Equivalent Load Method in Calculating Thermal Stresses during the Construction of Massive Monolithic Concrete Structures

The joined wing is a new concept of the airplane wing. The forewing and the aft wing are joined together in the joined wing. The joined wing can lead to increased aerodynamic performances and reduction of the structural weight. The structural behavior of the joined wing has a high geometric nonlinearity according to the external loads. Therefore, the nonlinear behavior should be considered in the optimization of the joined wing. It is well known that conventional nonlinear response optimization is extremely expensive; thus, the conventional method is almost impossible to use for large-scale structures such as the joined wing. In this research, geometric nonlinear response optimization of a joined wing is carried out by using equivalent loads. The used structure is a joined wing that is currently being developed in the U.S. Air Force Research Laboratory. Equivalent loads are the load sets that generate the same response field in linear analysis as that from nonlinear analysis. In the equivalent loads method, the external loads are transformed to the equivalent loads for linear static analysis, and linear response optimization is carried out based on the equivalent loads. The design is updated by the results of linear response optimization. Nonlinear analysis is carried out again and the process proceeds in a cyclic manner until the convergence criteria are satisfied. It was verified that the equivalent loads method is equivalent to a gradient-based method; therefore, the solution is the same as that of exact nonlinear response optimization. The fully stressed design method is also used for nonlinear response optimization of a joined wing. The results from the fully stressed design and the equivalent loads method are compared.

The performance evaluation of a thermal imager includes the comparison of a measurement to some specified temperature differential. It is uncommon to find a specification that is a function of absolute temperature. Since detectors respond to differential power, equivalent temperatures are presented with respect to an ambient (25°C background) differential temperature as a function of background temperature. The changes in the equivalent temperature difference are shown to be significant in both the near and far infrared regions ofthe spectrum. A simple curve is obtained to estimate the equivalent temperature difference for the far infrared region. The curve shape of the near infrared region varies too significantly to obtain any simple and accurate curve fit. The current thermal imager test methods should be reevaluated and specified in terms of background temperature.

Thermal load models for the static design of steel-concrete composite girders

An important element of the operation of high-temperature aggregates are modes that change over time. During these modes, maximum temperature changes are recorded in the cross-section of the lining of the aggregate. The difference in temperature leads to the formation of thermal stresses, which are the main reason for the repair of aggregates. During rapid heating, the inner layers of the lining are subjected to compressive stresses, while during rapid cooling, these layers experience tensile stresses. Under the same conditions, rapid cooling of the lining is more critical, since refractories have poor resistance to tension. The purpose of the study is to calculate and analyze the thermal stresses that arise during cooling of the casting ladle lining. The stresses are determined based on the calculation of the unsteady temperature field of the lining. Thermal stress values are necessary for analysis of the current cooling rates of casting ladles and subsequent development of optimal cooling modes for the lining. To solve the heat conductivity equation, a numerical method was chosen using an implicit four-point difference scheme. To study the cooling process of the casting ladle lining, temperature measurements were carried out in the zone of the greatest wear of the lining. Under conditions of natural convection, cooling of the casting ladle lining occurs unevenly. Cooling schedules during natural convection are characterized by significant unevenness and high rates of temperature decrease. The cooling rates of the inner surface of the lining at the initial stage of cooling significantly exceed the values recommended in the technical literature. Such cooling rates lead to the appearance of significant thermal stresses in the lining. For a refractory that has not been in service, the maximum thermal compressive stresses exceed the ultimate compressive strength by 1.27 times, and the tensile stresses exceed the corresponding limit values by 4.4 times. For refractories that have worked three fuses in the ladle lining, the maximum thermal compressive stresses exceed the ultimate compressive strength by 1.28 times, and the tensile stresses exceed the corresponding limit values by 3.19 times. The studied cooling modes for the casting ladle lining are unacceptable for operation. Cooling, taking into account the indicated rates, leads to the destruction of the lining material. To increase the resistance and duration of the working campaign of casting ladle linings, it is necessary to develop cooling modes for the lining at speeds at which the resulting thermal stresses do not exceed the strength of the refractory materials.

