I have tried to solve problems of this type before. One issue is the difference between the axial and bending stiffness. Generally cables have very high axial stiffness relative to the bending stiffness and this causes severe ill conditioning with any of the elements included in FEAP. When you solve the problem, how do you get the initial shape? do you solve the catenary problem and specify the nodal positions from this solution? Even if you do, when you ask FEAP to solve the problem it may have trouble converging (check of condition number for the stiffness reveals part of this -- one indicator is given by the equation solver in loss of significant digits during factoring of the stiffness matrix, this could be quite high). If you converge the solution for gravity (one trick is to use a transient solution with backward Euler for the transient and let the problem converge at a large time, use increasing dt from very small to very large as the solution should be like M u-dot + K*u = f). After getting close turn off transients and converge the rest of the way.
After getting a gravity solution, the strains are probably not large during transients and then the E-B (#1) element is probably ok to use -- however, I believe you will have serious problems still due to the ill conditioning.
At this point it is probably worthwhile looking at the literature for alternate formulations. Applications can be for anchor cables, long oil pipes (e.g., from drill platforms to sea bed), for references. In the past some of our colleagues from the Naval Architecture Department (no longer exists) worked on this -- Names are R. Pauling and W. Webster. I have not used any of these formulations - my memory says that the axial response is in terms of the force and the bending by displacements.
Good luck.
