The flow stress (in MPa) of a material is given by 500 e0.1 , Where e is true strain. The Young's modulus of elasticity of the material is 200 GPa. A block of thickness 100 mm made of this material is compressed to 95 mm thickness and then the load is removed. The final dimension of the block (in mm) is
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- Compare the engineering and true secant elastic moduli for the natural rubber in Example Problem 6.2 at an engineering strain of 6.0. Assume that the deformation is all elastic.The failure stress of a homogeneous steel bar having a diameter of 10 mm is 250 MPa. Using a factor of safety of 2.0 and if the elastic mođulus and length of the bar is 200 GPa and 2 m respectively, calculate the elongation in mm of the bar corresponding to the maximum load it can support. (А) 5 (в) 2.5 1.25 D) 0.625A steel bar, whose cross section is 0.60 inch by 4.10 inches, was tested in tension. An axial load of P = 31,025 lb. produced a deformation of 0.115 inch over a gauge length of 2.10 inches and a decrease of 0.0080 inch in the 0.60-inch thickness of the bar. a. Determine the lateral strain. b. Determine the axial strain. c. Determine the Poisson’s ratio v. d. Determine the decrease in the 4.05-in. cross-sectional dimension (in inches).
- At the proportional limit, the axial load of a 0.80-in-diameter bar was 5600 lb. A 2.30-in. gauge length on the bar has increased by 0.0044 inch. Determine the stress (in ksi) in the bar at the proportional limit. * 6 * Determine the strain in the bar. 7 Determine the elastic modulus (in ksi). * Ket2. 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.1500 KN 800 mm 70 mm 100 mm 1500 KN A bar has a length of 800 mm, width 100 mm, and thickness 70 mm, and is being subjected to 1500 KN of tension as shown. As a result, the length of the bar as increased to 802.5 mm and its width has decreased to 99.906 mm. Assume elastic behavior. a) Determine the Young's modulus (E) of the material b) Determine the Poisson's ratio (v) of the material c) Determine the Shear modulus (G) of the material d) Determine the new thickness of the bar in mm e) Determine the percentage change in the total volume of the bar
- The stress concentration occurs whenever there is an abrupt change in the cross-section of a component or there is any discontinuity in the material. The figure given below shows a flat plate with a hole of diameter d. The plate is fixed at one end and the other end is subjected to a tensile load of P = 44 kN due to which there is a change in length of 0.4 mm. The thickness of the plate is 11.5 mm. The maximum stress developed in the flat plate is 228 MPa. Take Young's modulus(E) = 210 GPa and theoretical stress concentration factor =2, Calculate the following values: i) Width of the plate (W2) in mm ( ii) Nominal Stress in MPa ( iii) Diameter of the hole (d) in mm7. A steel rod of diameter 10 mm carries an axial load of 10 kN. Consider the modulus of elasticity and Poisson's ratio of 20 GPa and 0.30 respectively. Calculate: a) the normal stress in the rod. b) the lateral strain in the rod. c) the change in diameter of the rod when the load is appliedA steel block has a length of 80 mm, width of 60 mm and thickness of 40 mm. The block is subjected to a uniform hydrostatic pressure of 180 kPa on all its faces. Modulus of elasticity E=200 GPa, Poisson’s ratio ?= 0.29. a.) Determine the bulk modulus of steel, b.) Determine the dilatation (e) of the material if e is the negative of the ratio of load to bulk modulus., and c.) Determine the change in volume of the steel block.
- The stress concentration occurs whenever there is an abrupt change in the cross-section of a component or there is any discontinuity in the material. The figure given below shows a flat plate with a hole of diameter d. The plate is fixed at one end and the other end is subjected to a tensile load of P = 41 kN due to which there is a change in length of 0.4 mm. The thickness of the plate is 11 mm. The maximum stress developed in the flat plate is 235 MPa. Take Young's modulus(E) = 210 GPa and theoretical stress concentration factor =2, Calculate the following values: i) Width of the plate (W2) in mm ii) Nominal Stress in MPa iii) Diameter of the hole (d) in mm Hole with stress concentration factor 2 35 mm W2 35 mm P 300 mm 350 mm- 250 mm3. The material is subjected to biaxial loading producing uniform normal stress ox and o, as shown. The strains are e, = -0.00065 and e, = -0.00040. Use E = 207 GPa and v = 0.35. Determine the following: (a) oz. Indicate tension or compression. Use 2 decimal places. (b) ơy. Indicate tension or compression. Use 2 decimal places. (c) Change in the thickness of the material. Indicate elongation or contraction. Use 5 decimal places and scientific notation of x 10-3 (Example: . (25 pts) x 10-3) y Oy x. Oy t = 16 mmBefore loading on the cylindrical brass rod, its length is L, = 0.3 m and its radius is r, = 30 mm. When this rod is pulled from its free end with a load of P = 60 kN, the radius becomes r = 29.998 mm. Calculate the change in length (AL) of the rod. Calculate the axial strain (ɛ) and the lateral strain (ɛ,). Calculate the Poisson's ratio (v) of the material. Calculate the shear modulus (G) of the material. o [MPa] SOLUTION L. 72 2r. O 0.00066