  We compute the expected strain power spectrum and energy density parameter of
the stochastic gravitational wave background (SGWB) created by a network of
long cosmic strings evolving during the whole cosmic history. As opposed to
other studies, the contribution of cosmic string loops is discarded and our
result provides a robust lower bound of the expected signal that is applicable
to most string models. Our approach uses Nambu-Goto numerical simulations,
running during the radiation, transition and matter eras, in which we compute
the two-point unequal-time anisotropic stress correlators. These ones act as
source terms in the linearised equations of motion for the tensor modes, that
we solve using an exact Green's function integrator. Today, we find that the
rescaled strain power spectrum $(k/\mathcal{H}_0)^2 \mathcal{P}_h$ peaks on
Hubble scales and exhibits, at large wavenumbers, high frequency oscillations
around a plateau of amplitude $100 (GU)^2$. Most of the high frequency power is
generated by the long strings present in the matter era, the radiation era
contribution being smaller.
