Taut cables such as those used in cable-stayed bridges are prone to exert a large amplitude response due to support motion. Support motion generally involve longitudinal and transverse components ...with respect to the cord. Such motions induce parametric and external excitation of the cable. For a certain excitation frequency, multimodal interaction due to simultaneous parametric and primary resonance can be expected. Previous studies have focused on changes in the boundary curves of the primary region of the parametric resonance affected by forced vibrations due to primary resonance. The hysteresis regions have not been determined; they have only been analyzed using the frequency-amplitude curves of the response. Moreover, the influence of the longitudinal and transverse displacement ratio has not been discussed thus far. This paper presents a complete formulation of the continuum equations of a cable model that is excited by support motion. A nonlinear discretized model that includes quadratic and cubic nonlinearities is obtained using the Galerkin method. Further, the analytical solution is determined using the method of multiple scales (MMS). By obtaining the expressions for the amplitudes and phases, the mathematical conditions are set for the amplitude of the parametric and primary resonance from which analytical expressions for the boundary curves of the interaction resonance region are derived. Local stability analysis is conducted for the steady-state response, and direct numerical integration is used for validating the frequency-amplitude curves obtained using the MMS. The solutions are verified using two independent numerical models. It is shown that the ratio of the transverse and longitudinal components of support motion significantly affects the resonance region, and several different response solutions can be obtained. It is also shown that different values of the mechanical cable parameters affect the resonance region and vibration amplitude.
A numerical analysis of part of the underground quarry of dimension stone with designed maximum dimensions of the rooms was carried out with the SAP2000 software based on the finite element method. ...The main objective of the analysis was to examine the preliminary stability and the influence of excavation on the redistribution of stresses in the surrounding rock masses, thus confirming the applicability of the tributary area method. The analytical solution with the tributary area method showed satisfactory agreement with the numerical calculations, and the results of the analytical calculations were on the safe side. The obtained results confirmed the predicted behaviour of the rock mass, which confirms the use of SAP2000 as a general-purpose software for civil engineering in the field of mining. The highest concentrations of stresses and strains are found in the edge areas of the pillars, so their correct design is crucial. The safety factor of the point with the highest stresses was determined and a value of 2.21 was obtained, thus fulfilling the stability condition. As for the influence on the surrounding area, stress changes of less than 10% were determined based on the solutions for the vertical stresses at a distance of 20 m from the underground excavation.
FUNDAMENTAL MODELS OF STRUCTURAL STABILITY Lazarevic, Antonia Jaguljnjak; Uros, Mario; Cengija, Ana
Rudarsko-geološko-naftni zbornik,
03/2017, Letnik:
32, Številka:
2
Journal Article
Odprti dostop
In this paper, basic structural stability phenomena are described. After some general comments about stability in the field of civil engineering, four elementary sources of nonlinearity are ...mentioned: of equilibrium equations, strain (geometry) relations, material (stress-strain) law, force and displacement boundary conditions. Four fundamental stability models are analysed, both ideal (perfect) and with geometric imperfection. Besides geometrically exact theory, initial post-buckling behaviour and linearization are briefly sketched. This paper is concluded with comments about the influence of plasticity.
An issue concerning the management of radioactive waste (RAW) in the Republic of Croatia continuously rises due to the lack of systematic solutions. In this paper, emphasis is being placed on the ...storage of RAW, as one of the important phases of RAW management. The current RAW storage facilities are not sufficient and there is a need for a new facility for low and intermediate level radioactive waste (LILW), since such waste accounts for the largest part of RAW. For this reason, a preliminary estimate for a one-storey structure was carried out, a potential storage facility of LILW that would be constructed at the location of Cerkezovac, Trgovska Gora, in the Republic of Croatia, as the currently most prominent location for the realization of the RAW storage facility. The geological characteristics of the site were analysed and, in accordance with the relevant regulations, a static design of the facility was made in the ETABS and SAFE program packages. The construction is a typical reinforced concrete structure, rectangular in plan (10.0 x 30.0 m) with a height of 5.9 m. The selected location meets the given parameters of geological characteristics, while the construction meets the given load and serviceability conditions defined by Eurocode (ultimate limit state and serviceability limit state). However, a more detailed analysis would be necessary if the decision to construct such a storage facility would be made.
