In present concrete work, basic measures to reduce segregation in terms of design, mix proportion and construction are routinely taken, and they are useful to prevent severe defects such as rock pocket and lost part. However, it is not clear if they prevent the blocking of coarse aggregate while passing between rebars and the settling of coarse aggregate during compaction with vibration, as well. In case these types of segregation phenomenon occur, the distribution of ratio of coarse aggregate to matrix mortar becomes non-uniform in a concrete structure. The authors previously reported that though this makes little difference in compressive strength and surface quality of concrete in a member, it makes much difference in amount of rise in temperature caused by heat of hydration, Young’s modulus and drying shrinkage strain.
In this study, ordinary concrete and high fluidity concrete were placed into wall forms with rebars. Coarse aggregate content which seems to have a major effect on passability and fine aggregate content in matrix mortar which seems to have a large effect on ability entraining coarse aggregate were changed in the experiment. Moreover, these effects on the two performances concerning passing between rebars, namely, passability between rebars (i.e. the ability that concrete can just pass between rebars), and segregation resistance while passing between rebars (i.e. the resistance to segregation of coarse aggregate arising from blocking by rebars), were investigated. The following findings were obtained as the results.
(1) When ordinary concrete passes the narrow space between rebars, the passability degrades and the segregation resistance slightly degrades with increasing coarse aggregate content.
(2) In case of ordinary concrete, the segregation resistance while passing narrow space between rebars degrades with decreasing fine aggregate content in matrix mortar, because yield value and viscosity of matrix mortar decrease and thereby the ability entraining coarse aggregate decreases.
(3) In case of high fluidity concrete with high performance AE water reducing agent containing viscosity modifying agent, as is well known, the passability between rebars without compaction by vibrator is higher than that of ordinary concrete. On the other hand, the segregation resistance while passing between rebars is lower than that of ordinary concrete. Furthermore, coarse aggregate content has little effect on these fact within the limits of bulk volume of 0.48 - 0.62 m3/m3.
(4) The relationship between the passability between rebars and the segregation resistance passing between rebars varies with types of concrete and fine aggregate content in matrix mortal. Namely, these are different performance.
A polyurethane waterproofing membrane is made through the process of applying liquid polyurethane on substrate and then being cured on site. Therefore, the control of thickness of a membrane is the most important matter of concern in construction management. As a membrane was made by the work of a workman using tools such as a trowel or a squeegee, the shape and size of application area of roof floor par a worker is considered to affect the thickness of a membrane.
This study is composed of the two works as follows, the experiment to know the effect of division of area before application and the one to make clear the suitable shape and size of area for a workman. In the first experiment, polyurethane material was applied on the exactly controlled area (4.0m×2.0m in size) and the not controlled area in a roof floor of an actual building. An observation during the work and a measurement of thickness of the membranes after cured revealed that the application work is consisted of the two steps of work such as pouring material on the substrate and then spreading it and indicating the shape and size of an area strictly before application is quite effective to make a membrane of enough thickness. In the second experiment, the effect of the shape and size of application area was furthermore discussed. As for pouring work, polyurethane material was flowed down from a small container in the areas of three levels of length such as 9.0m, 5.15m and 3.6m (0.8m, 1.4m and 2.0m long respectively) and then the weights of the material, cut into 10 pieces in length, were measured after completely curing. It was made clear the dispersion of weight was increased according to the increase of the length of an area.
As for spreading work, the area of three levels of width such as 0.8m, 1.4m and 2.0m (9.0m, 5.15m and 3.6m wide respectively) were prepared and the polyurethane material placed in the areas was spread by two kinds of tools, a trowel and a squeegee. And then distribution of thickness of cured membranes and working hours through the work were measured. According as the application width became wider, the dispersion of thickness of membranes noticeably increased but working hours slightly decreased for trowel application. For squeegee application, not so much change was observed in dispersion but working hours was increased.
By the above studies, the following results were obtained.
(1) Dividing the roof floor into suitable shape and size of an area before application is effective for making a membrane of even and enough thickness.
(2) For pouring work, the length of application an area influences on thickness of a membrane.
(3) For spreading work, width of an application area also influences on working hours as well as on thickness of a membrane.
(4) Three factors such as length and width of an area and working hours should be considered to decide a suitable application area.
Flat-plate roofs are expected to oscillate up and down during strong winds. When a structure is oscillating, unsteady wind forces acting on it are affected by interactions between displacement and the flow. Aerodynamic instabilities such as vortex-induced vibrations can arise depending on the shape and dynamic characteristics of the structure. To date, these unsteady wind forces acting on large cantilevered roofs and the characteristics of wind-induced oscillation have been investigated using forced vibration tests and aerodynamic vibration tests in two dimensions.
