Nominal Shear Stress Research Articles

Investigation of geometric and material effects on the fatigue performance of composite and steel adhesive joints

This study experimentally investigates the combined effect of several parameters on the fatigue behaviour of adhesive bonded single lap joints, including: substrate material (steel, glass fibre reinforced polymer (GFRP) and carbon fibre reinforced polymer (CFRP)); adhesive material (epoxy and methacrylate); as well as joint geometry (overlap length and adhesive thickness).Results showed that despite the lower bulk strength of the ductile methacrylate adhesive, in terms of the ratio of fatigue load to ultimate failure load, joints bonded by this adhesive had a higher fatigue performance when compared to joints bonded by the epoxy one, with differences in fatigue life of up to 20 times for the same load ratio. In a similar substrate configuration, flexible GFRP substrates reduced the fatigue life of the joints bonded by the methacrylate adhesive more than 10 times when compared to steel joints for the same load. However, in a dissimilar configuration, an increase in fatigue life was observed which, based on a finite element analysis, was attributed to the ductility of the adhesive and its effects on the stress field. In CFRP joints bonded by the epoxy adhesive, a deterioration in fatigue performance was observed due to the occurrence of interfacial failure.Regarding the geometrical factors, increasing overlap length led to a decrease of the fatigue life for the same nominal shear stress. Similar trend was obtained for adhesive thickness. A parametric analysis revealed that overlap length is the parameter that affects more the fatigue performance of the joints.

Flow Rate and Wall Shear Stress Characterization of a Biomimetic Aerosol Exposure System.

Current in vitro emissions and exposure systems lack biomimicry, use unrealistic flow conditions, produce unrealistic dose, and provide inaccurate biomechanical cues to cell cultures, limiting ability to correlate in vitro outcomes with in vivo health effects. A biomimetic in vitro system capable of puffing aerosol and clean air inhalation may empower researchers to investigate complex questions related to lung injury and disease. A biomimetic aerosol exposure system (BAES), including an electronic cigarette adapter, oral cavity module (OCM), and bifurcated exposure chamber (BEC) was designed and manufactured. The fraction of aerosol deposited in transit to a filter pad or lost as volatiles was 0.116±0.021 in a traditional emissions setup versus 0.098 ± 0.015 with the adapter. The observed flowrate was within 5% of programed flowrate for puffing (25 mL/s), puff-associated respiration (450 mL/s), and tidal inhalation (350 mL/s). The maximum flowrate observed in the fabricated BAES was 450 mL/s, exceeding the lower target nominal wall shear stress of 0.025 Pa upstream of the bifurcation and fell below the target of 0.02 Pa downstream. This in vitro system addresses several gaps observed in commercially available systems and may be used to study many inhaled aerosols. The current work illustrates how in silico models may be used to correlate results of an in vitro study to in vivo conditions, rather than attempting to design an in vitro system that performs exactly as the human respiratory tract.

Harnessing the synergy of grout and adhesive: Numerical prediction of load capacity in hybrid composite joints

This study examines grouted joints for offshore wind turbine systems, where gaps between steel pipes are filled with grout, relying on adhesion, friction and compression struts formed by shear keys. Concerns about the limited load carrying capacity of large diameter grouted joints in offshore structures have prompted investigation. Whilst adhesive bonds are recognized for load transfer in structural steel, the complete replacement of grouting with bonding alone is proving impractical for large gaps in offshore structures, posing challenges in terms of cost and handling. To address these challenges, the study presents an innovative hybrid grouted joint for steel structures that combines grout and adhesive layers. This novel approach replaces traditional large shear keys with distributed micro-shear keys — small granules embedded in the grout material. Under axial loading, the hybrid joint demonstrates robust performance, with a maximum nominal shear stress on the inner pipe of 30.1 MPa and consistent load capacity across tests. Average shear strength is in line with, and occasionally exceeds, expectations. Notably, the hybrid joint shows resilience in different configurations and maintains a low coefficient of variation of 5.5%, indicating consistent performance. When the influence of the adhesive material on the hybrid joint is examined, the effect on the joint stiffness is minimal, despite variations in adhesive stiffness. Sikadur 370, which has a higher modulus of elasticity than DuploTEC, shows similar deformation curves in the elastic region, emphasizing the robustness of the joint. Differences in the maximum loads are attributed to the thickness of the adhesive layer and the lower modulus of DuploTEC, resulting in different shear strengths. The proposed hybrid joint offers a promising solution to improve the performance of conventional grouts and adhesives in offshore structures. The study also formulates a failure criterion, performs numerical stress analysis, and models the effect of geometric dimensions, eccentricity, and misalignment on load capacity. The methodology’s accuracy in predicting load capacity, supported by numerical analysis and large-scale joint simulations, contributes to a comprehensive understanding of hybrid joint performance in engineering applications.

