We present three-dimensional simulations of field emission from an ideal open (10,0) carbon nanotube without adsorption, by using a transfer-matrix methodology. By introducing pseudopotentials for the representation of carbon atoms and by repeating periodically a basic unit of the nanotube, band-structure effects are manifested in the distribution of energies. The total-energy distributions of both the incident and field-emitted electrons present features, which are related to the gap of the semiconducting (10,0) nanotube, to a van Hove singularity, and to stationary waves in the structure. The transmission through the middle of the gap is exponentially decreasing, with each basic unit of the nanotube associated with a reduction of the current density at this particular energy value by a factor of 5.4. Except for the contribution associated with the van Hove singularity, all peaks are displaced to lower energies when the extraction field is increased.