Production of high-quality concrete and re-use of industrial by-products from the viewpoint of environmental conservation are social concern of Japan. Non-iron slag fine aggregates produced as a by-product treated in this study are ferro-nickel slag fine aggregate and copper slag fine aggregate.
 Currently, these non-iron slag fine aggregates are not actively utilized. However, recent research indicated that shrinkage reduction effect could be obtained by replacing natural aggregate with ferro-nickel slag fine aggregate and copper slag fine aggregate. This means the possibility to use it more effectively.
 In this research, authors aimed to clarify the strength characteristics and shrinkage reduction effect of concrete using non-iron slag fine aggregate. Strength test and drying shrinkage test were conducted. The effect of non-iron slag fine aggregate on the concrete on strength properties and shrinkage reduction effect was investigated. As a result, the compressive strength of concrete using non-iron slag fine aggregate was higher than that with natural aggregate. It was also shown that the shrinkage of concrete using nonferrous slag fine aggregate was lower than that using natural aggregate.
 Also, in this study, it was found that a reaction product was formed between the aggregate and the matrix paste. The compressive strength of concrete increased with increasing of volume content of reaction product. The shrinkage strain of concrete decreased with increasing of volume content of reaction product.
 There was no correlation between water absorption rate of non-iron slag fine aggregate and the dry shrinkage strain of concrete. Correlation was found between air-dried moisture content and specific surface area of non-iron slag fine aggregate. In addition, it was suggested that the shrinkage reduction effect of nonferrous slag fine aggregate are related to both of the specific surface area and the reaction layer volume formed at the interface between the nonferrous slag aggregate and the matrix paste. As a result, the shrinkage reduction effect of nonferrous slag fine aggregate could be evaluated by considering both the specific surface area and the reaction layer thickness. The drying shrinkage strain decreases with decrease of the specific surface area of the fine aggregate and the increase with the reaction layer thickness increases. Thus, the specific surface area of the aggregate and reaction product formed between the aggregate and the matrix paste contributed to reduce the shrinkage strain of the concrete. However, further consideration would be necessary for their quantitative contribution ratios.
 In addition, the authors proposed an equation for evaluating the effect of the aggregate on the shrinkage strain using compressive strength, mixing ratio and specific surface area at the mixing ratio of nonferrous slag fine aggregate. Prediction formula for compressive strength of concrete using ferro-nickel slag (HS) fine aggregate was described in equation (4) in chapter 4. The drying shrinkage strain of concrete using ferro-nickel slag (HS) fine aggregate was described in the equations (5), (6) and (7) in Chapter 5.

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 Background and Purpose
 Nowadays, the short-term heavy rains have been frequently occurring and an increase in number of flood disasters is unfortunately expected. The application of Porous concrete (POC) for pavements is thought to be an effective countermeasure against floods. However, at present the flow dynamics of water in POC is not well-understood for estimating and controlling the flow rate of rain. In POC application for road surfaces, it is important to understand the flow dynamics for permeability performance quantification and for prediction of the rainwater flow in residential areas.
 In this research, firstly the authors grasp hydraulic property of POC and construct a permeability model of POC in order to investigate the applicability of POC for pavements. Further, we research outflow delay effect of rainwater.
 The construction of non-linear permeability model
 Japan Concrete Institute suggests the constant level permeability test method for POC in saturated state to determine a permeability coefficient. In this method, the permeability coefficient is calculated from Darcy's law (see Eq. (1)). However, the relationship between the average flow velocity v and hydraulic gradient i is considered non-linear and was successfully estimated according to the Eq. (2).
 v = k_T·i (1)
 v = k'·i ^m (2)
 For example, when i is set in three levels, we get three different permeability indexes, k_T. On the other hand, only one value of k' is determined from Eq. (2). In this report, we supposed that the power index m is equal to 0.5 considering turbulent water flow, getting Eq. (3).