Effect of column size on punching behavior of flat slabs with square columns: Numerical investigation

This study investigates the punching behavior of slabs supported by square columns of various sizes at different effective slab depths. Within the research context, a finite element model of the slab-column connections is developed using ABAQUS and calibrated based on 15 test results from the literature. Subsequently, 84 slabs with square columns are simulated, and the effect of column size is assessed in terms of load-rotation behavior, shear stress distribution, cracking patterns, punching capacity, and nominal ultimate shear stress. The findings indicate that all slabs undergo brittle punching failure due to the damage near the column corner, which occurs before the ultimate shear stress is fully reached around the column perimeter. The shear stress of the slab along the column perimeter concentrates at the column corner, with this concentration being more pronounced in slabs supported by large square columns. Moreover, as the column size increases, the punching capacity consistently rises while the nominal ultimate shear stress initially decreases, with the decline of the nominal ultimate shear stress being more significant in thinner slabs. The punching capacity predicted by the finite element analysis is compared to the values derived from ACI 318-19, EC2, MC2010, and CSCT models. The findings suggest that these formulas do not adequately capture the influence of column size on punching capacity, prompting the proposal of a new formula that refines the consideration of column size effects.

Mean stress correction and fatigue failure criteria for hyperelastic adhesive joints

ABSTRACT The work investigates failure criteria and mean stress correction approaches for the fatigue lifetime prediction of two hyperelastic adhesives (a polyurethane, PU, and a silicon-modified polymer, SMP). Fatigue experiments are carried under constant amplitude cyclic loading at RT and 40°C/60% r.h with butt- and the thick-adherend-shear-test-joints at three stress ratios R = −1, 0.1 and 0.5. Three mean stress correction approaches are evaluated: Goodman (static strength based), Schütz (mean stress sensitivity based) and Kujawski & Ellyin (parameter optimisation based). Fatigue failure criteria considered are: Drucker-Prager (linear-relation with the hydrostatic stress), Beltrami (quadratic relationship with the hydrostatic stress), and a multivariable nominal shear and tensile stresses criterion (data-based). The comparison is based on prediction accuracy (R-squared of master SN curves) and complexity of parameter determination. The highest values of R-squared were obtained by the Kujawski and Ellyin correction, followed by Schütz and then Goodman. However, the complexity of parameter determination follows an opposite trend with Goodman being the lightest approach. Failure criteria yielded comparable results with the multivariable criterion having the advantage of not dealing with FEA, but being limited to joints with nearly uniform stress distribution. Finally, compared to Drucker-Prager, the Beltrami criterion had a more robust parameter determination.

Shear performance of reinforced concrete beams containing stirrups with lower bend defects

The reactive expansion caused by alkali-aggregate reactions and severe corrosion in a saline environment may both lead to fracture or complete section loss at the lower bends of stirrups and localized debonding of side-legs nearby. The effects of such bend fracture and the debonded length on the shear performance of a reinforced concrete beam were explored in laboratory experiments and through a finite element simulation. Bend-defects in the stirrups reduced the beam’s shear strength, and the reduction increased with the debonded length. And a parametric analysis indicated that the nominal shear stress carried by the stirrups with a given defect severity increased with section size, and the size effect of shear strength became less significant with increasing defect severity. An approach for predicting the shear strength of such defective beams was proposed based on a transparent and well-understood mechanical and physical model, and published test data confirm its accuracy and safety was confirmed by published test data on 35 beams of various sizes.

