For concrete in structures, moisture curing is important and has the large effect to the hydration of cement and the concrete properties after hardening. In the almost situations, moisture curing method of the vertical surface of wall and ceiling surface of under the slab are limited to cover with the sheathings. In the JASS 5 of AIJ, moisture curing period is specified prescribed days or compressive strength. Among these specifications, management due to compressive strength for moisture curing period is logical on the quality assurance of concrete and the working execution process. In the hot weather concreting, nevertheless, terminate of moisture curing at early age has apprehensiveness which is durability may be impaired. Then, in this research studied on the effects of moisture curing for concrete in structures from regarding to make wall model members, and considered management technique for moisture curing period from effects of the cement types and the water-cement ration.
Experiments were used 1,900 by 900 by 200 mm wall model members which made in summer and standard seasons. Moisture curing of members was used 12mm thick plywood for concrete formwork. Moisture curing terms were 1(2), 3, 5 and 7 days and removed plywood at these days. These wall model members were measured surface quality, compressive development and durability. Concrete using experiment wasmade in ready-mixed concrete plant, and these water-cement ratios were 0.45, 0.50 and 0.56.
As the results, effects of moisture curing periods were small on the concrete surface qualities of wall model members. That was, rebound number were same levels and coefficient of air permeability were Normal grade in spite of moisture curing periods. When removed plywood at 1 or 2 days, core compressive strength of those age were the above 10 N/mms that is management value of JASS 5. Furthermore, compressive strength differences of age 28 and 91 days were small due to different of moisture curing periods. Carbonation depth was large when terminated early moisture curing, but at over 3 days moisture curing periods, these values were same levels. However, effects of water-cement ratio for carbonation resistance were cleared than the moisture curing period.
On the evaluation for the effect of moisture curing for concrete in structures, strength development of concrete was confirmed enough too when moisture curing terminated early age. Moreover, carbonation depth of only water-cement ratio 0.56 of using ordinary portland cement was larger than the recommendation value of AIJ. As mentioned above, Water-cement ratio has an influence than the moisture curing period for carbonation resistance. Therefore, this report considered moisture curing period from the relationship between carbonation resistance and water-cement ratio. This relation was linearly, and the indoor water-cement ratios that satisfies the standard values of carbonation depth each planned service life class were 0.66 or less by short term, 0.55 or less by standard. These water-cement ratios were satisfied water-cement range that corresponding with durability design strength. From the above, if concrete proportion is designed to consider the durability design strength, durability for carbonation is considered to have enough resistance in spite of moisture curing period. In the hot weather concreting, from the above studying, when management for moisture curing period due to concrete compressive strength (10 N/mm^{2}), concrete in structure is assessed that ensure the strength development and durability after terminate moisture curing.
Colored concrete colored with pigments is used for building exterior walls and floor slabs. The amount of pigment added to such concrete is often based on the standard addition amount specified by the pigment manufacturer. However, a wide variety of materials and blends are used for concrete, and the dosage of pigment is adjusted as required. When determining the dosage of pigment, factors such as the water-binder ratio of concrete and color change over time must be taken into account, but there are very few research reports on such systematic experiments.
In the present study, focusing on the mortar portion, which is considered to determine the color of concrete, experimental verification was conducted on the effect of the amount of pigment used on the color of colored mortar. As a result, the following were found:
1) It was confirmed that there is an upper limit to the pigment substitution rate that can effectively color the powder mix and the hardened cement paste. Further, in experiments with cement paste, the upper limit of the pigment substitution rate was considered to be about 5% of the cement mass.
2) In the mortar experiment which in the pigment substitution rate under 5% was made, increase or decrease of pigment substitution rate could change the color value of the mortar effectively.
3) Within the scope of the experiment conducted this time, the shape of the specimens and which side was measured did not significantly affect the color values (L*a*b* values) of the mortar.
4) Lowering the water-binder ratio of the mortar was effective in preventing the color of the mortar from fading over time
Accurate estimation of roof snow load is important for safely ensuring the structural performance of buildings in snowy regions. Ground snow weight is a basic design factor used to calculate the roof snow load. In a previous model, the ground snow weight was estimated based on daily precipitation and average temperature. However, this model has a limitation in terms of its universality because it is necessary to optimize the coefficients used in the model by comparing the calculated result with observation data in advance.
