A thin plate is subjected to certain boundary conditions on its thin edges leading to the stress function $ = Ax?y* – By6 (a) Find the relationship between A and B for a valid stress function p. (b) Determine all the stress components Oxx, Oyy, Txy.
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- -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. a-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.-18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. 7.3-18 a=2I50kPa, ay=375kPa.Txy.=-460kPa
- A rubber ball (sec figure) is inflated to a pressure of 65 kPa. At that pressure, the diameter of the ball is 240 mm and the wall thickness is 1.25 mm. The rubber has a modulus of elasticity E = 3,7 MPa and Poisson's ratio v = 0.48. (a) Determine the maximum stress and strain in the ball, (b) If the strain must be limited to 0.425, Find the minimum required wall thickness of the ball.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 clementDuring 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.
- The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.Find the stresses in each direction, also find the change in volume of the block of dimension 120 mm x 60 mm x 43 mm, subjected to 3 mutually perpendicular loads. The load along length, breadth and depth directions are 10 kN (tensile), 25 kN (tensile), 13 kN (compressive) respectively, Take E as 180 GPa, Poisson's ratio as 0.3. The stress along length direction (Unit in kN/m2)= _____________ The stress along width direction (Unit in kN/m2)= _____________ The compressive stress along depth direction (Unit in kN/m2)= _____________ The change in volume of the block is (unit in mm3) = ______________In a biaxial state of stress, normal stress are 900 N/mm^2 and 100 N/mm^3 in x and y diretion respectively. Shear stress is 300 N/ mm ^2. The maximum principal stress will be,
- Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12 ksi, Sy = 17 ksi, and Sxy = 18 ksi.(a) Draw Mohr’s circle for this state of stress.(b) Determine the principal stresses (σp1>σp2σp1>σp2) and the maximum in-plane shear stress τmaxτmax acting at the point.(c) Find the smallest rotation angle θpθp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16)A state of stress at a point A is given by σx = 45 MPa, σy = 9.1 MPa, and τxy = -5.75 MPa. What is the maximum in-plane shear stress for the point A.A rectangular block of material is subjected to a tensile stress of 90 N/mm2 along X axis and acompressive stress of 45 N/mm2 on a plane at right angle to it, together with shear stresses of80 N/mm2 on the same plane. Calculate the direction of principal planes, the magnitude ofprincipal stresses and the magnitude of greatest shear stresses.