Concentrated Force Research Articles

Anisotropy and magnetoelasticity effects on the propagation of the SH-wave-induced semi-infinite crack in a magnetoelastic orthotropic medium

The crux of the present study is to investigate semi-infinite crack propagation in magnetoelastic strip influenced by propagating SH-wave under orthotropic geometrical configurations. The Wiener-Hopf (WH) technique and two-sided Fourier integral transforms (FIT) are applied in the proposed analytical model. A closed-form expression of the stress intensity factor (SIF) has been established for the constant concentrated force. The SIF in a magnetoelastic orthotropic strip is shown to be significantly affected by the crack length and crack speed, medium anisotropy, and magnetoelastic parameter. The proposed model is compared to the case of a magnetoelastic isotropic strip in order to demonstrate the effect of orthotropy as well as other anomalies. Among other observations, it is noted that regardless of whether orthotropy exists in the strip or not, the value of the SIF rises along with the crack speed until it reaches its maximum, at which point it rapidly declines.

Numerical analysis of curved steel plate girders subjected to patch loading

Curved steel plate girders are often utilized in bridges built in congested urban areas, where intricate plan alignments are required. Their performance and design is, however, more complex than that of equivalent straight girders, especially regarding concentrated forces: while AASHTO adopts a simplified and empirical approach for the design of curved steel girders, the Eurocode for plated structures EN 1993-1-5 does not address the patch loading design of steel plate girders curved in plan, being only applicable to straight girders. Therefore, it is necessary to carry out further research in order to achieve a better understanding of the behavior of curved steel plate girders so that suitable design approaches accounting for the specific response of these structures can be developed. This paper presents a comprehensive numerical study on curved steel plate I-girders subjected to patch loading, considering material and geometric nonlinearities as well as initial imperfections. The numerical models are developed by means of the advanced finite element software ABAQUS and validated against experimental tests available in the literature. The numerical results demonstrate that the elastic critical buckling loads increase with increasing span-to-plan radii, which can be conservatively estimated using the EN 1993-1-5 provisions for straight steel girders, and that the ultimate patch loading resistance decreases with the radius of curvature. Based on this, practical recommendations are proposed to extend the applicability of the design provisions prescribed in the next version of EN 1993-1-5 for straight steel I-girders to the case of curved steel I-girders.

Experimental investigation on the effect of nano-silica on reinforced concrete Beam-column connection subjected to Cyclic Loading

Beam-column joints are crucial load transmission zones because they face concentrated forces from both the beams and the columns. High shear and axial stresses caused by these concentrated forces in the area of the joint may result in decreased joint strength. This article proposes a new beam-to-column connection developed for precast concrete-resisting frames. Concrete mixtures are enhanced mechanically by adding nano silica as it increases compressive strength, flexural strength, and abrasion resistance. Within the concrete, it creates a solid, gel-like matrix that fills voids and strengthens the whole construction. In this study, three reinforced concrete beam-column joint specimens were cast with fly ash, the other three with nano-silica and fly ash, and one sample with nano-silica and a control mix without admixtures was cast. Specimen cast using fly ash and nano-silica is subjected to cyclic loading after 28 days of curing. A load capacity of 100 kN was imposed on the column during testing. It was observed that a gradual increase in fly ash decreased the compressive and flexural strength of the beam-column joints. This decrease in strength was addressed by adding 2.5% nano-silica. Nano silica acts as a nucleus to bond tightly with cement particles during hydration. The results showed that the flexural strength equivalent to that of a controlled specimen can be achieved by adding nano-silica at 2.5% and fly ash at 60%. The highest loading of 38.1 kN can be applied to the specimen with nano-silica without fly ash. Although a higher axial compression ratio can improve the bearing capacity and initial stiffness, it can also reduce deformation capacity and flexibility.