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without any rounding error. For such purposes, a corresponding system of equations should be ...exactly defined, either directly or by rationalising the numerically given input data. In the latter case, there is an initial round-off error, but this does not propagate during the solution process. If this system is exactly solved first and then using floating-point arithmetic, the convergence of the numerical method easily follows. As an example, the IRM–CG, which is an alternative to the Conjugate Gradient (CG) method and a special case of the more general Iterated Ritz Method (IRM), is verified. The method is not based on conjugacy; therefore, restarting strategies are not required, while an overrelaxation factor and preconditioning like techniques could be easily adopted. The exact arithmetic approach is introduced by means of a simple example and is then applied to small structural engineering problems. The perturbation of the displacement increment and the different condition numbers of the system matrix are used to check the stability of the algorithm. Interestingly, a large difference in the number of steps between the exact and numerical approaches is detected, even for well-conditioned systems. According to the tests, the IRM-CG may be considered to be stable and useful for not well-posed or well-posed but ill-conditioned models. Because the computer demands and execution time grow enormously with the number of unknowns using this strategy, three possibilities for larger systems are also provided.
Applied mathematics; Exact arithmetic; Benchmark; Rounding error; Iterated Ritz Method; Conjugate gradient method
A simple alternative to the conjugate gradient (CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear ...equations. This novel algorithm is not based on conjugacy; i.e., it is not necessary to maintain overall orthogonalities between various vectors from distant steps. This method is more stable than CG, and restarting techniques are not required. As in CG, only one matrix-vector multiplication is required per step with appropriate transformations. The algorithm is easily explained by energy considerations without appealing to the A-orthogonality in n-dimensional space. Finally, relaxation factor and preconditioning-like techniques can be adopted easily.
The distribution of stresses and strains during the portal section excavation for the right tube of the Sleme Tunnel is analysed by the Finite Element Method (FEM). Results of analyses obtained using ...2D and 3D models have been compared to in-situ measurements of tunnel convergence and ground surface settlements. Multistage excavations with pipe roof support of the working face were modelled. The numerical models verified that for this particular case a sufficiently safe and cost-efficient construction technology was applied.Original Abstract: Analizirano je stanja naprezanja i deformacija tijekom iskopa portable dionice desne cijevi tunela "Sleme" primjenom metode konacnih elemenata. Napravljena je usporedba rezultata proracuna ravninskog (2D) i prostornog (3D) modela s rezultatima terenskih mjerenja konvergencija u tunelu i slijeganja povrsine terena. Modelirani su visefazni iskopi s ojacanjem cela cijevnim krovom. Proracunski model je pokazao da je u navedenom slucaju primijenjena dovoljno sigurna i ekonomicna tehnologija iskopa.
U radu su na više interpretativan nego na formalan način svrstana i opisana tipična rješenja modela konstrukcije, s posebnim osvrtom na slabu formulaciju i njezino fizičko tumačenje, koje prema ...našemu mišljenju nedostaje u literaturi. Upozoreno je i na pogreške u približenju radi ustrajavanja na pretjeranoj glatkoći rješenja. Razmišljanja su potkrijepljena primjerima. Nadamo se da rad može pridonijeti shvaćanju biti aproksimacije praktičnih modela u građevinarstvu i zorno predočiti snagu slabe formulacije - temelja približnih postupaka proračuna.
The distribution of stresses and strains during the portal section excavation for the right tube of the Sleme Tunnel is analysed by the Finite Element Method (FEM). Results of analyses obtained using ...2D and 3D models have been compared to in-situ measurements of tunnel convergence and ground surface settlements. Multistage excavations with pipe roof support of the working face were modelled. The numerical models verified that for this particular case a sufficiently safe and cost-efficient construction technology was applied.
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