This study aims to develop a versatile and universally app licable method to estimate ground snow weight based on meteorological observation data and a heat balance model. The proposed model is based on the concept that the snow weight can be estimated by subtracting the snowmelt runoff from the total precipitation. The model proposed by Kondo and Yamazaki (1987) was used to calculate the amount of snowmelt. The ground snow weights were estimated through the proposed model using detailed meteorological observation data for Nagaoka, which is representative of a snowy city in Japan.
According to the estimation results, the threshold temperature of rain/snow, T_{SR} , used in the model did not significantly affect the error in the range of 1.1 to 2.0 °C. Additionally, the maximum water content values, CWV_{MAX}, of 5% and 10% did not show large differences in the estimation error. For the eight winter examples examined in this study, the average normalized mean square error (NMSE) was the smallest when T_{SR} was 1.4 °C and the maximum water content was 5%. Although the accuracy varies with the winter, the variations in the daily ground snow weight and 7-day increasing snow weight were correctly estimated with an error of approximately 20%. The maximum values of each winter were predicted within an error of approximately 10%.
By analyzing the heat balance components obtained by the model, it was confirmed that the snowmelt energy due to radiation mainly contributed to the decreasing snow weight. Under the conditions of the present study, the contributions of sensible and latent heat transport were small. An estimation method based on the heat balance model, as developed in this study, can be helpful for understanding the factors contributing to the variation in the snow weight. This is a great advantage of such a model.
The present method has a limitation in its applicability; that is, all meteorological factors required in the model are only available at very limited sites such as meteorological offices. To overcome this limitation, a method was examined through which unavailable meteorological factors were estimated by meteorological factors measured at AMeDAS observation points; this method was similar to extending AMeDAS meteorological data. As a result, it was shown that the present method can be applied with sufficient accuracy even at sites where only AMeDAS meteorological data are available.
In recent years, there have been an increasing number of cases where a tuned mass damper (TMD) has been adopted as a countermeasure against long-period ground motions for steel frame high-rise buildings. They are also used to improve habitability under small and medium earthquakes and strong winds, and their effectiveness has been reported based on observation records. To apply this kind of TMD to reinforced concrete (RC) buildings, it is necessary to consider period fluctuation, because the natural period of a RC structure becomes longer due to cracks generated under a large earthquake, and tuning deviation becomes a serious problem. In order to avoid deterioration of seismic control performance, the authors propose a new configuration of a semi-active tuned mass damper, as shown in Fig. 1. This system is suitable for a semi-active TMD with a large weight since its resonance period can be controlled only by switching the damping coefficient of the variable dampers. In the previous study, we described its principle and design method, and confirmed its response control performance. In this paper we focus on the control method for semi-active TMDs.
Two types of the control methods for the semi-active TMD have been described in previous studies. The first is to tune the TMD to the dominant frequency of the excitation. Nagarajaiah et al. proposed a control method that uses the short time Fourier transform to observe the dominant frequency, and adjust the resonant frequency of the TMD in real time. It is well known that tuning the TMD’s resonant frequency to the excitation frequency is effective when the excitation is a stationary sine wave. However, this control method does not work well under unsteady and wide frequency seismic motions. The second is to tune the TMD to the natural period of the main system estimated by system identification. Hori et al. proposed a control method that identifies the natural period of the building by a least squares method with a forgetting factor using an ARX model. However, in order to obtain appropriate results by system identification, trial and error process is necessary to set appropriate parameters. Therefore, in automatic control, it is impossible to immediately perform appropriate processing of observation records, and it is difficult to apply system identification to seismic control devices that require stability and redundancy.