Responses of wildfire-induced global black carbon pollution and radiative forcing to climate change

The impacts of climate change on wildfires have been studied extensively. Along with declining emissions from fossil fuel combustion due to anthropogenic emission control, black carbon (BC) released from wildfires is expected to contribute a more significant portion to its atmospheric burden. However, from a global perspective, little is known about the BC burden and radiative forcing caused by wildfires. Here, we report the results from the long-term wildfire-induced BC concentration and direct radiative forcing (DRF) from 1981 to 2010 globally simulated by an Earth System Model using an updated wildfire BC emission inventory. We show that wildfire-induced BC concentration and DRF varied significantly spatially and temporarily, with the highest in sub-Saharan Africa, attributable to its highest level of wildfire BC emission worldwide. The temporal trends of near-surface air temperature, precipitation, and evapotranspiration and their association with wildfire-induced BC concentration are explored using the multidimensional ensemble empirical mode decomposition. A statistically significant relation between changes in climate parameters and wildfire-induced BC concentration was found for 53% of the land grid cells, explaining on average 33% of the concentration variations. The result suggests that the wildfire-induced BC DRF, with an increasing trend, would be an important contributor to climate change, especially in sub-Saharan Africa. Occurrences of wildfires in the Amazon Basin respond most strongly to climate change and play an increasingly important role in changing the global climate.

Countermovement Jump Force-Time Curve Analyses: Reliability and Comparability Across Force Plate Systems.

Merrigan, JJ, Strang, A, Eckerle, J, Mackowski, N, Hierholzer, K, Ray, NT, Smith, R, Hagen, JA, and Briggs, RA. Countermovement jump force-time curve analyses: reliability and comparability across force plate systems. J Strength Cond Res XX(X): 000-000, 2023-Considering the growing prevalence of commercial force plates providing automated force-time analyses, understanding levels of agreement across force plate systems is warranted. Countermovement jump (CMJ) metrics across Vald ForceDecks (FD), Hawkin Dynamics (HD), and Sparta Science (SS) force plate systems were compared. Twenty-two subjects completed CMJ testing (∼128 comparisons) on each force plate system separately with rest between jumps. Baseline testing occurred 3 times and demonstrated poor test-retest reliability for modified reactive strength index (mRSI) and rate of force development (RFD). ForceDecks and HD comparisons yielded acceptable agreement for concentric/propulsive relative force and net impulse, jump height, eccentric/braking RFD, and mRSI, but systematic and proportionate bias existed for RFD. Sparta Science jump height and reactive strength index (RSI) demonstrated systematic overestimations compared with HD and FD, but jump height had acceptable agreement according to concordance correlation coefficients (CCC = 0.92-0.95). Agreement between SS load (eccentric RFD) and HD braking RFD was acceptable (CCC = 0.91), whereas agreement between SS load and FD deceleration RFD was considered acceptable (CCC = 0.81-0.87) but demonstrated systematic and proportionate bias. ForceDecks (CCC = 0.89) and HD (CCC = 0.85) average relative concentric/propulsive force yielded acceptable agreement with SS explode (average relative concentric force), but SS explode demonstrated systematically lower values than FD and HD. Sparta Science drive (concentric impulse) yielded acceptable agreement with HD relative propulsive impulse (CCC = 0.85), but not FD concentric impulse. Human performance practitioners need to be aware of inconsistencies among testing procedures and analyses across force plate systems, such as differences in metric definitions and units of measurement, before making comparisons across systems.

Determination of the form of a spiral spring in a free state

The object of research. This article deals with a spiral spring made of tape material with a rectilinear cross-section.
 Investigated problem. If one end of a metal ruler is pinched, and a certain force is applied to the other end, it will bend under the action of the generated moment. The magnitude of the moment depends on the applied force and the length of the ruler. Therefore, the amount of deflection will increase with the increase of these parameters, and the shape of the ruler may take the spiral form. After the termination of the external load, the ruler will regain its original shape, that is, it will become straight. However, such spiral springs do not exist in practice. For compact sizes, the spring in its free state also has a spiral shape. In this regard, the purpose of the study is to find the elastic axis of a tape spiral spring in a free state, which under the action of a concentrated force takes a given shape.
 The main scientific results. The shape of the spiral spring in the free state is determined, which under the action of the applied force acquires the desired shape, which does not lead to the occurrence of frictional forces between adjacent coils.
 The area of practical use of research results. Spiral springs are widely used. One example is mechanical clock movements and measuring devices, in which the determination of indicators depends on the applied force that "unwinds" or "twists" the spring.
 Innovative technological product. The paper calculates the elastic axis of a spiral spring in a free state according to its given final shape, taking into account the moment that arises as a result of the applied force at the end of the spring. For this, the nonlinear theory of absolutely elastic bending using the methods of differential geometry of curved lines as a function of the own length of the arc of the spring axis is applied.
 The scope of application of the innovative technological product. The results obtained in the study can be used in the manufacture of spiral springs for various purposes, as well as for the accumulation of potential energy in the absence of other sources

