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MATH3871 Assignment 2 UNSW
This is the second assignment for AER318 Dynamics. It has questions to practice and prepares you for the midterm. You are welcome.
Carleton University Department of Mechanical and Aerospace Engineering Winter 2017
MECH 3002 Machine Design and Practice Assignment due Friday, 3 March 2017 Assignment #2
A large rectangular sheet with a 1-in.-long central crack fractures when loaded to 80 ksi. Determine the fracture load for a similar sheet containing a 1.75-in. crack (see Figure A2.1). A2.1). A2.1
Figure A2.1
A2.2 A
plate of width 2 w = 8 in. and thickness t = 0.05 in is made of leaded beryllium ( S u = 98 ksi, S y=117 ksi) and the plate stress K Ic= 70 ksi !in. It is used in a boiler, where periodic inspection for cracks will be made. Estimate the highest load, P (Figure A2.2 ), that can be applied without causing sudden fracture when a central crack grows to a length, 2c, of 1.5 in.
Figure A2.2
Page 1 of 3
A machine component is loaded so that stresses at the critical location are "1 = 20 ksi, "2 = -15 ksi, and "3 = 0. The material is ductile, with yield strengths in tension and A2.3
compression of 60 ksi. What is the safety factor according to: (a)
the maximum- normal-stress theory?
(b)
the maximum-shear-stress theory?
(c)
the maximum- distortion-energy theory?
(d)
which theory would be expected to agree most closely with an actual test?
A2.4 A
round steel rod is subjected to axial tension of 50 MPa with superimposed torsion of 100 MPa. What is your best prediction of the safety factor with respect to initial yielding if the material has a tensile yield strength of 500 MPa (see Figure A2.4)?
Figure A2.4
A particular machine part is subjected in service to a maximum load of 10 kN. With the thought of providing a safety factor of 1.5, it is designed to withstand a load of 15 kN. If the maximum load encountered in various applications is normally distributed with a standard deviation of 2 kN, and if part strength is normally distributed with a standard deviation of 1.5 kN, what failure percentage would be expected in service? A2.5
Redesign the bolt loaded in tensile impact and shown in Figure A2.6 to increase the energy absorbing capacity by a factor of 3 or more. A2.6
Figure A2.6
Page 2 of 3
A2.7 Consider
a 3.5-in.-diameter steel bar having Su = 97 ksi and Sy = 68 ksi and machined surfaces. Estimate the fatigue strength for (1) 106 or more cycles and (2) 5*104 cycles for: (a) bending (b) axial (c) torsional loading Figure A2.8 shows (1) an unnotched bar and (2) a notched bar of the same minimum cross section. Both bars were machined from AISI 1050 normalized steel. For each bar, estimate (a) the value of static tensile load P causing fracture and (b) the value of alternating axial load ± P that would be just on the verge of producing eventual fatigue fracture (after perhaps 1 to 5 million cycles). A2.8
Figure A2.8
A2.9 Figure
A2.9 shows a shaft and the fluctuating nominal stress (in the center of the 50mm section) to which it is subjected. The shaft is made of steel having S u = 600 MPa and S y = 400 MPa. Estimate the safety factor with respect to eventual fatigue failure if (a) the stresses are bending, (b) the stresses are torsional.