The effect of the hardening process of a moisture-curing, one-component polyurethane sealants on the joint movement followability during curing was examined by experimental and analytical methods. In order to investigate the distribution of the rate of hardening in the depth direction from exposure surface, a bond breaker was applied to the upper or lower half of the adhesive surface between the sealant and the aluminum frame to prevent the adhesion of the specimen. Two types of sealants with different hardening rates were prepared for the experiment. U1 with normal hardening rate, M-U1 with faster hardening rate, respectively. According to the results of the tensile test, the tensile force was shared almost by the upper part of the sealant after 7 days of curing. After 14 days of curing, the upper part has more high strength than the lower part, but the hardening progresses to the lower part, and the elongation and strength was developed. M-U1 had a faster development of strength, and also had a higher strength.
The adhesive surfaces of the sealant and the aluminum frame were cut at each curing date of 3, 7, and 14 days as test specimens for testing the curing depth of the sealant. The penetration resistance was measured by a needle of 0.75 mm diameter into the cut surface. M-U1 was hardening faster and deeper than U1. A simulation program was proposed to model the penetration and reaction of moisture into the polyurethane and to predict the distribution of hardening rates in the depth direction. The prediction results were a good representation of the results of the penetration test.
Stress distribution analysis of the sealant under tensile force was performed by FEM using the distribution of hardening degree during curing. The maximum principal stress at the interface between the sealant and the aluminum frame was approximately 2.5 N/mm^{2} for U1. M-U1 is about 1.5 N/mm^{2}, which is about 40% smaller than U1. M-U1 had a faster hardening rate and higher strength than U1. However, M-U1 share a wider area of stresses due to the faster progression of hardening in the depth direction. Therefore, even if a tensile force occurs during the curing process, the effect of stress concentration is considered to be controlled. Since the maximum principal stress of M-U1 under a forced displacement of 10% is almost the same as that of U1 at 5%. The internal stress is reduced and the risk of peeling and rupture is considered to be low. From the above results, it can be seen that so as to reduce the influence of external forces during the curing process, it is important to formulate the materials so that curing proceeds uniformly in the depth direction, rather than simply increasing the reaction rate.
The random phase of artificial input ground motion model for structural design has non-ignorable influence on structural responses. For the case of using the statistical Green’s function method, the maximum acceleration of generated ground motion could fluctuate with the random phase of the elemental earthquake in the range of 20 to 30%. Therefore, the near-average model is often selected as the input ground motion model for structural design in considerably large set of ground motion models with different random phases. To overcome this inconvenience, a new method is presented for generating random input ground motion model expressed as non-stationary power spectral density function. The non-stationary power spectral density function of input ground motion model is synthesized from that of the elemental earthquake and the fault rupture process based on the application of the statistical or empirical Greenʼs function method. Furthermore, the method of estimating the standard deviation and average maximum response of non-linear structure under the random excitation characterized by the non-stationary power spectral density function is presented based on the random vibration theory and the equivalent linearization method. The efficiency of the presented method is investigated through some numerical simulations.
The non-stationary power spectral density function models of the hypothetical Nankai and Uemachi earthquakes are generated by the presented method; their root mean square acceleration time histories show good agreement with the results of Monte Carlo simulations (MCS). Furthermore, the non-linear responses of an 8-story RC building excited by these two input ground motion models is calculated based on the random vibration theory. The presented method gives good estimation of the expected value of the maximum response with the ductility factor less than about 2 for the case of the Nankai earthquake, whereas the discrepancy with the MCS results increases for large ductility factors concentrated in lower stories observed in the case of the Uemachi earthquake.
After Parkfield earthquake in 1966 and San Fernando earthquake in 1971, pulse-like ground motions with a long period and short duration have been observed near earthquake source faults, and structural damages due to these pulse-like ground motions have been reported after the large earthquake events, e.g. Northridge earthquake in 1994, Hyogoken-Nanbu earthquake in 1995, Taiwan Chi-Chi earthquake in 1999, Niigata-Chuetsu earthquake in 2004 and Kumamoto earthquake in 2016. The pulse-like ground motions with a predominant period of more than 1 second can damage two-story wooden houses, and many wooden houses were collapsed during Hyogoken-Nanbu earthquake in 1995.
