2. The Goodman diagram relates oa and om for fatigue failure after a specific number of cycles N₁, where da is the cyclic stress amplitude, and on the mean stress. For a steel specimen it is found that oa oa (0). [1- (om/OTS)] where Ors is the metal's tensile stress (375MPa), and a (0)~0.450Ts is the 107 cycle fatigue limit at zero mean stress. Assuming the specimen is cycled repeatedly between 0 stress and a peak stress, what is the maximum peak stress if failure in < 107 cycles is to be avoided? Ans: 233 MPa

An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 680 mm. The cross-sectional dimensions of the beam are b1 = 33 mm, d1 = 93 mm, b2 = 20 mm, d2 = 20 mm, and a = 6.5 mm. For this material, the allowable tensile bending stress is 16 MPa, and the allowable compressive bending stress is 9 MPa. Determine the %3D largest moment M that can be applied as shown to the beam. b2 M d2 d1 | A B L b1 Answer: M = i N•m

An aluminium specimen with an initial gauge diameter d, = 10 mm and gauge length, 1, = 100 mm is %3D subjected to tension test. A tensile force P= 50 kN is applied at the ends of the specimen as shown, resulting in an elongation of 1 mm in gauge length. The Poisson's ratio (µ) of the specimen is Take shear modulus of material, G = 25 GPa. Consider engineering stress-strain conditions. P

2.27. The stress components at a given point in an engineering component are es- timated to be oxy=4.1 ksi, ơyy=0 ksi, ơz =0.9 ksi, ory =-3.1ksi, ơyz = 1.2 ksi, Ozx =0 ksi. Estimate the factor of safety against yielding using von Mises' theory if the uniaxial yield stress of the material is Sy =17.2 ksi.