In general, silica fume is used as admixture to product high-strength concrete. On the other hand, researches on utilization of ground granulated blast furnace slag as an alternative material for silica fume have been begun in recent years. However, no researches has been conducted on long-term strength characteristics and durability of high -strength concrete using ground granulated blast furnace slag.
In this study, the long-term strength characteristics and durability of high-strength concrete using ground granulated blast furnace slag fine powder with specific surface area of 12000 and 16000 cm2/g (hereinafter referred to BFS concrete) were researched and compared with that of concrete using silica fume (hereinafter referred to SF concrete).
Results obtained from this study are summarized as follows.
1) From results of temperature rise tests using adiabatic curing specimens, temperature rise of BFS concrete is larger than that of SF concrete by 20% for water binder ratio of 22%, and by 12 to 14% for water binder ratio of 25%.
2) Compressive strength of concrete under standard curing was continued to increase up to the age of 8 years in both BFS concrete and SF concrete. In standard curing, the strength ratio of BFS concrete to the SF concrete was 0.89 to 1.09 in the period of 3 days to 8 years of age. In addition, the strength ratio of BFS concrete to the SF concrete was 0.93 to 1.08 at 8 years. The difference in strength ratio of both concretes was within range of ± 8%.
3) Compressive strength of core specimen was continued to increase up to the age of 20 years in both the BFS concrete and SF concrete. About the core specimens, the strength ratio of BFS concrete to the SF concrete was 0.94 to 1.06 in the period of 28 days to 20 years of age. In addition, the strength ratio of BFS concrete to the SF concrete was 0.96 to 1.05 at 20 years. The difference in strength ratio of both concretes was within range of ± 5%.
4) Shrinking of BFS concrete at the drying period of 10 years is smaller than that of SF concrete by 5 to 12%.
5) Carbonation depth at 20 years for outdoor exposure was 0mm in BFS concrete and SF concrete.
6) From the result of freezing and thawing test at 400 cycles, durability of BFS concrete was equal to or greater than that of SF concrete.
In the scope of this study, it is proved that ground granulated blast furnace slag with large specific surface area can be used as an alternative material for silica fume to product high-strength concrete.
In general, for evaluating the durability of concrete on exogenous type salt attack, standard values of diffusion coefficient and chloride ion content of concrete surface are used. These standard values are shown in the specification of Architectural Institute of Japan and Japan Society of Civil Engineers, however these are established on the basis of accelerated tests or exposure tests, because of the lack of the reports on the investigated date in actual buildings. Accordingly, using standard values are estimated on the safe side, but it is uneconomical, so cannot be applied hard.
This research is the rearrangement of the survey results which were conducted approximately 60 reinforced concrete buildings in 1985-88 by the Building Research Institute of the Ministry of Construction (Ministry of Land, Infrastructure and Transport) for the purpose of accumulating data on actual structures subject to the salt attacks.
These buildings were constructed before the notification of the regulation on total salt content in 1986, and located less than 2km from the coast. Furthermore, surface finishes of these buildings were sorted to undressed concrete or covered mortar. On these buildings, this research is examined using the distribution of total chloride ion content in concrete.
As the results, in the actual structures, chloride ion content of concrete surface is larger than the standard value of JASS 5 for durability design. On the other hand, the diffusion coefficient of concrete is smaller than the values of the accelerated test or exposure test. Moreover, it clarify that on the covered mortar, the diffusion coefficient is the same level with concrete.
Furthermore, in the actual structures, the peak of chloride ion distributes moves inside from surface in concrete, because of carbonation and so on. In this case, the treatment of the surface layer is not clear in conventional analysis for durability evaluation. In such a distribution of chloride ion, the diffusion coefficient of concrete is expected from analysis in which the provisional surface is set and the wholesome concrete is targeted.