Recently, as computer performance has improved, it has become possible to perform transient simulations of the flow around three-dimensional structures using computational fluid dynamics (CFD). CFD is capable of simultaneous and detailed investigation of three-dimensional wind pressure and velocity fields, which are difficult to investigate in conventional wind tunnel experiments. It is particularly suited for application to the unsteady wind forces caused by the interactions between an oscillating structure and the flow. However, the computational accuracy of surface pressures on oscillating structures simulated by three-dimensional CFD has rarely been examined.
The objective of the present study is to examine the relationship between unsteady wind forces and flow field around an oscillating flat-plate roof in detail using CFD. First, three-dimensional forced vibration test is carried out in a wind tunnel. The results confirm that there is a negative damping force on the roof when the non-dimensional frequency of the roof is relatively low. Moreover, the unsteady wind force on the roof varies depending on the cross section.
Next, the effectiveness of CFD with an overset mesh to simulate the flow around the oscillating roof is validated by comparing the numerical results with those of the wind tunnel tests. CFD is shown to be capable of approximating the wind tunnel results if the mesh range of the dependent region and the mesh resolution at the boundary between the master region and dependent region are set appropriately.
Finally, by applying complex proper orthogonal decomposition (CPOD) to the simultaneous wind pressure and velocity fields obtained in fine detail by CFD, the coherent structure of the fluctuating wind pressure field and the three-dimensional wind velocity field around an oscillating roof is extracted. CPOD is an effective technique for extracting any coherent structures in multivariate data and discussing the characteristics of various related phenomena. This analysis shows that the harmonic components of the unsteady wind force are caused by two-dimensional vortex shedding from windward edge of the roof when the non-dimensional frequency of the roof is relatively high. While, a negative damping force arises by the harmony of the roof oscillation and the three-dimensional vortex shedding when the non-dimensional frequency of the roof is relatively low.
In the engineering education, effective experiments are necessary to understand the phenomena in addition to the theoretical learning. Also in the earthquake engineering, it is difficult to understand the theory of the soil and building vibration without appropriate experiments due to its complexity including the concept of time and frequency. Thus the effective teaching materials are necessary for the architectural education.
In this study, a new shear vibration model using permanent magnets and ball bearings was developed. The model is constructed by stacking the layer consisting of the wooden board and permanent magnets via ball bearings alternatively. The restoring force appears as the horizontal component of the magnetic interaction between the magnets lower and upper the bearings. The model has the stable performance and the long natural period enough to visually recognize comparing to existing materials. Additionally, the model has a lot of features: inexpensiveness of materials, variable natural period, visible shear wave propagation, multiple applications to represent soil and building structures, and so on.
In this paper, basic characteristics of the model are revealed by the theoretical analysis, the static and dynamic tests, and the vibration experiment. The results obtained are as follows:
1) The restoring force shows almost linear and nonlinear characteristics for small and large relative story displacement, respectively. This is the same tendency as the actual soil and buildings. The stiffness of the model varies with the size of the bearing, the arrangement of the magnets, or the number of the magnets. High toughness is realized by using iron ball bearings, since they are magnetized between the lower and upper magnets due to high magnetic permeability.
2) The damping ratio of the model is almost constant with respect to the displacement amplitude. This is the same tendency as the actual soil and buildings, similarly to the restoring force characteristics. However, the effect of rolling resistance of the bearings becomes dominant for small displacement amplitude, causing the increase of the damping ratio.
3) By constructing the multilayered model simulating the high-rise building or the shear soil column, it becomes possible to visually observe the shear wave propagation in the model.
Large ground motions with seismic intensity of 7 were observed at Atsuma-cho Shikanuma (BBC) during the 2018 Hokkaido eastern Iburi earthquake (MJ6.7) although the hypocentral depth of 37 km was very deep as crustal earthquakes. Strong motions at KiK-net Oiwake (IBUH01) were also equivalent to seismic intensity of 7. We examined the causes of large ground motions to improve strong motion predictions for feature crustal earthquakes.
Firstly, we separated the source, path and site effects on strong motions by the spectral inversion using the main shock and aftershock records. The estimated Q for the path is modelled by 44f0.84 using frequency f. The estimated fmax for the main shock is 6 Hz. Both Q and fmax are average as crustal earthquakes. Empirical amplification factors for weak motions in frequencies 5-10 Hz are largest at IBUH01 among 33 stations. The amplification factor at IBUH01 during the main shock becomes smaller in frequencies 5-10 Hz but becomes larger at 2 Hz due to nonlinearity of shallow soils. The amplification at 2 Hz contributes to large peak at 2 Hz of spectra and seismic intensity of equivalent 7. The empirical amplification factors in frequencies 0.5-1 Hz are largest at three stations of KiK-net Atsuma (IBUH03), K-NET Ukawa (HKD126) and BBC. These stations are in a basin-like shape region where the thickness from the layer with S-wave velocity of 1.7 km/s to the layer with S-wave velocity of 0.35 km/s is thick (around 2.5 km). The predominant frequency of 0.8 Hz for weak motions shifts to 0.6 Hz at BBC and 0.3 Hz at IBUH03 during the main shock due to nonlinear site effects. At these stations the peak levels of the amplification factors become larger than those for weak motions. The large amplifications contribute to the large peak at 0.6 Hz and seismic intensity of 7 at BBC. Since the spectra at IBUH03 and IBUH01 in the boreholes have no clear peaks at 0.3 Hz and 2 Hz, respectively, these peaks are mainly generated by site responses.