 v = k'_{(m = 0.5)}·i ^0.5 (3)
 Eq. (4) was obtained as an approximation of index k'_{(m = 0.5)} from a series of test data, as a function of void ratio V_R and averaged size of aggregate φa. Here, as mentioned in previous report, the void ratio of POC under which POC becoming non-permeable, was found to be around 13%. Therefore, the intercept of x-axis was set to 13%.
 k'_{(m = 0.5)} = a·V_R−b (4)
 a = 0.0083φa+0.042
 b = 0.11φa+0.54
 Eq. (4) was generally applicable for the horizontal dynamic flow with infiltration surface and also result of the constant level vertical permeability test including the low hydraulic gradient.
 Drainage simulation of heavy rains in residential areas paved with POC
 The non-linear permeability formulas proposed for POC (Eq. (3) and Eq. (4)) were applied to the drainage simulation of heavy rain in a residential area. The reduction in amount at peak flow of water and the outflow delay effect due to the application of POC pavement was confirmed from the simulation result.

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 Long-duration earthquake with long-period characteristics and with strong ground shaking were observed in the 2003 Tokachi-Oki Earthquake and 2011 Tohoku Earthquake. Previous research mentioned that isolated buildings could be subjected to earthquakes whose periodic characteristics were close to the natural period of the isolated structure. The strength of lead rubber bearings (LRBs) can be reduced by “lead plug heating” caused by their absorption of seismic energy. So, it is important to characterize various dependencies of the yielding force of the LRBs to design isolated buildings that can cope with such earthquakes. The purpose of this study is to clarify this issue about the degradation of yielding force of LRB in the event of an earthquake and to propose a method to evaluate the yielding force of LRBs under cyclic loading experiments.
 We consider that the factors influencing the yielding force of LRBs are the intercept force of the rubber bearing (RB), rate of deformation of the LRB, and the temperature of the lead plug. In this paper, the yielding force of the LRB is defined as the sum of the intercept force of the RB and the yielding force of the lead plug (Fig. 1, Eq. (1)). First, the dependency tests for shear strain, shear strain rate, and environmental temperature, were carried out on the RB specimens (Tables 2, 3). From the RB tests, the evaluation formula for the intercept stress of RBs was described as Eq. (5) with high accuracy (Figs. 6, 8, 9). Then, as with the RB tests, the tests of various dependencies on the LRB specimens were carried out. The yielding force of the lead plug was calculated from the results of RB and LRB tests under the same conditions used in Eq. (1). From the above tests, it becomes clear that there is a close correlation between the yield stress of the lead plug and the temperature when considered per shear strain rate classification. The evaluation formula for the yielding stress of the lead plug was described with high accuracy as Eq. (6) in the range −25°C~300°C (Fig. 17).
 The proposed formulae (Eqs. (1), (5), and (6)) have less reduction in yielding stress for the temperature rise than previous research (Fig. 20). Previous evaluation equations about the relationship between the yielding stress of LRB and the temperature were described with an extrapolated high temperature range that lacked experimental data. Thus, the equation derived from previous research may be inaccurate if the temperature of the lead plug rises above any temperature previously confirmed by experiment.
 Dynamic loading tests were conducted for LRBs of various sizes from reduced to real in order to confirm the validity of the proposed formula. The experimental results were then compared with the data obtained from heat-mechanics interaction analysis that contain the proposed formula. Two kinds of analysis methods are used to consider the heat diffusion, namely the Constant Flux Solution (CFS) and the Finite Difference Method (FDM) (Fig. 21).
 From the examination above, it was confirmed that the proposed formula, which was applied to the heat-mechanics interaction analysis, could accurately predict the mechanical behavior and change of temperature of LRB under cyclic loading (Figs. 23~25).

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 We estimate static displacement and long-period pulse from strong motion records in the near fault region of the Mw7.0 2016 Kumamoto earthquake and compare them with previous prediction equations. In addition, we examine the relation between the observed data and the other parameters unused for the previous equations to aim for the improvement or development of prediction equations in the feature.