Various types of models that can represent the load-deformation relation or restoring force-deformation characteristics of shear walls or mainframes in wooden houses have been proposed. A bilinear + slip model, which consists of the normal bilinear hysteresis and slip-type hysteresis with tri-linear skeleton curve, is one of the restoring force-deformation characteristics for the time-history response analysis of the wooden structures or the shear walls.
In this paper, a double impulse input is introduced as a substitute for the main part of the pulse-like ground motions which can be modeled by a one-cycle sinusoidal wave or wavelets. Then, in order to estimate the maximum responses of the two-story wooden houses under the critical pulse-like ground motion, the closed-form solutions are derived for maximum deformation angles of a single-degree-of-freedom (SDOF) bilinear + slip model subjected to the critical double impulse input. The critical double impulse input can be defined as the double impulse input with the time interval which maximizes the maximum deformation after the second impulse, and the critical timing of the second impulse can be characterized as the zero restoring force timing. Similarly, the critical pulse-like ground motion can also be defined as the pulse-like ground motion which maximizes the earthquake response. Furthermore, two types of reduction methods of the two-degree-of-freedom (2DOF) bilinear + slip model into the SDOF bilinear + slip model are introduced, and the closed-form solutions for the critical responses and the reduction method can provide the simple evaluation method of the maximum deformation of the 2DOF wooden structures subjected to the critical pulse-like ground motion.
The validity of the double impulse as substituted for the pulse-like ground motions is investigated through the comparison with the elastic-plastic response of SDOF bilinear + slip model under the one-cycle sinusoidal wave in the critical case and actual recorded ground motions. The accuracy of the proposed estimation method of the critical earthquake response of the two-story wooden houses by using the closed-form solution and the reduction method into the SDOF system is checked through the comparison with the maximum displacement response of the 2DOF bilinear + slip model under the critical double impulse input and the critical one-cycle sinusoidal wave.
A hyperbolic paraboloidal (HP) shell with straight edge lines is generated by translating a straight line with varying the tilt of line. On the dynamic response behavior of the HP shells, there are few studies about the steel structure differently from the RC structure. In this paper, the effects of natural period ratios, mass ratios and input directions on the natural vibration characteristics and the seismic response behavior of HP lattice shells are made clear by the Complete Quadratic Combination (CQC) method. In addition, the evaluation methods for maximum seismic response accelerations of HP lattice shells taking natural period ratio, mass ratio and input direction into consideration are proposed. Furthermore, improvement of versatility of the response evaluation method is attempted by proposing the natural period estimation formula for HP lattice shells based on that for lattice shells on the previous study.
It is concluded as follows, from the above results.
1) When the depth span ratio d/L_{x} of shell roof exceeds 1/20 (the magnification of out of plane stiffness of roof=50 times), the effective mass ratio of antisymmetric one wave (O1) mode becomes the maximum in the vibration modes of model with only a roof structure. In the vibration modes of the model with a supporting substructure, higher-order modes appear when the natural period ratio R_{T} is less than about 0.2. However, as R_{T} becomes more than 0.2, the modes which O1 mode and the sway mode of supporting substructures are combined (O1±) appear. The sum of effective mass ratios of those modes becomes more than 94%. Even when the mass ratio R_{M} changes, O1± modes appear in the top 2 modes.
2) In the distributions of maximum response accelerations magnification factor of the model with only a roof structure, the distribution shapes are influenced by O1 mode. The distribution shapes are influenced by O1± modes also in the model with a supporting substructure, when R_{T} is less than about 5.0. While as R_{T} is 5.0 or more, the response accelerations are uniform in horizontal direction and do not occur in vertical direction. The maximum vertical response accelerations increase in the near of R_{T}=1.0. In addition, those increase following an increase of R_{M}.
3) The maximum response accelerations on roof structure of HP lattice shell with supporting substructure can be evaluated regardless of d/L_{x} by the response evaluation formulae considering the amplification factors expressed as a function of R_{T} calculated by the natural period of O1 mode and that of equivalent single mass system.