Stress state in perforated discs

The paper investigates the stress state in perforated discs by circular holes. Circular discs are subjected to two types of loadings: diametrical compression by concentrated forces and radial compression produced by an equivalent uniformly distributed load on the contour of the discs. The discs of radius 150 mm are perforated with two, four or 96 holes, of different radii between 1 mm and 50 mm or maximum possible. The stress distribution in the discs is studied according to the value of the radii of the holes and the distance between them. The stress concentration factors and their variation for the geometrical parameters of the concentrators are determined. The finite element method was used, which allows the modeling of the structure so that it is as close as possible to the real situation of the geometry and the way of application of the load.

Free Vibration Analysis of Elastically Restrained Tapered Beams with Concentrated Mass and Axial Force

This study proposes a new numerical method for the free vibration analysis of elastically restrained tapered Rayleigh beams with concentrated mass and axial force. The beam model had elastic support, concentrated mass at both ends, and axial force at the right end. The elastic supports were modeled as translational and rotational springs. The shear force and bending moment were determined under the assumption that the sum of the forces at arbitrary positions and the joint between the beam and elastic supports always becomes zero. Therefore, a frequency determinant is established considering the free-free end condition at both ends, but various boundary conditions were constructed by adjusting the values of the elastic springs in the frequency equation. This assumption simplified the deduction procedure, and the method’s efficiency was demonstrated through various comparisons. In particular, the value of compressive loading at which the first natural frequency vanished was investigated by considering the taper ratio based on the relationship between the elastic support and compressive loading. The analyzed results can be adopted as benchmark solutions for other approaches. The frequency determinant employs the transfer matrix method; however, numerical methods can easily be utilized in other approaches.

КРУЧЕНИЕ НИЖНЕГО ПОЯСА ПОДКРАНОВО-ПОДСТРОПИЛЬНОЙ ФЕРМЫ

The lower belt of the crane secondary truss, along which the crane moves, is made of a thin-walled box profile. The largest local concentrated crane forces applied with eccentricity to the lower belt of truss made of thin-walled welded box cause its restrained torsion. The calculation method of the crane secondary truss does not consider the inclusion in the work of the lower belt for torsion and horizontal bending of the webs. A beam with a span equal to the span of the crane secondary truss is taken as the design scheme of the lower belt along which the crane moves. In fact, the work of the belt during torsion is different from the work of the beam.
 The objectives of the work are to assess the impact on the operation of the lower belt during torsion of the webs and the upper belt and to clarify the methodology for calculating the lower belt. The study of the influence of webs on the angular malleability and torque of the lower belt has been carried out. Various ratios of the stiffness of the belt and the entire crane secondary truss are considered. The design scheme of the belt for the calculation of torsion is proposed – a beam angular elastic supports at the points of junction of the webs. The formula for determining the stiffness of elastic supports has been adopted. The error in determining the bending moments in the lower belt according to the proposed method relative to the results of numerical calculation of the rod design scheme of the entire crane secondary truss does not exceed 2%. The stresses in the lower belt, considering the torsion component, are analytically determined. The results were verified numerically using shell finite elements and a full-scale examination.

A novel LaAl1-xNbxO3 NTC ceramic with excellent stability for high-temperature thermistor

A series of LaAl1-xNbxO3 (0 ≤ x ≤ 0.100) samples were synthesized via the solid phase method. Characterization techniques including X-ray diffraction (XRD), scanning electron microscopy (SEM), and X-ray photoelectron spectroscopy (XPS) confirmed the formation of a solid solution in LaAl1-xNbxO3 (0 ≤ x ≤ 0.100) materials without the emergence of additional phases following Nb doping. Transmission electron microscopy (TEM) revealed distinct lattice fringes with a d value of 0.274 nm, corresponding to the (110) plane of LaAlO3 (PDF #82–0478). The introduction of Nb dopant caused distortions in the cell parameters of LaAlO3 due to ionic radius size effects, changes in Nb valence, fluctuations in oxygen vacancy concentration and Coulomb forces. Specifically, the lattice exhibited a shrinkage for 0 ≤ x ≤ 0.025, expansion for 0.025 <x ≤ 0.075, and subsequent shrinkage for 0.075 <x ≤ 0.100. Resistance measurements indicated that LaAl1-xNbxO3 (0 ≤ x ≤ 0.100) materials exhibited favorable negative temperature coefficient (NTC) characteristics in the temperature range of 600 °C–1400 °C. Hall measurements revealed that the materials functioned as P-type semiconductors with hole carriers, and Nb doping enhanced carrier concentration. Aging tests demonstrated that the aging drift rate of LaAl0.9Nb0.1O3 could be as low as 0.906% after aging it at 1000 °C for 500 h, a crucial parameter for practical applications of LaAl1-xNbxO3 (0 ≤ x ≤ 0.100) materials in high-temperature NTC applications.

