A Coriolis flowmeter having: a flow tube; connecting ring means (503, 1003, 1403) having a center opening through which said flow tube extends; a tubular balance bar (502, 1402A, 1402B) coaxial with said flow tube and surrounding an axial portion of said flow tube; axial end portions of said balance bar coaxial with and surrounding at least a portion of said connecting ring means; an inner circumferential surface (501, 1417) of said connecting ring means coupled to an outer circumferential surface of said flow tube; characterized in that: said tubular balance bar has a higher thermal coefficient of expansion than said flow tube and said connecting ring means; an outer circumferential surface (512, 1404) of said connecting ring means is tapered with a decreasing radius in a first direction with respect to the axial center of said flow tube; an inner circumferential surface (505, 1404) of said end portions of said balance bar has a taper that matches said taper of said connecting ring means; said tapered inner circumferential surface of said end portions of balance bar is affixed by braze material to said tapered outer circumferential surface of said connecting ring means; the higher thermal coefficient of expansion of said balance bar generates a compressive force against said connecting ring means and said flow tube. a flow tube; connecting ring means (503, 1003, 1403) having a center opening through which said flow tube extends; a tubular balance bar (502, 1402A, 1402B) coaxial with said flow tube and surrounding an axial portion of said flow tube; axial end portions of said balance bar coaxial with and surrounding at least a portion of said connecting ring means; an inner circumferential surface (501, 1417) of said connecting ring means coupled to an outer circumferential surface of said flow tube; characterized in that: said tubular balance bar has a higher thermal coefficient of expansion than said flow tube and said connecting ring means; an outer circumferential surface (512, 1404) of said connecting ring means is tapered with a decreasing radius in a first direction with respect to the axial center of said flow tube; an inner circumferential surface (505, 1404) of said end portions of said balance bar has a taper that matches said taper of said connecting ring means; said tapered inner circumferential surface of said end portions of balance bar is affixed by braze material to said tapered outer circumferential surface of said connecting ring means; the higher thermal coefficient of expansion of said balance bar generates a compressive force against said connecting ring means and said flow tube. said tubular balance bar has a higher thermal coefficient of expansion than said flow tube and said connecting ring means; an outer circumferential surface (512, 1404) of said connecting ring means is tapered with a decreasing radius in a first direction with respect to the axial center of said flow tube; an inner circumferential surface (505, 1404) of said end portions of said balance bar has a taper that matches said taper of said connecting ring means; said tapered inner circumferential surface of said end portions of balance bar is affixed by braze material to said tapered outer circumferential surface of said connecting ring means; the higher thermal coefficient of expansion of said balance bar generates a compressive force against said connecting ring means and said flow tube.