4) The maximum response accelerations subjected to earthquake motions with arbitrary direction can be evaluated by the square root of sum of squares for the response accelerations by the response evaluation formulae in the arch and suspension directions multiplied by cos^{2}φ and sin^{2}φ, respectively.
5) The response displacements and member stresses under the static seismic loads by response evaluation formulae considering R_{T}, R_{M} and input direction agree with those calculated by CQC method though the errors at some nodes and members are up to about 60%.
6) The natural periods can be calculated by the proposed natural period estimation formula for HP lattice shell with straight edge lines. By using the obtained natural period, the response values can be evaluated without executing the eigenvalue analyses.
Recently, application of Cross Laminated Timber (CLT) for medium and high-rise wooden structure is spreading rapidly even in Japan. It has been proposed not only CLT panel structures but also structures combined CLT panel with frame members which is used wood-based materials such as Glued Laminated Timber (Glulam) or Laminated Veneer Lumber (LVL) and so on. In a case of CLT is used as wall column and Glulam is used as beam, it is important that appropriate evaluation of deformation property between CLT and Glulam.
Wood has strong anisotropy, and material characteristics are completely different when subject to compressive stress in longitudinal direction or direction that perpendicular to the grain. Especially, it is known that stiffness and strength become low value in the case subject to partial compressive strain in direction of perpendicular to the grain. To evaluate deformation property of wooden structures, it is important that transact unique characteristics of wood such as mentioned above properly.
In this paper, the yield criterion and strain hardening rule using non-dimensional stresses for orthotropic materials such as wood proposed in previous papers are applied to numerical analysis of CLT-Glulam joint and comparison between result of analysis and experiment are shown.
Firstly, partial compression test of glulam is conducted and compared with numerical analysis. It is shown that method for decide material properties for analysis, which is that a certain value is decided from material experiment and other properties are calculated using ratio among material properties of wood proposed in previous studies. From the result of numerical analysis, stiffness and strength have not improved even though increase in size of specimen contrary to expectations.
Reason of the above result is expected to effect of inclination of annual rings in the end grain. Accordingly modeling method considering inclination of annual rings in the end grain is proposed and numerical experiment applied the method is performed. From the result of numerical experiment, if effect of inclination of annual rings is not considered, it is confirmed that obtained value from analysis is bigger than experimental value. In the case that width of glulam is 210mm, by the effect of inclination of annual rings, decrease 55% (from 519.05 N/mm^{2} to 235.59 N/mm^{2}) in Young’s modulus and 22% (from 2.74 N/mm^{2} to 2.14 N/mm^{2}) in yield stress. Moreover, result of compression test is shown and it is verified that Young’s modulus and yield stress decrease relatively even though size of specimen increase by effect of inclination of annual rings.
Finally, based on the above discussions, numerical analysis of partial compression test is conducted once again. The result of analysis is well corresponding to experimental result and appropriateness of the proposed method is confirmed. In the case that width of glulam is 150mm, by adjusting input data for analysis to experimental result, difference between analysis and experiment is only 1% (analysis: 701.26 N/mm^{2}, experiment: 711.05 N/mm^{2}) in Young’s modulus and 6% (analysis: 3.73 N/mm^{2}, experiment: 3.96 N/mm^{2}) in yield stress. It is clarified that whether considering inclination of annual rings in the end grain or not have great effect on result of numerical analysis. According to the result, effect of inclination of annual rings would be remarkable if width of glulam become larger and a part which annual rings inclining become wider.
1. Introduction
In June 2016, Ministry of Land, Infrastructure, Transport and Tourism has delivered countermeasures against the long-period ground motions caused by strong earthquakes along the Nankai trough^{3)}. However, the countermeasures do not cover high-rise buildings equal to or less than 60 m height that are not required earthquake response analyses in the seismic design. Hence, in this study, earthquake response analyses for such high-rise RC buildings were performed under ground motions assumed in the OS1 and OS2 regions to evaluate the base shear coefficients satisfying a safety demand. Furthermore, an estimation method of the required base shear coefficients proposed in the authors’ previous study^{4)} was applied to practically evaluate the results from the earthquake response analyses.
