The state of stress at a point in a member is shown on the rectangular stress element in (Figure 4) where the magnitudes of the stresses are |0x| = 171 MPa and | Txy| = 57 MPa. Determine the state of stress on an element rotated 100° clockwise from the element shown. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) σx' =, σy' =, Tx'y' = Submit ΜΕ ΑΣΦ vec ? MPa, MPa, MPa Figure > 4 of 6 >

Learning Goal: Part A - Orientation of the planes of maximum and minimum normal stress To determine the in-plane principal stresses and maximum shear stress along with their orientations and the average normal stress for an element in a given state of plane stress. Determine the orientation of the planes of maximum and minimum normal stress, 0p1 and 0,2, respectively. Use the value for Op2 that is negative. Then use this value to determine the value of Op1 Express your answers to four significant figures separated by a comma. The element of material below is subjected to the state of stress shown, where a = 120.0 MPa, b = 62.00 MPa. and c = 12.00 MPa (Figure 1) • View Available Hint(s) Πν ΑΣφ vec Opl, Op2 = Submit Figure 1 of 1 Part B - In-plane principal stresses a Determine the in-plane principal stresses for the element (as oriented in Part A), and calculate oj and o2 such that they correspond with 0pl and 0p2 Express your answers to four significant figures separated by a comma. >…

1. The state of stress in a machine element with respect to x-y axis is shown in Figure 1. The principal angle 0, (-20°) as shown in the figure defines the principal axes x' and y' (Note: orientation of stresses on the element is generic and is not related to the stress tensor). Oy 40 Txy MPa σε -20 Txy Txy 0, =-20° Figure 1 (a)(i) Draw the reference axes x, y, x', y' showing 0, (ii) Determine the four direction cosines that the principal directions make with the x-y axes. (b)Draw and label Mohr's circle for the state of stress shown identifying the following points on the circle: numerical values of the coordinates of (i) the center (oave, Txy), (ii) stresses from the given stress tensor (associated with the A and B planes. Note: Mohr's circle can be drawn with only ơ, oy ), (iii) the principal angle (0,), (iv) the principal stresses (61 02), (v) maximum shear stress (tmax). í (c)Determine the shear stress txy. (d)Show the stress tensor (normal and shear stresses) on a properly…

Use the stress transformation equations to determine the state of stress for the element shown if it were oriented 60° clockwise. 100 MPa. 75 MPa 150 MPa

The state of stress at a point in a member is shown on the element in Figure (1). Determine the following: 1) The stress components acting on the inclined plane AB (o and Ty'y'). 2) The principal normal stresses (op1, p2) and max in-plane shear stress (Tmax)- Do not calculate the angles of the planes of the principal stresses. Solve the problem using the equations. 8 ksi A Figure (1) 2 ksi B 5 ksi

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 MPа

The state of stress at a point in a member is shown on the element in Figure (1). Determine the following: 1) The stress components acting on the inclined plane AB (o and tx'y'). 2) The principal normal stresses (op1, p2) and max in-plane shear stress (Tmax). Do not calculate the angles of the planes of the principal stresses. Solve the problem using the equations. 8 ksi 2 ksi Figure (1) 60° B 5 ksi

85 In a pure shear condition, the maximum value of shear stress is observed to be 20 MPa for an element shown, subjected to above condition. The change in length of diagonal AB is μm. [Take G = 80 GPa] [Correct upto 2 decimal places] D 10 cm A 10 cm B () C

Principal stress: 01,2 Ox+0y tan20, = Txy 2 (Ox-0y)/2 2 maximum in-plane shear stress: Tmax *) : + Txy? tan20s -(0x-0y)/2 Ox+0y σανg Txy 2 The state of plane stress at a point is represented on the element shown in the figure below. (a) Determine the principal stresses acting on this point, and the corresponding orientation (angle). (b) Determine the maximum in-plane shear stress, and the corresponding orientation (angle). Also determine the associated average normal stress. Show your work. 57 MPa 28 MPa 42 MPa

Q.1 For the two- dimensional element normal stresses Ox and oy and shear stress txy is acting as shown in figure below. For the plane 'EF' which makes angle '0' form horizontal, prove that normal stress (on) and shear stress (Tn) at this plane is equal to: Oy + Ox, Oy – Ox On = 2 cos 20+ Tyy sin 20 2 Oy - Ox -sin 20 – Txy cos 20 2 Tn = N Tyx Txy B E