The clamping unit is used where an elongated carrier (6) is embraced by two elongated clamp pieces (2, 3) of light metal clamped together by screws, one clamp piece (3) having holes passing through it for screws, and being on a sliding path relative to the other. The material round the screw holes (10) is extended on one side to a support (12) which can be contacted by the screws (11). This support is faced by a surface (14) on the second clamping piece (2), set at an interval from the support so that thread segments are generated in the surface when the pieces are brought together and the screws of the thread-cutting type, are tightened, enabling the pieces to be braced together according to the degree of tightening of the screws. The difficulty of providing screw holes in exactly the correct placings is eliminated.
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