In this study, new field investigations such as PS logging, formation density logging and soil tests were conducted at IBRH13 (KiK-net Takahagi station), where ground motion records with more than 500 Gal were observed three times during near source earthquakes with the magnitude of around 6. Based on new field investigation data, an applicability of three types of equivalent-linear simulations for nonlinear site response estimation was examined by using three ground motion records with more than 500 Gal. As a result, it was found that the observed site responses were relatively well explained by the equivalent-linear simulation with frequency-dependent effective strain for damping factors. However, for the largest record over 1,000 Gal, all types of equivalent-linear simulations with the conventional effective strain coefficient of 0.65 were not effective to explain the characteristics of observed site responses. Moreover, an inversion method to optimize effective strain coefficients was proposed to expand an application strain range of equivalent-linear simulations. In the inversion, observed Fourier spectral amplification and response spectral amplification between the surface and GL-100m were used as target site responses. Optimization of effective strain coefficients was carried out by minimizing differences between target site responses and the ones from equivalent-linear simulations with frequency-dependent effective strain for damping factors. As a result, the optimized effective strain coefficients were identified as less than the conventional effective strain coefficient of 0.65 in the shallower layers. For the largest record over 1,000 Gal, it was demonstrated that the target site responses and waveform at surface ground were well explained by the estimated ones from equivalent-linear simulation with the optimized effective strain coefficients. Also, it was shown that the characteristics of converged damping factors were similar to the bi-linear type frequency-dependent model from the equivalent-linear simulation with frequency-dependent effective strain for damping factor. Furthermore, outcrop bedrock ground motion response spectra were evaluated by equivalent-linear simulations with optimized and conventional effective strain coefficients using observed bedrock record. From the comparison of those estimated outcrop bedrock ground motion response spectra, it was found that both cases were almost consistent with each other. Consequently, we infer that bedrock ground motion is hardly influenced by reflected waves in the case of during nonlinear soil behavior caused by strong ground motion with over 1,000 Gal at the surface ground. Whereas, it was demonstrated that surface ground motion was underestimated by equivalent-linear simulations with conventional effective strain coefficients using bedrock record. This discrepancy is due to the inaccuracy of nonlinear site response estimation by equivalent-linear simulation using conventional effective strain coefficients. In the case of estimating bedrock ground motion by using surface record, the estimated bedrock ground motion is also strongly affected by the quality of estimated nonlinear site response by equivalent-linear simulation. Therefore, the optimization of effective strain coefficients is also important to estimate bedrock ground motion by using surface record.
This report deals with the effect of damping on evaluation expectation of linear cumulative damage factor from ductility factor and cumulative ductility factor. In the evaluation of the linear cumulative damage factor, wave number and the probabilistic distribution of peak amplitudes are required. The wave number is evaluated referring to the closed form equation developed by Matsushima (1992)5). The probabilistic distribution of peak amplitudes is inferred from the displacements of center of oscillation per cycle. The displacement of center of oscillation is considered to follow the gamma distribution. The expectation of linear cumulative damage factor is given by single stochastic integral.
As a frame deforms under increasing external loads, relatively brittle member in the frame may fracture at an early point on the loading process. This causes sudden and considerable unbalanced force vector in the frame and then the released forces, which are axial force, bending moment, shear force and axial torsional moment of early fractured member, are redistributed into the remaining members of the frame. The elastoplastic incremental analysis to estimate the restoring force characteristics of a frame must be carried out with cancellation of above mentioned unbalanced force vector. However, it seems the dealing of those unbalanced force vector in the present most analysis codes is not necessarily clear and this reduces the reliability of the obtained values of horizontal load-carrying capacity.
In this paper a procedure to cancel a large unbalanced force vector in the elastoplastic incremental analysis of a frame is presented. The procedure is applicable only to the analysis method in which elastic and plastic components of deformations of each element can be separated explicitly from the largely deformed frame, e.g. the Fibered Plastic Hinge Method (FPHM)6), 7), 8). By using the procedure, redistribution of the released forces of early fractured relatively brittle member into the remaining members of the frame can be done, therefore, an accurate restoring force characteristics of the frame having both brittle and ductile members can be obtained. The validity and reliability of the procedure are demonstrated by the analysis of two-bay two-story steel frame.
