A bar clamp connection connects an elongated bar member, such as the handle of a dumbbell to a bar clamp. The bar clamp has a clamp body having an elongated open sided tube having a side opening sized to receive a predetermined elongated bar member therein. A tubular extension extends perpendicular from the open sided tube for attaching to a matching tubular member. A strip of hook and loop material has the hoop portion on one side of the material and the loop portion on the other side of the material and can be adhesively attached to the clamp body such that the strip of hook and loop material can be wrapped over the open side of the open sided tube having an elongated bar member therein and attached to the hook and loop material on the other side thereof. The hook and loop material is adhesively attached to the clamp body and also has an opening therein which is fitted over the clamp body tubular extension. The elongated bar member can be the handle of a dumbbell and one bar clamp body can be attached to each end of an elongated rod for supporting a dumbbell on each end thereof to thereby convert a pair of dumbbells into a barbell.