Alkaline arginine promotes the gentamicin-mediated killing of drug-resistant Salmonella by increasing NADH concentration and proton motive force.

Antimicrobial resistance, especially the development of multidrug-resistant strains, is an urgent public health threat. Antibiotic adjuvants have been shown to improve the treatment of resistant bacterial infections. We verified that exogenous L-arginine promoted the killing effect of gentamicin against Salmonella in vitro and in vivo, and measured intracellular ATP, NADH, and PMF of bacteria. Gene expression was determined using real-time quantitative PCR. This study found that alkaline arginine significantly increased gentamicin, tobramycin, kanamycin, and apramycin-mediated killing of drug-resistant Salmonella, including multidrug-resistant strains. Mechanistic studies showed that exogenous arginine was shown to increase the proton motive force, increasing the uptake of gentamicin and ultimately inducing bacterial cell death. Furthermore, in mouse infection model, arginine effectively improved gentamicin activity against Salmonella typhimurium. These findings confirm that arginine is a highly effective and harmless aminoglycoside adjuvant and provide important evidence for its use in combination with antimicrobial agents to treat drug-resistant bacterial infections.

Mechanical response of precast tunnel segments with steel and synthetic macro-fibers

Precast tunnel lining segments manufactured with synthetic macro-fibers and steel fibers as the primary reinforcement were tested under flexural and edge compression loading. Since steel fibers are usually prescribed as the primary reinforcement of tunnel sections, the dosage of synthetic fibers was determined by matching their residual flexural strength. The performance of tunnel segments was verified using the extensive data collected from instrumented deflection, crack growth, quantitative DIC, and strain gauge results and correlated with the load vs. deformation response. Results show that synthetic fibers can meet the design load requirements specified for the steel fibers reinforcement. Flexural test results indicate a 16% increase in macro-fiber content from 0.80% to 0.93% by weight resulting in a 32% increase in the residual strength of standard beam samples and a 41% increase in the residual strength of full sections. Compared to the steel fiber samples, samples with polymeric macro-fiber had a 6.5% higher average toughness. The full-scale load-deflection results were within 7% of the average values in each category of samples which is almost half the variation in the flexural ASTM C1609 results. The edge compression tests indicated that the mode of failure under concentrated jack forces is governed and dominated by the tensile lateral bursting stresses resulting from inefficient distribution of the load to the supporting edge.

Analytical analysis for horizontal displacement of pile anchor support structure considering prestress

The pile-anchor supporting structure is widely used in foundation pit engineering, it is particularly necessary for calculating lateral displacement of the pile-anchor supporting structure. The soil stress state is transformed by the additional stress caused by the prestress, thus the lateral displacement can be decreased own to pile-anchor supporting structure bearing active earth pressure had changed. Prestress as a concentrated force is decomposed into the horizontal component and vertical component, calculating the additional stress caused by the prestress and getting the formula of active earth pressure of considering the additional stress, setting up calculation model of the pile-anchor supporting structure. For typical examples of foundation pit engineering, the parameters are substituted into a program written based on derived formulas, and the elastic deformation superposition method is used to calculate the horizontal displacement of the pile anchor support structure. The comparison and verification is carried out by Finite element analysis. The influence of cohesion and friction angle on pile displacement, bending moment, and shear force has been studied. This study found that cohesion and friction angle have a significant impact on the displacement of pile anchor support structures.

