A pressure clamp for connecting pressure vessel segments can include a pair of semi-circular sections, which can be placed around the ends of the segments, so that there is a slight gap between the semi-circular sections. The inner surfaces of the semi-circular sections can be formed with two notches with beveled surfaces. The beveled surfaces can engage corresponding slanted surfaces on the segment ends, to urge the segments towards each other as the clamp is tightened. A pair of jack screws can be threaded through the semi-circular sections so that the jack screws extend slightly outwardly from one of the sections and contact the other section at the beginning of the tightening process, to establish an initial assembly gap. As fasteners tighten the clamp around the segment, the jack screws can be backed out to maintain a uniformly decreasing assembly gap between the semi-circular sections.