In the previous paper (Part 1) of this study, the weldability of high-strength reinforcing bars was evaluated from the viewpoint of the occurrence of weld cracks, and the effect of changes in the chemical compositions on weld cracks was experimentally investigated. As a result, it was found that when each index of chemical compositions such as carbon content (C), carbon equivalent (Ceq(1), Ceq(2)) and weld crack susceptibility composition (Pcm) was high, hot cracking (liquation cracking) occurred in the heat-affected zone near the bond.
In this paper (Part 2), we evaluated the weldability of high-strength reinforcing bars from the viewpoint of the occurrence of the fracture in the heat-affected zone, which is one of the important factors related to joint performance (toughness). The effect of changes of the chemical compositions on the fracture in heat-affected zone was investigated.
In the experiment in this report, the tensile tests of welded joint specimens were performed using several types of high-strength reinforcing bars having different chemical compositions to evaluate the occurrence of heat-affected zone fracture of the welded joints. At this time, a comparison was also made with the joints welded in a state of receiving the restraint stress.
Prior to the tensile tests of the welded joint, the hardness of the weld which may affect the fracture in the heat-affected zone was confirmed. In addition, the effect of the presence or absence of restraint stress during welding on the occurrence of weld cracking, which is considered to be one of the causes of the fracture in the heat-affected zone of the joint, was also confirmed.
Welding of the reinforcing bar joints in this experiment was performed so that the joint positions of the reinforcing bars were aligned with the groove of the rebar and the finish weld layer had a gentle shape in order to minimize the effect of stress concentration at welds.
As a result, the following became clear within the range of welding procedure conditions of this experiment.
1) Weld cracks (micro cracks) in the heat-affected zone near the bond can be evaluated by C and Pcm. When C becomes 0.32% or more and Pcm becomes 0.43% or more, they tend to occur.
2) There was no effect on the occurrence of welding cracks due to the presence or absence of the restraint stress of the reinforcing bar during welding.
3) The maximum hardness of the weld can be evaluated in terms of C and Pcm. When C exceeds 0.32% and Pcm exceeds 0.43%, the maximum hardness exceeds 350HV.
4) Heat-affected zone fracture of welded joints tends to occur rapidly when C is about 0.32% or more, Ceq(2) is 0.57% or more, and Pcm is 0.43% or more.
In 2014, in the Kanto-Koshin region many buildings were severely damaged by heavy rainfall after snowfall, a phenomenon called rain-on-snow.
Hence, to estimate rain-on-snow load on the roof, we are proposing a two-dimensional snow cover model. By observing recorded data, we assumed the model consists of three snow layers, the uppermost unsaturated layer does not contain much water, while the middle layer is a capillary force layer containing a large amount of water. The second layer does not cause outflow due to capillary force. The bottom is an outflow layer in which the water moves along the roof. The load was determined as the sum of the weights of three layers.
The thickness of the three layers is determined by the following method. First, several formulas were already existed for calculating the thickness of the capillary force layer, but the obtained values by these formulas are different from the measured values in Nagaoka this time. On the other hand, as indicated by conventional formula, we were able to confirm a tendency of inverse correlation between the thickness and particle size, the thickness of the layer increasing as the particle size decreasing. Here, depending on the particle size, we adopted 0.3 to 1.5 cm thickness of the capillary force layer. Second, the thickness of the outflow layer was obtained from the rainfall intensity, roof span, roof gradient and particle size. Third, the thickness of the unsaturated layer was the one obtained by subtracting the thicknesses of capillary force layer and the outflow layer from the overall thickness. To calculate the total thickness of all layers, we defined the density increment and the modified density increment. Since they showed a positive correlation regardless of snow condition, roof span or roof, we used this correlation to determine the total thickness.
We used two types of density in this model; unsaturated density and saturated density. Unsaturated density showed a strong correlation with the initial density in the experiment so we calculated unsaturated density using initial density in this model. The saturated layer density was approximately 850 kg/m³ regardless of the snow condition, roof span or roof gradient, so we adopted this value.
In estimating the transition of the increase in rain-on-snow load during rainfall, the amount of runoff from the bottom layer affects the estimation accuracy. In this calculation model, we used Darcy's law which is often used in the civil engineering field. In order to use this rule, the value of the permeability was required, which was obtained by the formula proposed by Shimizu.