This paper proposes a new control method that focuses on the absorbed energy by the TMD, and it solves the above mentioned problems. In this method, we set some virtual TMDs that correspond to the control mode of the variable TMD, and select the mode with maximum energy absorption rate. This control method is physically clear, and easy to apply since it needs only one observation point to operate. In this paper, we first present the analytical models and input waves and outline the control methods in previous studies, and discuss their performance. Next, we describe the concept and algorism of the proposed control method. Its principle is explained using time domain analysis, and it is confirmed that the proposed control method is stable against various situations. Finally, the seismic response analyses of simulated RC building model are operated. We confirm the superior response control performance of the Proposed TMD and the proposed control method by comparing it with those of conventional passive TMDs.
One of the main roles of passive dampers is to reduce structural damage, that is, to reduce interstory deformations. It is also well known that the damage of non-structural components and facilities as well as the structural damage delays the recovery of the damaged building. It is needed to develop a resilience-based design method.
The reduction of structural response by passive dampers and the increase of the strength of non-structural components and facilities lead to the enhancement of the resilience of buildings. The structural responses (floor acceleration and interstory deformation) and the damages of the non-structural components and facilities are strongly correlated because the structural responses are regarded as the inputs to the non-structural components and facilities. In addition, the reduction of floor acceleration also contributes to the reduction of material quantities and human damages. For these reasons, it appears effective to reduce the structural responses for preventing damage to the non-structural components and facilities and improving recoverability of building functions.
Recently, research on resilience and recovery time has been carried out extensively in the fields of architectural and civil engineering. However, researches on resilience and recovery time are still insufficient.
On the other hand, there have been many researches on the optimum placement of passive dampers. The genetic algorithm (GA), which is one of the useful methods of metaheuristics, has been adopted as a powerful means for structural optimization and vibration control. Since random numbers are used and searching is performed at multiple points in GA, it works effectively even when the objective function has discontinuity points and/or multiple peaks. It is also known that GA can easily perform multi-objective optimization. While a gene is usually expressed by 0 or 1 (binary expression) in ordinary GA, design variable vectors are directly treated to create new individuals in the real-coded genetic algorithm (real-coded GA). In addition, the binary expression is not required in the real-coded GA. However, an appropriate crossover is required in the real-coded GA to get good solutions for each problem.
The purpose of this paper is to propose both a model of the evaluation of building’s resilience and recovery time and a new optimal viscous damper placement method for targeted resilience. The evaluation model has the following features: 1) Building components (structural frame, non-structural components and facilities) are categorized into some systems from the viewpoint of function: 2) The recovery time is considered as a function of damages to building components and human resources to repair the components: 3) It is applicable to structural design. The design method proposed in this paper uses a kind of real-coded GA. The proposed method can reflect the uncertainty of the process to recover from damaged states (or the pace to recover) in a non-stochastic manner. Therefore, this uncertainty can be reflected in the damper design. The effective use of the constraint on the sum of added damper damping coefficients enables an efficient search for the solution. It is shown finally that the minimization of the recovery time with the limited ability (manpower) to repair the building components and the minimization of the recovery time with the full (unlimited) ability to repair the components correspond to the minimization of the total damage of the components and the minimization of the maximum damage among the components, respectively.
Recently, from viewpoint of Global Environment, timber, i.e., one of nature cycle materials, has been tried to be utilized as structural members of large timber buildings in Europe and North America. A representative timber of the members is Cross-laminated timber (CLT), however, CLT structural system very often restricts planning of building because of CLT being plate member. High-stiffness-strength-timber slender beam and column are significantly desired.
This study focuses a hybrid glulam timber with steel deformed bar (rebar) and Epoxy resin adhesive. Aim of this study is to propose an approach to predict elasto-plastic behavior of the hybrid timber column under lateral reversed cyclic loading, assumed to be attacked by big earthquake. The approach adopts a numerical calculation software for reinforced concrete(R/C) members, using Multi-spring model for R/C column yielded at its bottom by moment. The calculation results were verified with experimental results of hybrid columns previous reported in Reference 1, including skeleton curve, hysteresis loop, energy dissipation, and minimization of residual displacement.
The results are summarized as followings:
(i) The RC’s numerical calculation software is extremely useful for us to predict elasto-plastic behavior of the hybrid timber column because the column has no damages expect yielding of joint rebars between its column’ bottom and RC foundation, until 1/50 radian of maximum drifts.
