In a clamp device, a main clamp body includes an elongated tightening groove delimited by groove-forming wall sections. First and second lobe parts are disposed in the vicinity of end portions of two such tightening grooves. The main clamp body presents a ring shape when bolt and nut are mounted in position on the lobe parts disposed facing each other. Each of the lobe parts includes sidewall sections respectively contiguous to the groove delimiting wall sections that delimit the tightening groove. Each lobe part also includes a curved outer end wall section interconnecting the sidewall sections at an outer end of each lobe part and a seat surface wall section contiguous to the sidewall sections and to the outer end wall section. The seat surface wall section provides a bolt/nut seat surface. An arcuately shaped fulcrum part is formed on the curved outer end wall section of each lobe part.