2. Analytical buildings
Design concept of analytical building models are described. Major design parameters were the number of stories (12, 14 and 16) and lateral strengths (with different D_{s} in Eq. (2)). Table 2 shows the common structural details of the columns and beams for the building models with different numbers of stories. The member bending strengths were designed based on an overall collapse mechanism, as shown in Fig. 1, to satisfy the lateral strength (by Eq. (2)) under assigned D_{s}.
3. Earthquake response analyses
Analytical methods including modeling and numerical calculation methods are described. Two ground motions in the OS1 and OS2 regions were applied to earthquake response analyses. Within the analytical cases in the present study, in general, the inter-story drift responses were more severe under the OS2 ground motion for high-rise RC buildings. Furthermore, the base shear coefficients satisfying a safety demand of the maximum inter-story drift of 1/75 were identified, which is summarized in Table 5.
4. Estimation of demands on the base shear coefficients by the equivalent linearization method
The equivalent linearization method was applied to estimate the results from the earthquake response analyses. The procedure of the proposed estimation method^{4)} is illustrated, as shown in Fig. 7. It was also implemented for the analytical models. As a result, the estimations with Eq. (8) for practical design for RC buildings underestimated response reductions under hysteretic damping resulting in overestimation of the base shear coefficients to satisfy the safety demand, as shown in Table 6. Therefore, it was modified based on Eq. (12) presented by Kobayashi et al.^{16)} Consequently, the base shear coefficients required by the earthquake response analyses were well estimated by the proposed procedure with Eq. (12a), as shown in Table 8. In addition, suggestions for future study are provided to complete more accurate and simplified estimations.
5. Conclusions
Major findings from the present study are summarized based on the above research outcomes.
After an earthquake, it is important to judge the safety of buildings and make an efficient recovery plan. For that, it is necessary to know quantitatively the damage level and safety limit of buildings. An evaluation method of residual seismic capacity is described in the Japanese Standard for Post-earthquake Damage Level Classification of Buildings; however, the method does not consider the difference of deformation capacity of members such as walls and frames (columns and beams). Even though evaluation methods were proposed in previous research for the damage level and safety limit of RC buildings, the focus of the method has been mainly for moment-resting frames. Moreover, not enough experimental investigation has been done to verify the application of these methods. In this research, a new evaluation method for the collapse mechanism and safety limit of dual structures, which have members with different deformation capacity, was proposed. A shake-table test has been carried out to investigate the applicability of the proposed method to RC buildings consisting of moment resisting frames and shear walls.
The test specimen was a 1/4 scale model of a 4-story RC building with multi-story shear walls in both X- and Y-directions. The structure was designed to exhibit a total collapse mechanism (frame-sway mechanism) and so, plastic hinges were designed at the bottom of columns and walls in the first story and beam ends of each story. To investigate the difference of collapse mechanism in the X- and Y-directions, contribution ratio of shear wall to the whole seismic capacity was varied. In the X-direction, two shear walls were placed with the intention of making the failure of shear walls dominate the collapse mechanism of the whole structure (i.e., the failure point of walls corresponded to the global structural safety limit). In the Y-direction, only one shear wall was used such that failure of columns and beams would dominate the global collapse mechanism, which meant that failure of the wall would not correspond to the global structural safety limit. The design concept was quantitatively confirmed based on seismic capacity indices using results of nonlinear pushover analyses.
In the shake-table test, scaled artificial ground motions compatible with the Japanese standard spectrum were used as input. The damage of walls preceded in both directions and at the end of the test, the walls were severely damaged and the whole structure was close to collapse. The strength and the deformation capacity of the structure were higher than predicted by the analysis. Finally, the collapse mechanism and the safety limit of the specimen was evaluated. As a result, the collapse mechanism of the X-direction frame was wall-dominant and the wall failure point corresponded to the safety limit, consistent with the results obtained from analyses before the test. In the Y-direction, the collapse mechanism was also wall-dominant, even though a frame-dominant response was anticipated. It was estimated that the accumulated damage of columns and beams by former shakings degraded their seismic capacity after the wall collapse, which was not considered in the proposed analytical evaluation method, and so, the proposed method was improved considering the effect of accumulated damages of members simply. As a result, the collapse mechanism and safety limit reevaluated by the method was consistent with the test result and the applicability of the method was proved.
