Hi Laouzai,

I think the answer in general is "No". It is of course easy to model the origin-destination matrices for each type of vehicle, but the problem comes when you wish to construct the standard Beckmann "sum of integrals of link travel cost functions". Then the integral for one link will have as its argument some function of the number of cars and of the number of trucks on the link. And here is where the problem starts - in general there is NO symmetry in how an additional car on a traffic link affects a truck,and vice versa - an extra truck will most probably affect car traffic more than the other way around. This non-symmetry in how vehicle types affect each other will manifest itself in the Jacobian (matrix of partial derivatives) of the travel cost being asymmetric. This means that the Jacobian cannot be integrated, and, therefore, the standard Beckmann objective function is not well-defined. 

Thank you sir Michael Patriksson

in order to avoid the problem, I replace the total flow variable on link a,  xa by the two types of flows (cars and trucks ) noted va and wa respectively: xa =va+wa  and replace in the  objective function, the number of constraints will be doubled: the conditions of conservation of flows for each type.  In this case the model of beckman be treated by two different variables.