Secondary, we estimated the broadband source model composed of three strong motion generation areas by the empirical Green’s function method. We used records at 9 KiK-net stations in boreholes and 4 K-NET stations where effects of nonlinearity are small. It is found that the strong motion generation area SMGA2 with the stress drop of 74 MPa located at depths 21-25 km in the southern region of the fault is the main cause of large ground motions. BBC is the nearest station to SMGA2 and IBUH03 is also near SMGA2. Both stations are in the forward side from SMGA2. Records in borehole at IBUH03 are mostly reproduced by strong motions generated from SMGA2. SMGA2 starts to rupture about 7.7 s after the rupture of the small strong motion generation area SMGA1 located at the hypocenter. The other strong motion generation area SMGA3 with the stress drop of 52 MPa located at the same depths to SMGA2 in the northern region slightly contributes to the later part of S-wave potions especially at stations in backward side from SMGA2. Although the depths of SMGA2 and SMGA3 are about twice of the average as crustal earthquakes, the stress drops are 4-6 times of the average. The short period spectral level is more than 4 times of the average of crustal earthquakes and is the same level to intraslab earthquakes. These facts reveal that the large short period spectral level due to SMGAs with large stress drops located at 12-16 km shallower region from the hypocenter caused large ground motions during the main shock.
It has been shown that if a lead-rubber isolation bearing (LRB) repeatedly undergoes large deformation due to long periodic characteristics and a long-period earthquake accompanied by strong ground vibration, the lead core generates heat and the energy absorption performance of the LRB decreases.
There are two types of LRB: a single-core LRB with one lead core and a multi-core LRB with two or more lead cores distributed. The multi-core LRB can increases the surface area of the lead core without changing the total shear area of the lead core as compared with the single-core LRB. In other words, the heat dissipation characteristics of the lead core can be improved without changing its basic shear resistance.
To clarify the effectiveness of the distributed lead-core configurations of LRB on energy absorption during an earthquake, dynamic and cyclic loading experiments were conducted on actual-size multi-core LRB and single-core LRB of various shapes (Fig. 1).
The results of experiments showed that the energy absorption performance tends to decrease with larger diameter of the lead core, and that the multi-core LRB effectively restrains such decline of performance (Figs. 2, 3). It was also confirmed that the total thickness of the rubber layer has little influence on the energy absorption (Fig. 4, 5).
To conduct a heat-mechanics interaction analysis of the multi-core LRB, it is usually necessary to use a three-dimensional model, but this method requires much effort for creating a model and the computation time is long. Therefore, in this research, we propose a simple analysis method for multi-core LRB and show that the thermal interaction between lead cores is small. We confirmed the thermal interaction between the lead cores of the multi-core LRB by cyclic loading tests and also conducted an experiment on a specimen divided by the number of lead cores. (Fig. 12).
As a result, the rise in temperature inside the specimen located at the center between the lead cores of the multi-core LRB was slight, and the results of the experiments on the divided test specimens matched those of the specimen before being divided (Fig. 13 to 15). Since thermal interaction between lead cores hardly occurs in the multi-core LRB, it is considered that the Constant Flux Solution (CFS), which calculates by simplifying the heat dissipation path from the lead core, can be applied to heat-mechanics interaction analysis of the multi-core LRB. Furthermore, by replacing the divided specimen with an equivalent round model, the two-dimensional Finite Difference Method (FDM) model can be applied to the multi-core LRB (Figs. 16, 17).
From the above, CFS analysis and FDM analysis using the evaluation formulae (Equations (1) - (3)) proposed by the authors for the yield stress of the lead core were performed on the multi-core LRB. As a result, we confirmed that both analytical methods accurately predict the experimental results of the multi-core LRB (Figs. 18 to 23).
Based on the above, we clarified that the reduction of energy absorption due to repeated deformation of the LRB for a long time can be improved by the distributed lead-core configurations.
The Building Research Institute and the Japan 2x4 Home Builders Association jointly built a full-scale six-story wooden experimental building. The building was densely equipped with two types of accelerometers to investigate its dynamic characteristics in detail.
The experimental building has a wooden framing structure with a building area of 38.95 m2, a total floor area of 206.09 m2, and an eaves height of 16.91 m. The building is supported by eleven steel piles, each being 12 m in length. The floor plan and cross section of the building are illustrated in Fig. 1. Strong motion observation for this experimental building started in April 2016 using two types of instruments. One is a high-performance type equipped with a tri-axial force-balanced accelerometer. The other is an economical type equipped with a tri-axial MEMS (Micro Electronic Mechanical Systems) accelerometer. The sensor configuration is shown in Fig. 1. More than 100 strong motion data were recorded until December 2018. Event parameters and peak accelerations on the ground (GL), first floor (1F) and sixth floor (6F) of the major earthquakes are listed in Table 1.