Rancang Bangun Rangka dan Penggerak Mesin FDM Berbasis Arduino Tipe XZ-Head

FDM is an AM method that is currently being developed due to the flexibility of the object geometry that can be formed. This study aims to design the frame and drive of the XZ Head type FDM engine. Stress simulation was carried out to determine the safety factor in the frameXZ design. Lead screw parameters in the form of torque, shear stress, axial stress, and critical load were calculated to determine the torque requirement of the driving motor. The value of the linear axis of the stepper motor was calibrated to determine the dimensions of the printed output. Based on the simulation, the dynamic and static stresses on the XZ frame were 1.9 MPa and 2 MPa. The yield strength was 55 MPa with a safety factor of 28. The results of the calculation of the lead screw torque (TR) and (TL) were 18.27 N.mm and 6.60 N.mm. The calculated nominal shear stress of the screw () was 0.43 N/mm2, the axial loading stress () was -0.62 N/mm2, and the critical load (Wcr) was 9986.41 N. The difference in dimensions of the measurement results in the X and Z planes was 0.22 and 0.17 mm larger than the target dimensions of 20 mm.

Creep anisotropy of a 3rd generation nickel-base single crystal superalloy in the vicinity of [001] orientation

The effect of orientation on the creep behavior of a 3rd generation Ni-base single crystal superalloy with orientation deviated from [001] direction 10°∼20° was studied at 1100 °C/150 MPa and 850 °C/650 MPa. It is shown that the creep anisotropy almost disappears at 1100 °C/150 MPa for samples within 20° of [001]. Rafts with waving structures are formed in all samples which eliminate the various γ/γʹ microstructures caused by orientation deviation and hinder the matrix dislocation movement in similar ways. While the creep properties are highly anisotropic at 850 °C/650 MPa. The creep lives of samples close to [001]-[011] boundary are much longer than those of samples close to [001]−[1‾11] boundary, which is mainly caused by the activated slip systems at primary creep stage. Multiple <112>{111} slips are more likely to be activated in samples close to [001]-[011] boundary, and single <112>{111} slip system dominates the deformation of samples close to [001]−[1‾11] boundary. The phenomenon is rationalized in view of the nucleation and propagation of <112>{111} slip systems by means of the nominal resolved shear stress (RSS) analysis.

Failure Analysis of the Screw Press Machine

In this paper, an analysis of the mechanical components of the Screw Press Machine is carried out in the form of an analysis of the design of mechanical components, maintenance cycles and remaining life. From the design analysis of mechanical components, it is known that the stresses that occur in the screw are in the form of nominal shear stresses of 18.18 N/mm², axial stresses of -10.41 N/mm², bending stresses of 54.66 N/mm², and shear stresses acting on the base screw of 65.41 N/mm². The number of press cycles that occur in one hour is 121 cycles. Number in the press cycle that occurs in the worm screw press is 2.625x105 cycles. In field conditions with pressure fluctuating between 30-40 bars, the life time of using a worm screw press is around 2169.43 hours.

Frictional shear stress of ZnO nanowires on natural and pyrolytic graphite substrates

The friction behaviour of ZnO nanowires on natural graphite (NG) and highly oriented pyrolytic graphite (HOPG) substrates was tested in ambient conditions by use of optical microscopy based nanomanipulation. Nanowires on the step-free and waviness-free NG substrate exhibit a diameter-independent nominal frictional shear stress of 0.48 MPa, and this provides a benchmark for studying how the surface topography of graphite influences nanowire friction. Nanowires on the HOPG substrate present a significant diameter-dependent frictional shear stress, increasing from 0.25 to 2.78 MPa with the decrease of nanowire diameter from 485 to 142 nm. The waviness of HOPG has a limited effect on the nanowire friction, as a nanowire can fully conform to the substrate. The surface steps on the HOPG can significantly enhance the nanowire friction and lead to a much higher frictional shear stress than that on NG due to mechanical blocking and the presence of a Schwoebel barrier at step edges. The surface steps, however, can also generate small wedge-shaped gaps between a nanowire and substrate, and thus reduce the nanowire friction. With the decrease in nanowire diameter, the capacity for the nanowire to better conform to the substrate reduces the length of the wedge-shaped gaps, leading to the observed increase in nanowire friction. The results have improved our understanding of the unique friction behaviour of nanowires. Such an improved understanding is expected to benefit the design and operation of nanowire-friction-based devices, including bio-inspired fibrillar adhesives, soft grippers, rotary nanomotors, and triboelectric nanogenerators.