The springback behavior of cold formable steel of grade DP 1000 is assessed experimentally and numerically. Bending tests according to the VDA test specification are interrupted at three characteristic roller displacements, and the unloading characteristics are investigated. The tests are simulated with four different material models: i.) elastic plastic simulation with constant elastic modulus, ii.) elastic plastic simulation with plastic strain-dependent elastic modulus, iii.) damage mechanics simulation with constant elastic modulus, iv.) damage mechanics simulation with plastic strain-dependent elastic modulus. To provide the required input data for these simulations, the effect of plastic strain on the elastic modulus is studied based on uniaxial tensile tests, whereas the possible effect of ductile damage evolution on springback properties is numerically captured by the modified Bai-Wierzbicki model. The studies reveal that consideration of plastic strain effects on the elastic modulus adds a significant amount of accuracy to the numerical simulations, whereas the consideration of ductile damage does not improve the simulation results as much. This observation has to be related to the fact that steel DP 1000 is characterized by late damage initiation with rapid subsequent damage accumulation.

The purpose of this paper is to investigate several important methods of obtaining the equivalent loads in pre-stressed concrete structures, and to compare the advantages and limitations of each method. The methods devised in this study include the use of curvature of tendon, characteristics of primary moment, self-equilibrium condition and linear segments approximation of tendon. Several important numerical examples, including simple and continuous beams, are presented to show the differences among the methods. It is shown that the equivalent loading system is not uniquely determined depending on the approach adopted to calculate the equivalent loads, which results in different section forces even from the same pre-stressed concrete structure. The self-equilibrium conditions of the equivalent loading system are discussed, which indicates that some parasitic reactions may arise by some approximate equivalent loads even for the determinate structures. The present study indicates that the equivalent load method can be applied to various types of pre-stressed concrete members in a rational and efficient manner by carefully obtaining the equivalent loads.

The purpose of this paper is to investigate several important methods of obtaining the equivalent loads in pre-stressed concrete structures, and to compare the advantages and limitations of each method. The methods devised in this study include the use of curvature of tendon, characteristics of primary moment, self-equilibrium condition and linear segments approximation of tendon. Several important numerical examples, including simple and continuous beams, are presented to show the differences among the methods. It is shown that the equivalent loading system is not uniquely determined depending on the approach adopted to calculate the equivalent loads, which results in different section forces even from the same pre-stressed concrete structure. The self-equilibrium conditions of the equivalent loading system are discussed, which indicates that some parasitic reactions may arise by some approximate equivalent loads even for the determinate structures. The present study indicates that the equivalent load method can be applied to various types of pre-stressed concrete members in a rational and efficient manner by carefully obtaining the equivalent loads.

In this study, two different analysis methods were compared; the first is a linear static analysis method and the second is a linear dynamic analysis method. First one is the Equivalent Seismic Load Method, which is a linear static method where seismic loads can be obtained by applying a simple calculation. The second method, the Response Spectrum method, is a linear dynamic analysis method which obtains the seismic loads using more complex statistical calculations. For this analysis study, 18 structural models with 3 different building heights were analyzed according to the conditions of Equivalent Seismic Load Method and Response Spectrum Method specified in both TSC 2007 and TSC 2018 and base shear forces obtained as a result of these analyzes were compared. As a result of analysis; compared to the results obtained from TSC 2007, due to the effective stiffness coefficients specified in TSC 2018, it was observed that the base shear forces obtained for both methods were lower and the modal period values were longer in the analyzes applied according to TSC 2018. This means that the structural systems created with the designs according to TSC 2018 are more ductile than the structural systems created with the designs made according to TSC 2007. Base shear forces obtained by 2 different analysis methods applied according to regulations stated in both TSC 2018 and TSC 2007; it was observed that the base shear forces obtained by the Equivalent Seismic Load Method were higher than the results of the Response Spectrum Method.