From all strong motion data, the fundamental natural frequencies and damping ratios in two horizontal directions of the building were identified using a parameter optimization technique16). With a single-degree-of-freedom system, the natural frequency and damping ratio that had the most fitted response acceleration were determined using the grid search. Figure 2 indicates changes in natural frequency and damping ratio of the experimental building with time. The natural frequencies and damping ratios widely varied. There are three factors that affect dynamic characteristics of the building. Water pools, that were placed on each floor to substitute for the weight of finishing and live loads during the period from December 2016 to October 2017, had the effect of decreasing the natural frequencies and increasing the damping ratios of the building. Such effect was examined by the numerical analysis as shown in Fig. 3.
The upper and middle plots in Fig. 4 indicate natural frequencies and damping ratios identified using ambient vibration data. The seasonal fluctuation could be recognized in the natural frequencies. It seems that the fluctuation has correlation with the temperature and relative humidity indicated in the lower plot in Fig. 4. The influence of the temperature and relative humidity can be explained by the regression formula, Equations (5) and (6). To remove the influence of the temperature and relative humidity, the daily natural frequencies are converted to the values corresponding to the temperature of 15°C and relative humidity of 75% using the regression results. The converted natural frequencies are plotted in Fig. 5. The seasonal fluctuations of the natural frequencies were almost eliminated and the changes in the natural frequencies during the period with the additional loading were clarified.
The identified natural frequencies from the strong motion data were converted to the values corresponding to the temperature of 15°C and relative humidity of 75% as well and the relationships of the converted natural frequencies and damping factors to the maximum displacement angles defined by Equation (7) are plotted in Fig. 6. Looking at Fig. 6, the dependence of the dynamic characteristics on response amplitude could be clearly observed in the analytical result considering the effect of the sloshing, temperature and relative humidity. The natural frequencies decrease with increase of the response amplitude. In contrast, the damping ratios increase as the response amplitudes increase.
In the seismic design of nuclear power plant (NPP) buildings, the evaluation of basement uplift is an important factor. However, a lot of calculation time is required for these analyses with large finite element (FE) models, which then becomes a problem.
This study proposes a novel method to accelerate the uplift analysis for NPP buildings. The proposed method does not require an inverse matrix operation of the whole tangent stiffness matrix, which requires considerable computation time when using the tangent stiffness method. Instead, by using the inverse of the partial tangent stiffness matrix, the calculation time can be reduced
First, the outline and details of the method are described. Then, the results of the experiments that were performed to evaluate the proposed method are presented.
The findings of this study are as follows:
(1) The proposed method uses two inverse matrices to correct the displacement vector. One of them is the inverse of a partial matrix of only the degrees of freedom connected to nonlinear elements in a tangential stiffness matrix. The other method is the inverse matrix of the initial stiffness matrix. The proposed method can thus save on computational cost of the inverse matrix operation for the large total tangent stiffness matrix, which is required in the conventional tangential stiffness method, and reduces the overall computation time.
(2) The proposed method is applied to sample problems to validate the effectiveness. The results indicate that the proposed method can reduce calculation time to less than half of that required for the tangential stiffness method, while ensuring accuracy of the analysis regardless of the magnitude of uplift. In addition, it is important to make the squire partial matrix in which the size corresponds to the degree of freedom connecting the nonlinear elements. Furthermore, it is confirmed that the speedup effect of the proposed method increases as the model size increases.
In recent years, optimization methods are used for many computational design methods in the ﬁeld of architecture and architectural engineering. Optimization methods are roughly classiﬁed into heuristic methods typiﬁed by genetic algorithms and mathematical programming methods. Although the latter is inferior in versatility, it has an advantage that the calculation is fast. Along with the development of computers, mathematical programming methods have been developed dramatically and are used in various ﬁelds as a solution to optimization problems. Among them, the gradient method, which is the most classical method, is a method devised at the dawn of mathematical programming method, has been used for many years in various ﬁelds because of ease of algorithm implementation. Since the convergence is slow, a simple gradient method is rarely used nowadays. However, since the acceleration scheme of gradient methods greatly improve the convergence speed of the above solution, it has attracted attention in recent years as an effective solution method for solving a large scale problem. In fact, in ﬁelds other than the architectural engineering, accelerated gradient methods (AGM) are extensively used, for example, in machine learning for big data. In this paper, the computational performance of AGM is veriﬁed using a general benchmark problem. Furthermore, AGM is applied to equilibrium analysis of trusses with nonlinear elastic materials. Since solving the stiffness equation is synonymous with minimizing the total potential energy, equilibrium analysis can be formulated as a total potential energy minimization problem. AGM is used for solving such a problem and the effectiveness of the proposed method is discussed.
