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- 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 60If the angle of obliquity for the resultant stress at a plane which is 45° from the principal stress is 30° as shown in the figure then find the ratio of stress in x-direction to stress in y-direction. A-3.73 B 3.73 C 1.73 6² D 0.268 Correct Option B # 45%3 - A strain gauge is attached to the side of a beam, as shown by the cross-section view in the figure. When the beam is subjected to a specified uniform moment, the longitudinal strain measured by the gauge is -300μ. Plot the axial stress profile over the height of the cross- section. What is the magnitude of the moment that produced this strain gauge reading? Assume E = 75 GPa. 10↑ Strain gauge dimensions in mm 30 30 beamcross-section
- 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 mmThe stresses at a point in a bar are o1 = 28N/mm2 (tensile) and o2=12N/mm2 (compressive) as shown in Figure (a) Determine the normal, tangential and resultant stress in magnitude and direction on a plane inclined at 55° to the axis of the major stress. (b) Determine the maximum intensity of shear stress in the material at the point. (c) Also, solve the same problem using Mohr's circle method and compare the results. O2 Axis of Major Stress 55°2. 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 =
- 1.16 The stress-strain relationship shown in Figure P1.16 was obtained during the tensile test of an aluminum alloy specimen. 60,000 H Stress, psi 40,000 20,000 0 Figure P1.16 0.002 0.004 0.006 0.008 Strain, in./in. Determine the following: a. Young's modulus within the linear portion. b. Tangent modulus at a stress of 45,000 psi c. Yield stress using an offset of 0.002 strain d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used? 4The 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 mmA state of stress is specified in the figure shown. Determine the principal stress oy (mPa) if P =-20 mPa and y = 15 mPa P V
- A strain gage is installed in the longitudinaldirection on the surface of an aluminum beveragecan (see figure). The radius-to-thickness ratio of thecan is 200. When the lid of the can is popped open,the strain changes by ε0 = 187 X10-6.(a) What was the internal pressure p in the can?(Assume E =10 X106 psi and n = 0.33.)(b) What is the change in strain in the radialdirection when the lid is opened?q10At a point in a two dimensional stress system, the normal stress on two mutually perpendicular planes are o and o and shear stress is t One of the principal stresses will become zero when the value of shear stress Txy is (a) ±(0) (c) ±/0 +0yy (d) +/oo yyThe components of plane stress at a critical point on a steel shell are shown in the figure below. The yield stress (Gy) of the material in simple tension is 250 MPa. 60 MPa 40 MPa 70 MPa (a) Determine the magnitude of the principal stresses and maximum shear stress. Sketch these on appropriately orientated elements. (b) Calculate the factor of safety against yield on the basis of i. Tresca failure criterion ii. Von Mises failure criterion