Well Aamir bhai in static riks technique unlike the typical load or displacement technique in which at each step load is kept constant but in arc lenght technique to follow the arc lenght the load factor is at each iteration is modified so that to follow the required path .A few days ago i have read a example which says " imagine you're blindfolded and marching along a curved wall (and not allowed to deviate from curve). So, at any isntance you take ur stick and and try to tap in front of you. In this case, the horizontal projection of stick is search radius, and the distance you cover in one step is arc length".Now if you find that suitable load factor and you have initial arc lenght increment you can find the required load from it..
of Course the the constant LPF value will be your consideration .You can multiply this with your applied load to to find the current load .and in case f variation of load proportionality factor in the initial state .you can find the incremental load at each itteration by just multiply LPF with Load at each step((If you are applying load )).You can find more about this in Static riks analtical techniques method online .But this formula is modified more than twice i don't know which one is recent