First of all, the minimization problem of Rosenbrock function is solved as a benchmark problem to verify the computational performance of AGM. A quasi-Newton method based on the BFGS formula (BFGS), a truncated Newton method (TNC), a conjugate gradient method (CG) are compared with AGM. As a result of the veriﬁcation of the benchmark problem, it was shown that AGM can solve large-scale problems at the fastest speed.
Based on the result of the benchmark, using AGM for large-scale structural analysis with material nonlinearity is considered in this paper. Since solving the stiffness equation is equivalent to minimizing the total potential energy, equilibrium analysis can be formulated as a total potential energy minimization problem. The gradient of the total potential energy is equivalent to the unbalanced nodal force vector. Therefore, equilibrium analysis of trusses with nonlinear elastic materials is performed by applying AGM by utilizing unbalanced force as a gradient in this paper.
Equilibrium displacements of some three-dimensional truss structures which have a total of three restoring force characteristics of linear, bilinear, and high-order nonlinear are calculated by minimizing the total potential energy. As a result, it was observed that the AGM quickly converged to the optimum solution stably regardless of material properties. According to a comparison experiment between BFGS, TNC, and CG, it was conﬁrmed that AGM is the fastest in calculation time, especially for large scale truss structures.
In this paper, the effectiveness of AGM and its applicability to equilibrium analysis of trusses with nonlinear elastic materials were conﬁrmed.
This paper describes a new type of hysteresis model that is capable of generating various hysteresis loops. The seismic responses for structures depend on their force-displacement relationships. To improve the accuracy of seismic response prediction for the structures, the hysteresis models which are capable of calculating a force-displacement relationships closed to an actual phenomenon are essential.
The seismic fragility assessment has been performed to clarify the seismic performance. The fragility curves are calculated using the results of seismic response analysis obtained by incremental input ground motions. Their seismic responses contain the hysteresis loops that have the ultimate neighborhood of the structures. These seismic response analyses require the hysteresis models which can capture the hysteresis loops having strongly nonlinear characteristics. In general, modeling the hysteresis loops to be able to capture the ultimate state results in difficult because the hysteresis rules and the programing code to calculate their hysteresis loops are complex.
To overcome these problems, this paper proposes a newly hysteresis model which can capture the various nonlinear behaviors as a differential equation type. This hysteresis model can generate the hysteresis loops with strongly nonlinear skeleton-curves without the hysteresis law such as Masing’s laws because the hysteresis model can treat the any skeleton curves which are identified using an approximate polynomial based on the test results and so on. The feature will lead to improving the accuracy of seismic response prediction and the applicability of the seismic response including probabilistic assessment.
This paper is divided into three main groups. The first is to describe the constitutive equations of the proposed hysteresis model. The second is to demonstrate the validity of the hysteresis model by generating the various hysteresis loops and compares with the measured hysteresis loops. The third is to show the applicability of the hysteresis model into the seismic response analysis using a simple analytical model. The primary results are summarized as follows:
The proposed hysteresis model can:
1) Express the typical hysteresis loops which are generated by the previous hysteresis models consisting of the differential equation type.
2) Easily generate the various hysteresis loops, which contain the hysteresis loops that are varied due to the number of cyclic loading and the experienced maximum displacement.
3) Accurately capture the measured hysteresis loops having strongly nonlinear characteristics.
4) Easily apply to the seismic response analysis as an initial problem even if the target skeleton curve has nonlinear characteristics.
1. Introduction The plate bending problem of flat plate is the basis of static analysis and vibration analysis of three dimensional wall structure and folded plate structure. Development of elements having high accuracy with few elements is one of the essence of the finite element method. A rectangular flat plate bending element is easy to use and its shape function is determined in a simple way. The generalized coordinates of each node of the bending plane plate element are three degrees of freedom, displacement, and rotation in two directions. A rectangular four-node element has a total of 12 degrees of freedom. The ACM element defines the shape function using the low order polynomial of Pascal's triangle. Several adaptive elements with the same degree of freedom have been developed, but it is hard to find out which gives solutions with good precision . Since weak points of rectangular bending flat plate elements with 4 nodes and 12 degrees of freedom are conforming conditions between neighbouring elements, this paper imposes the following two conditions to improve these conditions, and aims to advance the element performance.
Condition 1 :The rotation in the normal direction of each side of the quadrilateral element coincides with the adjacent element at both ends. Here, we introduce the condition that the rotation in the normal direction at the midpoint of the side is the average value of the rotation at both ends.
Condition 2 :Completely eliminates the influence of the node displacement of this element on the rotation in the normal direction of each side of this element.
