After being rotated through an angle 0, the stress elements σx and Tx'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: 0x = 0x cos² 0 +σy sin² 0 + Txy (2 sin 0 cos 0) (σy -σx) sin cos 0 + Txy (cos² 0 - sin² 0) Tx'y' = Using the trigonometric identities Figure 6 of 6 Part D - Clockwise Rotation of a Stress Element with No Shear Stress 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 |σx | = 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) ΜΕ ΑΣΦ vec - σx =σy =,Tx'y' = 22.6, 19.6, 17.7 Submit Previous Answers στ × Incorrect; Try Again; 5 attempts remaining Use the angle of rotation required to move the +x axis to the +x' axis. You may want to review Hint 2. The original stresses and rotation angle. ? ksi, ksi, ksi
After being rotated through an angle 0, the stress elements σx and Tx'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: 0x = 0x cos² 0 +σy sin² 0 + Txy (2 sin 0 cos 0) (σy -σx) sin cos 0 + Txy (cos² 0 - sin² 0) Tx'y' = Using the trigonometric identities Figure 6 of 6 Part D - Clockwise Rotation of a Stress Element with No Shear Stress 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 |σx | = 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) ΜΕ ΑΣΦ vec - σx =σy =,Tx'y' = 22.6, 19.6, 17.7 Submit Previous Answers στ × Incorrect; Try Again; 5 attempts remaining Use the angle of rotation required to move the +x axis to the +x' axis. You may want to review Hint 2. The original stresses and rotation angle. ? ksi, ksi, ksi
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:After being rotated through an angle 0, the stress
elements σx and Tx'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:
0x = 0x cos² 0 +σy sin² 0 + Txy (2 sin 0 cos 0)
(σy -σx) sin cos 0 + Txy (cos² 0 - sin² 0)
Tx'y'
=
Using the trigonometric identities
Figure
6 of 6
Part D - Clockwise Rotation of a Stress Element with No Shear Stress
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 |σx | = 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)
ΜΕ ΑΣΦ
vec
-
σx =σy =,Tx'y' = 22.6, 19.6, 17.7
Submit
Previous Answers
στ
× Incorrect; Try Again; 5 attempts remaining
Use the angle of rotation required to move the +x axis to the +x' axis.
You may want to review Hint 2. The original stresses and rotation angle.
?
ksi, ksi, ksi
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