Experimental study on flocculation and sedimentation characteristics of cohesive fine sediment measured using ultrasound in the Pearl River Estuary

Flocculation-settling of cohesive fine sediment is the main cause of sediment deposition and changes in topography and geomorphology in estuaries. However, studies on estuary morphology have often focused on a single influencing factor, and sediment deposition characteristics under disturbances in sediment concentration, moisture content, and external forces have rarely been considered simultaneously. The authors propose an ultrasound-assisted flocculation-settling method to analyze the various factor affecting cohesive sediment. The current study examined the sedimentation patterns of cohesive sediment with a sediment content concentration of 30%–80% through ultrasound experiments. The results show that when the sediment concentration is 40%–50%, the best effect on flocculation and sedimentation is induced by ultrasound waves. The corresponding settling height at the clear-muddy water interface is 3.05–3.45 cm, and the settling rate is 0.161–0.173 cm/min. Finally, using ultrasound waves, a moisture content of the sediment concentration of 30%–80% was analyzed based on wet and dry conditions. Taking a sediment concentration of 50% as an example, the maximum values of the variation in the water contents of the upper, middle, and lower layers of the wet basis were 0.82%, 0.51%, and 0.37%, respectively, whereas those of the upper, middle, and lower layers of the dry basis were 4.77%, 1.07%, and 0.60%, respectively. Thus, the moisture content of dry and wet sediment varied as follows: Wupper > Wmiddle > Wlower. The current research results can provide a theoretical basis and technical reference for siltation in channels, harbors, and reservoirs; the evolution of submarine deltas and coastal beaches; transportation of fluid mud; and the treatment of hyper-concentrated sediment flows.

Vertical Jump Testing after Anterior Cruciate Ligament Reconstruction: A Systematic Review and Meta-analysis.

Recently, there has been a call for vertical jump testing via force-plate analysis to be included in the assessment of individuals after anterior cruciate ligament reconstruction (ACLR) and as part of return-to-play criteria. However, a synthesis of current literature is needed to help guide clinicians on what tests to perform, which force-plate metrics to assess, and how these may change over the time course of rehabilitation. Four online databases were searched from inception to July 2022. The Downs and Black checklist was used to assess study quality. Multilevel meta-analyses and meta-regressions were undertaken in conjunction with a best evidence synthesis. Forty-two articles were included, capturing 2375 participants with a history of ACLR. Reconstructed limbs displayed 1) lower peak eccentric forces, concentric forces, landing forces, and lower eccentric and concentric impulses (standardized means difference [SMD] = -1.84 to -0.46) than uninjured contralateral limbs during bilateral countermovement jumps (CMJ) and drop vertical jumps (DVJ); 2) lower jump heights and reactive strength indices (RSI), and longer contact times than uninjured contralateral limbs during unilateral CMJ and DVJ (SMD = -0.86 to 0.26); and 3) lower jump heights, RSI, and longer contact times during bilateral and unilateral CMJ, and unilateral DVJ, than uninjured controls (SMD = -1.19 to 1.08). Meta-regression revealed that time postsurgery was a significant moderator ( P < 0.05) for 1) bilateral CMJ height, peak concentric force, and peak landing force; 2) between-limb differences in unilateral CMJ height; and 3) differences in unilateral DVJ height, RSI, and contact time between reconstructed limbs and healthy controls with no history of injury. Individuals with a history of ACLR display chronic deficits in vertical jumping performance during a range of bilateral and unilateral tasks, which may have implications for return-to-play criteria and the design of interventions targeted at restoring long-term deficits in explosive lower limb strength after ACLR.

Analytical study on the propagation of semi-infinite crack due to SH-wave in pre-stressed magnetoelastic orthotropic strip

This study deals with the propagation of semi-infinite crack impacted by SH-wave propagation in a pre-stressed magnetoelastic orthotropic strip (PMOS). The proposed analytical model makes use of the Wiener-Hopf (WH) approach and two-sided Fourier integral transforms (FIT). The exact formulation of the stress intensity factor (SIF) for constant concentrated force (CCF) has been established in closed form. The effect of influencing factors, including the crack length, crack speed, magnetoelastic parameter, horizontal compressive pre-stress (HCP)/horizontal tensile pre-stress (HTP), vertical compressive pre-stress (VCP)/vertical tensile pre-stress (VTP), and anisotropy parameter on the SIF in the considered strip has been unraveled. The proposed model is compared with the case of a pre-stressed magnetoelastic isotropic strip (PMIS) and some peculiarities, along with the influence of orthotropy have been reported. The significant results reported in the present manuscript reveal that magnetoelasticity and pre-stress is a prominent factor impacting crack propagation in elastic material with orthotropy configuration properties and has a significant impact on the SIF, which has not been taken into account in the existing literature on the subject of fracture mechanics. The present investigation helps with structural and reliability analysis, fracture propagation, material durability and failure of engineering structures.

