Simple Design Formulas Research Articles

Experimental Study on the Behavior of Polyurethane Springs for Compression Members

In this study, the characteristics of the compression behavior of polyurethane springs that can be used as compression members of seismic devices, such as dampers and seismic isolators, were identified, and the effect of the design variables on the performance points of polyurethane springs was investigated. Compressive stiffness and specimen size were set as the design variables of the polyurethane spring, and the performance indicators were set as maximum force, residual strain, and energy dissipation. A total of 40 specimens with different conditions were fabricated and a cyclic loading test was performed to obtain the force-displacement curve of the polyurethane spring and to check the performance indicator. Significant strength degradation was confirmed after the first cycle by repeated loading, and it was confirmed that compressive stiffness and size demonstrated a linear proportional relationship with maximum force. In addition, the design variables did not make a significant change to the recovered strain, including residual strain, and residual strain of about 1% to 3% occurred. Energy dissipation showed a tendency to decrease by about 60% with strength degradation after the first cycle, and this also demonstrated no relationship with the design variables. Finally, the relationship between the design variables and performance indicators set in this study was reviewed and suggestions are presented for developing a simple design formula for polyurethane springs.

Activation model for various punching shear reinforcement types in flat slabs and column bases optimized for design

Various types of punching shear reinforcement have been developed during the past decades to increase the punching capacity and ductility of slab-column connections. Due to diverse geometries and thus varying anchorage conditions, the effectiveness of these elements contributing to total punching resistance can differ significantly. Generally, the degree of activation of shear reinforcement can be described by contributions of anchorage and of bond. Yet, most of current punching design provisions follow a simplified, empirical approach. Despite its mechanical background, the punching design according to the next generation of Eurocode 2 still does not consider the effect of better anchorage of, for example, double headed studs compared to simple stirrups.In this paper, an extended activation formula for flat slabs as well as column bases is proposed as refinement for the next generation of Eurocode 2. This unifying approach considers different anchorage categories and thus enables more progressive design results. After discussing the background of possible activation scenarios, the effects of bond and anchorage in cracked concrete and the kinematic deformation behavior of slabs subjected to punching are identified as governing constraints. The major focus is on the transformation process from mechanical considerations to a simplified design formula to ensure practical applicability.

Design of concrete fracture property by average aggregate size

This study presents a design methodology for concrete fracture properties, linking the average aggregate size dav to the tensile strength ft and fracture toughness KIC for a given cement grade and water/cement (W/C) ratio. Two different concrete mixes with dav = 3.5 and 7 mm were tested and analyzed. Similar peak load Pmax values were obtained under three-point-bending conditions, but with different “ductility”. Variations of ft &KIC with dav were established by a simple design formula, which can be used to tailor bulk concrete fracture properties for specific purposes. A statistical method was introduced to estimate the effective dav if only the maximum aggregate size dmax was given. Comprehensive fracture data in literature were analyzed to demonstrate the estimation of dav from dmax. The purposely designed concrete mixes and data in literature show the significance of dav design even after the cement grade and W/C ratio are fixed.

Stability checks of columns and beams n braced Frames using elastic effective lengths.(Dept.C)

Checking for stability of columns and beams in braced frames is based on the elastic effective lengths. Simple design formulae. for checking the stability of the individual Pin-ended columns, are derived, where the effective length is equal to the line structure length. In this paper the problem of checking the stability of single braced frames, by using the equivalent column approach is considered. i.e the stability check of the total braced frame is replaced by stability cheeks of the individual Columns. Requirements necessary for the beans of a simple braced frame are sought, when the column is checked for stability using the elastic effective length.

Coupled ultimate capacity of CFRP confined concrete-filled steel tube columns under compression-bending-torsion load

Carbon fiber reinforced polymer confined concrete-filled steel tube (CFRP-CFST) columns are having promising utilization in offshore structures, which are usually subjected to the combination of axial forces, bending moments, and torsional moments. This paper thus presents a finite element (FE) study on CFRP-CFST columns under combined compression-bending-torsion load. The comprehensive FE modelling was established and then validated by the experimental data. Analysis of typical failure modes, load-deformation relations and full-range behavior was performed based on the FE simulation. Meanwhile, parametric analysis was conducted to reveal the sensitive parameters as well as their influence on the structural behavior and ultimate capacity of CFRP-CFST columns. Finally, correlation relations which can reasonably characterize the coupled ultimate capacity of columns were obtained and validated. Correspondingly, simplified design formulae for predicting the ultimate capacity correlation of CFRP-CFST columns under compression-bending-torsion load were proposed.

