Two dimensional stress system on a block made of a material with Poisson's ratio of 0.3 is shown in fig. A O B 60 N/mm² The limiting magnitude of the stress so as to result in no change in length AB of the block N/mm². is
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- The stale of plane stress at a point is represented by the stress element shown in Fig. Q1. Determine the principal stresses and draw the corresponding stress element. Q1 50 MPa 80 MPa 80 MPa 25 MPa 50 MPa Answer: 0= 54,6 MPa with ep1 = 100.5 Omin = -84.6 MPa with ep2 = 10.5 %3! %3DQ. 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 6014. For a linear elastic material with Young's modulus E=20 MPa: a) Calculate the amount of longitudinal strain ewhen a specimen made of this material is subjected to uniaxial tension at the stress level o =6 КРа. b) Draw the stress-strain diagrams corresponding to the respective loading protocols e1(t) and ɛ 2(t) given in the figure below Loading e (1) Loading e:(t) Ei (t) (1) 0.04 10 20 t(s)
- The 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°The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle 0, locating the X-axis is assumed to be positive when measured from the x-axis in counter-clockwise direction y = 120 MPa 40 MPa Oxy 50 MPa %3D 30% Oyy = 35.6 MPa The absolute magnitude of the shear stress component o,xy (in MPa, round off to one decimal nlace) in x-y coordinate system isThe 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 mm
- a L₁ C 3 of 6 > Determine the orientation of the planes maximum and minimum normal stress, ₂1 and ₂2. respectively. Use the value for 8,2 that is negative. Then use this value to determine the value of 8,1. Express your answers to four significant figures separated by a comma. ► View Available Hint(s) VAΣo↓ vec ? 8p1, 8p2= Submit Part B - In-plane principal stresses Determine the in-plane principal stresses for the element (as oriented in Part A), and calculate 01 and 2 such that they correspond with 81 and 8,2. Express your answers to four significant figures separated by a comma. ► View Available Hint(s) IVE ΑΣΦ vec ? 5 OThe stiffened top skin of a wing structure is modelled as a panel has simply supported edges as shown in the figure below. a The sheet is 4.7 mm thick and the stringers are spaced at b 0.6 m. Assume the dimension of the panel in spanwise direction is much longer than the chordwise direction. The material constants are: E 70 x 10' N/m2, Poisson's ratio v 0.34. Determine the spanwise stress at which the sheet between the stringers will begin to buckle. Give your answer in MPa to three decimal places.Q.5 A component of machine made of steel which resist a biaxial state of stress o,= -120 MPa and t = 100 MPa. Check whether this part is safe or fail using 1. Max. principal stress theory 2. Max principal strain theory 3. Max. distortion energy theory.
- A rígid steel bar is supported by three rods as shown. There is no strain in the rods before the load P is applied. After load Pis applied, the normal strain in rods (1) is 2120 μm/m. Assume initial rod lengths of L1 = 1,250 mm and L2 = 2,000 mm. Determine the normal strain in rod (2). (1) (2) Rigid bar 1325 μm/m O 1546 μm/m O 1790 μm/m 1712 μm/m 1435 μm/m P L₂ O (1)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 =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