HW _3 Solutions

# HW _3 Solutions - 2(661.67 kg·m/s 2(9.81 m/s 2 = 67.4 kg =...

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CE 3020 Construction Materials Dr. Kurtis SOLUTIONS Question 1 Determine the mode I fracture stress ( σ f ) for: (a) a wide glass plate containing a crack 2 mm long; Assume shape factor Y=1, and K Ic =0.7 MPa for glass. ANS. MPa a Y K Ic f 5 . 12 001 . 0 7 . 0 = = = π π σ (b) a flaw-free glass fiber Assume shape factor Y=1, and K Ic =0.7 MPa for glass. ANS. a = atomic spacing = 1x10 -8 in = 2.54x10 -10 m MPa a Y K Ic f 800 , 24 10 54 . 2 7 . 0 10 = × = = - π π σ Question 2 Could you hang from the glass successfully for one minute? ANS: Depends on how much you weigh! There are 2 ways to solve this problem: (1) you can run the calculations using your weight OR (2) you can solve for the maximum you could weigh before the plate would fracture (thus, avoiding revealing your weight!). Using method (2) and knowing Y=1 for a center-cracked plate: MPa m a Y K Ic f 21 . 5 0081 . 0 MPa 83 . 0 = = = π π σ = 5.21 x 10 6 N/m 2 P = σ f (A) = (5.21 x 10 6 N/m 2 )(1.27x10 -4 m 2 ) = 661.67 N = 661.67 kg·m/s

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Unformatted text preview: 2 (661.67 kg·m/s 2 )/(9.81 m/s 2 ) = 67.4 kg = 148.6 lbs. So, if you weigh 148.6 lbs. or less, according to LEFM, you could win \$10 Million! Question 3 A fatigue test is made with a mean stress of 15,000 psi and a stress amplitude of 20,000 psi. Calculate the maximum and minimum stresses. ) ( 5 ); ( 35 40 20 2 30 15 2 min max min max min max min max min max n compressio ksi tension ksi ksi ksi ksi ksi amplitude mean-= = =-=-= = + = + = σ Question 4 From the S-N curve: Cycles σ ampl N f 100,000 40ksi infinite 20,000 60ksi 10 6 let y = number of years; set Miner’s Law equal to 1 at failure ( 1 ) 020 . 10 000 , 20 000 , 100 6 = + = + ∞ = ∑ y y N n i y = 50 years to failure under the given loading conditions....
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