Achromatic optical system with diffractive-refractive hybrid lenses for multifocusing of ultrashort pulse beams.

We report an achromatic cascade optical system for multifocusing ultrashort pulse beams with a diffractive beam splitter. Distortion compensation requires the removal of pulse front distortions from arrayed pulses, which originate from beam-radius-dependent group delay dispersions. The inclusion of hybrid diffractive-refractive lenses can effectively manage system dispersions. Simple design formulas are derived using the ray-matrix analysis and the designed system is evaluated using 20-fs pulses. We confirm that the hybridized system can remove not only chromatic aberrations but also pulse front distortions, hence improving the system spatio-temporal focusing resolutions. The proposed pulse delivery technique enhances the practicality of materials processing with ultrashort pulses.

A parametric study on the stability of fiber reinforced rubber bearings under combined axial and shear loads

Fiber Reinforced Bearings (FRBs) have proven to be a valuable rubber-based base isolation technology in which flexible fiber reinforcements are used to replace the steel layers commonly adopted for the manufacturing of Laminated Rubber Bearings (LRBs). Thanks to the low weight and cost of FRBs, these devices could prove to be instrumental for the promotion of base isolation applications to houses and residential buildings of developing countries of the world in seismic regions. This study is based on the results of a large set of Finite Element Analyses (FEAs) aimed to assessing the performance of FRBs under combined axial and shear loads. The aim of this work is that of filling a lack of knowledge regarding the lateral displacement capacity of FRBs: research studies available in literature do not consider the effects of axial pressure, material properties, primary and secondary shape factors on the response of these devices under combined axial and lateral loads. Conclusions of this study underline that the simple design formula commonly adopted for the design of FRBs underestimate the effect of the axial pressure in limiting the lateral displacement capacity of the bearings. Moreover, available simplified formula, do not offer an accurate estimate of the force response of these bearings under combined loads. Additional FEAs are needed to extend the results of this study to bearings of other shapes, including circular and square isolators.

Bounds to the pull-in voltage of a MEMS/NEMS beam with surface elasticity

The problem of pull-in instability of a cantilever micro- or nano-switch under electrostatic forces has attracted considerable attention in the literature, given its importance in designing micro- and nano-electromechanical systems (MEMS and NEMS). The non-linear nature of the problem supports the typical approach that relies on numerical or semi-analytical tools to approximate the solution.By contrast, we determine fully analytical upper and lower bounds to the pull-in instability phenomenon for a cantilever beam under the action of electrostatic, van der Waals or Casimir forces. In particular, the novel contribution of this works consists in accounting for size effects analytically, in the spirit of surface elasticity, which adds considerable complication to the problem, allowing for a nonconvex beam deflection. Surface energy effects are generally ignored in classical elasticity, although they are known to become relevant for very small structures and especially at the nano-scale, owing to their large surface/volume ratio. Closed form lower and upper bounds are given for the pull-in characteristics, that allow to discuss the role of several tuneable parameters. Indeed, the evolution of the cantilever tip deflection is presented as a function of the applied voltage up to the occurrence of pull-in and the contribution of van der Waals and Casimir intermolecular interactions is discussed. It is found that intermolecular forces strongly decrease the pull-in voltage, while surface elasticity works in the opposite direction and stabilizes the system. The accuracy of the bounding solutions, measured in terms of the difference between upper and lower analytical bounds, is generally very good, although it rapidly deteriorates as the effect of surface elasticity becomes more pronounced. Finally, approximated closed-form relations are developed to yield simple and accurate design formulae: in particular, they provide estimates for the minimum theoretical gap and for the maximum operable length for a free-standing cantilever in the presence of the effects of surface elasticity and intermolecular interactions. Results may be especially useful for designing and optimizing NEMS switches.

Experimental study on mechanical behavior of double-layer toughened sandwich glass with two-side simple support

To study the mechanical behavior of double-layer toughened sandwich glass with two-side simple support under out-of-plane bending, a total of sixty-four specimens with different test parameters were experimentally investigated in this paper. The main parameters of specimens include thickness of single layer, supporting width, and loading length. It was demonstrated that the specimens failed with all pieces of cracks combined together as an entire unit rather than to separate into a large number of glass fragments. What's more, the cracks appeared only in the lower layer of the toughened sandwich glass, extending in a way similar to the spider web. The ultimate bending strength and bending stiffness of the toughened sandwich glass are enhanced with the increase of the thickness of single layer, the supporting width, and the loading length. Among the above parameters, the thickness of single layer plays a leading role in enhancing the ultimate bending strength and bending stiffness of the toughened sandwich glass. Nevertheless, the supporting width only has a slight effect on improving the ultimate bending strength and bending stiffness. Based on the bending theory of thin plates, the simplified design formulas were presented to evaluate the ultimate bending strength of double-layer toughened sandwich glass with two-side simple support under out-of-plane bending, which was verified to be reasonable and accurate.