2., 3. Characteristics of a rectangular flat plate bending element with 12 degrees of freedom
4. Numerical analyses and verification A shape function of a rectangular flat plate bending element having 4 nodes and 12 degrees of freedom satisfying these two conditions can be constructed by using a basis function expressed by the formula (10.2). The resulting shape function is shown in equation (11.1). In order to demonstrate the performance of the rectangular element developed here, four benchmark tests are carried out using six element meshes. Considering the symmetric condition, 1/4 of the analysis model is set as the analysis target. For element division, the same elements 1 × 1, 2 × 2, 3 × 3, 5 × 5, 7 × 7, and 9 × 9 were used in two directions.
4.1. Simply supported square plate under a uniform vertical load q
4.2. Simply supported square plate under loading a force P at the central point.
4.3. Natural frequencies of a simply supported square plate
4.4. Deflection of square plate with built-in edges under loading force P at the central point.
This analysis was done to compare accuracy with the solution BCIZ-SQ element developed recently and ANDES 4 element. 1 × 1, 2 × 2, 4 × 4, 8 × 8, and 16 × 16 element meshes were used. This discussion is shown in section 4.4.
5. Conclusion We analyzed the incompatibility of the existing rectangular flat plate bending element with 4 nodes and 12 degrees of freedom and found two conditions to improve incompatibility and aimed for advanced element performance. These conditions lead to improvement of element basis functions, and developed high precision elements with identical degrees of freedom. Static analysis and natural frequency were analyzed, and the performance obtained from the existing solution was compared with the performance. We verified that the developed element will be a rectangular flat plate bending element with high performance.
This paper discusses about stability in sliding of conventional slide-bearings supporting steel spatial roofs on the lower concrete structures.
In many gymnasiums in Japan, a spatial steel roof is installed on the lower concrete frame via bearings. The conventional detail of such roof bearings is similar to that of an exposed column base used in multistory buildings. It is composed of anchor bolts embedded into the lower concrete frame and a base plate. Base mortar is also used below the base plate. However, different from an exposed column base, roof bearings are usually designed to be mobile in one direction. to reduce the stress due to thrust or thermal strain. The mobility is also to avoid forced the deformation due to out-of-plane vibration of the lower RC frame. In this paper, such mobile bearing is called as “slide-bearing”. In a conventional slide bearing, slot hole (called as the “loose hole” in this paper) is hollowed out in the base plate for anchor bolts and a PTFE pad was sheeted to reduce the friction at the bottom of the base plate.
Many slide bearings in steel spatial roofs were destroyed during the 2011 Tohoku Great Earthquake. However, no abrasion of sliding was found in some destroyed bearings. Moreover, in our experimental study to reproduce the damage, a test body did not slide and large rotation arose. Based on these observations, we conducted further experimental study to investigate the conditions on stability of slide.
Six full-scale tests were conducted where the three influential conditions, the eccentricity of the horizontal force line, the pre-tension of anchor bolts and the vertical constant load were parametrically changed and combined. In each test, cyclic increasing forced displacement was given horizontally. Where the horizontal force line was low, the bearings slid stably and the horizontal force was small without fluctuation. However, significant rotation of bearings caused with slide and the horizontal force rapidly increased accompanying the rotation where the horizontal force line was high and the eccentricity was large. Friction between the top surface of the base plate and the washer of anchor bolts was found to be very influential on slide behavior in spite that it is usually neglected in the structural design.
Based on these observations in the above experimental study, the slide behavior was modeled and formulated based on a simple equilibrium between the forces and moments acting on the base plate. From the stability of horizontal force, the stability condition in slide was derived as a non-dimensioned eccentricity of the horizontal force line. The experimental results were evaluated applying the equation for the stable slide condition. It was found that, the test condition where the large rotation caused did not satisfied the condition for stable slide.
In the authors’ previous study3) on weak beam-strong column type RC moment-resisting frames (Figs. 1 and 2), buckling of longitudinal rebars was visually observed at the beam ends at large drift ratios (Fig. 4 and Photo 1). This result indicated that the buckling of beam longitudinal rebars was related to the safety limit (collapse preventaion performance) of weak beam-strong column type frames. However, to date, no method is presented to quantitatively evaluate the ultimate performance of RC frames at the buckling of beam longitudinal rebars. Hence, numerical and practical evaluation methods for the buckling of beam longitudinal rebars are proposed and verified through comparisons with the previous test3), as described above, and an additional one.
2. Experimental investigations
A prototype building of this study was introduced (Fig. 1), then the preceded tests of two moment-resisting frame specimens with/without RC secondary walls partially representing the prototype building were summarized (Figs. 2 to 4 and Photo 1). From the tests, buckling of the beam longitudinal rebars was visually observed after peeling off of the cover concrete at the ends of the beams (Photo 1). It indicated that the buckling of the beam longitudinal rebars affected the ultimate performance of the specimens.
