths near the hole, notch, or element edges have a relatively small influence on the beam strength. Parametric studies indicate net shear failure (mode II) and tensile failure perpendicular to the beam axis as the critical failure modes in most of the considered cases, indicating their strong underestimation in design verifications according to the analytical model.

A Unified Design Proposal for Shear Stress Prediction in Crossing Areas for Cross Laminated Timber at In-Plane Shear and Beam Loading Conditions

A Unified Design Proposal for Shear Stress Prediction in Crossing Areas for Cross Laminated Timber at In-Plane Shear and Beam Loading Conditions

Variational Self-Consistent Theory for Beam-Loaded Cavities

A variational theory is presented for beam loading in microwave cavities. The beam-field interaction is formulated as a dynamical interaction whose stationarity according to Hamilton's principle will naturally lead to steady-state solutions that indicate how a cavity's resonant frequency, $Q$, and optimal coupling coefficient will detune as a result of the beam loading. A driven cavity Lagrangian is derived from first principles, including the effects of cavity-wall losses, input power, and beam interaction. The general formulation is applied to a typical klystron input cavity to predict the appropriate detuning parameters required to maximize the gain (or modulation depth) in the average Lorentz factor boost, $⟨\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}⟩$. Numerical examples are presented, showing agreement with the general detuning trends previously observed in the literature. The developed formulation carries several advantages for the analysis and design of beam-loaded cavity structures. It provides a self-consistent model for the dynamical (nonlinear) beam-field interaction, a procedure for maximizing gain under beam-loading conditions, and a useful set of parameters to guide cavity-shape optimization during the design of beam-loaded systems. Enhanced clarity of the physical picture underlying the problem seems to be gained using this approach, allowing straightforward inclusion or exclusion of different field configurations in the calculation and expressing the final results in terms of measurable quantities. Two field configurations are discussed for the klystron input cavity, using finite magnetic confinement or no confinement at all. Formulating the problem in a language that is directly accessible to the powerful techniques found in Hamiltonian dynamics and canonical transformations may potentially carry an additional advantage in terms of analytical computational gains, under suitable conditions.

Functional Overview of the RF Power System for the LIPAc RFQ

Design, development, manufacturing, and test activities of the RF power system (RFPS) for Linear IFMIF Prototype Accelerator (LIPAc) were completed in Europe. Installation and commissioning activities were carried out at the International Fusion Materials Irradiation Facility-Engineering Validation and Engineering Design Activities (IFMIF/EVEDA) site in Rokkasho, Japan. Challenging IFMIF requirements led to a number of innovations during design and development. Commissioning required a major effort on calibration and fine setting and led to development of new functionalities. The RFPS was validated under full power and 125-mA deuteron beam loading conditions, in the radio frequency quadrupole (RFQ), demonstrating good performance. This article is an overview about how technical challenges impacted the prototype RFPS design and its functional evolution during commissioning, cavity conditioning, and beam operation of the RFQ.

Optimal Beam Loading in a Laser-Plasma Accelerator.

Applications of laser-plasma accelerators demand low energy spread beams and high-efficiency operation. Achieving both requires flattening the accelerating fields by controlled beam loading of the plasma wave. Here, we optimize the generation of an electron bunch via localized ionization injection, such that the combination of injected current profile and averaged acceleration dynamics results in optimal beam loading conditions. This enables the reproducible production of 1.2% rms energy spread bunches with 282MeV and 44pC at an estimated energy-transfer efficiency of ∼19%. We correlate shot-to-shot variations to reveal the phase space dynamics and train a neural network that predicts the beam quality as a function of the drive laser.

Experimental and numerical investigations of cross-laminated timber elements at in-plane beam loading conditions

Abstract Cross laminated timber (CLT) at in-plane beam loading conditions presents a complex stress state wherefore several failure modes and geometry parameters need to be considered in design. The work presented here includes experimental investigations of CLT beams for comparison and validation of an analytical model and design proposals previously suggested by the authors. All relevant failure modes are considered; bending failure and shear failure modes I, II and III. The main focus is, however, on shear failure mode III relating to shear failure in the crossing areas between orthogonally bonded longitudinal and transversal lamination. The analytical model presented is an improvement of the analytical model which has been suggested to be used as the basis for design equations for the next version of Eurocode 5. The two design proposals presented are based on that improved analytical model. Experimental results show good agreement with the improved model and both design proposals. In order to study the influence of different lamination placements and varying lamination widths, comparisons between the improved analytical model and FE-analyses regarding magnitude and distribution of internal forces are presented and good agreement is obtained. Experimental and analytical results indicate only a small influence of reduced lamination widths close to the beam edges. This is a finding which is of practical interest since CLT beams in general are cut from larger elements, with no consideration of the location of the individual laminations with respect to the edges of the beam.

Cross laminated timber at in-plane beam loading – Comparison of model predictions and FE-analyses

The work presented concerns validation of a specific analytical model for Cross Laminated Timber (CLT) at in-plane beam loading conditions. The original model (model A) has previously been presented in the literature and is also suggested to be used as a basis for design equations for the next version of Eurocode 5. An improved version (model B) of that original model (model A), regarding basic assumptions relating to the internal force distribution, has recently been presented in the literature. Here, comparisons between the original model (model A), the improved model (model B) and FE-analyses regarding magnitude and distribution of internal forces are presented. The main focus is on forces and torsional moments acting in the crossing areas between longitudinal and transversal laminations and relevant for shear mode III failure, meaning the relative sliding and rotation between two flat-side bonded laminations. The results show that the improved analytical model (model B) outperforms the original model (model A) in terms of giving predictions very close to the predictions of the FE-model. A further extension of the improved model (model B) regarding distribution of forces and torsional moments in the beam width direction is also presented.