Effective slab width for beam-end flexural strength of composite frames with circular-section columns

The calculation of the ultimate loading capacity of composite frame beams is an important step in the design of composite frame structural systems. This paper puts forward the Compression-on-Column-Face, Compression-on-Transverse-Beam and Tension-on-Transverse-Beam mechanisms to explain the mechanism of the circular-section column frame in the ultimate loading state, and an extensive parametric analysis is conducted on a series of typical composite beam–column joint subassemblies using the nonlinear finite-element simulation method. First, an elasto-plastic elaborate finite element model is established to conduct the parametric analysis of the exterior joint of the circular-section column frame under negative and positive moment. Furthermore, based on the parametric analysis, the simplified design formulae of the slab effective width are derived. The proposed formulae and numerical results are compared for the effective slab width for composite frames with circular-section columns, and the relative errors are little. In addition, the applicability of the formulae to calculate the effective slab width at the interior joints in the circular-section column frame is verified. Finally, this paper compares the proposed formulae with formulae in the current design codes, and the proposed formulae provide the most accurate results to predict the effective slab width and ultimate loading capacity.

Elastic buckling analysis of rectangular longitudinally profiled (LP) steel plates under uniform compression

Longitudinally profiled (LP) steel plates are plates rolled to variable thickness along the rolling direction in order to suit practical loading distributions in construction applications. The elastic buckling load of LP steel plates is different to normal flat plates due to the change in thickness and it is hard to find analytical solutions to the governing equation. In this paper, the elastic buckling coefficients of rectangular LP plates were calculated using the Galerkin and Rayleigh-Ritz method (GRM). The plates were under uniform compression and four typical boundary conditions were considered. The element expression of the feature matrix was obtained by theoretical derivation and the elastic buckling coefficients were obtained by calculating the eigenvalues of the feature matrix numerically with MATLAB. Numerical models of LP plates were developed to validate the derivation. Upon validation it was further found that the elastic buckling coefficients of LP plates can be approximately expressed by those of constant thickness steel plates together with variable thickness coefficients. A series of approximation formulae of elastic buckling coefficients of LP rectangular steel plates were proposed. Simplified design formulae of elastic buckling coefficients of LP plates were proposed for the first time to promote the application of LP plates in engineering practice.

Investigation on flexural behavior of double-layer toughened sandwich glass with trilateral simple support

This paper presents experimental investigations on the flexural behavior of double-layer toughened sandwich glass with trilateral simple support. A total of sixty-four pieces of toughened sandwich glass with different thickness of single layer, supporting width, and loading length were subjected to out-of-plane flexural loading tests. It was demonstrated that the specimens failed with all pieces of cracks combined together as an entire unit rather than to separate into a large number of glass fragments. The cracks appeared only at the lower layer of toughened sandwich glass and the upper layer of the toughened sandwich glass was integral and undamaged. The ultimate capacity and flexural rigidity of the toughened sandwich glass are enhanced with increasing the thickness of single layer, supporting width, and loading length. Among all studied parameters, the thickness of single layer exerts the largest influence on the ultimate capacity and flexural rigidity of toughened sandwich glass, while the effect of supporting width is quite limited. A simplified design formula was put forward to predict the ultimate capacity of double-layer toughened sandwich glass with trilateral simple support under out-of-plane flexural loading, which was verified to be reasonable and accurate.

Multi-index distortion control of steel-concrete composite tub-girders considering interior cross-frame deformation

Excessive distortion of the cross section may occur and induce significant distortional warping stresses when the steel-concrete composite trapezoidal box girders are subjected to eccentric loads. The most effective solution to control distortion is to install sufficient internal cross-frames. However, current design methods generally omit the deformation of the cross-frames. In addition, most design guidelines limit the distortion control index to a specific value, which may result in quite conservative design. Therefore, this paper aims to propose a method for distortion control of steel-concrete composite box-girders with deformable interior cross-frames considering various distortion control indices and limit values. In accordance with current studies and design specifications, three distortion control indices are selected for investigation in this research. Equations for the distortion of composite trapezoidal box girders with cantilever overhangs are first derived based on the energy-variation method. Accordingly, an efficient modeling strategy using the Beams on Elastic Foundation (BEF) analogy is developed. Subsequently, extensive parametric analyses are conducted to obtain simplified design formulas of the control indices, which well fit the numerical results. Therefore, the effective design methods for the cross-frames to control distortion are proposed, where various indices and shear deformation of inner cross-frames are considered. Analyses of bridge design examples demonstrate that the proposed method is both efficient and universally applicable to provide appropriate number and size of cross-frames to control distortion of composite tub-girders in practical design.