Lateral behavior of trapezoidally corrugated wall plates in steel plate shear walls, Part 2: Shear strength and post-peak behavior

This research focuses on the shear strength and post-peak behavior of trapezoidally corrugated wall plates in vertically or horizontally Corrugated Steel Plate Shear Walls (CoSPSWs) through nonlinear pushover analyses. Results showed that different from flat wall plates, corrugated wall plates could develop a shear strength close to the shear yield strength at relatively low lateral drifts, and the lateral load-drift curves usually experienced a descending stage, which was closely related to the elastic shear buckling stress, the dominant shear buckling mode, and the shear yield strength. Corrugated wall plates with higher elastic shear buckling stress, dominant global shear bucking mode, or lower shear yield strength would generally have slightly higher peak nominal shear stress ratio and much higher ductility than wall plates with lower elastic shear buckling stress, dominant interactive or local shear bucking mode, or higher shear yield strength. A shear slenderness ratio λs was then introduced as the square root of the ratio between the shear yield strength and the elastic shear buckling stress, and simplified lateral load-drift curves were proposed for corrugated wall plates with different dominant shear buckling modes and range of λs values. The proposed curves could accurately predict the initial lateral stiffness, the shear strength as well as the post-peak descending behavior of corrugated wall plates.

Evaluation of design equations for out-of-plane shear strength of deep concrete sections in nuclear power plant buildings

Reinforced concrete walls in nuclear power plant buildings, which are generally more than one-meter thick, are typically designed to resist out-of-plane shearing force using concrete resistance only, namely, through-thickness shear reinforcement is not provided. Standard ASCE 43, which addresses design of safety-related nuclear facilities in the United States, references ACI 349 for design of reinforced concrete nuclear structures and components, with exceptions as deemed necessary. The code ACI 349–13, assumes, identically to ACI 318–08 and ACI 318–14, that the nominal shear stress capacity of longitudinally reinforced concrete sections is independent of cross-section depth: an assumption not supported by data. In the last revision cycle of ASCE 43, the ACI 349–13 design equation for concrete shear stress capacity was evaluated for conformance with the performance target of the standard, namely, a 98% or higher probability of exceedance, and found to be inadequate. A correction to the ACI 349–13 equation was developed and implemented in ASCE 43–19 to account for the effects of effective depth and longitudinal reinforcement ratio on concrete shear stress capacity. In parallel with the revision of shear provisions in ASCE 43, a size-effect modification factor, λs, was introduced in ACI 318–19 to account for the reduction in concrete shear stress capacity with increasing effective depth. In this paper, the technical basis for the correction factor included in ASCE 43–19 is developed and the ACI 318–19 equation is assessed to judge whether it achieves the ASCE 43 performance target. The assessment utilized the test data of longitudinally reinforced beams assembled by Reineck and his co-workers for slender sections (ratio of shear span-to-effective depth greater than or equal to 2.4) and non-slender sections (ratio of shear span-to-effective depth less than 2.4). For slender sections, the probability of exceedance of the ASCE 43–19 (ACI 318–19) design strength is greater than 98% (99%). For non-slender sections, the exceedance probabilities are greater than 99%. Because the ACI 318–19 equation meets the ASCE 43 performance target for both slender and non-slender sections, the correction invoked in ASCE 43–19 could be retired once ACI 349 adopts the shear provisions of ACI 318–19 for longitudinally reinforced concrete.

Static and fatigue behavior of shear stud connection embedded in UHPC

In the UHPC-steel composite bridge deck, the thickness of UHPC layer is usually only 40–50 mm, so short headed studs are used for shear connection of the interface between UHPC and steel deck. In this paper, the refined finite element (FE) model of push-out specimen is established to explore failure mode of the stud connection, damage concentration location of UHPC and load-slip behavior of UHPC-steel interface. Verified against the existing test results, FE parameter analysis is conducted, and shear strength formula and load-slip relationship of short headed stud embedded in UHPC are proposed. With the consideration of reduction effect of group studs, the shear strength formula of single stud can be used to simplify the calculation safely. A nominal shear stress S-N curve with 95% survival probability is proposed, fitted by the International Institute of Welding (IIW) recommended method. Based on the fracture mechanics method, a fatigue life evaluation formula of stud under influence of multiple factors is established. By the comparative analysis between the proposed formulas and the existing codified formulas for stud connection in ordinary concrete, the recommended formula for the fatigue strength of stud in UHPC is proposed.