An accelerated explicit method and GPU parallel computing program of finite element method (FEM) are developed for simulating transient thermal stress and welding deformation in large scale models. In the accelerated explicit method, a two-stage computation scheme is employed. The first computation stage is based on a dynamic explicit method considering the characteristics of the welding mechanical process by controlling both the temperature increment and time scaling parameter. In the second computation stage, a static equilibrium computation scheme is implemented after thermal loading to obtain a static solution of transient thermal stress and welding deformation. It has been demonstrated that the developed GPU parallel computing program has a good scalability for large scale models of more than 20 million degrees of freedom (DOFs). The validity of the accelerated explicit method is verified by comparing the transient thermal deformation and residual stresses with those computed by the implicit FEM and experimental measurements. Finally, the thermal stress and strain in an automotive engine cradle model with more than 12 million DOFs were efficiently computed and the results are discussed.

This chapter begins with some general considerations on the thermoelasticityThermoelasticity of auxetic solids, followed by the thermal elasticity of 3D auxetic solids with geometrical constraintsGeometrical constraints . Thereafter, the thermoelasticity of beams and plates arising from a given temperature profile is furnished. Based on a set of dimensionless thermal stressesThermal stress for application in auxetic platesPlates and shells, it was found that thermal stresses reduce as the material becomes more auxetic at constant Young’s modulusYoung’s modulus (E), and constant shear modulus (G), but the thermal stresses increase as the material becomes more auxetic at constant bulk modulusBulk modulus (K). In the case of constant product of EGK, the thermal stress is maximum at Poisson’s ratio of 0.303, but diminishes at Poisson’s ratios of −1 and 0.5. In most cases of solids considered in this chapter, the thermal stresses are minimized in the auxetic region. Finally a summary of thermal conductivityThermal conductivity study in multi-re-entrantRe-entrant honeycombs by Innocenti and Scarpa (J Compos Mater 43(21):2419–2439, 2009) is given, in which the results suggest that auxetic honeycomb configurations exhibit higher out-of-plane conductivity, strong in-plane thermal anisotropyThermal anisotropy , and the lowest peak temperatures during heat transfer between the bottom and top faces of honeycomb panels.

An equivalent constant-amplitude cyclic loading method for random vehicle load is proposed based on the concept of energy equivalence. The filtered compound Poisson process is adopted to describe random vehicle load, through which the vehicle load spectrum is gained. The total dissipated energy due to fatigue loads subjected to concrete structures is deduced by introducing a multi-scale model, in which the energy dissipation induced by the nano-cracks level is presented, and the energy transition from nano to macro scales is derived. By assuming that the total energy dissipation under random loading equals that under equivalent constant-amplitude loading, the equivalent load ratio and amplitude as well as the number of equivalent cycles for random vehicle load are obtained. To validate the effectiveness of the proposed method, a set of numerical simulations is presented. The fatigue damage accumulations for concrete structures under both the random load and the equivalent loads converted by the proposed method and the classic root mean square method are calculated. By comparing with the root mean square method, the accuracy and advantage of the proposed equivalent load model are verified.

Nonlinear unloading plays an important role in predicting springback during plastic forming process. To improve the accuracy of springback prediction which could provide a guide for precision forming, uniaxial tensile tests and uniaxial loading–unloading–loading tensile tests on SUS304 stainless steel were carried out. The flow stress mathematical model and chord modulus mathematical model were calibrated according to the test results. A constant elastic modulus three-point bending finite element model () and a constant elastic modulus roll forming finite element model () were established in MSC.MARC. The chord modulus was output by the PLOTV subroutine to determine the mean modulus of different regions, and the mean modulus three-point bending finite element model () and the mean modulus roll forming finite element model () were defined. The constant modulus finite element model () simulation results and the mean modulus finite element model () simulation results were compared with the three-point bending tests and roll forming tests test results. The difference between the simulation results and the test results was small, indicating that the mean modulus was feasible to predict the springback, which verified the suitability of the .