The obtained findings are as follows:
1. Using the present procedure, a discontinuous restoring force characteristics of the frame having both brittle and ductile members can be obtained.
2. A final behavior of the restoring force characteristics of the present example frame approaches to that of the frame excluded initially the fractured members. This agrees qualitatively with the schematic diagram presented in Commentary on Structural Regulations of the Building Standard Law of Japan 2015 Edition1).
3. The reliability of the horizontal load-carrying capacity of a frame obtained by the analysis without unbalanced force cancellation may not be sufficient.
Simulated earthquake motions whose response spectrums meet the multi target response spectrums are often used while designing earthquake resistant nuclear power plant facilities. Therefore, it is advantageous to utilize simulated ground motions with phase characteristics of actual earthquake ground motions in the design of nuclear power plant facilities. Several methods exist for the generation of these motions. However, these methods cannot maintain phase properties of the simulated earthquake motions. A method to generate simulated earthquake motions that meets both the multi target response spectrum and phase property requirements does not exist.
This study proposed a novel method for generation of simulated earthquake motions considering actual earthquake phase properties and multi target response spectrums. This method is equivalent to the modal iterative error correction method which is effective for solving inverse problems with strong discontinuities. Therefore, this study proposed an improvement of this method for spectrum fitting.
The findings of this study are as follows:
(1) A novel method for generation of simulated earthquake motions that considers actual earthquake phase properties and multi target response spectrums was developed. In this method, the simulated earthquake motion was expressed by sine wave convolution. Subsequently, the sine wave amplitudes were changed (while maintaining constant phase property) using the modal iterative error correction method to fit the target spectrums.
(2) The proposed method was applied to sample problems to confirm its accuracy. The results indicate that the simulated seismic motion accurately represented phase characteristics of the actual earthquake. Additionally, two acceleration response spectrums were also created. However, depending on the setting of the phase characteristics, there is no suitable simulated ground motion. Therefore, it should be noted that the simulated seismic ground motion may not converge sufficiently in such cases.
Steel composite concrete pile was developed consisting of double steel tubes, with an inner steel tube installed on the inside face of concrete of an SC pile (hereafter referred to as “WSC pile”) for enhancing deformation capacity. The inner steel tube restricts peel-off of concrete in the steel tube during crushing, which is an issue with the SC pile, and enhances the constraining effect of concrete thereby improving the deformation capacity of the WSC pile.
This paper reports a series of bending shear tests performed to study the deformation capacity of WSC pile under high compressive load and axial tensile load. Bending shear tests were conducted in three series: “A series” tests for confirming the effect of double steel tubes; “B series” tests for validating the effect on the deformation capacity of WSC pile due to change in the axial force ratio; and “C series” tests to assess the restoring force model of WSC pipe considering the results of the A series and B series tests. Findings from the test results of the different series were as follows:
(1) In the SC pile, bearing capacity dropped steeply and toughness reduced with the peel-off of concrete from the crushed internal surface. In the WSC pile using double steel tubes, the peel-off of internal surface of concrete was prevented and bearing capacity did not drop steeply after it reached the peak due to the effect of the inner steel tube.
(2) In the range of axial force ratio of -0.31 to +0.32, the WSC pile had adequate deformation capacity with ductility factor exceeding 6.0 and also exceeding the limit of deformation angle of 1/50 radians. To ensure adequate deformation capacity, it was observed that inner steel tube with diameter to thickness ratio ti/ri ≧0.04 must be used to restrict the buckling advance in the said tube.
(3) Assessment method using reliable bending moment rMu was proposed as the restoring force model of the WSC pile, and the validity of this model was confirmed.