 We derive velocity and displacement time history from acceleration time history of K-NET, KiK-net, JMA-95 type and local government strong motion records. Then we estimated the static displacement D_p, the period of long-period (>2 s) velocity pulse T_p and the PGV for the maximum D_p direction (Fling-P).
 Tp of Fling-P component at Nishihara village with the distance is near 0 km is 2.6 s and the average of T_p at eight stations with the distance less than 15 km is 3.1 s. The average of T_p at 16 stations with the distance less than 30 km is 4.0 s. One cosine-shape pulse at the S wave potion is observed in the extremely near fault region. On the other hand the fling step is started between P wave and S wave portions at stations with the distance longer than 15 km and so the T_p becomes longer. T_p predicted from equations by Kamai et al. (2014) and Burks and Baker (2016) are 5.5 s and 3.5 s, respectively. These two equations were developed using data with the distance less than 30 km or more and modeled by only Mw. Kamai et al. used synthetic data for scenario earthquakes. Burks and Baker used both synthetic data and strong motion records. However no records of crustal earthquakes in Japan were used. T_p equations could be improved by using the distance as one of predictors and T_p obtained from the Kumamoto earthquake as data. T_p of vertical component is almost the same to T_p of Fling-P component.
 PGV of Fling-P and vertical components agree with previous equations on the average. However PGV of Fling-P component at Nishihara village is 277 cm/s, which is larger than the average plus the standard deviation of the equation by Si and Midorikawa (1999). The PGV ratios of Fling-P component to the orthogonal component are 2 or 2.5 times at three stations with the distance less than 1 km and become smaller to unity as the distance is longer. PGV of vertical component at Nishihara village is 152 cm/s. This is larger than the average plus the standard deviation of the equation by Satoh (2008).
 D_p of Fling-P component observed at Nishihara village is 154 cm. Predicted D_p by four previous equations in which the average slip is predicted using Mw are 80 to 90 cm at the distance of 0 km. On the other hand the predicted D_p in which the average slip is predicted using the fault area and Mw is consistent to D_p observed in the distance from 0 to 30 km. The D_p predicted by the best equation are 141 cm at a distance of 0 km and 56 cm at a distance of 10 km in the hanging-wall side. When the ratio of the distance along the strike direction from the fault edge is smaller, the observed D_p becomes smaller. This feature is consistent to a previous rupture shape model developed for slip distribution from point measurements of rupture displacement of many faults. This parameter would be a good predictor to improve the D_p equation. D_p of vertical component at Nishihara village is 179 cm. However, there were no equations of D_p and T_p for vertical component considering normal-slip.

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 1. Introduction
 A large number of steel roof bearings in RC gymnasia were damaged at the 2011 Tohoku Earthquake and 2016 Kumamoto Earthquake, mainly due to the out-of-plane response of cantilevered RC walls. In this paper, a PTFE sliding bearing, a friction damper bearing and a rubber sheet bearing with thick leveling mortar are fabricated and dynamic loading tests are carried out. Using the experimental results, the response of the RC walls under not only longitudinal input ground motions, but also transverse direction is confirmed by numerical simulations.
 2. Specimens and experimental methods
 A PTFE sliding bearing, a friction damper bearing and a rubber sheet bearing are fabricated with 0.8 times scale. Mortar thickness of PTFE sliding bearing and friction damper bearing is 60 mm, more than three times of anchor bolt diameter, and rubber sheet thickness is also 60 mm. Vertical load evaluating roof weight is set on the top of the specimens by H-section jigs and PC bars. First, dynamic loading tests are carried out by applying sine waves with various amplitudes and frequencies, followed by ultimate loading tests.