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Adoption of double-wall straight-tube steam generators (SGs) made of Mod.9Cr-1Mo steel is planned for next-generation fast breeder reactors (FBRs) in Japan. One of the major concerns with the SG is the structural integrity of the tubesheet. During a transient event, a maximum thermal stress may be induced by the temperature distribution in the tubesheet, and the magnitude of the stress depends on the configuration of the tubesheet. Therefore, the stress generation mechanism of a tubesheet was studied through finite element (FE) analysis. Semispherical tubesheet models were investigated for the first survey of the thermal stress mechanism. The calculated results of the semispherical tubesheet model indicated an extensive peak stress around the outermost hole. The recognized thermal stress mechanism of a semispherical tubesheet is as follows: (1) The dominant thermal stress is hoop stress caused by the temperature difference between the perforated and surrounding regions. (2) The thermal stress is insensitive to the size of the specific portion, although it is dominated by an interaction mechanism between the perforated and surrounding regions. (3) The stress concentration around the edge of the holes generates a peak stress. (4) The amplitude of the peak stress depends on the tubesheet penetration angle, and the stress concentration becomes greatest near the outermost hole. Based on the above stress generation mechanism, we proposed a stress-mitigated tubesheet, a center-flattened spherical tubesheet (CFST), as an improved configuration. The calculated peak stress of the CFST was smaller than that of the semispherical tubesheet. Further investigation revealed the detailed stress generation mechanism of the CFST during a thermal transient. There were, in fact, two different comparable thermal peak stress mechanisms observed for the CFST. Both the location and magnitude of the maximum peak stress depended on the steam temperature histories during the thermal transient. The radial stress caused by structural discontinuity, which was located at the outermost hole, depended on the rate (dT/dt) of the steam temperature change. The hoop stress caused by the interaction between the perforated and surrounding regions, which occurred at the first inner layer hole (with respect to the outermost layer holes) depended on the range (ΔT) of the steam temperature change.

Adoption of double-wall-straight tube steam generators made of Mod.9Cr-1Mo steel is planned for next generation fast breeder reactors in Japan. One of the major concerns relevant to the SG is structural integrity of tubesheets. In the reactor transient operation, thermal stress is induced by the temperature distribution in tubesheet and the magnitude of it depends on configurations of tubesheet. Stress generation mechanism of tubesheets was revealed through Finite Element analysis. Semi-spherical tubesheet models were investigated for the first survey of the thermal stress mechanism. As calculated results, semi-spherical tubesheet model gave the extensive peak stress around the outermost hole. Recognized thermal stress mechanism of semi-spherical tubesheet is as follows. (1) Dominant thermal stress is hoop stress caused by temperature difference between the perforated region and surrounding region. (2) Thermal stress is insensitive to size of specific portion, although is dominated by interaction mechanism between perforated and surrounded regions. (3) Stress concentration around hole’s edge generates peak stress. (4) Amplitude of peak stress depends on the tubesheet penetration angle and stress concentration becomes high near the outermost hole. Based on the above stress generation mechanism, authors proposed a stress mitigated tubesheet. It is center flatted spherical tubesheet (FST) as improved configuration. Calculated peak stress of FST was smaller than that of semi-spherical tubesheet. Further investigation revealed the detailed stress generation mechanism of FST during thermal transient. There were two different comparable thermal peak stress mechanisms in FST. Both location and magnitude of maximum peak stress depend on sodium temperature histories at thermal transient. One depends on the range (ΔT) of sodium temperature change. This type of peak stress was radial stress caused by the structural discontinuity, and it was located at the outermost hole. The other depends on the rate (dT/dt) of sodium temperature change. This type of peak stress was hoop stress caused by interaction between perforated region and surrounding region, and it was located at the one inner layer hole from outermost layer holes.