Abstract: A clamp for anchoring a safety tether to an I-beam. Two opposed jaws are drawn together and spread apart by turning a screw passing through both jaws. The screw is journaled in one jaw and threaded into and entirely through the other jaw. The screw is positively retained to both jaws, so that the clamp is prevented from separating into two constituent parts. The jaws are arranged to remain properly aligned with one another. Because of the fixed alignment of the jaws and the single part construction, the clamp is readily placed in position by a steelworker. In a preferred embodiment, a cranked handle is geared to the screw, so that the screw can be turned from directly above the clamp. This avoids the necessity of reaching out to either side of the beam, above open space high up on a building skeleton. The jaws are configured to accommodate I-beam or H-beam flanges of different thicknesses. An eye bolt enables attachment to a safety tether. Provision may be made for accepting a plurality of eye bolts.