In a material the principal stresses are 60 MN/m², 48 MN/m² and -36 MN/m². When the 1 find the total strain energy per unit volume. values of E = 200 GN/m² and 3 = 0.3
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- Q.70 ox= X The state of stress at a point is given by : = 80 MPa, oy=100 MPa = and txy = 60 MPa. If the yield strength for the material is 150 MPa, as determined in a uniaxial test, then the maximum shear stress is, nearly A 75.5 MPa B с D 127.4 MPa 119.3 MPa 104.0 MPaThe state of plane strain at a point is ɛ = 800 × 10-6, ɛ, = 200 x 10-6 and y. = -600 x 10-6. If material %3D properties are E = 200 GPa and µ = 0.30, then the major principal stress is (nearest integer) MPа.ox The state of stress at a given point in a material component is = 120 MPa; Oy = - 80 MPa and t = 60 MPa The loading on the component is increased so that stresses are increased to values which are k times the given values. Determine the maximum value of k if the material can withstand maximum normal and shear stresses of 300 MPa and 200 MPa respectively. 1 11
- Acube of material is subjected to the following direct stress system: , = +120 N/mm², o, = + 80 N/mm² and o̟=-100 N/mm². If Young's modulus, E, is 200 000 N/mm² and Poisson's ratio, v, is 0.3 calculate the direct strain in the x, y and z directions and hence the volumetric strain in the cube.a. At a point in a given material the three dimensional state of stress is given by ox = oy oz = 10 MPa ,Txy F 20 MPa, Tyz = %3D !! TXZ = 10 MPa. Compute the principle planes if the corresponding principles stresses are, ol = 37.3 MPa, c2 = 10MPA, o3 =2.7 MPa %3D %3D b. , What no2. A copper rod of diameter 12 mm is subjected to a compressive force of 8 kN. The change in diameter happens to be 4.5 x 103 mm. Determine the strain along the length of the material and the Poisson's ratio when E = 110 GPa.
- Q. No .3 On the free surface of an aluminum [E = 10,000 ksi; v = 0.33] component, the strain rosette shown in the figure was used to obtain the following normal strain data: = -500 µɛ, E = -220 µe, and &e = +600 µɛ. Determine the normal stress that acts along an axis that is rotated at an angle of 0= 45° coun- terclockwise from the positive x axis. 60 60 60A homogenous isotropic material of size 20 cm x cm x 20 cm is placed inside a rigid box of internal dimension 20 x 20 x 20 cm. The top of the box is open and the material inside is subjected to a uniform compressive stress of 10 N/mm² from the top. Assuming there is no friction between the surface of contact, find the stresses on the side faces of the material. Also find maximum shear stress, the normal stresses on the plane of maximum shear stress and the change of volume of the material. Young's modulus E is 1 x 105 N/mm² and Poisson's ratio, m = 0.3 for the material. S 10 N/mm² 20 cm 20 cm-Problem 2: A brittle material has the properties Sut=30 kpsi and Suc=90 kpsi. Using the brittle Coulomb- Mohr and modified-Mohr theories, determine the factor of safety for the following states of plane stress. 0z=215 kpsi, oy=10 kpsi, txy=215 kpsi
- A plate in equilibrium is subjected to uniform stresses along its edges with magnitude o = 30 %3D MPa and ow = 50 MPa as shown in the figure. %3D = 50 MPa %3D O = 30 MPa XX ple The Young's modulus of the material is 2 x 1011 N/m2 and the Poisson's ratio is 0.3. If o is negligibly small and assumed to be zero, then the strain Ezz isA critical point in a part made of a ductile material is subject to the following state of plane stress: 15ksi, 30 ksi, 15 ksi, Ox,min = -35 ksi, Oy,min = 30 ksi, Txy,min = -15 ksi. Ох,max бу,max Тxy,max %3D There are no stress concentrations. The load line is propositional. The material has a yield strength of Sy = 130 ksi, an ultimate strength of Su = 200 ksi, and a fully corrected endurance limit of Sn : 75 ksi. Calculate the: (a) Static factor of safety using the MSSTF, (b) Static factor of safety using the DETF, (c) Fatigue factor of safety using the Soderberg criterion, (d) Fatigue factor of safety using the Goodman criterion, (e) Fatigue factor of safety using the ASME elliptic criterion.At an axial load of 22 kN, a 15-mm-thick x 45-mm-wide polyimide polymer bar elongates 4.0 mm while the bar width contracts 0.15 mm. The bar is 260-mm long. At the 22-kN load, the stress in the polymer bar is less than its proportional limit. Determine Poisson's ratio. O 0.175 O 0.217 O 0.297 0.235 O 0.280