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In the simple case of bosonic closed string theory with one of the twenty-five spatial directions being a circle of radius $R$, one has to take the field-theory limit $R\gg\sqrt{\alpha^{\prime}}$ to study the low-energy physics. The corresponding massless spectrum, which does not have the winding number and internal momenta excitation, is obtained when the left-moving and right-moving oscillator numbers equal to one, i.e.  $N_L=N_R=1$. This condition characterizes the strong constraint solutions in Double Field Theory. When, in the context of this letter,  one considers instead $N_L\neq N_R$, then the strong constraint solution is not enough to take into account the massless states with nontrivial internal momentum and winding number. This stringy effect in the low-energy limit should be expected from a perturbation in the parameter $\sqrt{\alpha^{\prime}}/R$. We use a linear gauge transformation to construct the quadratic action with a new mass term for the state $(N_L, N_R)=(2, 0), (0, 2)$, and the action is T-dual invariant. By obtaining a gauge transformation for a non-linear extension, a constraint acting on fields can be uniquely defined in triple-products. Finally, we show that the stringy effects only appear in the higher dimensional compact dimensions.