Large, reconfigurable and light orbiting structures are necessary to accomplish a number of tasks, such as the ones related to astronomy and fundamental physics missions, where very large telescope or other sensor arrays are needed. Given the technical limits imposed to the mass at launch, a mostly studied solution can be found in the formation of many satellites controlled in such a way that they can be considered as a virtual structure. This is possible only if synchronized and very accurate control is accomplished. The present paper focuses on the alternative solution represented by the space webs, intended as a set of small corner satellites connected by tethers: along the ropes of the web small robotic systems can move like spiders to position and re-locate, at will, pieces of hardware devoted to specific missions. In this sense, this work is the natural prosecution of previous studies of the same authors, where the advantages, drawbacks and possible solutions have been analyzed. In fact, the presence of rigid links would add the advantage of a simpler control strategy to the typical benefits of formation flying. Unfortunately, there is no stable configuration for an orbiting two dimensional web made by light, flexible tethers, since it cannot support compression forces caused by the gravity gradient. However, if the net is initially rotating (at a sufficiently high velocity) in the orbital plane, the centrifugal force counteracting the gravity gradient compression leads to a stable motion. Residual shape deformations are still present: in order to increase the desired shape stability of the web, it is possible to introduce a coordinated attitude control of the corner satellites, as an example by means of reaction wheels. This paper shows some preliminary results on the dynamics of tethers which are subjected to a torque at their tip. The analysis requires to add to previous models the attitude of the corner spacecraft as well as of the section the tethers are divided in. At this step, tethers are modeled as axial springs with no compression resistance. The paper, based on a performing code specifically written, reports the results for a number of simulations in order to provide helpful insight in this unusual dynamics