Comparing the estimated values using this model with the measured values in Nagaoka and Shinjo, they matched with high accuracy even in various environments with different snow conditions and roof shapes. Through our model, we were able to obtain quite a similar result to not just measured values but also to of an actual phenomenon. By assuming the capillary force layer, we succeeded in modeling of the actual phenomenon, where snow on the top end of the roof holds water the phenomenon cannot be described by the formula proposed by Colbeck. It was also confirmed that our model could be performed with high accuracy even when there was granular snow whose properties were significantly different from other snow.
In this study, the nonlinear seismic response analysis model of a human body was developed using shaking table tests. Next, the relationship between human’s displacement of the center of pressure (CoP) and the action difficulty during earthquake was evaluated based on the human model and questionnaire survey for residents of the super high-rise residential buildings. Furthermore, several aspects of human behavior in an RC super high-rise building were investigated based on the results of the seismic response analysis of the building. Finally, a method was proposed to evaluate human injuries in a super high-rise building during an earthquake.
Based on the results, the following conclusions were obtained.
1) We proposed a simple method to evaluate the action difficulty from the maximum displacement of the CoP calculated by the seismic response analysis model of the human body.
2) Based on the results of the analysis employed using the seismic response analysis model of an RC super high-rise building, it was shown that there is a good correlation between the maximum absolute velocity of the floor response of the building and the human response.
3) The study proposed a simple evaluation method to obtain the maximum relative displacement of the CoP with respect to the floor, maximum displacement and velocity of the human head from the maximum absolute velocity of the floor response during an earthquake.
4) A higher floor has a higher maximum absolute velocity of the floor response. Thus, the potential for incurring human injuries increases with greater proximity to the higher floor.
5) Even if the maximum story drift angle of the building does not exceed the design criterion of 1/100, humans can suffer injury, such as from collisions with obstacles or from falling.
Further studies are required to evaluate the variation in human behavior due to individual differences, as well as to examine the validity of the analytical result of the human model when extreme shaking is provided as input to the model.
Elastic behaviors of uniformly twist-formed or pre-twisted bars with a narrow rectangular cross section under axial compression, as shown in Fig. 1, are analytically and experimentally investigated. The analysis is based on the fiber hypothesis invented by Wagner (1936). The experiment is performed employing steel flat bars.
The analytical solutions are derived from the kinematics of inclined straight fibers constituting the twist-formed bar as illustrated in Fig. 2 applying the method of energy principles. The potential energy is represented by Eq.(5), in which the fiber strain energy U1 of Eq.(2) or (3) and the Saint-Venant’s twisting energy U2 of Eq.(4) are incorporated as the internal works. It is noted that the fiber apart further from the center axis undergoes a larger vertical displacement during the twisting motion as quantified by Eq.(1), and consequently a smaller fiber strain during the axial contractive motion of the bar. The principle of minimum potential energy brings the equilibrium Eqs.(6) and (7), and finally the twisting rigidity Kθ defined as Eq.(9) and the axial rigidity Kδ as Eq.(10) are given by Eqs.(11) and (12), respectively. These results indicate that compressive loading generates incremental twisting in the same direction of the pre-twist and that the compressive rigidity is smaller than that of a flat bar in the absence of pre-twist, in other words, the apparent Young’s modulus is smaller than the material’s one as indicated by Eq.(14). These solutions are compared with those of Knowles & Reissner (1960) and Rosen (1983) introduced in Appendix A, and the differences are found small in Appendix B, because the shell’s bending action by Knowles & Reissner and the nonlinear effect by Rosen are slight. Furthermore, the author’s approach clarifies that the axial compressive stresses are parabolically distributed in the cross section such that largest at the mid-width and smallest at the edges as formulated by Eq.(15) or (16), which was undiscovered in the previous studies. The axial stress and shear stress at mid-width in Fig. 3 are quantified by Eqs.(17) and (18), respectively, and then the orientation of the principal stress (the max compressive stress) is given by Eq.(19).