(ii) Skelton curves, reversed cyclic hysteresis loops, and amount of energy dissipation of the columns have been precisely predicted to the experimental results.
(iii) The length of the Multi-spring model for plastic hinge of the column could be recommended to be 7/8 of its column’ depth.
(iv) Equivalent viscous damping factor of the column and final residual displacement in quasi-static free vibration immediately after target displacement, under the column bottom yielding, also were predicted on safe side.
Nuclear power plants are required to act as barriers to gases, liquids, and to hold negative pressure during the earthquakes. The maximum crack width is frequently used as the damage indicator of these properties, but the authors think it is inadequate to evaluate the shielding performance of nuclear power plants by means of the maximum crack width. The nonlinear finite element (FE) analysis is widely used for simulating the seismic behavior and crack patterns of reinforced concrete (RC) structures. However, it is difficult to predict crack width and crack spacing through conventional nonlinear FE analysis with smeared crack concept.
Therefore, a series of cyclic loading test on RC shear wall specimens were conducted to obtain validation data on the crack width, length, and spacing. Five specimens, with each having a wall of 1280 mm × 800 mm area and 85 or 100 mm thickness, were constructed. Two columns, a base stub, and a loading stub were attached to the wall of each specimen. The variables of the specimens were as follows: the shear reinforcing bar ratio (1.0% or 0.5%), reinforcing bar arrangement type (double or single), and diameter of reinforcement bar (D6 or D10). The compressive strength of concrete was approximately 30 N/mm^{2}. The specimens were subjected to horizontal cyclic load under constant axial force. When the drift angle reached peak points (±0.1%, ±0.15%, ±0.2%, ±0.25%, ±0.3%) and each unloading points in the cyclic load, the crack width and length of the wall were comprehensively measured using a crack scale. The experimental results show that the maximum crack width and crack spacing depend on reinforcement bar arrangements, such as the reinforcement bar ratio, rebar diameter, rebar spacing, and arrangement type. However, crack area, which is defined as the product of the crack width and crack length, is unaffected by these factors but correlated to the drift angle of the wall.
Furthermore, nonlinear FE analyses were conducted using widely-used smeared crack model to simulate the test results. The horizontal load and drift angle relationships of the FE analysis agree well with the experimental ones. In order to estimate the crack area from the FE analysis results, the increase in the wall area was calculated using two methods. One is based on the nodal displacement, whereas the other is based on the normal strain of the element. The increase in the wall area evaluated using these two methods correspond to the actual crack areas of the specimens. However, the method based on the normal strain of the element is supposed to be more rational because it is able to exclude the thermal expansion and shrinkage.
It is concluded that the quantitative tendency of the relationship between the wall drift angle and crack area can be evaluated through nonlinear FE analysis, but the accuracy of the evaluation method needs to be improved further.
In the case of repair and reinforcement of an R/C structural frame, and installation of new members for extension and reconstruction, it is necessary to anchor main bars and wall reinforcement bars of new members to the existing frame.
In this case, the anchor is required to reliably transfer the tension of the rebar to the existing frame. The purpose of this research is to propose a post-installed headed rebar anchor method with high reliability both in structural performance and workability, and to evaluate the anchorage performance of the method.
In the third part of the authors’ research, a shear experiment was conducted to clarify the structural performance of the post-installed rebar anchor with small headed plate under the combined load of tension and shear. In the test, shear force was applied to a joint surface where the rebars were anchored with the proposed method. The number of test specimens was 10, and the parameters of the test were anchoring method, concrete strength, tensile load level, and edge size (rebar spacing).
The following results were obtained.
(1) The shear resistance of the post-installed rebar anchor of the proposed method is similar to that of the cast-in-place rebar even when its diameter is large or concrete strength are different, and the shear resistance is dominated by the dowel action.
(2) The allowable shear load (stress) can be evaluated by applying the steel structure bolt method for the fracture of rebar and the bearing strength of concrete for the failure of anchor area. The displacement can be controlled to 1 mm or less at the long-term allowable load and about 5 mm or less at the short-term allowable load even when the tensile force is applied.
