Static Load-deflection Curves Research Articles

A NEW METHOD FOR GENERATING VIRTUAL MODELS OF NONLINEAR HELICAL SPRINGS BASED ON A RIGOROUS MATHEMATICAL MODEL

This paper presents a new method for generating nonlinear helical spring geometries based on a rigorous mathematical formulation. The model was developed for two scenarios for modifying a spring with a stepped helix angle: for a fixed helix angle of the active coils and for a fixed overall height of the spring. It allows the development of compression spring geometries with non-linear load-deflection curves, while maintaining predetermined values of selected geometrical parameters such as the number of passive and active coils and the total height or helix angle of the linear segment of the active coils. Based on the proposed models, Python scripts were developed that can be implemented in any CAD software offering scripting capabilities or equipped with Application Programming Interfaces. Examples of scripts that use the developed model to generate the geometry of selected springs are presented. FEM analyses of quasi-static compression tests carried out for these spring models have shown that, using the proposed tools, springs with a wide range of variation in static load-deflection curves can be obtained, including progressive springs with a high degree of nonlinearity in the characteristics. The obtained load-deflection curves can be described with a high degree of accuracy by power function. The proposed method can find applications in both machine design and spring manufacturing.

Axial–Flexural Interaction in Axially Restrained Beams in Progressive Collapse Column-Removal Scenarios

Progressive collapse alternate path scenarios are often characterized by restrained beam configurations that provide resistance to structural collapse after column removal. While various methods have been presented to model the behavior of restrained beams, opportunities exist for mechanics-based estimation of the complete static and dynamic load-deflection curves. This paper presents an axially restrained beam (ARB) model that incorporates axial–flexural interaction throughout the entire static load-deflection curve including the elastic material range, the plastic flexural dominant range, the range beyond plastic flexure with increasing catenary effect, and the full catenary range. Energy methods are applied to static load-deflection curves to determine dynamic load-deflection relationships. A parametric study was conducted to assess the accuracy of the ARB method compared to nonlinear, dynamic time history finite-element (FE) analyses. The model compares favorably to results of FE models with average estimates of dynamic deflection within 2.1% for ideal moment connections and 7.7% for configurations combining simple and moment resisting connections.

Investigation of the Young's Modulus and the Residual Stress of 4H-SiC Circular Membranes on 4H-SiC Substrates.

The stress state is a crucial parameter for the design of innovative microelectromechanical systems based on silicon carbide (SiC) material. Hence, mechanical properties of such structures highly depend on the fabrication process. Despite significant progresses in thin-film growth and fabrication process, monitoring the strain of the suspended SiC thin-films is still challenging. However, 3C-SiC membranes on silicon (Si) substrates have been demonstrated, but due to the low quality of the SiC/Si heteroepitaxy, high levels of residual strains were always observed. In order to achieve promising self-standing films with low residual stress, an alternative micromachining technique based on electrochemical etching of high quality homoepitaxy 4H-SiC layers was evaluated. This work is dedicated to the determination of their mechanical properties and more specifically, to the characterization of a 4H-SiC freestanding film with a circular shape. An inverse problem method was implemented, where experimental results obtained from bulge test are fitted with theoretical static load-deflection curves of the stressed membrane. To assess data validity, the dynamic behavior of the membrane was also investigated: Experimentally, by means of laser Doppler vibrometry (LDV) and theoretically, by means of finite element computations. The two methods provided very similar results since one obtained a Young’s modulus of 410 GPa and a residual stress value of 41 MPa from bulge test against 400 GPa and 30 MPa for the LDV analysis. The determined Young’s modulus is in good agreement with literature values. Moreover, residual stress values demonstrate that the fabrication of low-stressed SiC films is achievable thanks to the micromachining process developed.

Representation of damage caused by fragmentation impact in design and analysis of reinforced concrete barriers

This paper presents methodology and calculation models that aim to enable a more realistic design of reinforced concrete (RC) protective barriers. The proposed methodology considers the global effect of fragmentation impact, which is commonly neglected in current design procedures. The analysis considers a non-uniform, two-zone damage model over the span, where the damage caused by fragment strikes is represented in the model in terms of reduced equivalent cross-section heights. It is shown that one of these zones, denoted ‘intense strip’, is significantly more damaged than the other zone. This representation of a damaged barrier, inside and outside the intense strip, should be considered for its global analysis. The proposed model was validated by comparison of its predictions with measured static load-deflection curves of plate specimens, which had been damaged by fragmentation impact in previously performed field tests. The models that are described in this paper, which provide an equivalent slab dimensions, can be used in further, more realistic dynamic analysis of the structural behavior of RC elements, subjected to combined blast and fragmentation loading.

Chord rotation demand for effective catenary action of RC beams under gravitational loadings

Many experimental and analytical studies have been conducted with beam-column subassemblages composed of a two-span beam to investigate the progressive collapse resistance of RC frames. Most study results reveal a strength-decreased transition phase in the nonlinear static load-deflection curve, which may induce dynamic snap-through response and increase the chord rotation demand for effective catenary action (ECA). In this study, the nonlinear static response is idealized as a piecewise linear curve and analytical pseudo-static response is derived for each linearized region to investigate the rotation demands for the ECA of the two-span RC beams. With analytical parameters determined from several published test results, numerical analysis results indicate that the rotation demand of 0.20 rad recommended in the design guidelines does not always guarantee the ECA. A higher rotation demand may be induced for the two-span beams designed with smaller span-to-depth ratios and it is better to use their peak arch resistance (PAR) as the collapse strength. A tensile reinforcement ratio not greater than 1.0% and a span-to-depth ratio not less than 7.0 are suggested for the two-span RC beams bridging the removed column if the ECA is expected for the collapse resistance. Also, complementary pseudo-static analysis is advised to verify the ECA under realistic dynamic column loss even though the static PAR is recovered in the nonlinear static response. A practical empirical formula is provided to estimate an approximate rotation demand for the ECA.

