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.A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?
- The state of stress at a point under plane stress condition is Ox = 100 MPa, Oy = 50 MPa, Txy = 20 MPa %3D The radius of the Mohr's circle representing the given state of stress in MPa is: O 32.02 O5071 O60 23 O 100.92The state of stress at a point under plane stress 40 MPa, Oyy condition is Ox = = 100 MPa and Txy 40 MPa. This radius the Mohr's circle representing the given state of stress in MPa is:Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with "full' details Draw the Planes of Principal and Maximum Shear Stresses Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw → S Txy= -5 ksi Ox = 10 Ksi Tyx = 5 Ksi 10 5 -20 -10 5 10 15 20 5 10 Tccw → S'
- you can provide handwritten solution also. At a point in a material under stress, the intensity of the resultant stress on a certain plane is 60 N/mm2 (tensile) inclined 30o to normal of that plane. The stress on a plane at right angle to this has a normal tensile component ofintensity 40 N/mm2.Using the Mohr’s circle calculate, resultant stress on the second plane, the principal planes and stress, plane of maximum shear and its intensity.At point O of a part subjected to plane stress made of steel material (E = 210 GPa and %3D ww v= 0.3) The tensile components are given below. 240 %3D - 30 MPa *yz yz a) The principal stress components (01, 02 and o3) and their angles with respect to the x-y-z axes of the planes where they are formed calculate b) Calculate the maximum shear stress (tmax) and the angles of the plane in which it is formed with respect to the x-y-z axes. c) Drawthe 2-D and 3-D Mohr circles for the stress components. d) At point O in a section plane passing through point O and having an angle of 30° counterclockwise with the +x-axis Calculate the resulting stress components. e) Calculate the strain components (Exx, EW, Ezz, YXV, YXz and Yyz) and draw the 2-D and 3-D Mohr circles for the strain components.Consider the following plane stress state: Ox=30 MPa, y= -60 MPa, Txy= 30 MPa cw Calculate the following: 1. The coordinates of the center of the Mohr's circle C The location of the center of the Mohr's circle Cis ( 2. Principal normal stresses (01, 02) The principal normal stresses are σ₁ = 39.08 3. Maximum shear stress (7) The maximum shear stress is 54.08 MPa. 4. The angle from the x axis to 0₁ (p) The angle from the x axis to 0₁ (p) is -16.85 5. The angle from the x axis to 7 (s) The angle from the x axis to T (s) is 28.15 6. The radius of the Mohr's circle The radius of the Mohr's circle is 54.08. ✰ MPa. MPa and 02 = -69.08 MPa. O -15 MPa, CW CCW O MPa).
- Rod AB is fixed at side A with a length of 500m and a diameter of 20m. On side B, the rod experiences a torque of 2kN-m a compressive force of 10KN and a transverse force of 12kN. a) Find the stress state at center point C. b) Draw mohrs circle for the stress state. (Be sure to include principal values, A, B, sigma1 and sigma2) T= d%=20m 250m ZKN-m IOKN 7. A, 500m I2KNA large thin rectangular plate is subjected to certain traction boundary conditions on its thin edges. The following stress function is proposed for this problem: 2 p(x,y) = A x¹ + B x²y² + Cy² (i) use the biharmonic equation to find restrictions, if any, on values of A, B, and C (ii) calculate all stress components (iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and Poisson's ratio E and y, respectively. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x=+a and y=+bCalcuate Bending From Point A to Point B and Point A to Point C, Calcuate torsion From Point A to Point C. Draw a FBD from point A to point B and another for point A to C indicating what stresses are been calculate. Use the stress tensor and stress cube to Indicate what forces are acting at point A. Force apply at point B is 70lb Distacen from Point A to B is 12 in or 1 feet long Distacen from Point A to C is 3 in Handle diameter 0.625 in