This study proposes a disaster resilient structural design of reinforced concrete buildings with ordinary construction approach, and demonstrates the seismic capacity by the full-scale test on five-story reinforced concrete buildings. In this design, the building produces base shear coefficient higher than 0.55 by utilizing wing wall, spandrel wall, and hanging wall. The target damage level under extreme ground motion is less than slight for buildings, and grade I for each member. This method improves the strength and stiffness of the moment resisting frame and reduces the deformation during earthquakes. That can minimize the damage on each member.
The full-scale specimen is a five-story reinforced concrete building with 1×2 bays and height of 18.7m. The wall frame has large openings in the longitudinal direction. The span length is 6.0m and story height is 3.5m. Columns have 700 mm square section, and beams have 500×700 mm section. The width of the attached wall section is 200 mm. A series of 4 actuators located on the roof level and 6 actuators located on the 4th-floor level. Those actuators pinched the center of the floor slab from the upper and lower level. The relation between base shear and the overturning moment is given by a ratio of external force on the 4th floor and roof is equalize to that given by an external force with inverted triangle load distribution. The cyclic loading peak is controlled by the total drift on the roof level. The test demonstrates the up to 3.0 times over calculated strength of base shear coefficient 0.3 of bare- frame. The story drifts are concentrate prominent on 2nd and 3rd floor and its collapse mechanism form the partial collapse. The strain of the main reinforcement of the bare-frame yielded in the 0.5% total drift loading cycle, where a limit of elastic is 0.25% total drift loading cycle. The damage levels based on the residual seismic capacity on the hysteretic curve is slight at 0.25% total drift loading cycle, and the base shear coefficient at the 0.25% total drift loading cycle is 0.67.
Focusing on a strength reduction factor related to door openings provided in AIJ standards in 2010, a series of experimental studies was performed with multi-story shear wall specimens with different configurations of door openings. In this study, besides the former specimen with eccentricallyaligned door openings, two specimens were designed to fail between the door openings. The observed strengths of all specimens agreed well with the values predicted using the index proposed by the authors' previous study. Furthermore, a specimen with shear margin of 1.2 obtained using the proposed index was tested, and its effectiveness for the assurance design was verified.
In this study, tensile tests of notched flat plates are conducted. The purpose of this experiment is to reveal the relationship between stress concentration factor α 3.5-9.3 and fracture critical stress of notched tensile specimens of spheroidal graphite cast iron and the relationship between maximum first principal stress and stress concentration factor α in spheroidal graphite cast iron. Table 1 shows stress-concentration factor α of previous and this studies. Stress-concentration factor α is calculated from equation (1). Stress-concentration factor α of previous studies only 2 and 10. This study, considering α between 3.5 and 9.3. Notched tensile specimens are made of the castings shown in Fig. 1 by cutting. Fig. 3 presents the notched tensile test specimen and clip gauges mounting position. It is measured notch displacement of specimens. The shape of notched tensile specimens are indicated in the Table 2. Notched tensile specimen has 8 different shape notches. All of these specimens, length is 550mm, width is 90mm, thickness is 20mm, notch depth c is 5mm and 10mm, and notch bottom radius ρ is 0.25mm, 0.5mm, 1mm, and 2mm.
Specimens of round bar tensile tests is shown in the Fig. 4. The results are indicated in the Table 3 and Fig. 5. Fig. 5 is stress-strain relationships of notched tensile specimens.
Fig. 6 shows the load-displacement relationships. The list of notched tensile test results are indicated in the Table 4. Notch round bar tensile test was conducted to calculate fracture critical stress. The test specimen and analysis model are shown in the Fig. 8 and Fig. 9. The list of notch round bar tensile test is shown in the table 5 and Fig. 10.
Fig. 11 shows the analysis model of notched tensile specimen. As indicated in the Fig. 12, the load-deformation relationships are relative to experimental results. The difference between the maximum first principal stress of tensile analysis and fracture critical stress was under 13%. It is shown in the Table 6. Fig. 13 shows eccentricity analysis of 10-0.5(1).