3. Quantification of the safety limit (collapse prevention performance) of RC beams based on longitudinal rebar buckling
A numerical method to evaluate buckling occurrence of beam longitudinal rebars was proposed by comparing the stress-strain behavior of the beam longitudinal rebar with the buckling resistance by Eqs. 2 and 6. Thus, one of the specimens described in Chapter 2 was replaced by an idealized numerical model (Figs. 8 and 9) and numerically analyzed (Figs. 10 and 11). The analysis gave a good agreement for a drift at the beam longitudinal rebar buckling with that from the experiment (Fig. 13).
4. Simplification for application to practical design
Since the neutral axis on cross-sections of general RC beams is likely to be close to rebar under compression, the strain of the beam longitudinal rebars described in Chapter 3 was assumed to be zero under the maximum compression. This assumption simplifies the evaluation method proposed in the previous chapter and provides a practical evaluation method for the ultimate performance of RC beams at the buckling of beam longitudinal rebars by Eqs. 9 and 10. An estimated ultimate hinge rotation by the practical method was also verified to show a good agreement with the experimental result (Table 4).
5. Additional verification based on a full-scale RC beam test
An experimental study was performed using a full-scale beam specimen focusing on buckling of longitudinal rebars. This specimen also showed buckling behavior of the longitudinal rebars at the member end (Photo 2), then deteriorated (Fig. 23). The hinge rotation angle at the buckling of longitudinal rebars was evaluated as 1.26%rad based on the practical method proposed in Chapter 4. Consequently, the estimation was consistent to the experimental result (Table 8).
The present paper experimentally showed the safety limit (collapse prevention performance) for RC beams with buckling of longitudinal rebars; thus, proposed numerical and parctical evaluation methods. The proposed methods well evaluated the ultimate hinge rotations of the beam specimens at the longitudinal rebar buckling.
In order to simulate the behavior of reinforced concrete members failing in flexure, analytical procedures based on the flexural theory have been popularly used. In the procedure the Ramberg Osgood hysteresis model is popularly used for the stress-strain relationship of the longitudinal reinforcing bars. As for the concrete model, concrete confinement by transverse reinforcement is the most important aspect and many confined models have been proposed. On the other hand, other aspects concerning the material models have been highlighted recently, such as concrete confinement of thin members or buckling of longitudinal reinforcement.
In this study analytical studies regarding the moment-curvature relationships of reinforced concrete columns have been conducted herein. A fiber model is used that considers the buckling of the longitudinal bars and concrete confinement from the rigid base stub.
2. ANALYSIS OBJECTS
The analysis objects were four reinforced concrete columns failing in flexure with comparatively large amount of longitudinal reinforcement that were previously tested and reported. The column specimens were subjected to a constant or varying axial force and anti-symmetric moment reversals. The shear span length and ratio were 600mm and 2.73. The deformation capacity of the column was designed in accordance with the buckling of the longitudinal reinforcing bars.
3. BUCKLING MODEL
In general the buckling length of the longitudinal reinforcement in the RC members extends over several times the spacing of the transverse reinforcement. The buckling mode represents the buckling length divided by the hoop spacing. A buckling model for the longitudinal reinforcing bars of the RC columns, which accounts for the buckling mode, was already proposed by Kato et al. (1995). In this study the model is used. The Ramberg Osgood hysteresis model by Jennings (1963) is used for the stress-strain relationship of the longitudinal reinforcing bars with some modification. The reversed Ramberg Osgood function is applied in the region after buckling.
4. CONCRETE MODEL
The authors reported that the real flexural behavior of the columns could not be simulated with sufficient accuracy using the concrete model confined only by hoop reinforcement (Kato (1992)). This was because the compressive failure zone of the concrete was limited locally to the near-critical sections with the members subjected to the moment and shear force, and the concrete confinement from the rigid base stubs could not be disregarded. The previous research by Kato et al. (1998) proposed a stress-strain relationship model of concrete that is confined by hoop reinforcement. This model is used herein to represent the stress-strain relationship of the concrete confined by transverse reinforcement and a rigid base stub.
The simulated moment curvature relationships and the hysteresis energy dissipated during the loading were compared to observation. The main conclusion is that the results of the simulated moment-curvature behavior using the fiber model matched the test results, thus, indicating the effectiveness of the proposed buckling and confinement models.
Shear walls in which sheets with burring holes aligned along the vertical direction are fastened to frame members, are applied to multi-story buildings in seismically active regions. A sheet for the standard 2.73-high-walls is 2.73-m-long × 0.455-m-wide × 1.2mm-thickness with seven cold-formed burring holes with the diameter of 200mm, which are created by cold pressing a sheet with small-radius holes. A burring hole contains rib (curvature radius: 10mm and 5mm height cylinder) to make edge-stiffened circular hole. A configuration with burrs on the inside and smooth on the outside enables the construction of omitting the machining of holes for equipment and thinner walls of simplified attachments of finishing.