Cross laminated timber at in-plane beam loading – Prediction of shear stresses in crossing areas

Cross Laminated Timber (CLT) at in-plane beam loading conditions present a very complex stress state and many failure modes need to be considered in design. The work presented here aims at finding improvements of a specific analytical model for stress analysis and strength verification that has been suggested in literature and which is also suggested as a basis for design equations for the next version of Eurocode 5. Although the model has appealing properties it suffers from some drawbacks related to the assumed distributions of internal forces which, based on comparison to finite element analysis, appear to be inaccurate. The main focus in this paper is on model predictions regarding the distribution and magnitude of internal forces acting in the crossing areas between longitudinal and transversal laminations. The proposed modified model assumptions regarding the distribution of lamination shear forces, which in turn influence the forces acting in the crossing areas, are suggested to be taken into account in design of CLT beams.

Slenderness Effects in Reinforced Concrete Beams

Although slenderness in reinforced concrete (RC) beams can lead to possible instability failure without warning, detailed provisions are not specified in current concrete design codes to account for these slenderness effects. The existing recommendations are limited to prescriptions of limiting slenderness ratios which are semi-empirical in nature. No reduction in flexural moment capacity is recommended for beams whose slenderness approaches these limits. This paper addresses these shortcomings for rectangular beams. In a recent paper, the authors proposed a formulation to predict the critical buckling moment, which is found to agree closely with experimental results. Based on this formulation, an expression for limiting slenderness ratio (to predict sudden buckling failure) is explicitly derived for under-reinforced rectangular RC beams. The proposed expression for limiting slenderness ratio accounts for beam end conditions, loading conditions, concrete strengths and steel, as well as tension and compression reinforcement and transverse reinforcement ratios. It is found that a wide range of slenderness limits is feasible for different sets of design variables, in contrast to the constant value prescribed in the existing codes of practice for specified end conditions. Experimental studies were carried out on eight moderately slender beams. Results indicated that, like steel beams, even moderately slender RC beams exhibit slenderness effects such as lateral deflections and twist. The ultimate moment capacity is found to reduce on account of these effects. Based on the test results, it is recommended that a conservative moment reduction factor be applied on the ultimate moment capacity of beams.

A Finite Element Analysis of the Stress Intensity Resulting from Single-Edge Precracked Beam Loading Conditions

Abstract The single-edge precracked-beam (SEPB) fracture toughness method has been investigated using finite element methods to analyze the stress intensity (KI) resulting from variations in bridge span, punch length, and virtual crack length. A two-dimensional half-plane, semi-infinite model was used to approximate the stress intensity from a fit of the nodal displacements of a crack face under SEPB loading conditions. The finite element method models the crack in situ, using six-node triangular elements specified around a singular point that simulates the crack tip. The analysis reveals that for increasing virtual crack length (a), the stress intensity increases to a maximum where ΔKI/Δa = 0. With further increasing virtual crack length, the stress intensity decreases. The inflection point ai, KIi differs for varying span and fixed punch length, and for varying punch lengths with fixed span. The resulting stress intensities per new ton force loading are presented in tabular and graphical form. The presented series of graphs can be used to explore variations in precracking parameters. This finite element analysis provides useful data for those developing or adopting the SEPB fracture toughness measurement technique.

Semi-Active Multimatrix Reflector Antennas

ABSTRACT This paper covers recent work on a novel concept for multibeam transmit reflector antennas, called semi-active antennas since the feed array elements are not directly connected to the power modules, as in an active antennas, but separated from them by several multiport hybrid couplers. By controlling the phase of the low level equi-amplitude signals at the inputs of the amplifiers, these can be directed to selected feeds in the focal area of the reflector to generate multiple fixed or movable pencil or shaped beams. More or less channels can be routed into the beams by low level switching at the beam forming network input ports. Under all beam pointing and beam loading conditions, all amplifiers operate at nominal power, therefore with optimum efficiency. The basic principle of this new antenna architecture is presented and discussed and designs are evaluated for regional and global coverage satellite applications.

Improved method for calculating strain energy release rate based on beam theory

The Timoshenko beam theory was used to model cracked beams and to calculate the total strain-energy release rate. The root rotations of the beam segments at the crack tip were estimated based on an approximate two-dimensional elasticity solution. By including the strain energy released due to the root rotations of the beams during crack extension, the strain-energy release rate obtained using beam theory agrees very well with the two-dimensional finite element solution. Numerical examples were given for various beam geometries and loading conditions. Comparisons with existing beam models were also given.

YIG tuners for RF cavities

Tuning of RF accelerator cavities in electron storage rings is needed to maintain accelerating gap voltage under varying beam loading conditions. A type of ferrite tuner based on the stripline configuration has been tested at the National Synchrotron Light Source. The tuner is basically a short-circuited ferrite-loaded transmission line which is inductively coupled to the RF cavity to be tuned. The use of substituted yttrium-iron-garnet (YIG) allows for custom tailoring the saturation magnetization to the specific application and thus minimizing the bias field requirement. The design goal for the tuner was to achieve a tuning range of 50 kHz. Linear tunability of 78 kHz was demonstrated, exceeding the goals set for the tuner. Results of testing the YIG tuner are presented. >

Energy characteristics of a short-pulse S-band industrial linac

The time-averaged and time-dependent energy spectra of an S-band, standing-wave industrial linac with direct injection are examined during steady-state and stored-energy mode operation. The effective fill-time for the structure under heavy beam-loading conditions is found to be significantly shorter than that predicted from an unloaded structure.