There have been many kinds of troubles of bolted joints, such as loosening and fatigue failure of bolts. The main reason of these troubles is a lack of initial fastened stress. As a prevention of these troubles the post-yield fastening method of boltedjoints has attracted the attention recently. This post-yield fastening method has many advantages such as higher load-capacity of bolted joints and stability of initial fastening stress. This method is being used in variable industrial fields and contributing to the improvement of reliability and to the reduction of the size of the bolt. In this paper the fatigue strength and loosening behevior of elastic and post yield fastened joints under off-axial loading condition are studied analytically and experimentally. The deformation behavior of bolted joints under off-axial loading condition is analysed with following procedures. Below the load at which the side edges open, the relation between incremental is linear. This relation is analysed already in VDI 2230. On the other hand, over this load the stress of bolt and applied load relation between incremental bolt stress and applied load become nonlinear, which case is not analysed in VDI 2230 yet. In this paper this relation is derived using the equivalent fastened body, which is definend taking account of the opend contact surface. These analytical relations, linear and nonlinear, were confirmed experimentally. Using these relations between incremental bolt stress and applied load the fatigue strength of bolted joints were estimated analytically and confirmed by the fatigue test. Moreover, the loosening behavior of bolted joints were obtained by measuring the bolt stresses during the fatigue test.
From these studies following conclusions are obtained.
(1) The fatgue strength of post-yield fastened joints is about 50% higher than that of elastically fastened joint.
(2) The drop of fastening stress by loosening of post-yield fastened joint during the fatigue tests is almost the same as that of elastically fastened joint.

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When an earthquake hits, a part of the bottom plate of the flat-bottom cylindrical tank which has no anchor device, or anchor rigidity of which is week, will be lifted up from the foundation due to overturning moment. As a result, the axial compressive force of shell bottom course will increase and such a damage of shell plate as “Elephant Foot Bulge” will be caused.
In this report, an effective method is developed in order to calculate quantitatively the rate of increase in the axial compressive force of shell plate as the ratio “C_A” of the compressive force calculated in case of considering the uplift of opposite side bottom plate to that in neglecting the uplift. And the characteristics of main factors which have influence on “C_A” are examined in the calculation example for a fullscale tank.
Firstly, a static rocking analysis model for calculating “C_A” is shown, in which the rigidity in the vertical direction of anchor and foundation right below shell plate is replaced with the springs of elasticperfectly plastic type, and the uplift resistance force due to the liquid pressure on the uplifted part of bottom plate is considered to act on the lower edge of shell plate. The axial compressive force of shell bottom course in tilt side can be obtained with the equilibrium equations concerning the overturning moment and the vertical forces, such as anchor reaction force, foundation reaction force, uplift resistance force and tank self weight.
Secondly, from the comparison between this model calculation and the static tilt test of a thin bottom plate model tank which has 2, 034mm in diameter, it is shown that the calculation results are good agreement with the test results.
Last, the characteristics of main factors having influence on “C_A” are examined by parametric studies for a 75, 000m³ LNG storage tank. From these studies, it is clarified that; As the seismic loading becomes larger, the value of “C_A” increases. The less the rigidity of anchor becomes and/or the more that of foundation right below shell plate becomes, the higher the value of “C_A” grows. In the calculation example for the 75, 000m³ LNG storage tank which is designed with current seismic design code in Japan, the change rate of “C_A” is small within the range of the seismic loading usually applied with design code, and the absolute value of “C_A” nearly equals that of the case in which the uplift of bottom plate is disregarded.

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Models for foundation vibration analysis are reviewed in the paper. The models reviewed were examined their accuracy by vibration tests and earthquake observations of foundations and have been frequently used in dynamic design of structures. The models are the following four and classified to continuous and discrete ones.
Continuous model for surface footing.
Continuous model for deep foundation.
Discrete model for pile foundation.
Finite element model.
The characteristics of the models are as follows.
The ground of the first model is uniform and elastic.
Accuracy of the model significantly depends on how to select equivalent uniform elastic contants when analysing non-uniform real ground, which is a problem to be solbed in the model.
The second model has a tendency to give two or three times greater stiffness. A problem to be solved for the model is how to reduce accurately and reasonably the stiffness.
The third model has been most frequently used in practical design of structures with pile foundation for its small number of unknowns and low costs of computer. But accuracy of the model greatly depends on damping evaluation of ground, whose methods are not yet established.
The fourth model is versatile and usually gives fairly good accuracy even for non-uniform ground. But because of great number of unknowns, the model requires great costs of computer and application of the model is restricted to designs of important and high-class structures.

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