A Simplified Calculation Method of Length Adjustment of Datum Strand for the Main Cable with Small Sag

Table 3

Comparison of length adjustment results for datum strand in side span with different sag-span ratios.

Sag to span ratio	Sag f0 (m)	Exact solution ΔS (mm)	Perfect solution of parabola theory ΔS (mm)	Traditional simplified formula		The improved simplified formula I		The improved simplified formula II
				ΔS (mm)	Error (%)	ΔS (mm)	Error (%)	ΔS (mm)	Error (%)
1/8	37.25	48.2564	48.1414	49.8407	3.5	49.9282	3.7	49.9354	3.7
1/10	29.8	/	39.0885	39.8610	2.0	40.0019	2.3	40.0090	2.4
1/20	14.9	/	20.3755	19.9017	−2.3	20.4884	0.6	20.4955	0.6
1/35.98	8.2830	12.9359	12.9419	11.0379	−14.7	12.9611	0.1	12.9682	0.2
1/50	5.9600	/	11.6553	7.9261	−32.0	11.6624	0.1	11.6696	0.1
1/70	4.2571	/	13.0155	5.6450	−56.6	13.0180	0.0	13.0251	0.1
1/100	2.9800	19.0276	19.1201	3.9343	−79.4	19.1209	0.0	19.1280	0.0