4.16. Show that the linear stress-rate of strain relation given by Eq. (4-53) implies that stress tensor is symmetric.
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- Displacement components at a point in a solid u(x, y,t) = 2y²x+2t v(x, y, t) = 8y'x + 5t2 w(x, y, t) = 3zy'x + 5xt² |3D a) the strain tensor, b) stress tensor c) Find out if the strain satisfies the fit equations?PROBLEM SET 1 A rigid bar AB is hinged to a vertical wall and supported horizontally by a tie bar CD as shown in the figure, The tie bar has a cross sectional area A=0.10in² and its allowable stress in tension is 20,000 psi. Find the safe value of the magnitude of the load P and the corresponding vertical deflection AB of point B. The tie-bar has a modulus of elasticity of E=30x106 psi. P B C 4ft D A 3ftProblem 3.4 The stress tensor has components at point P in ksi units as specified by the matrix 3 -6 [tij] = 3 6. 9. -6 -6 Determine: (a) the stress vector on the plane at P whose normal vector is 1 n = (êj + 4ế2 + 8ế3) , (b) the magnitude of this stress vector, (c) the component of the stress vector in the direction of the normal, (d) the angle in degrees between the stress vector and the normal.
- 1. Given stress on an element as shown. a) Using both Analytical method and Graphical method Determine ) σ1, σε ii) The maximum shear stress b) Using pole method of finding stress determine stress on a plane inclined at 30° clockwise from the major principal stress plane 40 MPа B 75 MPа 75 MPа А 20 MPа 40 MPаQuestion 2 The stress acting on two planes at a point is indicated in Fig. 2. Determine using the stress transformation equations: a) the shear stress on plane a- a and sketch the orientation of the element with the relevant stress components. b) the principal stresses at the point (sketch of orientation of the element in principal direction not required). Hint: Associate plane b - b with the x - y and plane a - a with the x'-y' coordinate system. b [MPa] 80 Ta 90° 45° 60 60° b Figure 2: plane stress statePart C - Counterclockwise Rotation of a Stress Element Figure 5 of 6 The state of stress at a point in a member is shown on the rectangular stress element in (Figure 5) where the magnitudes of the stresses are |0z| = 13 ksi, Joy = 23 ksi, and |Tzy| = 12 ksi. Determine the state of stress on an element rotated 45° counterclockwise from the element shown. Express your answers, separated by commas, to three significant figures. • View Available Hint(s) Vol AEO I vec Or =, oy =, Tự'y = ksi, ksi, ksi Submit Pearson
- PROBLEM 1: The frame shown in the figure is carrying a traingular distributed load. Pins at A and B are forced in single shear while the pin at C is forced in double shear. If the allowable tensile stress of bar BC is 300 MPa and the allowable shear stress of pins is 150MP3; (a) The cross sectional area of BC (b) The required diameters of pins A, B and C as multiples of mm. w = 8 kN/m 6 m 5 m 3 mTwo dimensional stress tensor at a point is given by a matrix *][* [100 30 30 20 The maximum shear stress is MPa MPa.The strain components Ex, Ey, and y,yare given for a point in a body subjected to plane strain. Using Mohr's circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle 0, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 0 µE, ɛy = 400 µɛ, Yxy = 220 µrad. Enter the angle such that -45° s0,s+45°. Answer: Ep1 = με Ep2 = με Ymax in-plane= prad Yabsolute max. prad 0, =
- QUESTION 2 An element in plane stress is subjected to stresses; Ox , Oy, and Txy (FIGURE 2). Using Analytic method, determine the stresses acting on an element oriented at an angle 0. (Note: The angle 0 is positive when counter clockwise and negative when clockwise) i. Normal Stress (ox', oy ') ii. Normal Shear Stress (Txy') iii. Shear Stress Maximum (t max ) iv. Show the stresses on a sketch of an element oriented at the angle 0. 100 MPa 50 MPa 150 MPa 60° 150 MPa 150 MPa FIGURE 2Learning Goal: To determine the effects of certain geometric shapes, namely fillets and circular cutouts, on the stress distributions inside a rigid body and to determine the maximum applicable axial force in the same rigid body while considering these stress concentrations. The member shown below is made of steel (oallow = 20.0 ksi ) that is 2.75 in thick. The member is subjected to an axial force P that is applied at both ends. Let r = 1.25 in , w = 5 in , h = 2.5 in , and d = 1 in .Q. No. 4: The state of plane stress at a point is represented by the stress element shown in figure.Analyze the element for stresses acting on an element oriented at 30° clockwise with respect to the original element.