point, another plane B, inclined at 45°, on the normal aly Mohr's stress circle technique to find the princip and B relative to the principal planes.
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- EB and FG are two planes inside a soil element ABCD as shown in Figure 10.50. Stress conditions on the two planes are Plane EB: EB = 25 kN/m2; EB = +10 kN/m2 Plane FG: FG = 10 kN/m2; FG = 5 kN/m2 (Note: Mohrs circle sign conventions for stresses are used above) Given ; = 25, determine: a. The maximum and minimum principal stresses b. The angle between the planes EB and FG c. The external stresses on planes AB and BC that would cause the above internal stresses on planes EB and FG6) Across Plane #1, the state of stress is measured as: On 1.1 kb and os 0.4 kb Across Plane #2 which is at right angles to Plane #1, the state of stress is: On 0.7 kb and os=- = -0.4 kb Assuming that one principal stress lies parallel to the intersection of the planes, a. What are the values of o1 and 03? b. What is the angle between 1 and the normal of plane #1? c. Draw Planes 1 and 2 with respect to the principal stresses, 01 and 03.. At a point, the major principal stress is 5000 psf compression and the minor principal stress is 2000 psf compression. (a) Draw the Mohr's circle for this stress combination. (b) Find the maximum shear stress, and also indicate the value of normal stress acting on this same plane. (c) Determine the values of the normal and shear stress acting on a plane that is 60° from the major principal plane. 2. At a point, the major principal stress is 80 psi compression and the minor principal stress is 20 psi compression. (a) Draw the Mohr's circle for this stress combination. (b) What is the maximum shear stress acting at the point, and what value of normal stress acts on this same plane? (c) Determine the value of the normal and shear stress acting on a plane that is 60° from the minor principal plane. 13. The major and minor principal stresses acting at a point are 80 psi compression and 20 psi tension. (a) Draw the Mohr's circle for this stress combination. (b) What is the maximum shear…
- Determine the absolute maximum shear stress for each of the following plane stress states for which the principal stresses are given.(a) σp1 = 2540 psi, σp2 = -2120 psi, σp3 = 0(b) σp1 = 63 MPa, σp2 = 53 MPa, σp3 = 0Problem 2: The stresses shown act at a point on the free surface off a stressed body. a) Determine the principal stresses and the maximum in-plane shear stress acting at the point b) Show these stresses in an appropriate sketch. c) Determine the normal stresses on and ot and the shear stress Tnt that act on the rotated stress element. 53 MPa 16 MPa 47 MPa 35⁰At a point in a stressed material, the major principal stress is 66 kPa compression and the minor principal stress is 34 kPa tension. (a) Use the Mohr’s circle to determine the shear and normal stress on a plane 45° ccw from the major principal plane. (b) Determine the stress combination acting on the plane 75° ccw from the major principal plane.
- 3. (a) A prismatic bar is subjected to an axial compressive stress of 85N/mm. Determine the i. Stresses acting on the plane which is at an angle e= 40° with reference to the x-axis. ii. Magnitudes of maximum, and minimum normal stresses induced and the position of their planes Us" ii. Magnitude of normal Stress on the plane of maximum shear stressSIMPLE STRESSES 340 mm Two plates are connected by bolts as shown in the figure. Compute the maximum axial stress that each plate will handle. The allowable shear stress of each bolt is 50 MPa and the diameter of each bolt is 20 mm. F F 150 mm 册 F 50 mm 340 mmThe stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 22.6 ksi, Sy = 2.2 ksi, and Sxy = 3.8 ksi. Assume β=33∘β=33∘. Determine the normal stresses σxσx and σyσy and the shear stress τxyτxy at the point.
- The two-dimensional state of stress is given as = 10 MPa, 0 = 5 MPa and T₁ = 2.5 MPa. Determine the following on a plane inclined at an angle of 30° from the x-plane in anticlockwise direction. (i) Normal stress, (ii) shear stress, (iii) resultant stress and (iv) principal stresses. 30° 12.5 (a) 2.5 -10 normal on plane AB 6.30 30° (b) xA high-strength steel [E = 188 GPa] tube having an outside diameter of 67 mm and a wall thickness of 4.1 mm is bent into a circular curve having a 42-m radius of curvature. Determine the maximum magnitude of the bending stress max developed in the tube. Answer: Omax = i MPa.2. At a point, the major principal stress is 80 psi compression and the minor principal stress is 20 psi compression. (a) Draw the Mohr's circle for this stress combination. (b) What is the maximum shear stress acting at the point, and what value of normal stress acts on this same plane? (c) Determine the value of the normal and shear stress acting on a plane that is 60° from the minor principal plane. 13. The major and minor principal stresses acting at a point are 80 psi compression and 20 psi tension. (a) Draw the Mohr's circle for this stress combination. (b) What is the maximum shear stress acting at the point, and what value of normal stress acts on the plane? (c) Determine the value of the shear and normal stress acting on a plane that is 30° from the major principal plane. 14. At a point, the normal and shear stresses acting on one plane are 8000 psf compression and 2000 psf, respectively. On a perpendicular plane, the normal and shear stress combination is 2000 psf compression…