Inelastic Response Under Combined Bending and Tension

This chapter deals with the mechanics of inelastic bending in the presence of tension. Bending a circular tube ovalizes its cross sections and leads to a limit-load instability. Bending in the presence of tension can aggravate the growth of ovalization. Two types of combined bending-tension loading have been identified. The first is encountered in a suspended line, where the tension is used to control the shape of the suspended section. In this case, the tension is reacted by a distributed force normal to the axis of the tube that occurs because of the weight of the pipe and the buoyancy force. The transverse force acts at the axis of the tube and thus does not influence ovality. In this type of loading, the tension interacts with the bending (and possibly pressure) through an inelastic action by aggravating the state of stress. In the second type of combined bending-tension loading, the pipe is bent over a rigid surface, in which case the tension is reacted by a distributed force acting on the surface of the bent tube. This type of loading is encountered, for example, by a pipeline passing over a curved stinger and when winding or unwinding a line on a reel.