Conveyor slat bottom flanges (78, 80) are positioned vertically between side portions of upper and lower clamp members (52, 54). The upper clamp member (52) is within the conveyor slat (70) and its side portions are above the conveyor slat flanges (78, 80). The lower clamp member (54) is welded or otherwise secured to a transverse drive beam (56). Its side portions are below the conveyor slat bottom flanges (78, 80). Bolts (164) project upwardly through openings in the transverse drive beam (56) and the lower clamp member (54) and thread into threaded openings (160) in the upper clamp member (52). Or, bolts (170) extend downwardly from the upper clamp part (52) through openings in the lower clamp part (54) and openings in the drive beam (56), to nuts (170) that are below the drive beam (56). Tightening of the bolts (170) causes the conveyor slat bottom flanges (78, 80) to be clamped between the two clamp members (52, 54). This secures the conveyor slats (70) to the transverse drive beam (56) without the need of forming fastener holes in the top (72) of the conveyor slat (70).