(3) At the maximum load, the increase of load is small due to the effect of cyclic loadings, but the ductility is large due to the yielding of the rebar. The ultimate shear capacity can be evaluated by the existing evaluation method considering the reduction due to cyclic loading.
(4) The shear force-displacement relationship can be evaluated using the existing evaluation method for the dowel action of the PCa connection by modifying its horizontal reaction coefficient of concrete when tensile force is applied.
The purpose of this research is to drive the evaluation formula of coupled local buckling strength of H-shaped members under pure compression. To clarify the interaction among plate elements, multiple studies have been conducted. As a result, the evaluation formulae for maximum strength are established and expressed by empirical equations or regression analysis equations . However, most equations were not able to explain the local buckling behavior of H-shaped members because the local buckling behavior is complicated. To solve this problem, Prof. Ikarashi proposed a displacement function using a Fourier series to drive an evaluation formula based on the energy method. By using the Fourier series, the buckling deﬂection can be described even if combined stresses act on H-shaped members. In this paper, the evaluation formula is proposed based on the energy method, as well as Prof. Ikarashi did. The diﬀerence between Prof. Ikarashi’s researches and this research is the displacement function. The exponentiation of the trigonometric function is used as a particular buckling displacement function. Because the function is fast-converging compared to the Fourier function, it is possible that the buckling deﬂection can be described by only three terms. Additionally, the function can describe elastic web-ﬂange interaction amongst the elements comprising the cross section. As a result, the closed-form evaluation formula of H-shaped members is proposed. To verify the reliability and the eﬀectiveness of the proposed formula, modal analysis based on the ﬁnite element method (FEM) is conducted.
From this research, the following are found.
1) The proposed displacement function in the web-height direction is expressed by the linear sum of the trigonometric function with three terms: a sine half-wave that expresses the buckling displacement under simple support conditions, a cosine half-wave that expresses buckling displacement under clamped support conditions, and a power trigonometric function. The proposed displacement function converges the buckling displacement faster than the partial sum of the Fourier series with higher accuracy.
2) Boundaries exist where the web buckling coeﬃcient k_{w} becomes 4.00 or 6.98 where the ﬂange buckling coeﬃcient ratio k_{f}/k_{f}_{0} relative to the buckling coeﬃcient under the support condition of one free edge and three simple-supported edges becomes 1.00, and where the ratio of the buckling wavelength λ_{w}/k has a linear relationship in the coordinate axis of the width-to-thickness ratio of the plate elements of the web and the ﬂanges. Each boundary line changes with the cross-sectional aspect ratio B/H, and the buckling behavior can be classiﬁed into four types as per these boundary lines.
3) In the wide ﬂange cross-section, the web buckling coeﬃcient becomes less than 4.0, and the cross-sections show that local buckling of the ﬂanges occurs before that of the web. The web and ﬂanges simultaneously buckle in the cross-section when the web buckling coeﬃcient is higher than 4.0.
4) Based on the proposed web displacement function, the coupled local buckling strength of the H-shaped member under pure compression can be derived using the direct method as a closed-form solution. The results of the eigenvalue analysis on Eq. (25) using FEM for evaluating the coupled local buckling strength in this study indicate an average value of 0.9906, an average coeﬃcient of variation of 0.01186, and a maximum error of 4.39%. Therefore, the formula proposed in Eq. (25) can be used to accurately evaluate the coupled local buckling strength.
1. Introduction
The objective of this study is to examine 1) the validity of the effective length factors based on the stability index, 2) the properties of stability index, 3) the relations among the effective lengths obtained from different buckling conditions, and 4) the applicability of the stability index by using the G factor. The targets are rectangular plane frames, and total 168 cases for one-span and 2-8 stories frames, and total 48 cases for two-spans frames are examined, taking the condition of the column base, number of story, stiffness ratio, stiffness ratio reduction factor, and distribution of the story shear as the parameters as shown in Figs. 3, 4 and 5.
2. Effective length factors and stability index
Effective length factors _{SI}γ is calculated by Eqs. (6) and (9) for the overall structural system, and _{SI}γ * are calculated by Eq. (11) for each story. Effective length factors _{G}γ by G factor method are obtained from Eqs. (12) and (15). The exact effective length factors γ _{exact} accord to the factors shown in references 10) and 11). On the other hand, approximate stability index is calculated from the Eq. (27) by using G factor.
