  As an application of the new realistic three-dimensional (3D) formalism
reported recently for three-nucleon (3N) bound states, an attempt is made to
study the effect of three-nucleon forces (3NFs) in triton binding energy in a
non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral
equations with the inclusion of 3NFs, which are formulated as function of
vector Jacobi momenta, specifically the magnitudes of the momenta and the angle
between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in
operator forms which can be incorporated in our 3D formalism. The comparison
with numerical results in both, novel 3D and standard PW schemes, shows that
non PW calculations avoid the very involved angular momentum algebra occurring
for the permutations and transformations and it is more efficient and less
cumbersome for considering the 3NF.