Fig. 15 shows the relationship between the maximum first principal stress of tensile analysis _{P}σ and stress- concentration factor α. It is the linear relationships.
From the results of test and analysis, following findings were obtained.
(1) The difference between the maximum first principal stress of tensile analysis and fracture critical stress was under 13%. Therefore, in the scope of this study, fracture critical stress is relative to brittle fracture of spheroidal graphite cast iron.
(2) By analysis imitating eccentricity, fracture critical stress is applicable to brittle fracture of spheroidal graphite cast iron when the eccentricity of difference is 1.2 of left _{d}σ/right _{d}σ in elastic range, as same as nothing eccentricity.
(3) Including this study and previous studies, the relationship between the maximum first principal stress of tensile analysis _{P}σ and stress-concentration factor α is linear in stress-concentration factor α 2.2~10.8.
(4) By the results of notched specimen tensile test, the larger stress-concentration factorα, the smaller the displacement of fracture. Specimens with smaller stress-concentration factors tend to vary in maximum displacement comparing specimens of the same shape.
Connection of which the beam web is connected to the gusset plate of column through high strength bolts is considered as a pin connection in structural design. In previous study, fundamental structural behaviors were investigated by conducting experiment of the pin detailed connection. Further, in experiment of tension-only braced frames, it was confirmed that beam-column assemblies which had pin detailed connections at the beam ends hardly resisted in lateral force. On the other hand, in the case of a beam with concrete slab, it is expected that stiffness and strength of the connections increase by restricting a rotation of the pin detailed connections and lateral force of beam-column assembly become larger. However, it is unclear that how much is the influence of the concrete slab on structural behavior of the connection.
In this study, cyclic loading tests of pin detailed connections which has concrete slab were carried out in order to investigate the effect of concrete slab on structural behavior at the connections. In addition, full-scale frame tests were conducted to clarify the influences of concrete slab on structural behavior of braced frame in which beams were subjected to compressive force.
In the connection tests, specimens are cantilever beams in length of about 0.8m which are consisted of steel beam and gusset plate. Test parameters are presence or absence of concrete slab and bolt spacing of the connection. As a result, the pin detailed connections with concrete slab exerted a greater rotational stiffness and strength under positive bending. On the other hand, the same behavior as the connection without concrete slab was shown under negative bending. For the rotational stiffness under positive bending, evaluation model is represented by using local spring stiffness around bolt holes and elastic stiffness of concrete slab, and it was confirmed that the model can evaluate the experimental values. For flexural strength under positive bending, evaluation models of yield strength and ultimate strength based on strain distributions are shown, it was found that they can evaluate the test results. Finally, envelope curve model for connection behavior under positive bending is proposed, and it was shown that its model enable to evaluate the test results.
On the other hands, in the frame tests, specimens are 2 story-1 bay full-scale braced frame which have pin detailed connections at beam-ends. Test parameter is presence or absence of concrete slab on beams. Test results show that horizontal stiffness and strength of specimen with concrete slab was greatly larger to be compared that of a specimen without concrete slab. It indicates that bending moments at beam-end connections increase due to compressive resistances of the concrete slabs, and lateral strength of the beam-column subassemblies increases. Additionally, in the frame test, the maximum strength of connections with concrete slab was about 1.8 times larger than that in connection tests. This is because the concrete slab in braced frame is subjected to compressive force from braces and its force is eccentric to steel beam. At last, using the envelope curve model obtained from connection tests, push-over analysis of a braced frame with concrete slab was conducted. The result represented that the analysis model can evaluate the envelope curve obtained from test result if additional moment due to presence of concrete slab is considered.
The sway buckling mode occurs when a steel frame with unrestricted relative story displacement is subjected to vertical loads. The sway buckling mode involves a large relative story displacement, and all beams are deformed into an s-shape. In this study, a formula to calculate the elastic buckling load of a column is proposed when sway buckling occurs in a non-uniform frame. The proposed formula can calculate not only the elastic buckling load of columns in an unbraced frame with the sway buckling mode, but also that in a braced frame.