3. Results
Comparisons of effective length factor between _{SI}γ and γ _{exact} are shown in Fig. 8. Effects of story shear distribution and column base are shown in Figs. 11, 12 and Fig. 13, respectively. Effective length factors (_{SI}γ, _{SI}γ *and _{G}γ ) are shown in Figs. 14, 15 and 16. Comparison between the stability index SI obtained by the first-order lateral load analysis and approximate _{G}SI obtained by G factor is shown in Figs. 17 and 18.
4. Conclusions
The conclusions derived from this study are as follows:
1) Effective length factors _{SI}γ obtained by using the stability index agree fairly well with the exact factors γ _{exact} about within 5% error (see Fig. 8).
2) The buckling-associated-story where the stability index becomes maximum is shown in Figs. 9, 10 and Fig. A3.
3) The effects of the story shear distribution on the stability index are hardly observed (see Figs. 11 and 12).
4) For frames with 4 stories or more, the stability index above the 4th story is almost same among the fixed base and pin base frame (see Fig. 13).
5) As to the exception of the lowest and highest story, the effective length factors _{G}γ obtained by G factor method agree well with the factors _{SI}γ * obtained by the stability index method used the buckling condition equation as the story buckling (see Figs. 14, 15 and 16).
6) The approximate stability index obtained by G factor can be applicable instead of the stability index (see Figs. 17 and 18).
A structural design algorism to find superior solutions using the multiple start local search (MSLS) method for steel buildings associated with buckling restrained braces (BRBs) is proposed. The strengths and locations of BRBs in addition to the section sizes of structural members are considered as discrete design variables. The steel volume including BRBs is minimized as an objective function. The superior solutions satisfy serviceability constraints under the allowable stress design against sustained and moderate earthquake loads, as well as limit-state constraints under the “calculation of resistance and limit-state” (CRLS) for large earthquakes. The limit-state is defined as the maximum inter-story drift ratio of 1.5 %. The BRBs and main frames remain elastic under the moderate earthquake load with the base shear coefficient of 0.2. In addition to these constraints, standard design constraints such as the width-to-thickness ratio, strong column weak beam conditions and 0.5 % of the lateral drift ratio constraint under the moderate earthquake load are also considered. Applying the proposed method, the entire seismic resisting systems of the buildings composed of the main frames and BRBs are designed taking into consideration the seismic energy dissipation effect of BRBs using CRLS.
The superior solutions of a seven-story office building in the space frame system (SFS) and perimeter frame system (PFS) are derived, where the columns are square hollow structural sections and most of the beam-to-column connections are moment connections in SFS, and the columns are I-shaped sections and the moment connections are limitedly used in the perimeter frames in PFS. The steel volume in the superior solutions with PFS is 5 % lower than that with PFS. The total steel volumes including BRBs in both systems are lower than the statistics and the location of BRBs is obtained in a checkered pattern, which is rational for avoiding axial force concentration in columns under lateral forces.
The ratios of seismic lateral forces carried by BRBs in the elastic state are approximately 70-100 %, which is higher than the standard design. Most of the BRBs yield slightly over a moderate earthquake load and it is seen that the hysteresis seismic energy dissipation effect is maximized. The maximum ductility factors of BRBs and beams in large earthquakes are approximately 8 and 2, respectively, and the most columns remain elastic. The predicted responses by CRLS reasonably agree with the simulated responses by response history analyses under simulated seismic ground motions for large (Level 2) earthquakes. The key values in simulations of the superior solutions such as the inter-story drift ratio and cumulative ductility factors of the main structural members (columns and beams) and BRBs are within the standard practical design criteria. It is confirmed that the superior solutions are successfully designed satisfying almost all of the practical structural design constraints. Through these evaluations, the efficiency of the proposed MSLS algorism is validated.
The ultimate lateral strengths calculated by pushover analyses are slightly lower and close to the code required ultimate lateral strength. The rationale of the three design procedures against earthquakes, CRLS, response history analyses and ultimate lateral strength calculations is confirmed for the steel buildings associated with BRBs through the evaluations of the obtained superior solutions.
