Bending stiffness- door bars

Multiple tubes in the same plane are required to prevent side intrusion. The builder is left with several options as to tubing diameter and wall thickness. This spreadsheet compares idealized properties of the tubes to give an idea of how adding extra elements would affect weight of the assembly, or overall bending stiffness. (Stiffness largely drives energy absorption unless the tubes buckle or otherwise plastically deform)

				Number of Tubes
constant	OD (inches)	thickness	I	1	2	3		Relative mass per unit length		Stiffness to mass ratio
0.04900	1.50000	0.095	0.10376	0.1038	0.2075	0.3113		0.4191		0.2476
0.04900	1.50000	0.120	0.12456	0.1246	0.2491	0.3737		0.5200		0.2395
0.04900	1.75000	0.095	0.16937	0.1694	0.3387	0.5081		0.4937		0.3431
0.04900	1.75000	0.120	0.20482	0.2048	0.4096	0.6145		0.6142		0.3335
0.04900	2.00000	0.083	0.22964	0.2296	0.4593	0.6889		0.4996		0.4596