An I-beam clamp, used for engaging the bottom flange of an I-beam or bar joist, includes a pair of threaded rods and a pair of brackets that can be moved relative to each other along the threaded rods. One of the brackets, a clamp bracket, has a set screw configured to engage a top surface of the I-beam flange, to hold the clamp in place once it is installed on the I-beam. The other of the brackets, a nut bracket, has half-threaded portions for selectively engaging the threaded rods, to hold the nut bracket in place relative to the threaded rods, and to disengage from the threaded rods, in order to allow positioning of the nut bracket along the threaded rods. The nut bracket may include a spring clip or other device to provide force to bias into engagement the threaded rods with the half-threaded portions.