 3. Results of dynamic loading tests and ultimate loading tests
 From dynamic loading tests, PTFE sliding bearing slipped at 13 kN. Friction damper bearing showed two-stage sliding yield strength due to the rotation of base plate. Rubber sheet bearing showed stable hysteresis curve by sliding and shear deformation under 70 kN vertical load. When sliding yield strength of friction damper bearing exceeded the ultimate strength of RC parts during dynamic loading tests, RC parts cracked. From ultimate loading tests, RC parts of all bearings cracked at the horizontal force less than the ultimate strength defined in AIJ recommendation. After fracture of RC part, strength of bearings increased again by tensile action of anchor bolts.
 4. Verification of response reduction effects of bearings
 Hysteresis curves of PTFE sliding bearing and friction damper bearing are modeled by bi-linear model and that of rubber sheet bearing are modeled by powered expression and Masing rule. Effective response reduction effects of friction damper and rubber sheet bearing were verified by numerical simulations of steel roof bearings supported by RC substructures.
 5. Conclusions
 1) Sliding yield strength of PTFE sliding bearing was about 13 kN and that of friction damper bearing is about 80 kN in the 0.8 times scale models, and hysteresis curves of them showed rigid-plastic relationships even though mortar thickness is 60 mm. In addition, sliding yield strength 80 kN included the strength rise by 33 % by rotation of base plate.
 2) Rubber sheet bearing showed stable hysteresis curve under 70 kN vertical load under high axial pressure, however, slippage limited the maximum shear force especially under low axial pressure.
 3) When relative displacement exceeds the limit of loose hole or sliding yield strength of friction damper bearing exceeds the ultimate strength of RC parts, RC anchorage of all bearings cracked at the horizontal force less than the ultimate strength defined in AIJ recommendation.
 4) Effective response reduction effects of friction damper bearing and rubber sheet bearing are verified by numerical simulations.

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 In November and December 2015, NIED tested a ten-story reinforced concrete building frame on the E-Defense, three-dimensional shaking table, in order to verify a foundation system of the building that would ensure continued use of the building even after an extreme major earthquake motion. The shaking table tests were conducted under 1995 Kobe earthquake motion to obtain the test data from the building specimen equipped with a simple base sliding mechanism using cast iron plates on concrete faces.
 The dimensions of the specimen were 15.7 meter in the longitudinal direction and 9.7 meter in the transverse direction on the 1st floor, and 13.5 meter in the longitudinal direction and 9.5 meter in the transverse direction on standard floors.
 The longitudinal direction had three spans at 4.0 meter each, whereas the transverse direction had three spans with 3.1, 1.8, and 3.1 meter long. The floor heights were 2.80 meter for the 1st floor, 2.60 meter for the 2nd to 4th floors, 2.55 meter for the 5th to 7th floors, and 2.50 meter for the 8th to 10th floors. The specimen height was 27.45 meter from the shaking table floor surface, with an aspect ratio of about 3.4. The longitudinal direction was a simple moment-resisting frame structure composed of beams and columns, whereas the transverse direction was a frame structure with a wall-frame structure with a multi-story shear wall at the middle span from the 1st to 7th story. The floor slab was 120 millimeter thick. A special foundation detail was used with plates made of cast iron were placed at the bottom of the specimen's footing beam on 16 column locations, so that reduce the responses of the upper floors would be reduced during a major earthquake. Therefore, clearances of more than 450 millimeter were provided around the footing beam and stiff rubber cushion were installed for cushioning in order to prevent impact loading.
 In the test, the base was observed sliding while base uplift occurred, which might have promoted the base sliding and caused rotational movement with eccentric distributions of friction resistances. The maximum story drift angle generated in the specimen under 100% amplitude of the JMA-Kobe excitation was 0.0060 rad, and after that crack width were less than 0.05 millimeter on almost all members. The maximum slip dislocation were 84 millimeter, 189 millimeter and 149 millimeter at the center of specimen under 25%, 50% and 100% amplitudes of the input intensity to the original record, respectively. Friction coefficient was estimated as 0.10 - 0.23. The measured base uplifting displacements were 5 millimeter, 14 millimeter, 29 millimeter and 40 millimeter at the corner of specimen under 10%. 25%, 50% and 100% intensity, respectively.