The authors have proposed effective steel connections achieving high bending stiffness and strength for timber grid-shell structures in the previous research. They are composed of joints with T-section or H-section brackets connected to glued laminated timber section members through lag-screw bolts at flanges, their bending stiffness and strength have proved to be much higher than the ones of conventional connections. However, their performance against negative out-of-plane and in-plane directions which affect the shell buckling strength are not clear yet. In this research, the bending performance of the proposed connections against negative out-of-plane and in-plane directions are confirmed through real-size mock-up tests. They are compared to the performance against positive out-of-plane. Formulas for evaluating the stiffness and strength of the connections against these directions are proposed, and their validity are verified by comparing with the test results.
First, detailed analysis methods evaluating negative out-of-plane and in-plane stiffness and strength are constructed based on equilibrium of forces between steel bracket and timber beam and their compatibility condition. Next, approximating the process of neutral axis iteration, simplified formulas are demonstrated. Also, assuming the neutral axis at the center of the connections, further simplified equations for stiffness and strength are proposed. Then, real-sized mock-up specimens for the proposed connections are constructed, and simple bending tests in negative out-of-plane and in-plane directions are carried out. Their bending moment – rotational angle relationships are compared with the proposed formulas and their validity is confirmed.
As results, the following conclusions are obtained.
1) TB300 (T-section bracket with 300mm length) exhibited higher bending stiffness and strength in negative out-of-plane direction than those in positive direction. TB400 (T-section with 400mm length) exhibited lower bending stiffness but higher strength in negative out-of-plane direction.
2) For in-plane bending tests, all specimens showed much lower rotational stiffness and strength than those in out-of-plane directions. Those of TB440 and HB (H-section bracket) exhibited nearly twice than those of TB300, which is caused by the effects of shear resistance of lag-screw bolts.
3) Comparing with the test results, the proposed detailed analysis methods well evaluate bending moment – rotational angle relationship, while the ultimate strengths are a little overestimated. In addition, proposed simple formulas estimate the test results in safer sides, and considered as valid for practical use.
4) TB300 has higher rotational stiffness and strength in negative out-of-plane direction than the ones in positive out-of-plane direction. However, TB440 has lower rotational stiffness and higher strength in negative out-of-plane direction than the ones in positive out-of-plane direction. As for in-plane rotational stiffness and strength, they are lower than the ones in out-of-plane direction. Therefore, the difference of rotational stiffness in out-of-plane/in-plane directions has to be considered when evaluating buckling strength of timber grid-shell structures.
Regarding the in-plane shear strength of CLT, the authors proposed the modified formula CLT beam proposed by M.Flaig et al3). The equation of shear strength proposed by M.Flaig well matched to the test results that performed by Japanese cedar CLT. To apply that for the other species, Japanese larch and Sakhalin fir were used as specimen, here, and in-plane shear strain distribution along the cross section were measured to study about shape factor of CLT.
The experimental investigations described below include torsional shear test with CLT block and rolling shear test with inner layer. The series of these were performed in order to determine the torsional and rolling shear strengths of glued layer. Series of test, three species, Japanese Larch, Japanese Cedar and Sakhalin Fir were intended to investigate the relationship between strength and density.
These two strengths were required to obtain the in-plane shear strength of CLT panel. The other required strength, shear strength of parallel and perpendicular to the grain direction of laminae, were referred to Japanese Standard.
Experimental methods of in-plane shear for panels were developed with several methods. We adopted horizontal loading test with real size two rail shear method. Cross laminated timber panel were cut in H shape. Middle narrow part was intended to deform shear and the others were no-deformation area. Experimental and calculated values generally show good agreement.