The proposed formula is derived using the principle of virtual work. An important assumption in deriving the proposed formula is that the infinitesimal virtual work increment of the internal force in the sway buckling mode under vertical loads is equal to that in the deformation under a horizontal load. The proposed formula is shown in Equation (19): The following two interesting conclusions are obtained from this formula: The sum of the column axial forces in the story when sway buckling occurs is approximately constant regardless of the column axial force distribution, and it is approximately proportional to the horizontal stiffness of the frame.
The accuracy of the calculation result of the proposed formula was verified using one-story four-bay unbraced and braced frames. It was shown that the calculation result of the buckling load of columns by the proposed formula had an error of 1.7% compared with the result of the buckling eigenvalue analysis for one-story four-bay unbraced frames. In the verification using one-story four-bay frames with braces, the relationship between the growth ratio of the horizontal stiffness of the frame due to the braces and the buckling mode of the frame and the buckling axial force of a column was determined. Consequently, by combining the proposed formula with the method for calculating the elastic buckling axial force of a column in the non-sway buckling mode, the elastic buckling axial force, which agrees well with the buckling eigenvalue analysis result was obtained. Here, the non-sway buckling mode is a buckling mode in which a relative story displacement barely occurs.
Sakamoto and Wakabayashi's methods are known as methods for calculating the elastic buckling load in the sway buckling mode. However, Sakamoto's method cannot be applied to frames with braces. Furthermore, it is shown that Wakabayashi's method has a larger error compared with the proposed formula. Meanwhile, the formula proposed in this study is applicable to not only one-story unbraced frames, but also to one-story braced frames. The elastic buckling load of the sway buckling mode can be calculated, which has fewer errors compared with the buckling eigenvalue results. The proposed formula may be applied to any multi-story multi-bay frame or any frame with multi-story halls. In future studies, the method will be further developed.
Most of school gymnasiums which are composed of braced steel frame are expected to play a role as a disaster prevention base and public shelter in severe earthquakes. Therefore, it is necessary to establish seismic repairs that can be used continuously after earthquakes, although a damage reduction is also important. In the previous study, the damage evaluation based on the residual out-of-plane deformation has been established by an experimental study. This paper focuses on the seismic repair by retightening turnbuckle brace, and examined (1) performance recovery, (2) internal forces, and (3) workability.
Firstly, performance recovery by retightening turnbuckle brace was investigated by a cyclic loading experiment. In this experimental program, after "damage loading" to damage to the braces, seismic repairs were performed. After that, "repair loading" was conducted to confirm the performance recovery. It was found that the turnbuckle can be retightened even if the maximum story drift ratio (R_{max}) reached to 4.0%. In addition, from the comparison of hysteresis curves, it became clear that the performance of brace was recovered by retightening the turnbuckle. However, even though multiple seismic repairs restored the maximum strength and yield strength, the elastic stiffness was reduced.
Secondly, the out-of-plane bending moment as the internal force was discussed. It was indicated by the experiment that the out-of-plane bending moment in tension depends on the eccentric distance. The distance can be obtained by the structural model proposed in this paper. Moreover, the out-of-plane bending moment in tension is restrained by making the thickness of the gusset plate and the diameter of brace equal in size. On the other hand, in compression, the out-of-plane bending moment needs to be considered in the case of a brace with a large diameter.
Lastly, the torque in retightening the damaged turnbuckle was investigated from the viewpoint of workability. It became clear that repairing out-of-plane deformation is easier than introducing axial force. Considering retightening the damaged turnbuckle with a 1m rod, the nominal diameter is M24 or smaller when the damaged brace is repaired and M20 or smaller when an axial force is introduced. In addition, after the multiple repairs, the torque coefficient is almost constant that the screw part of the turnbuckle was not damaged and the workability was not affected even after multiple retightening.
A square hollow section member is generally used as a column in steel structures. Local buckling is known to affect the large deformation behavior. Local buckling is more likely to occur when the width-thickness ratio of the plate elements is large. Therefore, an octagonal cross sectional member that can reduce the width-thickness ratio of the plate elements and reduce the material is expected to be column.