 According to the response analysis, that was executed in order to verify the cause of base rotational dislocation, base rotational angle was enhanced by axial force fluctuation of each bearing. Based on Equivalent Linear Response Spectrum method, spectral displacement of base slip test was reduced to 0.22 times in frame direction and 0.24 times in wall direction compared to the fixed bases test.

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 In the joints of seismic retrofitting structures, post-installed anchors are generally used. The concrete surfaces at the joints are roughened through a chipping process using a vibration drill in order to achieve the shear force stipulated in the Japanese guidelines for the seismic retrofitting of structures. However, there are no unified rules for concrete roughening in terms of shear force or the shape of the roughened surface. On the other hand, some previous studies focused on shear stress transfer mechanisms of cracked concrete surfaces. According to these research, we can estimate the shear stresses and normal stresses interacting on the entire cracked surfaces by integrating the contact stress over the area of the entire interface. Therefore, we conducted shear loading tests, and measurements of the roughened surface were taken. We then constructed a mechanical model based on the constitutive law that describes the shear stress transfer mechanisms of cracked concrete surface.
 Eight test specimens were prepared. We roughened the concrete surfaces of the eight specimens. For the test specimens, the existing member was modelled by a rectangular block with dimensions 580 mm × 400 mm × 200 mm. After roughening an area of 375 mm × 200 mm centered on the concrete surface, grouting mortar of dimensions 375 mm × 200 mm × 200 mm was cast on the surface.
 The test parameters considered here were the roughed concrete depth as well as the ratios between the roughened area and the surface area (0.10, 0.20, 0.30, 0.50, and 0.75). We took measurements of the roughened surface using laser displacement sensors. The measurement intervals were set to 0.04 mm in the x-direction and 0.5 mm in the y-direction. For the shear loading tests, we controlled the shear displacement and applied repeated cyclic loading. The constant normal stress was set to a constant value of 0.48 N/mm².
 We constructed a mechanical model of the roughened concrete surface using the Bujadaham model (Bujadaham 1991). This model takes into account the stress transfer mechanisms of the cracked surface. The angle density function Ω(θ) in the Bujadaham model was set as Ω(θ) = 0.5cosθ However, it was not known whether or not we could use this defined angle density function for the roughened concrete surface. Therefore, we evaluated Ω(θ) using the three-dimensional data obtained from the shape measurements of the roughened surface. Additionally, we proposed Ω(θ) using the shape measurement results. The test and calculation results were in agreement. However, the contact stress in the Bujadaham model adopted an elasto-plastic model, we newly constructed the model between contact stress and contact displacement for the roughened concrete surface. In the proposed contact stress model, the stress softening behavior in the roughened concrete was considered.
 We constructed a mechanical model representing the roughened concrete surface and compared the experimental and analytical values. By using a constitutive equation that expresses the shear transfer mechanism of a cracked surface, and that takes into account the contact stress and friction on the local surface, the shear and vertical stresses of specimens with a roughened concrete area ratio of up to 0.3 can be evaluated. However, for specimens with a roughened concrete area ratio of 0.5 or 0.75, the shear and vertical stresses are underestimated. Thus, we were not able to express the specimens of shear failure modes using the proposed model. This problem will be a focus of future research.

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 The brace joint fracture was observed in several severe earthquakes which occurred in the past. That's because fracture prevention of a brace joint wasn't considered by old seismic design code. The important problem to promote seismic retrofit works of a brace joint in the future is compact and fire-less seismic retrofit method which doesn't use a welding and gas-cutting. In this paper, fire-less seismic retrofit method which consists of prestressing steel bar, concrete and cover plate was proposed targeted for the existing H-shaped steel brace joint designed by old seismic design code. This seismic retrofit method aims at fracture prevention of an existence joint by an added load transmission route by reinforcement part. A series of loading test and a series of FEM analysis were carried out to consider strength improvement effect of this method and validity of the strength evaluation and each part design method. As a result, the following knowledge was obtained. The slipping strength of the existence brace and the concrete surface which were a dominant factor of the reinforcement part strength was proportional to the compression force introduced into prestressing steels bars. The reinforced joint strength exceeded the existing joint maximum strength, and the effect of the strength improvement was confirmed. The reinforcement part strength was evaluated as the slipping strength at the concrete surface, and the reinforced joint strength was evaluated as the simple sum of the existence joint maximum strength and the reinforcement part slipping strength.