Design method for steel deck plates under quasi-static patch loads with allowable plastic deformations

Plastic deformation of plates in steel deck structures under heavy vehicle or helicopter wheel loads is common in ships and offshore structures, and is therefore of significant interest to designers of ro-ro/cargo ships, helicopter-carrying ships and offshore platforms. To provide insight into the plastic deformation of plates, the nonlinear elasto-plastic response of stiffened steel plates loaded quasi-statically by a central rigid rectangular indenter is investigated both experimentally and numerically. The numerically-determined stiffened plate permanent deflections compare well with those obtained experimentally. The concept of applying the elasto-plastic method to the design of deck plates under wheel patch loads is introduced, and the design principle of wheel patch loaded plating is studied together with the design criteria. A simple design formula to determine plating thickness is proposed based on an acceptable level of permanent set. Ship-mounted helideck plating design cases are given to illustrate the elasto-plastic method, and comparisons are made between the thicknesses derived using the proposed design formula and those found from Lloyd's Register (LR), Bureau Veritas (BV) and DNV-GL rule requirements.

Experimental and numerical study on creep and shrinkage effects of ultra high-performance concrete beam

Compared with normal concrete, ultra high-performance concrete (UHPC) is of increasing interest for bridge engineering because of its superior tensile strength, compressive strength, and significantly enhanced durability. The creep and shrinkage effect have a significant influence on the long-term behavior of UHPC. However, the existing research on the time-dependent behavior of UHPC is still limited. In this research, based on numerical integration method, the ABAQUS user subroutine for simulating creep and shrinkage of both normal concrete (NC) and UHPC were developed by the recursive algorithm of adjacent stress increment in the time history. The accuracy of developed user subroutine was validated by creep and shrinkage test of reinforced NC beams. Subsequently, the long-term creep and shrinkage test of UHPC specimens was conducted with stress to strength ratio of 20%, 30%, and 40%, respectively. Based on the test results and the CEB-FIP Model code 1990, the simplified design formulas for predicting creep and shrinkage of UHPC were proposed respectively based on the developed UHPC material. In the proposed design formulas, the final shrinkage strain was 145 με, and the final creep coefficient was 0.46 for the developed UHPC specimens based on the test environment condition. The comparison between the test result and proposed formulas indicated good applicability and accuracy of the proposed formulas. Based on the developed ABAQUS user subroutine and the proposed design formula for creep and shrinkage, the finite element (FE) models of RC beam and UHPC beam were developed. The influence of creep and shrinkage on the long-term mechanical behavior of simply supported prestressed beams were investigated.

An investigation into prying models in tension clips

Models of the prying phenomena can be split into two types; simple analytical and semi-empirical. Simple analytical models are based on assumptions that allow for rough sizing, but do not address important prying phenomena. Semi-empirical models attempt to holistically address the various phenomena arising from prying, but are pragmatically focused on matching tested data and arriving at simple design formulae rather than accurately modelling the physical phenomena. A comparison of these two types of modelling philosophies is presented, addressing both their advantages and disadvantages. Since most tested data is from the civil engineering-side of the structural fraternity, they apply to end-plate connections with relatively ’thick’ bases (> 10 mm). The aerospace industry uses ’thin’ ( <3 mm) bolted tension ’T-clips’ extensively to transfer ’light’ loads. Accurately predicting the load in the fastener, as well as the bending and shear distribution throughout the clip, is therefore important; especially for fatigue considerations. To achieve this objective, a method is proposed that assumes the clip to rest on an infinitely stiff, tensionless Winkler foundation. The corner radius is modelled using Castigliano's 2nd theorem to accurately predict the shear and moment distribution throughout the clip. The fastener is modelled as both an axial and torsional spring, allowing for extension and rotation of the fastener, and to establish the point of first contact of the clip with the foundation. Fastener preload is also included in the model. Finally, the maximum applied force at which the clip initiates plastic hinges is also predicted. The proposed method predicts the centroid of the prying load distribution to be a function of base thickness, with significantly larger prying force reacted by the fastener in ’thin’ bases. Predicted results for ’thin’ (<3 mm) aluminium clips match those of 1D Nastran beam models (CBARs) on CGAP elements, as well as a 3D Marc non-linear contact model, closer than any other model found in the literature.

