Out-of-Phase Cyclic Loads

Assume that a component, for example a tensile specimen, made of a viscoelastic material is loaded cyclically with angular frequency w. After some initial transient effects, the strain will also oscillate with the same angular frequency lu. Due to the time-dependence of elastic deformation, stress and strain are out of phase because the strain follows the current stress only with some delay. The following time-dependence is assumed for stress and strain ... 

Fig. 9.2 Non-proportional loads in an axle subjected to cyclic traction F and torque T out-of-phase that a generate out-of-phase stress components, b principal directions are continuousiy...

Kanazawa, K, Miller, K.J., Brown, M.W. Cyclic deformation of 1 % Cr-Mo-V steel under out-of-phase loads. Fatigue Eng. Mater. Struct. 2, 217-228 (1979)... 

Cyclic stress state Stress amplitude, mean stress, biaxiaUty, in-phase or out-of-phase shear stress, and load sequence. 

Several of the above analyses have to be carried out for different load combinations at different times in order to find the critical safety factor. For example, local contact stresses between the base and soil may be predominant in installation phase before the voids have been grouted. Similarly, the shear strength of the soil reduces after several years of production owing to cyclic loading to lower than it was shortly after the installation. Typical loads and overturning moments for a foimdation stability analysis is shown in Figure 10.33. 

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