Experiment on Natural Frequency Change of Reinforced Concrete Members under Low Cycle Loading

Table 5

Frequency change equations and damage rate equations of test members.

Specimen category		Equation
		Frequency change equation	Damage rate equation
A = 30 mm	Z-1 (T = 1.875 s)	ω = 0.0027N^2 − 0.5725N + 78.079	V = 2 ∗ 0.0027N − 0.5725
	Z-2 (T = 2.4 s)	ω = 0.0009N^2 − 0.2582N + 78.747	V = 2 ∗ 0.0009N − 0.2582
	Z-3 (T = 3.0 s)	ω = −0.0024N^2 − 0.2918N + 80.029	V = 2 ∗ (−0.0024)N − 0.2918
	J-1 (T = 1.875 s)	ω = 0.0051N^2 − 0.7685N + 82.852	V = 2 ∗ 0.0051N − 0.7685
	J-2 (T = 2.4 s)	ω = 0.0012N^2 − 0.2823N + 85.962	V = 2 ∗ 0.0012N − 0.2823
	J-3 (T = 3.0 s)	ω = 0.0064N^2 − 0.9811N + 86.278	V = 2 ∗ 0.0064N − 0.9811
	M-1 (T = 1.875 s)	ω = 0.005N^2 − 0.873N + 88.11	V=2 ∗ 0.005N − 0.873
	M-2 (T = 2.4 s)	ω = 0.001N^2 − 0.225N + 96.91	V = 2 ∗ 0.001N − 0.225
	M-3(T = 3.0 s)	ω = 0.002N^2 − 0.386N + 92.10	V = 2 ∗ 0.002N − 0.386
A = 24 mm	Z-4 (T = 1.875 s)	ω = 0.003 N^2 − 0.341N + 88.40	V = 2 ∗ 0.003N − 0.341
	Z-5 (T = 2.4 s)	ω = 0.002 N^2 − 0.264N + 85.62	V = 2 ∗ 0.002N − 0.264
	Z-6 (T = 3.0 s)	ω = 0.014N^2 − 0.877N + 90.20	V = 2 ∗ 0.0014N − 0.877
	J-4 (T = 1.875 s)	ω = 0.0078N^2 − 1.2601N + 95.533	V = 2 ∗ 0.0078N − 1.2601
	J-5 (T = 2.4 s)	ω = 0.0018N^2 − 0.3531N + 97.122	V = 2 ∗ 0.0018N − 0.3531
	J-6 (T = 3.0 s)	ω = 0.0015N^2 − 0.286N + 96.913	V = 2 ∗ 0.0015N − 0.286
	M-4 (T = 1.875 s)	ω = 0.001N^2 − 0.238N + 102.5	V = 2 ∗ 0.001N − 0.238
	M-5 (T = 2.4 s)	ω = 0.001N^2 − 0.239N + 109.0	V = 2 ∗ 0.001N − 0.239
	M-6 (T = 3.0 s)	ω = 0.001N^2 − 0.214N + 106.6	V = 2 ∗ 0.001N − 0.214
A = 18 mm	Z-7 (T = 1.875 s)	ω = 0.0015N^2 − 0.2305N + 101.74	V = 2 ∗ 0.0015N − 0.2305
	Z-8 (T = 2.4 s)	ω = 0.0015N^2 − 0.2532N + 99.158	V = 2 ∗ 0.0015N − 0.2532
	Z-9 (T = 3.0 s)	ω = 0.0009N^2 − 0.1555N + 97.336	V = 2 ∗ 0.0009N − 0.1555
	J-7 (T = 1.875 s)	ω = 0.0012N^2 − 0.2003N + 98.11	V = 2 ∗ 0.0012N − 0.2003
	J-8 (T = 2.4 s)	ω = 0.0011N^2 − 0.255N + 87.926	V = 2 ∗ 0.0011N − 0.255
	J-9 (T = 3.0 s)	ω = 0.0019N^2 − 0.3883N + 86.874	V = 2 ∗ 0.0019N − 0.3883
	M-7 (T = 1.875 s)	ω = 0.001N^2 − 0.204N + 116.3	V = 2 ∗ 0.001N − 0.204
	M-8 (T = 2.4 s)	ω = 0.001N^2 − 0.216N + 115.2	V = 2 ∗ 0.001N − 0.216
	M-9 (T = 3.0 s)	ω = 0.001N^2 − 0.222N + 113.5	V = 2 ∗ 0.001N − 0.222