Experiment was carried out to verify the analytical solutions. The specimens were twist-formed from steel flat bars whose compressive stress-strain curves on un-twisted condition are in Fig. 4. Eight specimens were prepared as shown in Table 1 with various pre-twist angles, which were measured as in Fig. 5. Each specimen was setup as shown in Fig. 6, and four displacement meters were installed to measure the incremental twist angle and three-element rosette gauges were pasted on both sides at the mid-height. Experimental results were plotted as follows: load vs. twist angle per unit length in Fig. 7, load vs. axial contraction per unit length in Fig. 8, load vs. axial stress concentration in Fig. 9, load vs. ratio of shear to axial stress in Fig. 10, and load vs. principal axis orientation in Fig. 11. Major elastic properties obtained from the experiment are summarized in Table 1.
The theoretical solutions are compared with the experimental data in Fig. 12 to Fig. 16 for five properties. The agreements are not perfect due to unavoidable imperfections in the specimen and the setup, but basic trends are comparable. Conclusively, the solutions derived from the simple mechanical model will be useful for the design of twist-formed bars in practice.
In some cases, wooden columns have penetration holes in addition to notches for attaching points or nuki (penetrating tie beams). In such a case, it is desirable to consider the effect of this cross-section defect to ensure the safety of the structure. However, in the wooden structure design standard, there is no description of the effect of the through-hole provided in the column.
Therefore, the design method for the compression material with the through-hole and the cross-section defect is not clarified. From this point of view, to grasp the effect of penetration holes and notches on the buckling state of columns, compressive force tests were carried out by setting through-holes and notches in a nearly full-scale column of 86 × 86 × 2780. Linear and nonlinear FEM analyses were conducted to verify the validity, and it was revealed that the analytical results about both the buckling and load-deformation curve accorded with experimental results accurately. Parametric simulations using load column with through-hole or notches were conducted and the validity of the analysis was verified and the obtained results regarding the effect of through-hole and notches on the buckling load of columns were as follows;
1. It is shown that the load-displacement and load-strain curves leading to the buckling of notched or penetrated columns can be predicted by nonlinear buckling analysis.
2. When the through-holes are located at the center of the column without eccentricity, the buckling load is reduced by about 10% at the maximum, even if the number of penetration holes increases. Further, even if the through-hole is arranged eccentrically from the material shaft, even if the compression side of the section having the eccentricity ratio (x/B) remaining is eccentrically located so as not to buckle, the decrease in the buckling load is only about 25% at the buckling load 0.2 or 0.8, and it can be said that the influence of the through-hole on the buckling is not so large.
3. In the case of a column having a notch in the same position on both sides, the buckling load decreases in almost proportion to the ratio x/B of the notch depth to the width of the sound part. It was suggested that the buckling load of notched columns depends on the presence or absence of cracks in the corner of the notches and that the buckling load of notched columns varies.
On behavior of the pile-cap embedding prefabricate pile, many experiments and investigations of failure mode were conducted. However, the design-method of the pile-cap embedding the prefabricate pile and the method of evaluating the maximum bending strength are less well understood. This paper reports that the bending resisting mechanism of the pile-cap in cases where a single prefabricate pile is embedded by a single pile-cap.
Bending resisting mechanisms are two type, lever mechanism of embedded pile and anchor mechanism on head face of pile. Lever mechanism resists the bending moment on the side surface of the prefabricate pile. Mteu0 (the ultimate bending moment from lever mechanism) is derived from the bearing strength of the concrete or the tensile strength of the horizontal re-bar to resist lever mechanism. Anchor mechanism is based on the anchoring re-bar on the head face of the pile and the axial force. MHu0 (the ultimate bending moment from anchor mechanism) is given by the bearing strength of the concrete.
As the results of previous experiments which are SC-pile bending-shear tests with no axial force, no anchoring re-bar and changing ℓ (the embedded length) and the SC-pile bending-shear test with ℓ = 0mm, the authors have determined that the coefficient ßte related to lever mechanism is 1.5 and the coefficient ßH related to anchor mechanism is 1.8.
Mu0 (the ultimate bending moment of under surface of pile-cap) is calculated by the accumulative strength of MHu0 and Mteu0. To confirm those resisting mechanism, we conducted bending-shear tests with SC-pile having thick steel pipe (steel pipe 400φ×19), changing axial force, shear-span ratio, embedded length and re-bar arrangement. As results, we ascertain that the Mu0 accumulative of MHu0 and Mteu0 can evaluate the maximum bending moment of the experimental result safely.
