A clamping device (1) is adapted to receive and retain a portion (21) of a strip (20), and to actively tighten itself around the strip portion (21) under the influence of a pulling force. This is functioning in such a way that the higher the pulling force, the higher the force with which pushing parts (31) of the clamping device (1) are pushed. This results in a firm clamping connection. On the basis of this functioning, the clamping device (1) can be embodied in a form which has an open side, while maintaining a high capacity of withstanding loads. This results in the advantageous property that the strip (20) can be placed in and removed from the clamping device (1) in a sideward direction. This allows for detachment and reuse, and increases speed and convenience of use. The strip (20) does not need to be inserted in a closed shape. Various other applications than in a tie wrap (10) are possible for the clamping device (1), including applications in tension belts.