Compressions of magnetorheological fluids under instantaneous magnetic field and constant area

Compressions of magnetorheological (MR) fluids have been carried out under instantaneous magnetic fields. The yield strength of the MR fluid in compressive mode has been derived by assuming that it was a transformed shear flow in Bi-visous model. The compressive stresses have experimentally studied under different magnetic fields, different initial gap distances and different compressive velocities. The nominal yield shear stresses of the compressed MR fluid under different influential factors have been calculated. The compressive stress increased in a power law as the applied magnetic field increased, while it decreased as the initial gap distance and the compressive velocity increased. With the increase of magnetic field, the difference between the nominal yield shear stress curves increased, and the exponents of the power law increased with the increase of the magnetic field strengths. A larger initial gap distance and a lower compressive velocity resulted in a higher nominal yield shear stress under the same instantaneous magnetic field. The achieved results of the nominal yield shear stress with magnetic field seemed to deviate from the prediction of dipole model, and the chain structure aggregation effect, the sealing effect and the friction effect by compression should be considered.

Panting Fatigue of Trapezoidal Corrugated Steel Webs with Mixed-Mode Cracks

Trapezoidal corrugated steel webs under panting fatigue are represented by repeated cyclical out-of-plane deflections of their subpanel with mixed-mode cracks. Compared to stiffened flat webs, notable fatigue crack formation could take place along with local deflection. Fatigue tests were conducted for nine composite girders with slender webs and varied corrugation dimensions. Nearly all test girders showed notable local and interactive shear buckling at the corrugated web panel and the panting fatigue cracks are formed under repeated cyclical deflection while the compression and tension flanges remain intact. Fatigue cracks are initiated at the junction between the vertical (longer) edge of the subpanel and the boundary of the out-of-plane deflection region. The crack propagation paths appear to deviate from the original vertical edge due to buckling induced out-of-plane deflection under mixed-mode stress condition. The test results demonstrate that the Category B’ and Category E suggested by the AASHTO LRFD bridge fatigue design provisions related to the principal stress range and the nominal membrane shear stress range respectively can be considered for the prediction of the fatigue life of trapezoidal Corrugated steel webs in test girders. An appropriate allowance of both the shear stress along the vertical web edge and tension stress from the diagonal plastified tension band is given for the mixed-mode stress intensity factor. The proposed fatigue life prediction allowing for mixed-mode crack growth mostly compares well with test results and its further improvement for the case with higher web panel slenderness ratio is discussed.

Constraint and size effects in confined layer plasticity

Plane strain finite element analyses are used to model the experiments of Mu et al. (2014, 2016) for a thin metal layer confined between elastic solids. The thin metal layer undergoes elastic–plastic deformations, here modeled by strain gradient plasticity, while the rest of the solid deforms only elastically. Plane strain is assumed and finite strains are accounted for. The microscopic boundary condition at the band interface is initially taken to be zero plastic strain increment, but plastic straining at the interface is allowed when the plastic strain gradient at the interface has exceeded a critical value. When the narrow metal band is inclined 45° relative to the direction of compression of the solid, simple shear develops in the band and predictions are rather similar to those of a one-dimensional analysis for an infinite band. For a band at 90° the elastic parts give significant constraint on plastic flow, the stress fields are non-uniform along the band and the average nominal compressive stress shows strong sensitivity to the layer thickness and to the width of the specimen. Remarkably good qualitative, and in some cases quantitative, agreement is found with the experimental observations of Mu et al. (2014, 2016). Considering also other band angles, both the average nominal shear and compressive stress show variations with the angle.

Discussion on Calculation Method of Shear Bearing Capacity of HSC Beams Without Web Reinforcement under Concentrated Loads

In order to investigate the main influencing factors and development rules of the shear performance of high strength concrete (HSC) beams without web reinforcement under concentrated loads, analyze and compare the rationality of the China and American Code formulas and Zsutty formula, in this paper, 303 sets of experimental data about the shear test of HSC beams without web reinforcement at home and abroad were selected, based on these experimental data, the calculation method of the shear capacity of HSC beams without web reinforcement was discussed. The results showed that the measured shear bearing capacity of HSC beams without web reinforcement gradually increases with the decrease of the shear-span ratio. The nominal shear stress of HSC beams without web reinforcement gradually increases with the increase of concrete strength, the increase of longitudinal reinforcement ratio and the decrease of section height. The shear bearing capacity formula proposed by Zsutty is the most accurate prediction than other formulas. Based on the experimental data and considering the influence of the longitudinal reinforcement ratio on the shear bearing capacity of structure, a new calculation formula for the shear bearing capacity of HSC beams without web reinforcement under concentrated loads was obtained by regression analyze, and this formula is more comprehensive than the other three calculation formulas, moreover, the calculation results are more reasonable.

