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- - A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.At a point on the web of a girder on an overhead bridge crane in a manufacturing facility, the stresses arc known to be x = —4300 psi, a = 1700 psi, and r = 3100 psi (the sign convention for these stresses is shown in Fig, 7-1). A stress clement located at the same point in the structure (but oriented at a counterclockwise angle 0, with respect to the _y axis) is subjected to the stresses shown in the figure {b, r», and 2100 psi). Assuming that the angle 8Xis between zero and 90°, calculate the normal stress trA, the shear stress ta, and the angle BvThe hollow drill pipe for an oil well (sec figure) is 6,2 in. in outer diameter and 0.75 in. in thickness. Just above the bit, the compressive force in the pipe (due to the weight of the pipe) is 62 kips and the torque (due to drilling) is 185 kip-in. Determine the maximum tensile, compressive, and shear stresses in the drill pipe.
- A copper rod of length L = 18.0 in. is to be twisted by torques T (see figure) until the angle of rotation between the ends of the rod is 3.0°. (a) If the allowable shear strain in the copper is 0.0006 rad, what is the maximum permissible diameter of the rod? (b) If the rod diameter is 0.5 in., what is the minimum permissible length of the rod?A close ends long thin walled cylindrical shell is subjected to an internal pressure. What is the ratio of the hoop stress to longitudinal stress developed in the shell ?2. At a point in a brocket, the stresses on two mutually perpendicular planes are 180 MN/m? (tensile) and 70 MN/m2 (Compressive). The shear stress across the planes is 65 MN/m2. Find the following by Mohr's Circle method and compare with Analytical solutions: (i)The Normal stress on a plane making an angle of 50° with the plane of first stress. (ii)Shear stress on the plane (iii) Maximum shear stress (iv) Resultant stress and it's direction. (v) Major and minor principal stresses.
- A 30 ?? square plate is subjected to uniform pressure as shown in Figure.1. The 2D loading stressesare described. If the modulus of elasticity is 200 ??? and the lateral constant (Poisson's ratio ? = 0.3). Estimatethe change in length in the vertical, horizontal and diagonal sides as well as determine the volumetric strain.Illustrate the effect of two-dimensionalstrain by constructing appropriate sketches (before and after deformation).Repeat the analysis for lower value of pressure and higher value in the range of [20 -100 MPa] and comment onthe overall results.P solid, see Fig below. The outer diameter of the hollow and solid sections is 6 cm and the inner A circular metal bar with a 15 cm long section being hollow and a 30cm long section being diameter of the hollow section is 3.5 cm. The bar is loaded to an extension of 5 mm and then unloaded. o MPa The stress-strain curve of the metal is shown in the diagram below: solod -hollow квост. Calculate: a) Maximum load, P b) Length after unloading Бет 3.5 cm 250 P 10 = .01 .02 .03 € 6cmQ4 (a) A thin eylinder 95 mm internal diameter, 500 mm long with walls 4.5 mm thick is subjected to an internal of 9 MN/m2. If E = 200 GPa and v = 0.25, and assuming rigid end plates. Calculate: (i) The change in volume. (ii) The change of internal diameter and change in length. (iii) The value of hoop and longitudinal stresses.
- ompletion QUESTION 8 The stepped down circular bar with diameters 2d and d is subjected to a tensile axial force aligned with its axis. The ratio of direct stress in segment AB to direct stress in segments BC is: OIE 2d O a. 2:1 O b. 1:4 Oc. 4:1 O d. 1:2 QUESTION 9 The segments AB and BC of composite bar constructed of the same steel have identical cross-sectiona in ouhinntod to a comnressive axial load. The raPart (1): A 30 ?? square plate is subjected to uniform pressure as shown in Figure.1. The 2D loading stresses are described. If the modulus of elasticity is 200 ??? and the lateral constant (Poisson's ratio ? = 0.3). Estimate the change in length in the vertical, horizontal and diagonal sides as well as determine the volumetric strain. Illustrate the effect of two-dimensionalstrain by constructing appropriate sketches (before and after deformation).Repeat the analysis for lower value of pressure and higher value in the range of [20 -100 MPa] and comment on the overall resultsQuestion: Find schematically the normal and shear stresses in the plane when the element in the plane stress state is rotated 30 degrees counterclockwise with the Mohr circle.