* 'Determine the ox 30 MPa 10 MPa 20 MPa The state of plane stress at a point is represented on the upper element shown in the figure. The lower element oriented 40° from the position shown. x 40°
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- An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec figure). On this inclined clement, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an clement whose sides are parallel to the \y axes, that is, determine crv, tr(_, and t, Show the results on a sketch of an clement oriented at B .-26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. aAssume that the normal strains x and y , for an clement in plane stress (see figure) are measured with strain gages. (a) Obtain a formula for the normal strain x in the : direction in terms x , y and Poisson’s ratio v. (b) Obtain a formula for the dilatation L’ in terms of x , y and Poisson’s ratio v.
- -18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (see figure). Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.The state of plane stress at a point is represented on the element shown in the figure. The element oriented 40° 'counterclockwise. Find the value of ox 30 MPa 20 MPa -10 MPa +55.2 Mpa +11.4 Mpa -37.9 Mpa +24.7 Mpa -11.4 Mpa +37.9 Mpa -55.2 Mpa -24.7 Mpa +45.9 Mpa -45.9 Mpa5/5 find the normal stress at left of point C A 100 C 40 kN 50 kN 40 mm 70 10 kN 20 mm 30 mm 100 mm 300 mm 300 mm 200mm B.
- 100 kN and 200 kN to the rectangular column in the figure Two forces act in intensity. A and B according to given on the stress element by finding the stresses at show. 100 kN 200 kN 140 80 120At a point in a component, the state of stress is shown on the element below. Assume that the stress magnitudes are sy- 8544 psi and Sy = 4835 psi. The stresses act in the directions indicated in the figure. Determine the magnitude of the absolute maximum shear stress that acts at the point. Answer: Tmax=i psi %3DThe state of plane stress at a point is represented by the element shown in the figure. Oy o, = 200 Mpa oy = 450 Mpa Txy Try 3D200 Мра Click here to see all formulas Ox Part A - Determine the maximum principal stress in Mpa. O 253 О 355 O 507 O 760 O 608 Submit Request Answer O O O O O
- State of stress at the wall and the roof of the following circular opening bafore the excavation is (a] = |0 4. Find the induced stress components at point a. R W with respect to the given x-y coordinate systerm, and expresst them in the matrix form. b. Find the total stresses at point W, and give them in matrix form. c. Repeat (a) and (b) for the roof. d. Find the stresses oy, Ciy, and tyy at point A which is located at a radial distance twice the radius of the tunnel.100 kN Two forces, 100 kN and 200 kN, act on the rectangular column in the figure. Find the stresses at A and B points according to the given and show them on the stress element. 200 kN 140 80 120Problem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.