Problems E-mail : russin10@yonsei.ac.kr H.P. : 010-3066-6339 신재혁

1. An annealed–steel tensile specimen (E = 200 GPa) has a 12 mm minimum diameter and a 50 mm-gage length. Maximum load is reached at 7,000 kg (=68.6 kN), and fracture occurs at 4,500 kg(=44.1 kN). What is the tensile strength? Why does fracture occurs at a lower load than maximum load? What is the deformation when a tensile stress of 100 MPa is applied?

2. A wire 300 m long elongates by 3 cm when a tensile force of 200 N is applied. What is the modulus of elasticity (in MPa) if the diameter of the wire is 5 mm?

3. A cylinder of cast iron 12 mm in diameter by 50 mm long is tested in compression. Failure occurs at an axial load of 22,000 kg on a plane inclined 40° to the axis of the cylinder. Calculate the shearing stress on the plane of failure.

4. Determine the shear stress τy′x′ for the x′ axis inclined at θ=30° to the x axis. The stress state is given by

5. A cubic crystal is loaded with a tensile stress of 2 5. A cubic crystal is loaded with a tensile stress of 2.8 MPa applied along the [210] direction, as shown in Figure. Find the shear stress on the (111) plane in the direction.

6. Find the principal stresses and the orientation of the axis of principal stress with the x,y axes for the following situations: (a) σx = + 340 Mpa σy = + 34 Mpa τxy = - 55 Mpa (b) σx = - 410 Mpa τxy = + 170 Mpa

7. Construct a Mohr’s circle of stress for each of the plane-stress conditions given in Prob. 6.

8. A body is loaded under stresses, σx = 150 MPa, σy = 60 MPa, τxy = 20 MPa, σz = τyz = τzx = 0. Find the three principal stresses, sketch the three-dimensional Mohr’s circle diagram for this stress state, and find the largest shear stress in the body.

9. On a plate of materials (E=170GPa, v=0 9. On a plate of materials (E=170GPa, v=0.25) strain gages are arranged as shown. When the plate is loaded, the gages read e1=1,860 x 10-6, e2=185 x 10-6, and e3 = 1,330 x 10-6. y What is the largest normal stress? What is the smallest normal stress? What is the largest shear stress? 45° 30° x 30°

10. Young’s modulus (E) of a cubic single crystal as a function of orientation is given by where l1, l2, and l3 are the direction cosines between the direction hkl and [100], [010], and [001], respectively. For copper, E111 = 19 GPa and E100 = 66 GPa. Calculate Young’s modulus for a copper single crystal in the [110] direction.

11. For iron, C11 = 237 GN/m2, C12 = 141 GN/m2, and C44 = 116 N/m2. Determine the respective compliances for Fe.