Pilot tests were conducted on a reinforced concrete (RC) frame that had lightly RC wall piers with a steel slit damper for their effective use. In the pilot tests, when the damper was applied to the lightly RC wall piers, a damping effect was observed without adversely affecting the RC frame and the lightly RC wall piers. This showed the effectiveness of the proposed system. However, the damper force was not stabilized because of the damage to the connection between the lightly RC wall piers and the steel slit damper, the axial force acting on the lightly RC wall piers, etc. To solve these problems, a steel rod damper rationally applied to the lightly RC wall piers was used, and component tests of the lightly RC wall piers and subassemblage tests of the RC frame with lightly RC wall piers were conducted. Through these tests, the structural behavior was confirmed.
Component tests were conducted on four specimens using the steel rod damper proposed for application to the lightly RC wall piers as a parameter. As a result, the proposed steel rod damper became a stable restoring force without causing significant damage to the lightly RC wall piers. In addition, a method for evaluating the damper force was examined.
From the results of the component tests, the most rational and simply detailed steel rod damper was selected; the tests were conducted on the RC frame subassemblage with lightly RC wall piers. The parameters for the test specimens were different methods of fixing the steel rod damper to the lightly RC wall piers. There are two fixing methods: one with a joint in which the damper axis direction is unconstrained, and one with adhesion and fixing in the axial direction.
The test results of both specimens show that steel rod dampers start to dissipate energy at an early stage with story drift ratios much smaller than those at yielding RC frames. In the specimen in which the steel rod damper was fixed to the lightly RC wall piers, the stress was increased by the rope effect in the large deformation zone. By installing an axially unconstrained steel rod damper onto lightly RC wall piers designed considering the input shear force from the damper, it is possible to increase the damping effect without causing damage. The part with the largest steel rod damper curvature was not the concrete face but the position where it penetrated the concrete.
Local buckling is one of critical behaviors to determine the plastic flexural strength and deformation capacity of rectangular hollow structural (RHS) section steel columns. Several researchers have proposed numerical models to capture the strength deterioration of the RHS columns under axial loads due to local buckling. The authors proposed a fiber model using a phenomenological model (phenomenological fiber model) to simulate the yield area extends to a broad axial range from the end. This study presents the accuracy of the fiber model for RHS columns under cyclic high axial loading compared to stick or FEM models.
2. Composition of Phenomenological Fiber Model
The composition of the phenomenological fiber model is constituted based on the numerical simulations of RHS columns subjected to shear forces with axial loads. 10 specimens, based on a past research article, are referred to clarify the accuracy of the phenomenological fiber model, to develop the yield lines of local buckling of RHS section. The collapse mode of local buckling forms a kind of hip roof shape on the steel tube wall, and the lengths of each yield line are estimated by numerical and tests results. The stress-strain relationship of the fiber element of the phenomenological fiber model is almost identical with the shell elements of the FEM models, except for 33 width-thickness ratio RHS columns.
3. Validation of Phenomenological Fiber Model with Numerical Model for RHS Columns
The accuracy of the phenomenological fiber model for RHS columns, subjected to shear forces under high constant or variable axial loads, is validated by FEM numerical results. 12 models of the RHS columns are created using shell elements based on the specimens in the Chapter 2. The phenomenological fiber model captures the strength, the force-deformation relationship, and the local buckling behavior of the FEM numerical results under high axial loads, except for the 33 width-thickness ratio RHS columns.
4. Validation of Phenomenological Fiber Model with Test results Based for RHS Axial Members
The accuracy of the phenomenological fiber model for RHS axial members is examined. 8 specimens are extracted from a past research article as samples for the validation. The phenomenological fiber model almost captures the buckling strength, overall flexural and local buckling behavior of the test results.
5. Validation of Phenomenological Fiber Model with Test Results and Other Analytical Model Based for RHS Columns
The accuracy of the phenomenological fiber model for RHS columns subjected to shear forces under axial loads is validated by tests and FEM numerical results. 25 specimens are extracted from 9 past research articles as samples for the validation. The results of the phenomenological models are almost identical with the results of the test results, as well as those calculated by another phenomenological model developed by the extended skeleton curve theory, except for the 33 width-thickness ratio RHS columns.
