126. If the principal stresses at a point in an elastic material are 2f tensile, 1.5f tensile and f compressive. What is the value of fat failure using maximum principal stress theory? (Take the elastic limit in simple tension as 210 N/mm² and u = 0.3)
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- 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 mm2. For the state of stress shown, determine the range of value of for which the normal is equal to or less than 100 MPa and 50 MPa. stress x' + 90 MPa 60 MPa =The stress–strain diagram for the material of a column can be approximated as shown. Plot P/A vs. KL/r for the column.
- Q: A piece of material is subjected to tensile stress of 70 N/mm² in one direction and a compressive stress of 50 N/mm² in a direction at right angles to the previous one. Find fully the stresses on a plane the normal of which makes an angle of 40 degree with the 70 N/mm2 stress.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 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 applied
- Question- Principal stress at a point in an elastic material are 1.50 (tensile), o (tensile) and 0.50 (compressive). The elastic limit in tension is 210 MPa and poisson's ratio=0.3. Find the value of o at the failure when computed by the maximum principal strain theory.Steel cylinder has 200 mm mean diameter with a wall 1 mm thick and 310 mm long. Determine the circumferential and longitudinal stresses that occur on the cylinder if the maximum pressure difference allowed between the inside and outside must not exceed 100 MPa. Determine the effects of three dimensional loading by determine volumetric strain and change in volume for the first steel cylinder. Modulus of elasticity E= (210 GPa), Poisson's ratio 0.30. 7A beam with varying load is shown at the figure below. If the beam properties are given, what is the final stress at top of the beam at midspan where total losses of the prestressing force is 21% (MPa)
- 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 barProblem: A steel rod with a cross-sectional area of 180 mm2² is stretched between two fixed points. The tensile load at 25°C is 3,600N. Assume thermal coefficient equal to 11.7 x 106 mm/ (mm°C) and E= 200 GPa. a. What is the temperature at which the stress will be zero? b. What is tthe temperature at which the compressive stress will be 48 MPa?A load of 1000 N is applied as shown in figure, given cross-sectional area of bar 1 & 2 is 100 mm² & 80 mm2, young modulus of elasticity E₁ = 120 GPa, E₂ = 150 GPa. Calculate the minimum normal stress (in MPa) (1) (2) P= P= 1000 N