Seismic behaviour of a through-beam connection between concrete-filled steel tubular columns and reinforced concrete beams

Abstract This paper aims to investigate the seismic and post-seismic behaviour of a new and innovative type of through-beam connection between a concrete-filled steel tubular (CFST) column and a reinforced concrete (RC) beam. In this new connection system, the steel tube is completely or partially cut with the cut or openings being at the corresponding beam location, with the longitudinal steel reinforcing bars for the beam remaining continuous through the connection region. A strengthening ring beam is used to enlarge the connection zone in order to compensate for the possible decrease of the axial load carrying capacity as a result of the discontinuity of the steel tube that encases the column. Cyclic loading tests and subsequent axial compressive tests are reported on six beam–column specimens. Based on the experimental results, the hysteretic response, the skeletal and post-cyclic static load–deflection curves, the strain, ductility, strength and the stiffness degradation and energy dissipation are discussed. The favourable seismic performance of the connection is demonstrated in the tests. A finite element model is then developed and validated by a comparison with the experimental results. The relative effects of the reinforcement ratio of the frame beam and the ring beam, and the axial compressive force in the column on the seismic behaviour of the connection are elucidated through parametric studies.

Snapping of a Planar Elastica With Fixed End Slopes

In this paper, we study the deformation and stability of a planar elastica. One end of the elastica is clamped and fixed in space. The other end of the elastica is also clamped, but the clamp itself is allowed to slide along a linear track with a slope different from that of the fixed clamp. The elastica deforms after it is subjected to an external pushing force on the moving clamp. It is observed that when the pushing force reaches a critical value, snapping may occur as the elastica jumps from one configuration to another remotely away from the original one. In the theoretical investigation, we calculate the static load-deflection curve for a specified slope difference between the fixed clamp and the moving clamp. To study the stability of the equilibrium configuration, we superpose the equilibrium configuration with a small perturbation and calculate the natural frequencies of the deformed elastica. An experimental setup is designed to measure the load-deflection curve and the natural frequencies of the elastica. The measured load-deflection relation agrees with the theoretical prediction very well. On the other hand, the measured natural frequencies do not agree very well with the theoretical prediction, unless the mass of the moving clamp is taken into account.

直列皿ばねの振動特性

This paper describes the experimental results on the dynamic behavior of the Belleville springs stacked in series with washers and some process for deducing its dynamic character from the static load-deflection curve. Comparing the experimental results with those of the calculation, it is concluded that:(1) For demonstrating the hysteresis phenomena on a static load-deflection curves of the Belleville springs stacked in series with washers, it is necessary to take the frictional force between the contact surfaces into consideration. Thus, the experimental results agree fairly well with the calculated ones.(2) It is found that both the dynamic spring constants and the equivalent damping coefficients change in accordance with the amplitudes as well as the exciting frequencies, and those take the minimum values in the vicinity of the resonant frequency. And it can be said that vibration characteristics are the non-linear ones with soft-spring tendency.(3) According to the process described in this paper, it is possible to deduce the dynamic character of the Belleville springs stacked in series quantitatively from the calculation.

建築物の床のかたさおよびその評価方法に関する研究 : その 2. 床のかたさに関する心理学的尺度と物理量の対応および床のかたさの評価式・最適値の提示

The main purpose of this paper is to relate the scale of the sense on Hardness to the physical value of a building floor. The result are as follows. 1. We could relate the scale of the sense on Hardness to the deflection energy, being obtained from the static load-deflection curves of model floors. 2. We could obtain the equation for estimating the Hardness of a building floor using the deflection energy. 3. We could indicate the most suitable physical value of Hardness of a building floor.

The concept of snap-buckling illustrated by a simple model

The purpose of this paper is the development of a mathematical model which contains one degree of freedom and which illustrates, in a simplified manner, the complex problem of “snap-buckling” of slightly curved membranes and thin spherical shells. The model consists of the classical “Mises truss” with the addition of rotational springs at the joints of the truss. The resultant system is then analysed statically and dynamically. Static load-deflection curves are described, as well as curves for snap-buckling loads and corresponding critical displacements. Phase-plane curves are investigated for a more complete interpretation of stability conditions.

Measurement of the Dynamic Stiffness and Loss Factor of Elastic Mounts as a Function of Static Load

The dynamic stiffness of a number of elastic mounts commonly used in floating floor applications was measured as a function of the static load. The paper reports on the measurement method and on the measured data obtained. The measurements indicated that the dynamic stiffness for cork, neoprene, and precompressed glass fiber mounts increases with increasing static load. The dynamic stiffness was found to be independent of frequency in the region of from 20 Hz to 2 kHz. An inspection of the static-load deflection curves indicated that the tangent of the static-load deflection curves does not agree with the measured dynamic stiffness, the latter being 2 to 3 times larger. [The work was supported by the Korfund Dynamics Corporation.]

Arching Action Theory of Masonry Walls

Proposed theory to explain and predict relatively great strength of masonry walls constrained between essentially rigid supports; comparison with available test data on lateral loading of brick beams; theory used to obtain static load deflection curves for masonry beams of solid cross section; results compare reasonably well with test data available on brick beams.