High-Performance Steel Bars and Fibers as Concrete Reinforcement for Seismic-Resistant Frames

Table 5

Properties of SDOF systems considered.

System^a; MPa (ksi)	No.	Period of; vibration^b; 𝑇, s	Spectral acceleration; coefficient^c; 𝑆𝐴,g	Strength; ratio^d; 𝑆𝑅	Yield strength; coefficient^e; 𝐶𝑦
Grade 410 (60)	1	0.60	1.00	1/3	0.33
	2			1/6	0.17
	3	0.90	0.83	1/3	0.28
	4			1/6	0.14
	5	1.20	0.63	1/3	0.21
	6			1/6	0.10
Grade 670 (97)	7	0.69	1.00		0.33
	8				0.17
	9	1.04	0.72		0.28
	10				0.14
	11	1.39	0.54		0.21
	12				0.10
Grade 830 (120)	13	0.85	0.88		0.33
	14				0.17
	15	1.27	0.59		0.28
	16				0.14
	17	1.70	0.44		0.21
	18				0.10

^aGrade-670 and Grade-830 systems represent equivalent alternatives to Grade-410 systems. All systems target identical strength; however, the stiffness of Grade-670 or Grade-830 systems is 0.75 or 0.50 times the stiffness of Grade-60 systems. In all cases, the postyield stiffness was defined as 5% of the initial stiffness.
^bTarget periods of vibration for Grade-410 systems are set to 0.6, 0.9, and 1.2 s for a unit mass, from which the stiffness is derived. The stiffness of Grade-670 or Grade-830 systems is 0.75 or 0.50 times that of Grade-410 systems.
^cLinear-response acceleration (divided by g) of a 5%-damped SDOF system of period 𝑇. It is defined using 𝑆_𝐴=𝑆_𝐷1/𝑇≤𝑆_𝐷𝑆, where 𝑆_𝐷𝑆=1.0 and 𝑆_𝐷1=0.75, refer to ASCE/SEI 7-10 [20].
^dYield force, 𝑉_𝑦, of nonlinear SDOF system (of initial period 𝑇) divided by the force induced in a 5%-damped linear SDOF system of period 𝑇.
^e𝐶_𝑦=𝑆_𝐴⋅𝑆𝑅=𝑉_𝑦/𝑊, where 𝑆𝑅 is the strength ratio and 𝑆_𝐴 is the spectral acceleration coefficient obtained from the design spectrum (5% damping coefficient) for a system of period 𝑇. The value of 𝐶_𝑦 corresponds to the yield strength, 𝑉_𝑦, divided by the weight, 𝑊, of the SDOF system.