Compressive behavior of CFRP-confined partially encased concrete columns under axial loading

This paper reports the compressive behavior of CFRP-confined partially encased concrete columns under axial loading. Nine CFRP-confined partially encased concrete columns and three partially encased concrete columns are axially tested. The failure modes, load versus displacement relationship, axial bearing capacity, ductility and initial stiffness are presented and analyzed. The results show that CFRP-confined partially encased concrete columns present a better mechanical performance than those without CFRP sheets confining (i.e. partially encased concrete columns). CFRP-confined partially encased concrete columns are eventually failed due to the local buckling of steel flange with rupture of CFRP sheet or without rupture of CFRP sheet. The ductility and axial bearing capacity of columns can be improved with increasing number of CFRP sheet layers. A simplified design formula of CFRP-confined partially encased concrete columns is proposed, which can satisfactorily agree with the test results.

Numerical analysis of buried trench in screening surface vibration

In practical engineering, open trenches would be covered by soil or plate for greenery and safety reasons, which inevitably turns them into buried trenches. It is necessary to reassess the screening efficiency of these buried trenches. A plane strain model is then established to describe wave propagation in ground. The influences of geometrical parameters normalized by Rayleigh wavelength (LR) are investigated, followed by a simplified design formula to estimate the screening capacity of buried trenches. Results show that the buried depth and trench depth play dominant roles in screening effect whereas the influence of trench width is small. Furthermore, four kinds of extending plates mounted on top of buried trenches are considered. It can be found that extending plates would significantly increase the screening performance of the barrier system. The source- and receiver-oriented extending plate are found to be the more effective measures and make a more contribution to wave screening when buried depth is around 0.2–0.3LR.

Tuned inerter dampers for civil structures subjected to earthquake ground motions: optimum design and seismic performance

Tuned inerter damper (TID) is a promising passive vibration control device in earthquake engineering because it achieves a large inertance-to-mass ratio without requiring a large space and thus can effectively decrease the cost. This paper presents a theoretical and numerical study of a structure-TID system subjected to earthquake ground motions. Using the fixed-point theory, we derived simple design formulas for the TID when it attached to a single-degree-of-freedom system subjected to ground acceleration excitations. Analytical and numerical results demonstrate that the optimally designed TID using the proposed parameters is capable of suppressing the displacement response of structures with natural period ranging from 0.3 s to 5 s, and the performance positively relates to the inertance-to-mass ratio used. Particularly, a TID with a large inertance-to-mass ratio can significantly prolong the fundamental period of a structure-TID system, which is similar to a seismic isolation system. The optimally designed TID can effectively mitigate the absolute acceleration response of short-to-moderate period structures, but is far less likely to be effective for long-period structures. It is suggested that a value of less than one is used for the inertance-to-mass ratio of long-period structures if one intended to mitigate both displacement and absolute acceleration responses. In addition, numerical results illustrate that an optimal inertance-to-mass ratio exists when a single TID is applied to a multi-degree-of-freedom building structure. The results also indicate that the emerging TID outperforms the conventional tuned mass damper for seismic response control because the former device introduce no additional seismic energy to the system and is more robust due to large inertance-to-mass ratio used.

Analytical behaviour and design of square CFDST subjected to local bearing force

This paper presents a finite element analysis (FEA) model for the behaviour of square concrete filled double skin steel tube (CFDST) under local bearing force. Feasibility of the developed FEA model was validated extensively against available experimental results. The predicted results obtained from the FEA modelling were found to match well with those observed from the tests in terms of failure patterns, load versus deformation curves and bearing capacities. The full-range load-transferring mechanism of square CFDST under local bearing force was then analyzed using the FEA model. Comprehensive parametric studies were also carried out to investigate the effect of various parameters on the bearing capacity of square CFDST subjected to local bearing force. The evaluated parameters mainly included the hollow ratio of CFDST, geometric configuration of the bearing member (BM) and the CFDST, the width to thickness ratio of steel tubes, and the strengths of steel and concrete materials. Based on the parametric analysis results, simplified design formulae were proposed for calculating the bearing capacity of square CFDST under local bearing force. Validated through the reported experimental data, the proposed formulae were featured with a reasonable accuracy and could be adopted in the practical design of square CFDST members subjected to local bearing force.