The objective of this study is to examine the conditions for attainment of the full plastic moment. The ultimate strengths of square steel tubular beam-columns are obtained by the analytical work, where the moment gradient ratio and stability index are selected as the parameters. The stress-strain relation is assumed to be elastic-perfectly plastic. From the analytical results, the conditions are proposed which is composed axial load ratio, slenderness ratio and moment gradient ratio.
2. AIJ Recommendations for Limit State Design and for Plastic Design of Steel Structures
Provisions of the Beam-columns prescribed in the AIJ Recommendations for Limit State Design and for Plastic Design of Steel Structures are summarized. Some points to consider are described.
3. Analytical work
Analytical model is shown in Figure 2, and square steel tubular beam-columns are subjected to constant vertical load and monotonic increasing moment M1 and kM1. The stress-strain relation is assumed to be elastic-perfectly plastic. As the analytical parameter, the moment gradient ratio and the stability index are selected. The strengths of square steel tubular beam-columns are obtained by the shooting method.
4. Results and Discussion
Moment M1-slope θ1 relations are shown in Figure 8, and the maximum flexural strengths M1max are obtained. In Figure 11 λc-ny relations are shown, where white circle and black circle indicate that maximum moment M1>0.95Mpc and 0.95Mpc >M1>0.9Mpc, respectively. Marks x indicate 0.9Mpc >M1. From Figure 11 the condition that assures attainment of the full plastic moment is obtained by Eq. (26), and the κ-nyλc2 relations are shown in Figure 12.
The conclusions derived from the analytical work are as follows:
1) Equation (26) are proposed as the condition for attainment of full plastic moment (Fig. 12). This equation is composed of axial load ratio, slenderness ratio and moment gradient ratio.
2) The limit value (B-t)/lc and lc/(B-t) for attainment of the full plastic moment are presented by Eq.(29) and Fig. 13.
In recent years, it has been actively researched to improve the seismic performance of houses by using shear walls with energy absorption even in houses.
In this paper, we focused on U-shaped steel devices that are also used in seismic isolation devices. It is well known that U-shapes have very high ductility due to the use of energy absorption through bending deformation. Therefore, it can be used as a connection method incorporated as a damping member of an H-shaped beam-column joint, or as a damping member between an interpolation panel of a lightweight wall and vertical frame members. In previous studies, a U-shaped damper with a relatively large ratio of radius-to-thickness was used in order to take advantage of excellent energy absorption performance. On the other hand, in this paper, we propose a shear wall aiming to utilize the energy absorption capacity of U-shaped damper by amplifying device deformation. In this case, the number of devices installed on the shear wall is reduced, and the shape of the proposed U-shaped damper has a smaller ratio of radius to thickness and a larger ratio of width to thickness compared to previous studies. Therefore, the effect of these form factors on U-shaped devices needs to be clarified.
First, elemental tests were conducted on U-shaped devices to clarify the basic performance and the effects of shape factor on elasto-plastic behavior. The U-shaped device exhibited stable spindle-type hysteresis and excellent performance as a damper.
In addition, we tried to derive evaluation formulae for elastic stiffness and plastic strength required for the design of U-shaped devices. The elastic stiffness was calculated from elastic strain energy, and the collapse load was calculated based on limit analysis. As a result of comparing the calculated values with the experimental values, design formulae that can evaluate the experimental values could be derived.
Finally, a shear test was carried out on the shear wall with the U-shaped device installed to confirm its performance as a shear wall. Regardless of the position where the U-shaped device was installed, energy could be absorbed by being deformed evenly, and it exhibited excellent deformation performance as a shear wall. In addition, the device evaluation formulae (elastic stiffness and plastic strength) are extended to shear wall evaluation. The results show that the elastic stiffness and the plastic strength of the shear wall including the frame can be evaluated using the proposed design formulae.
The objective of this study is to examine the perspective of stability design of plane steel frames and review the core indexes for stability problems prescribed by some recommendations. After the indexes are compared with each other, the method to obtain the effective length factor by using a stability index is presented. It is shown that the effective length factors obtained from the method agree with the correct one to accuracy of about 5%.
2. Indexes for stability design
Indexes for the frame stability of "AIJ Recommendations for Plastic Design of Steel Structures", AISC "Specification for Structural Steel Buildings" and "Eurocode 3 Design of Steel Structures" are compared and relationships among them are shown as Eq. (16). Defining the stability index referred to SI as the ratio PΔ moment to story moment, the stability index SI for a sub-assemblage frame is expressed as Eq. (18), and the criterion for the buckling becomes SI is equal to unit as shown in Fig. 2.