Optimum design of vibration absorber for cracked beam under the effect of moving concentrated force utilizing genetic optimization algorithm

Optimum design of vibration absorber for cracked beam under the effect of moving concentrated force utilizing genetic optimization algorithm

Numerical investigation of convergence of Fourier series, poly-nomials, and method of finite elements

Purpose. To compare the efficiency of using finite elements with variable and averaged mechanical and geometric parameters and to investigate the convergence of results obtained by the semi-analytical finite element method (SAFEM) using Fourier series and polynomials with the results obtained by the finite element method (FEM). The methods. The construction and development of an algorithm for studying the stress-strain state of spatial bodies with variable and averaged mechanical and geometric parameters were carried out based on SAFEM. Findings. Solvability indicators of SAFEM were obtained for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters. Numerical convergence studies of results obtained using SAFEM with Fourier series, polynomials, and the finite element method were conducted for a benchmark example, which was the Boussinesq problem for a half-space subjected to a concentrated force. The results indicate that the convergence of the investigated coordinate functions in the considered problem is of the first order. The originality. The obtained solvability indicators of SAFEM for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters allow for the study of various classes of problems. Numerical convergence studies using Fourier series, polynomials, and the finite element method were conducted for the benchmark example. Practical implementation. The practical significance lies in the development of a methodology for determining the stress-strain state of relevant spatial elements of structures with variable and averaged mechanical and geometric parameters subjected to arbitrarily distributed spatial loads.

Application of generalised functions and Fourier’s integral transformation in modelling the effect of a moving load on a beam resting on an elastic foundation

The paper is dedicated to modelling the behaviour of an infinitely long beam resting on a solid elastic foundation under the concentrated moving load effect. The modelling is carried out in the context of determining the high-speed vehicle stock impact on the track structure. When developing the method of problem solving, the known elasticity theory factors, wave-propagation theory, complex variable theory, as well as integral transformations of generalised functions were used. The mobile concentrated force is represented by the Dirac delta function. The Fourier’s integral transformation is used to solve the equation of motion and determine the beam defect. Contour integration using Cauchy residue theorem is applied to calculate the defect values in the original space. The general dependence form the beam defect on the load velocity is determined. It is shown that the defect values in the beam increase with moving load increasing speed. It is shown how the moving load velocity affects the character of the beam defect time dependence. Solutions are given for Euler-Bernoulli, Rayleigh and Timoshenko models of beams on an elastic base. The considered mathematical models behaviour is compared. It is shown that the character of beam interaction with the moving load, the defect values, as well as the reaching critical velocities character do not differ significantly for the considered beam models. The character of reaching the maximum defect in the application area of the mobile load is analysed. It is shown that the maximum defect values of beams on an elastic base occur after the moving load. The presented methodology can be used to evaluate the impact of rolling stock on the track structure, including the design of high-speed lines.

Insights into the occurrence of transverse bending stresses in web plates of crane runway girders

AbstractCrane runway girders are installed in industrial buildings to carry heavy loads from crane operation. The wheels of the bridge crane introduce concentrated forces in the crane runway girder via the rails. This leads to local vertical stresses in the web plates of the crane runway girders in addition to the global bending stresses. The local stresses at the top of the web usually become crucial for the fatigue design of the girder. The potential eccentricity of vertical wheel loads as well as additional horizontal forces from operation of the crane can lead to torsional rotations of the rail and the top flange and subsequently to transverse bending of the web plate of the crane runway girder. In the current design model of EN 1993‐6, the rotation at the top of the web plate is described by assuming the rail and the top flange of the girder acting as a bar under torsion, supported continuously by the bending stiffness of the web. Within this paper the existing model for the rotations is improved and it is shown that these modifications lead to more accuracy in comparison with numerical finite element calculations. It is also shown that the current simplified procedure for calculating the resulting stresses in the web is not able to adequately describe the real stresses for all practical cases. It is found that the quality of the stress predictions can significantly be improved by considering the web as a simply supported plate with the previously identified rotations on its top edge.