A beam clamp for attachment to a flange of a structural building member and from which to support or brace a service component. The beam clamp has a clamp body, and a set screw. The clamp body includes a first jaw section with at least one mounting through hole, a second jaw section, a joining section that interconnects the first and second jaw sections, and a transverse opening that is to receive the flange. A contact surface on the second jaw section is formed with surface irregularities providing a roughness that enhances engagement of the contact surface with the flange. In use of the beam clamp, the contact surface is in contact with the flange of the structural member, the set screw is installed in the mounting through hole, and the flange is secured within transverse opening between the tip of the set screw and the contact surface.