This paper presents the accuracy of the phenomenological fiber model for evaluating the buckling behavior. As a result, the phenomenological fiber model could capture the strength, the force-deformation relationship, and the local buckling behavior of the RHS columns subjected to shear forces with high axial loads. This phenomenological fiber model also simulates the overall flexural and local buckling behavior of RHS axial members, except for RHS sections larger than and equal to 33 width-thickness ratio.
Few experiments have evaluated joints wherein a steel beam is simply embedded in the concrete columns, and a method for evaluating the bearing strength has not yet to be established. A previous study8) described the results of embedded type column-to-footing connection tests and a strength evaluation model that considers the resistance due to bearing and friction forces outside the flange. An adequate consideration has not been given to the stress transfer mechanisms distinctively to H-shaped steel members, such as the distribution of the bearing force and the friction force on the inside of the flange, and the evaluation accuracy of bearing strength has yet to be established.
To evaluate the bearing strength of beam embedded joints in steel reinforced concrete wall columns, this study proposes a strength evaluation formula based on the bearing and friction resistance mechanisms. A stress transfer mechanism is also proposed, which considers bearing force both inside and outside the flange, as shown in Fig. 5.
A total of five beam-column joint specimens at half scale of the actual structure were tested under cyclic loading conditions to simulate seismic loads, while the test parameters included the width, depth, and the embedded length of the steel beam. Bearing failure occurred in specimens with a 1.0–1.15 ratio of embedded beam length to beam depth. Fig. 9 depicts the relationship between beam shear force versus drift angle for each force direction in the specimens subjected to the bearing failure test. Based on the results of the bearing strength evaluation of the specimens, the proposed formula proved to evaluate strength characteristics with a high degree of accuracy.
The contribution ratio of the bending moment caused by bearing resistance and frictional resistance was calculated using the data of the bearing failure specimens based on the evaluation model of the bearing and friction forces of the beam embedded joints, as shown in Fig. 13. Results of this study indicated that the experimental value of the contribution ratio of the bending moment can be effectively evaluated by the proposed model. However, future research must focus on the development of an accurate method of calculating the bending moment due to the frictional resistance near the maximum bearing failure.
The bearing stress distributions in the beam embedded joint considering the top and bottom flanges were also calculated, and this calculation was based on the evaluation model shown in Fig. 16. A comparison of the bearing stress distributions with the test results also led to the validation of the proposed model.
Accuracy of the proposed model was evaluated by comparing the proposed evaluation formula with a previously developed evaluation formula for the specimens in past experiments. The proposed formula was able to evaluate the bearing failure strength with a high degree of accuracy compared with the previous formula.
To improve the bearing failure behavior of interior S beam－RC column joint, joint details using perfobond plate shear connectors were proposed. In this study, perfobond plate connectors were attached on the upper and bottom flanges of the embedded steel beam on parallel with the steel flange as show in the Fig. 1.
Objective of this study is to propose bearing design formulae taken account of the effect of perfobond plate connectors based on the stress transferring mechanism and resistance mechanism proposed by author’s previous study.
RCS beam‐column joint is assumed to be composed of the inner panel with the steel flange width and the outer panel outside the flange, and ultimate strength of the joint is assumed to be estimated by superposing that of the inner panel and the outer panel. Resistance mechanism is shown in Fig. 2. As shown in Fig 2(a), the inner panel is resisted by prying action. Accordingly, it is considered that perfobond plate connectors act for preventing rotation of the steel beam.
On the other hand, the outer panel is assumed to be resisted by a combination of the arch mechanism and truss mechanism as shown in Fig. 2 (b). The ultimate strength of the outer panel is obtained by superposing that of the arch mechanism and the truss mechanism. The ultimate strength of the outer panel is controlled by the strength transferred from the inner panel to the outer panel. The strength transferred from the inner panel to the outer panel is developed by the strength C of the horizontal strut-and-tie mechanism and the strength Mt of the torsion between the inner panel and the outer panel as shown in Fig. 2 (b). Based on these mechanisms, bearing strength pMb was given by formulae (1 ) ～ ( 3 ).