Estimations of Stress Concentration Factors (Cw/Kts) For Helical Circular/Square Cross Sectional Tension-Compression Springs And Artificial Neural Network Modelling

Springs are used for various purposes in machine design as they can store energy under load, due to their elastic deformation characteristics. There are many types and profiles of springs. For a round wire helical compression or tension spring of small pitch angle, the Wahl factor, a correction factor (Cw) taking into account curvature and direct shear stress, is generally used in the design. The corresponding stress concentration factors, which may be useful for mechanics of materials problems, are obtained by taking the nominal shear stress τnom as the sum of the torsional stress (τ) and the direct shear stress (τ) for round wire. In the case of the wire of square cross-section, τnom is the sum of the torsional stress and the direct shear stress. For design calculations it is recommended that the simpler Wahl factor be used. The same value of max will be obtained whether one uses Cw or Kts. This study contains the determination of stress concentration factor and Wahl factor. For this aim, stress concentration factor charts were converted numerical values for round and square wires. These values were collected in an excel file. ANN (Artificial Neural Networks) model was developed using the data. It is an easy and convenient method, ANN model, was presented for the determination of stress concentration and Wahl factor for spring design.

Big-and-dull or small-and-sharp: A comparison of specific energy, wheel wear, surface-generation mechanisms and surface characteristics when grinding with Al2O3 and CBN to achieve a given surface roughness

• For the same R a , small & sharp give much lower specific energies than big & dull. • For the same R a , small & sharp give slightly lower R t values than big & dull. • Ground surfaces are Gaussian, for all grit sizes and dressing. • The normalized grit shear stress is the force per grit per unit grit area. • Larger, dull-dressed CBN requires frequent dressing. An investigation was made into the effect of grit size and dressing conditions on specific energy, surface-finish characteristics and wheel wear, with a focus on whether smaller, sharp-dressed grits and larger, dull-dressed grits produce different specific energies and surface-finish distributions, even for the same R a surface-roughness. Grinding tests were performed and measurements were made of grinding forces, wheel wear, R a , R t and surface-height distributions. Observations were made of SEM photos of ground surfaces. Results show that, for a given R a surface roughness, smaller, sharp-dressed Al 2 O 3 grits give significantly lower specific energies and slightly lower R t values than larger, dull-dressed grits over a large range of grit sizes. This has significant implications in terms of thermal-damage risk and cycle times. Also, using larger, dull-dressed CBN grits requires too-frequent dressing in order to maintain surface roughness. A new concept is developed, the nominal bond shear stress , which can be used to quantify the risk of grit fracture or bond fracture in a single grit. The fundamental relationships between grit size, grit sharpness and contact mechanisms are discussed and practical recommendations are given.

Enhancement of shear strength of bonded post-tensioned beams using inverted-U shaped reinforcements

At cracked stage, the post-tensioned concrete beams resist shear through a different set of mechanisms, the accepted mechanisms are: interface shear transfer, dowel action of longitudinal reinforcements, shear transfer in compression zone, transversal reinforcements, and vertical component of the force in the draped of prestressing strands. To increase the shear capacity in such beams, special shear reinforcements can be used. This paper presents the results of an experimental investigation on shear strength for bonded post-tensioned concrete beams (PTB) reinforced with inverted-U shaped reinforcement; those results were compared with beams provided with stirrups reinforcements. Based on ACI code, the nominal shear stress in transversal reinforcement is limited to 8 fc' psi (0.67 fc'MPa), but however it does not differentiate between the types of shear reinforcements. The results indicate that the nominal shear stress in inverted-U shaped and stirrups reinforcements are 14.4 fc' psi (1.2 fc'MPa) and 12.72 fc' psi (1.06 fc'MPa), which it gives approximately 13 % increase in shearing strength. Good correlations exist between the predicted and the actual experimental results.