the Mohr's circle
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- At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clement-27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile stress The stresses on element A oriented at angle ?? x1=45° aresy1= 75 psi. tx1y1= 275 psi. . Find the state of stress on the element lilt is rotated clockwise to align the x3 axis with the horizontal x axis.A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
- A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses with a magnitude of 42 MPa in the horizontal direction and tensile stresses with a magnitude of 9.5 MPa in the vertical direction (sec figure part b). Also, shear stresses with a magnitude of 15.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40g from the horizontal. Show these stresses on a sketch of an element oriented at this angle.During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
- 4 In a plane stress condition, the components of stress at a point are ox= 20 MPa, oy = 80 MPa and Oxy = 40 MPa the maximum shear stress (in MPa) at the point isThe principal tensile stress at a point across two mutually perpendicular planes are 100 N/mm2 and 40 N/mm2. The normal, tangential and resultant stresses on a plane inclined at 20° to the axis of the minor principal stress by analytical method is2- The state of stresses at a point are defined as follows. Find the normal and shear stress vector components (O₂. ) on a plane tangent to a cylinder of diameter D and coaxial with x-axis (Z-axis) at point (B.y.B). Also, determine the octahedral shear stress. Stu. Nom. D B Y 30 45 60 5.0 2.0 1.5 Ju = 45 20 50 MPa 60 50 10
- 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.3. An axial pull of 35000 N is acting on a bar consisting of three lengths as shown below. If the Young's Modulus is 2.1 x 105 N/mm2. Determine (i) Stresses in each section, and; (ii) Total extension of the bar. Section 3 Section 2 Section 1 35000 N 35000 N 2 cm DIA 3 cm DIA 5 cm DIA k-20 cm- 25 cm -22 cm-1-A bar of square cross section is subjected to point loads of P1, P2, P3 and P4 as shown here. Find the magnitude of the force P3 necessary for the equilibrium, if P1= 110 kN, P2 = 210 kN & P4 = 190 kN. Also, determine the stresses in each section & the net change in the length of steel bar. square of size a1=50mm, L1=30 cm, size a2 = 40mm, L2=39 cm, size a3=50 mm & L3 =32 cm Take E = 166 GPa. The force P3 to make it to equilibrium in kN is The Stress in section 1 in N/mm2 is The Compressive Stress in section 2 in N/mm2 is The stress in section 3 in N/mm2 is The total change in length in x10-3 mm is