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 1. Introduction
 The structural requirement of truss towers is generally determined by the wind load. However, large seismic ground motions were observed in several great earthquakes, which results that the truss towers shall be designed to resist the larger ground motions than the previous Japanese building code. This study presents the effect of the member fracture and strength deterioration of structural members on the ultimate seismic performance of a truss tower is examined. Components loading test of circular hollow sections and collapse analysis provide that the member fracture and strength deterioration are critical to determine the ultimate seismic performance when the extremely large ground motions.
 2. Cyclic loading test on CHS specimens with a large diameter-to-thickness ratio
 The buckling behavior and the cumulative deformation capacity of CHS members in truss towers are investigated by cyclic loading tests. The diameter-to-thickness ratio of the specimens is fixed to 63.5, and the slenderness ratio is 40 and 85. As a result, the position of local buckling is not necessarily observed at the center of CHS member, and the deformation shape of the section at local buckling zone is similar to the cylindrical shell buckling rather than flexural buckling.
 3. Revision of a phenomenological buckling hysteresis rule
 Several revisions of the analytical model "Shibata-Wakabayashi model" to simulate phenomenological buckling hysteresis are discussed. The strength deterioration due to the plastic hinge at local buckling region is additionally examined in this section taking the effect of the diameter-to-thickness ratio into account. The revised Shibata-Wakabayashi model captured the experimental test more precisely than the previous models.
 4. Development of fracture evaluation method of CHS members
 The strain concentration method proposed by the authors is revised based on the position and deformation of local buckling obtained by the test of CHS specimens. Accuracy of the strain concentration method to measure the plastic strain at local buckling zone is improved by the revised evaluation model.
 5. Collapse analysis on the truss tower
 The ultimate seismic response of the truss towers with smoke stacks using the IDA analysis. When the revised analytical model of the buckling hysteresis rule is used in the time history analysis, the damage of the truss tower is more significant than that using the previous model. When the scale factor of the input ground motion is 4.0 ~ 5.0, the truss tower collapses due to the strength deterioration of the smoke stack.
 6. Conclusions
 This research investigated the damage evaluation of truss tower structure taking member fracture and strength deterioration into account. The results are summarized as follows.
 1) For the CHS with 63.5 diameter-to-thickness ratio and 40 or 85 slenderness ratio, fracture is initiated from the local buckling zone of the CHS even when the strength of the connection is smaller than the requirement of the Japanese building code.
 2) When the revised analytical model of the buckling hysteresis rule is used in the time history analysis, the damage of the truss tower is more significant than that using the previous model.
 3) When the scale factor of the input ground motion is 4.0 ~ 5.0, the truss tower collapses due to the strength deterioration of the smoke stack. (524 words / max. 600 words)

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 A steel-framed house is constructed using walls and floors made of plywood board panels and light-gauge cold-formed steel frames fastened with drill screws. The seismic performance of steel-framed houses prlmarily depends on the force-deformation relation of shear walls. Most conventional plywood shear walls show poor ductility because they tend to suddenly lose strength owing to the breaking of screws or punching out of the board when the deflection angle becomes around 1/30[rad]. Therefore, the energy absorbing ability of these walls is very low because of their pinching property in load-deflection relationships. The objective of this research is to improve the structural performance of shear walls in steel-framed houses by employing built-in friction dampers.