3. Effective length factor using the SI
Method to obtain the effective length factor of multi-story multi-bay plane frames is presented by use of Eqs. (21) - (28). The stability index SI of i-th story is defined as Eq. (20), and the story with maximum SI becomes the critical story. The buckling load of the story can be calculated by the Eq. (23). The effective length factors of the each column are obtained by Eqs. (24) - (28). Examples of sub-assemblage frame, portal frame with asymmetric columns or vertical load and 6 stories frame are presented, together with the G factor method. As to the multi-story frames, two types of the distribution of story shear are selected. As the results, the effective length factors fairly well agree with the correct values obtained by using the buckling slope-deflection method.
The conclusions derived from this study are as follows:
1) Indexes of some recommendations are compared and relationships among them are presented as Eq. (16).
2) Method to obtain the effective length factor of multi-story multi-bay plane frames is presented by use of Eqs. (21) - (28). The effective length factors obtained from the method agree with the correct values to an accuracy of about 5%.
Bending moments due to superstructure-derived axial and shear force act on flange plate and fastening bolts, which are used to join rubber bearing to seismic building frame and foundation. Previous studies had confirmed the tensile force of bolt and the von Mises stresses on flange by the loading tests of rubber bearing with diameters of 800 mm and less. Additionally, these studies determined the pressure distributions of the rubber interior using finite element methods, as well as derived formulas for calculating the tensile force generated in bolt in cases where prying actions are formed due to the tensile axial forces of building. However, the phenomenon in which the area decreases in the vertically overlapping rubber along with the shearing deformation results in the concentration of vertical load on a single portion of the flange, and the differences between previous calculation formula for flange bending stress by using the tensile force of bolt and real-world scenarios, had been pointed out but not investigated quantitatively.
Therefore, we performed biaxial loading tests on two types of natural rubber bearing with diameters of 800 mm and 1300 mm. By the loading conditions ranged from only tensile deformation to compressive stress of at least 20 MPa, we investigated the effects of vertical and horizontal load on flange stresses and tensile force of bolt. The flange stress was evaluated by attaching the strain gauges on the flange diameter in the shear deformation direction and determined by using the maximum principal stress.
The results show that the tensile stresses of bolt in rubber bearing 800mm where there are significant decreases in the vertical overlapping area accompanying horizontal deformation, are high during high compressive stress and large shear strain. Large prying forces generate in the rubber bearing were confirmed, similar to predictions made by one of previous calculation methods, with the calculated and measured values being close to each another. The results also demonstrate that even the maximum tensile force of bolt is within a factor of approximately 1.5 of the allowable stress. However, significant variations are often observed for the tensile force of bolt introduced by tightening, even when the torque wrench is used. Therefore, the design that incorporate reserve strength are necessary by factoring the prying action of fasten bolt for seismic building and foundation.
The flange stresses locally increase in the domain of the decreasing overlapping rubber area with the shearing deformation in each rubber bearings. Some of these trends can be predicted when the flange is modeled as a beam of infinite length horizontally laid across an elastic foundation. When this prediction method is used for calculations in other rubber bearing, then the flange stresses are predicted to be decided not only rubber diameter, but also stiffness of steel plates in rubber bearing, the basic coefficient as foundation, and reduction rate of overlapping rubber area. Therefore, rubber bearing flange should be designed in consideration of vertical load from the superstructure and stiffness of foundation. In the future, it will be necessary to verify various effects and improve this prediction method of flange stress.
The mechanism of rotational embedment of traditional wooden strut is analyzed on the basis of loading tests of struts. Formulation of restoring force characteristics of traditional wooden strut joints is established by Elasto-plastic Pasternak Model proposed by the authors. Then the formulation is discussed and verified with rotational embedment test results of struts.
The BCIZ element is the most common triangular plate bending elements with nine DOF. It is hard to say that the element has sufficient performance when the number of element mesh is small. The basis functions for the triangular elements include functions that can be selected appropriately. A higher-order function terms similar to these functions is added to improve element performance. The solution obtained from the developed element was compared with solutions obtained from the conventional elements, and it was proved that the element exhibited high performance.