Figure (a) y 1 of 6 Part C - Counterclockwise Rotation of a Stress Element 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 |σ| = 10 ksi, |σy| = 29 ksi, and |7zy | = 6 ksi. Determine the state of stress on an element rotated 40° counterclockwise from the element shown. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) ΕΧΕΙ ΑΣΦ ↓↑ vec σ =σy = Ta'y = 23.76, 15.24,7.56 Submit Previous Answers × Incorrect; Try Again; 5 attempts remaining Part D - Clockwise Rotation of a Stress Element with No Shear Stress ? ksi, ksi, ksi The state of stress at a point in a member is shown on the rectangular stress element in (Figure 6) where the magnitudes of the stresses are |σ| = 29 ksi and |σy| = 26 ksi. Determine the state of stress on an element rotated such that the +x axis is 20° below the x axis of the original stress element. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) ΕΠΙ ΑΣΦ ↓↑ vec σ = σy' = Tz'y' = Submit Provide Feedback ? ksi, ksi, ksi Part A - State of Stress on an Inclined Plane Learning Goal: To be able to identify the initial stresses and the angle of rotation, including the correct signs, and use these in the stress- transformation equations to find the stress on a plane or element at a different angle than the original. The method of calculating the state of stress on an inclined plane is tedious, prone to error, and incomplete--if we calculate σ and Tz'y', we have to do a separate calculation to determine σy. Consider the stress element (a) shown in (Figure 1). After being rotated through an angle 0, the stress elements σ and Tr'y' can be calculated by the inclined-plane method by letting the inclined plane be the y' axis. (Figure 2) Balancing the sums of the forces in the primed coordinate system yields two equations: σ =σ cos² +σy sin² 0 + Try (2 sin cos 0) Try (σyσ) sin 0 cos 0+ Tzy (cos2 0 - sin2 0) Using the trigonometric identities 2 sin 0 cos 0 = sin(20), sin² 0 = (1 - cos(20))/2, and cos² 0 = (1 + cos(20))/2 and the fact that the +y' axis is always 90° counterclockwise from the +x axis, we can derive the equations: The state of stress at a point in a member is shown on the rectangular stress element in (Figure 3); the magnitudes of the stresses are |σ| = 92 MPa, |oy| = 39 MPa, and |Tzy| = 57 MPa. Using the stress-transformation equations, determine the state of stress on the inclined plane AB. Express your answers, separated by a comma, to three significant figures. ▸ View Available Hint(s) σ =, Tx'y' = Submit ΜΕ ΑΣΦ vec ? MPa, MPa σ = 2 2 + cos(20) + Tzy sin(20) Oxtoy στον 2 Oy = Tz'y = 2 στ cos(20) Tzy sin(20) Jay) sin(20) + Try Cos(20) 2 These stress-transformation equations allow us to eliminate the geometric work that was involved in the incline-plane method of stress transformation and provides us with all three stresses in the primed coordinate system. In deriving these equations, we have used the standard sign convention that a normal stress, σ, is positive if it points outward from the stress element, a shear, T, is positive if, on the face through with the +x axis passes, it points in the +y direction, and angles, (-180°, 180°), are positive if they are counterclockwise from the +x axis. Part B - Clockwise Rotation of a Stress Element with Only One Normal Stress 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 |σ| = 171 MPa and |Try | = 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) σ =, σy' =, Tz'y' = Submit ΜΕ ΑΣΦ ↓↑ vec ? MPa, MPa, MPa