Although there have been many previous studies on octagonal cross sectional members, none have examined the inelastic behavior of octagonal cross sectional members subjected to shear bending. In this study, the plastic deformation capacity of an octagonal cross sectional member subjected to shear bending is clarified based on the actual behavior of the member, and an evaluation method is proposed.
In this study, the buckling coefficient of an octagonal cross sectional member under compression or bending is calculated by eigenvalue analysis using the finite element method, and a buckling coefficient evaluation formula for octagonal cross sectional members under compression or bending is proposed.
In addition, the plastic deformation capacity of the octagonal cross sectional members was confirmed by the large deformation analysis of the cantilevered column form under axial and bending shear forces for the octagonal cross sectional members. In the comparison, the effect of the length of both members on the large deformation behavior was studied, and the plastic deformation capacity was investigated using a square hollow section member with the same thickness-width ratio of the plates. Next, in order to investigate the effect of the maximum value of initial imperfections on the plastic deformation capacity, a large deformation analysis is performed using the maximum value of initial imperfections as a parameter.
In order to understand the actual behavior of the octagonal cross section members, the plastic deformation capacity of the octagonal cross section members was confirmed by cantilevered bending shear tests and compared with the plastic deformation capacity of the square cross section members with equal width and length.
The buckling coefficient evaluation formula for octagonal cross section members obtained in this study is applied to the new width-thickness ratio for square cross-section members proposed in Reference 2), and the plastic deformation capacity evaluation formula using the new width-thickness ratio for square cross section members proposed in this study is examined whether it is possible to evaluate the plastic deformation performance of octagonal cross section members obtained by large deformation analysis and loading tests. The effect of the initial imperfection on the plastic deformation capacity of the square and octagonal cross section members is taken into account.
The authors have designed and developed steel-concrete (SC) columns without reinforcement bars. The SC columns are composed of only cruciform steel and concrete, and they had an octagonal cross-section. In a previous work, an experiment was conducted on SC columns (section dimension: 190 mm × 190 mm) under cyclic and horizontal loads to investigate their earthquake-resistant performance. The experiment could not consider the scale effect of the concrete, which makes it difficult to evaluate the compressive strength of the concrete. In this study, four large-scale SC specimens were tested to investigate the scale effect of the concrete. The large-scale SC specimens were of dimensions 500 mm × 500 mm, and the shear span ratio of the SC columns was three. The experimental variables considered include the size of the cruciform steel, compressive strength of the concrete, and axial-load ratio. The small-scale specimens were tested with both ends fixed, whereas, the cantilever type was adopted for the large-scale specimens. The loading device was designed to subject the columns to an axial load N and horizontal load Q. The tests were conducted using a universal testing machine. For all the tests, the specimens were subjected to a constant axial load while the horizontal load was applied. The displacement amplitudes were increased uniformly and repeated two times at each amplitude peak.
All specimens under an axial-load ratio n = 0.3 exhibited a very ductile behavior until the end of the test. Contrarily, under a high axial-load ratio of above 0.5, an abrupt degradation in the flexural strength was observed at a rotation angle R = 2.0%. The experimental maximum strength of the large-scale specimens exceeded the plastic-collapse mechanism line obtained by assuming a plastic hinge being formed at the fixed end of the column. The superposed strength was calculated from the yield strength of the steel and the compressive strength of the concrete. For the small- and large-scale specimens, no significant difference was observed in the axial strain and failure mode. The comparisons of the experimental results of the small- and large-scale specimens suggest that the scale effect of the concrete has little effect on the structural performance of SC.
The flexural strength calculated based on the superposed strength or linear distribution of strain was assumed to be the estimated short-term allowable flexural strength of the SC columns. The flexural strength calculated based on the superposed strength was in good agreement with the flexural strength at the yield point of the steel flange in the tests. The rotation angle R at short-term allowable flexural strength was approximately 0.5%.
An analysis on the elastic–plastic behavior of the SC columns was also conducted using the method that takes into account the concrete confined by the cruciform steel. The effect of the concrete confined by the cruciform steel was obtained from the axial compressive-test results of the small-scale specimens. Although the analytical results were somewhat underestimated compared with the experimental results, they pursued well with the experimental results up to a large deformation.