 First, basic performance tests were conducted on a friction damper. The friction force was found to be sufficiently stable when the lubricated coating steel sheets were tightened with high-strength bolts. Furthermore, the insertion of disk springs and square washers on the bolt shank was found to be effective in reducing the fluctuation and decrease of the bolt tension during the friction damper sliding. Since the friction force of the damper has a linear relationship with the bolt tension, it can be arbitrarily adjusted by changing the bolt tension.
 Next, a tension control method for the bolts used in the damper was studied. A method to control the bolt tension by adjusting the diameter of the pintail fracture groove of the torque-shear-type high-strength bolt was proposed. This method enables the accurate and reliable provision of an arbitrary bolt tension to the friction damper.
 Furthermore, static loading tests were conducted on full-scale built-in friction shear walls with varying bolt tension. It was found that the walls have a high and stable energy absorption capability as compared with general plywood shear walls. It is also possible to design With reduced wall quantity while suppressing stress by employing dominant design characteristic values.
 Finally, a numerical analysis model of the built-in friction shear wall was constructed using the loading test results. By using this analysis model, it is possible to analyze the restoring force characteristics corresponding to the change in the bolt tension of the walls.

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This paper propose an improved evaluation to calculate local buckling, global buckling and coupled buckling strength of trapezoidal corrugated steel web under shear loads. First, the local buckling and the global buckling are studied respectively, then the interaction among local buckling, global buckling and coupled buckling strength is demonstrated. The local buckling strength is defined as an upper limit, and this upper limit is amended down by expecting a decreasing rate to calculate the coupled buckling strength. The proposed work gives good agreements with numerical analysis results, which can be applied to a wide geometric range.

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 The formula of ultimate shear strength of headed stud is shown in the design recomendations in Japan. However, the shear strength based on the design formula is not corresponded to the ultimate shear strength obtained by the push-out tests if both the specified design strength of concrete and the Young's modulus are large. In previous studies, some calculation method of ultimate shear strength of headed stud have been considered, but these methods are completely changed from the design formula. Considering structural design, the formula of ultimate shear strength should be simple and easy to use.
 This study proposed the new method of the ultimate shear strength of headed stud by multiplying simply modified coefficient to the design formula. In the first step, the database of ultimate shear strength and some elements affected the strength are organized. In the database, basic correlations of main elements are considered. The elements of _sca, E_c, and F_c which are already used in design formula have large variabilities, but the average values of them are able to use the representative value. The ratio length to diameter (L/d) and the tension strength of headed stud (F_u) also have large variabilities. As the tensile strength of stud material determined by standard is used as F_u when buildings are designed, and the real value of F_u is seldom obtained. Moreover, large shear displacement of composite structures as much as the headed stud occurring the tensile strength is not considered in design. Therefore, in this study, F_u is treated as one of element, not required element.
 Based on the above confirmation of each correlation, a series of the multiple regression analysis for some elements in database are conducted. Using the combination of the elements in the case which the adjusted R-Square value is best, the modified coefficient is created separately both in case of flat slab and deck slab. In flat slab, the modified coefficient include _sca, E_c, F_c, L/d, and F_u. In order to simplify, and correspond to the ultimate shear strength obtained in test, E_c, F_c, and F_u are changed to real number using by the average values. The correlation coefficient between modified formula and the ultimate shear strength obtained in test increased.
 In deck slab, the modified coefficient include E_c, F_c, L/d, n_d, b_d, and H_d. However, using the average value of E_c, n_d, and H_d are poor correlation to the ultimate shear strength obtained in test. Therefore, the part of calculation of E_c, n_d, and H_d is represented by E_c. The correlation coefficient between these modified formula and the ultimate shear strength obtained in test also increased.
 The proposed formulas in this study do not depended on the diameter of headed stud, the construction direction of deck, pitch or gage of headed studs, however, they are enough effective to calculate the ultimate shear strength close to the ultimate shear strength obtained by the push-out tests. The calculation is simple because all needs are that the calculation of the modified coefficient. Therefore, the formulas are also useful because of rising the accuracy of the structural design of headed stud.

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