In-plane shear experiments and finite element analyses revealed that the walls that receive the in-plane shear force allow shear stress to concentrate in intervals between the burring holes. The walls changed from the elastic to plastic region and maintained stable strength. The walls at 1/300 story angle had stress concentrations at the intervals. The walls at 1/100 story angle experienced out-of-plane deformation at the all intervals simultaneously. The deformations were limited in the intervals and a large out-of-plane waveform in a sheet was effectively prevented owing to the ring-shaped ribs of the holes. The effects of cross-rails which are designed to strengthen the bearing capacities of the studs, on the shear walls were clarified by experiments and analyses.
Shear stiffness of the wall was gradually decreasing according to the deformation increasing of the wall, even in the elastic region, regardless of cross-rails. The burrs of steel sheets on the one side of the sheets created the asymmetry and the directions of principal stress flows on the sheets varied in three dimensions. Therefor out of plane deformations occurred on the sheets and inclined tension fields occurred in the intervals between the burring holes like post shear buckling behavior that Dr. Basler proposed for plate-girder designs. Ultimate strength of the wall depended on tension fields restrained by cross-rails.
In this paper, new design methods are proposed for evaluating the stiffness of the walls using the idea of decreasing the band-width of the inclined tension fields with the effect of the cross-rails. The design formula to evaluate the shear strength of the wall at a story angle of 0 to 1/200 was developed and the values obtained using the formula lie almost the same values obtained through experiments. The large deformation behavior was also depended on the tension fields on the intervals between the holes. The shear strength at a story angle of 1/200 to 1/100 was increased by the studs restrained by cross-rails. The effect of cross-rails maintained wall strength stable in inelastic region. The tension in the interval between the burring holes was balanced with the compression resisted by burring holes and horizontal shear forces at screw connections created by studs and cross-rails. The design formula to evaluate the shear strength of the wall at a story angle of 1/200 to 1/100 was developed and the values obtained using the formula lie almost the same values obtained through experiments.
Superior design solutions of section sizes in seven-story steel buildings are obtained for three types of structural systems: (1) a space frame system with rectangular HSS columns (SFS), (2) perimeter frame systems (PFS) with I-shaped columns (PFSH), (3) PFS with rectangular HSS columns (PFSB). Moment connections are used in most beam-to-column connections in SFS, while they are limitedly used in the perimeter frames in PFS. SFS is a commonly used structural system in Japan, whereas PFSH is commonly used in other countries. In this research, structural characteristics of SFS, PFSH and additionally PFSB are evaluated for evenly rationally designed office buildings using an optimization algorithm. The superior solutions are derived by multiple start local search (MSLS), minimizing steel volumes. The solutions satisfy multiple requirements of the allowable stress design and ultimate lateral strength. The discrete design variables are the section sizes of grouped structural members. Approximately 100 constraints and 40 variables are applied. Dealing with these large numbers, the proposed MSLS algorithm works and superior solutions are obtained for various types of buildings, such as moment frame, braced frame and mixed frame buildings, in the three types of structural systems, SFS, PFSH and PFSB. Pipes or buckling restrained braces (BRB) are used in the braced frame buildings. The findings are as follows:
(1) Superior solutions for moment frame buildings are obtained for the base-shear coefficient of the ultimate lateral strength, CQUN1, as 0.3 and 0.6. Although the value of 0.6 for CQUN1 is given by referring to responses in the time-history analyses for very rare (L2) earthquake ground motions, the superior design solutions do not satisfy the standard design criteria against L2 earthquakes. The maximum inter-story drift ratios are 1.4-1.5%, which are greater than the standard criteria of 1.0%. PFSH can be advantageous for the moment frame building in terms of steel volume.
(2) Superior solutions of the braced frame building are obtained for 0.35 and 1.0 of CQUN1. The sections of the braces are steel pipes. The differences of steel volumes between PFSH, SFS and PFSB are relatively small. The steel volume is slightly lower in SFS and PFSB, because axial forces are the primarily derived member forces under earthquake lateral load in these braced frame buildings and rectangular HSS columns are advantageous. The CQUN1 value needed for the L2 time-history analysis is nearly 1.0, which is very different from the 0.35 required by the design standard.
(3) Superior design solutions using BRBs are obtained for the braced frame building with 0.5 of CQUN1. The steel volume in SFS and PFSB is slightly lower, as observed in the braced frame building with pipes. The steel volume excluding the braces in the superior solutions with BRBs is 70-90% of that with pipes for the braces (CQUN1 =1.0).
(4) A comparison of the superior design solutions for mixed structures shows that the steel volume of SFS solution is higher than those of PFSs. Irregularity in the beam spans or different lateral systems in two horizontal directions causes an increase in the steel volume in SFS, controlled by some critical constraints, such as uniform beam height in a single floor and strong column weak beam ratio.
Superior design solutions are obtained by using the optimization algorithm but not based on engineers’ personal experience. Therefore, although the number of cases studied in this research is limited, the discussion and findings comparing these different structural systems are of interest.