To my surprise, I still see papers/publications in which 4P bending tests on asphaltic beams were used with a controlled haversine deflection. Nothing wrong as long as you are aware of the fact that after a few cycles the load signal has changed from a haversine at the start into a pure sine signal. This implies that you are bending a bent beam. And the strain in the beam is also a sine. This is due to the fact that asphalt is a visco-elastic material. And for comparing fatigue tests the tensile strain amplitude is related to half the peak-peak value of the haversine signal. By gluing strain gages at the bottom and top of the beam you will see that the strain signals are opposite. The application of a haversine deflection has an advantage. In a traditional 4PB test with a pure sine signal, all horizontal movements of the supports/clamps are directed inwards to the center. This results in a repeated half-sine movement for the supports which is from a mechanical point of view awfully. In practice I measured it and it turned out to be a deformed sine signal. However, using a haversine deflection the horizontal movements will be pure sines. I think using a haversine deflection signal will allow going to frequencies of 30 Hz and higher.