The advantages of concrete-filled steel-tube (CFT) columns include high strength and remarkable ductility, since the steel tube provides confinement to the concrete while the concrete prevents local buckling of the steel tube. CFT column composite frame systems with steel beams have been widely used in bending moment-resisting frame systems for mainly office buildings. CFT columns at typical floors are short and have small ratios of buckling length to cross section depth, and those at entrances of lower floors are slender and have large ratios of buckling length to cross section depth. CFT columns from short to slender have been used in buildings. In order to verify the structural safety of CFT structures in the ultimate state against huge earthquakes, etc., a restoring force characteristic model incorporating strength reduction after ultimate strength is required. The stress states of CFT columns applied to buildings are in a state of flexural-shear stress, and the structures are designed for the predominant flexural yielding. It is thought that accurate evaluation of a bending moment-deformation relationship under axial force will lead to design of columns that have the features of CFT columns. For a restoring force characteristic model, which is the basis of the bending moment-rotation angle relationship of CFT columns from short to slender, it is important to devise a simple model incorporating a reduction of strength after ultimate strength.
This paper proposes a new simplified restoring force characteristic model of a bending moment-rotation angle relationship for square CFT beam-columns to estimate the elasto-plastic flexural-shear behavior of beam-columns from short to slender. The square CFT beam-column model incorporates a reduction in strength after ultimate strength. The proposed simplified model is a multi-linear model having a crack strength point, a yield strength point, an ultimate strength point and strength reduction points. In the proposed model, each flexural strength is calculated by a general superposed strength method, and new multiple regression formulas for each rotation angle are proposed based on results of cyclic and monotonic loading tests from previous researches. Predictions from the proposed model of the bending moment-rotation angle are found to agree approximately with experimental results up to large rotation angles.
Regarding practical fire resistant designs for steel structures in Japan, the performance-based design represented by the AIJ Recommendations for Fire Resistant Design of Steel Structures is rarely used, on the other hand, the specification-based design code (route A) on the Building Standard Low of Japan is widely applied to determine specification of fire proofing material used for the steel member, which has been verified by the fire resistant performance-evaluation test (hereinafter referred to as fire test). The fire test condition differs from the actual condition of fully-developed compartment fire occurred in a building, in particular, regarding the fire temperature and time relationships, the boundary and loading conditions for the heated steel member. Furthermore, the fire loads in the compartment room, mechanical properties of steels at elevated temperatures, and dead and live loads applied to the member possess the large dispersion. To evaluate the safety side performance of protected steel beam based on the specification-based design code, the large loading values at the fire test are used in comparison with the actual condition, however, that probabilistic fire safety at the fully developed compartment fire has not been clarified. To improve the fire resistant safety of the protected steel members applied for many steel buildings, the reliability evaluation on the specification-based design code is of importance.
The main purpose of this study is to evaluate the failure probability of the protected steel beam based on the specification-based design code in a case when the fully-developed compartment fire occurred, by using the theoretical probabilistic calculation model which has been proposed by the authors. To determine the thickness of fire proofing material that satisfies each required performance (1, 2, or 3 hours fire resistance performance) at the fire test, the numerical simulation using the Monte Carlo method considering the dispersions of steel strength and possessing fire resistance time is conducted. The failure probability of protected steel beam with the above required thickness arranged in the fire compartment room are evaluated by the parametric calculations considering the dispersions of fire loads, steel strength, and dead and live loads, respectively.
The main conclusions of this paper are summarized as follows:
1) The failure probability of protected steel beam based on the specification-design code strongly depends on the intended use of compartment room with the changeable fire load values and the applied vertical loads. The selection of specification of fire proofing material based on the specification-based design code, that is, the classification of 1, 2, or 3 hours fire resistance performance based on the Building Standard Law of Japan, is not reasonable to decrease the failure probability at the building fire.
2) The improved specification-based design considering the effects on both intended use of compartment room and loads applied to the steel beam was proposed. By using the proposed design, the failure probability can be rationally decreased in comparison with the current specification-based design code.