To clarify effectiveness of the proposed joint details, eight specimens were tested. The overall dimensions of the specimen, the cross sections and reinforcement details are shown in Fig. 3. The beams were all continuous through the column. The transverse reinforcement ratio of the joints was 0.181% and 0.815%. In addition, the specimens with the transverse reinforcement ratio of 0.204% were planned in consideration of practical design. The overall test program was shown in Table 1.
Hysteresis loops are shown in Fig. 4. The vertical axis represents the applied load at the end of the beam. The horizontal axis gives the deflection of the beam relative to the column at the end of the beam. For all specimens, the hysteresis loop shows the reversed S-shape.
Fig. 5 shows the envelope curve for hysteresis loops. Deterioration of the strength after the maximum load was very small. Bearing strength of specimens with perfobond plate connectors was larger than that of specimen without perfobond plate connectors. Bearing strength of the specimen with reinforcing bars inserted in the hole was almost same to the specimen without reinforcing bars. From the test results, double shear strength concrete connector a hole was 0.76 times compression strength of concrete.
The comparison of the calculated value obtained by the proposed formulae with the test results is shown in Fig. 7. The calculated values were shown to be in good agreement with the test results.
In this study, firstly, the multiplicative viscoplasticity model shown in Part 1 was briefly explained, and the material constants at 350 oC were identified using experimental data from isothermal rate controlled tensile tests(1) for the Japanese steel SM490. Material constants of the multiplicative viscoplastic model at 400<T<700 oC were previously identified. In the previous papers, Part 1 and 2, it was assumed that the temperature was constant over the duration of creep tests, and no verification of the viscoplastic model was made for varying temperature conditions as in the building fires. In order to simulate more closely the conditions existing in a real fire, the verification of viscoplastic model for varying temperature condition is need to be considered.
Secondly, in section 3, numerical simulations of the three kind of uniaxial tests under constant stress levels,  Creep tests at constant temperatures,  Creep tests under step-wise varying temperatures,  Creep tests under linearly increasing temperature change with temperature rate 5 oC/min, were carried out and the calculated results were compared with the corresponding experimental measurements to verify the applicability of viscoplastic model for varying temperature conditions. The creep tests for the Japanese steel SM490 in simulation ,  and  were carried out in reference 3, 4 and this paper respectively.
The purpose of simulation  is to verify the accuracy of viscoplastic model at constant temperature conditions, and those of simulations  and  are to verify the accuracy of viscoplastic model at varying temperature conditions based on the assumption of the mechanical equation of state. The discrepancy between the prediction and the measurement of simulation  is useful to consider the results of simulation  and .
From the analytical results and the discussions the following are concluded:
1) In the case of simulation , the validity of the multiplicative viscoplastic constitutive model for the prediction of creep tests under constant loads at elevated temperatures were verified, and the data for investigating the results of simulations  and  was obtained.
2) In the case of simulations , the strain increment just after the rise of temperature change (+25 oC) was predicted slightly bigger, and conversely the strain at final time of duration (150 minutes) was predicted smaller. Also it was shown that the trend of simulations  can be explained by making use of the results of simulation .
3) In order to accumulate the experimental data for creep test under constant loads at continuously varying temperatures, new creep tests under constant loads at linearly increasing temperature (rate of temperature rise 5 oC/min) were carried in this study.
4) In the case of simulation , although the viscoplastic model predicted the test value slightly bigger, it was explained that the viscoplastic model give the appropriate result because the difference between measured and calculated temperatures of same strain level was comparatively small from the practical point of view . Also it was shown that the trend of simulation  can be explained by making use of the results of simulations  and .