Pipeline systems under thermal loads are frequently used in different industries, such as the power plants and petrochemicals. Unlike the analytical method of elastic center, which is capable to analyze only one branch of pipeline with pipe members parallel to the coordinate system, the method of stiffness removes these limitations. In this article the stiffness method is introduced for the analysis of pipeline systems. Based on this method, the piping system may include any number of piping braches. The straight pipe elements in the branch may have any general orientation and the bend elements may have any arbitrary angle. The computer program designed based on this method may compute the nodal displacements at the ends of the straight or bend elements and present three components for loads and three components for moments. Once the free-body diagram of each piping elements with nodal forces and moments are drawn, then the engineering codes are employed to design the piping system for safe operation.

In this paper a new ribbed bracing system (RBS) is proposed capable of performing as a variable stiffness system that can be used for controlling structural deformations and frequency shifting to compensate seismic energy. RBS has two important advantages. Because of ribbed system, the compressive member is rigidly moved like a piston and a cylinder and therefore it is a buckling prevented system. Also it is possible to use this system as a semi-active system by considering the story drifts and global structural damage and control the system if it is necessary to be open or closed based on the operational criteria assigned in the system. RBS has no need to any actuator and large power supply, but just a battery-size power supply to switch the ribbed mechanism to be on or off. RBS is composed of a ribbed supplemental part and a normal wind-bracing on each floor. Considering an appropriate criterion based on the storey drift, minimum number of bracing systems will be active on the height of structure during earthquake. In contrast with completely closed RBS (CC-RBS) by on-off bracing system arranged along the height of the building cause period shifting of the structure to the larger value. Three stages are considered in the numerical studies: conventional bracing frame (CBF), CC-RBS and semi-active RBS (SA-RBS). Damage indices and Fourier transforms are calculated in order to discuss on the efficiency of the proposed system. Nonlinear dynamic analysis of system has been carried out and structural behaviour has been investigated.Numerical results show the efficiency of CC-RBS in reducing structural damage and improving seismic energy. Also base shear is reduced when SA-RBS is used and structural damage is more uniform in this case.

The track stiffness experienced by a train will vary along the track. Sometimes the stiffness variation may be very large within a short distance. One example is when an unsupported sleeper is hanging in the rail. Track stiffness is then, locally at that sleeper, very low. At insulated joints the bending stiffness of the rail has a discontinuity implying a discontinuity also of the track stiffness. A third example of an abrupt change of track stiffness is the transition from an embankment to a bridge. At switches both mass and stiffness change rapidly. The variations of track stiffness will induce variations in the wheel/rail contact force. This will intensify track degradation such as increased wear, fatigue, track settlement due to permanent deformation of the ballast and the substructure, and so on. As soon as the track geometry starts to deteriorate, the variations of the wheel/rail interaction forces will increase, and the track deterioration rate increases. In the work reported here the possibility to smooth out track stiffness variations is discussed. It is demonstrated that by modifying the stiffness variations along the track, for example by use of grouting or under-sleeper pads, the variations of the wheel/rail contact force may be considerably reduced.

Flexural stiffness of a single load-induced crack is determined. Modal analysis is performed on the beam prior and after each load stage. Mode shapes are extracted and eigenvectors used to determine the mode shape equations. Global flexural stiffness is derived by utilizing the regressed variable l and the local flexural stiffness is derived by applying the centered-finite-divided-difference formula on the regressed data. The global stiffness decreases with increasing severity of the crack. Results compared with values computed using the load-deflection plot showed similar trends. The algorithm may be used as a technique for detecting crack damage in reinforced concrete.