Using any of the bilinear transform, matched pole-zero, or impulse invariance techniques in converting a continuous-time system
2 answers:
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Answer:
A) ( N ) = 1.54
B) N ( Goodman ) = 1.133, N ( Morrow) = 1.35
Explanation:
width of steel bar = 25-mm
thickness of steel bar = 10-mm
diameter = 6-mm
load on plate = between 12 kN AND 28 kN
notch sensitivity = 0.83
A ) Fatigue factor of safety based on yielding criteria
= δa + δm = = 91.03 + 227.58 = 490 / N
therefore Fatigue number of safety ( N ) = 1.54
δa (amplitude stress ) = kf ( Fa/A) = 2.162 * ( 8*10^3 / 190 ) = 91.03 MPa
A = area of steel bar = 190 mm^2 , Fa = amplitude load = 8 KN , kf = 2.162
δm (mean stress ) = kf ( Fm/A ) = (2.162 * 20*10^3 )/ 190 = 227.58 MPa
Fm = mean load = 20 *10^3
B) Fatigue factor of safety based on Goodman and Morrow criteria
δa / Se + δm / Sut = 1 / N
= 91.03 / 183.15 + 227.58 / 590 = 1 /N
Hence N = 1.133 ( based on Goodman criteria )
note : Se = endurance limit (calculated) = 183.15 , Sut = 590
applying Morrow criteria
N = 1 / ( δa/Se) + (δm/ δf )
= 1 / ( 91.03 / 183.15 ) + (227.58 / 935 )
= 1.35