Cable force estimation of cables with small sag considering inclination angle effect

Advances in Bridge Engineering

Table 9 Force estimation result of Cable I

EC	Angle (°)	FF (Hz)	RCF (MN)	Hinged-Hinged		Fixed-Fixed		Identified
EC	Angle (°)	FF (Hz)	RCF (MN)	T_j(MN)	RE(%)	T_g(MN)	RE(%)	T₁(MN)	RE(%)
\( {K}_{rot}^{\hbox{'}} \)	0	0.440	2.9036	2.8705	−1.14	2.8654	−1.31	2.8680	−1.23
	30	0.436		2.8655	−1.31	2.8600	−1.50	2.8627	−1.41
	60	0.429		2.8848	−0.65	2.8790	−0.85	2.8819	−0.75
	90	0.426		2.9137	0.35	2.9086	0.17	2.9112	0.26
\( {K}_{rot}^{\hbox{'}\hbox{'}} \)	0	0.440	2.9036	2.8705	− 1.14	2.8654	− 1.31	2.8680	− 1.23
	30	0.436		2.8655	−1.31	2.8600	−1.50	2.8627	−1.41
	60	0.429		2.8848	−0.65	2.8790	−0.85	2.8819	−0.75
	90	0.426		2.9137	0.35	2.9086	0.17	2.9112	0.26
\( {K}_{rot}^{\hbox{'}\hbox{'}\hbox{'}} \)	0	0.440	2.9036	2.8705	−1.14	2.8654	−1.31	2.8680	−1.23
	30	0.436		2.8655	−1.31	2.8600	−1.50	2.8627	−1.41
	60	0.429		2.8848	−0.65	2.8790	−0.85	2.8819	−0.75
	90	0.426		2.9137	0.35	2.9086	0.17	2.9112	0.26

Note: EB denotes elastic boundary; FF denotes fundamental frequency; RCF denotes reference cable force; RE denotes relative error