Mechanics 1O - 2.001 MECHANICS AND MATERIALS I Lecture#12...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
2.001 - MECHANICS AND MATERIALS I Lecture # 10/23/2006 Prof. Carol Livermore MULTI-AXIAL STRESS AND STRAIN Recall: Internal Forces and Moments Axial stress from uniaxial loading P σ = A Note: σ is an average axial stress. For slender (long, thin) objects A is either uniform or slowly-varying . 1 12
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
What about a more general case? Note: dF is not in general parallel to ˆ n . 2
Image of page 2
dF ( i ) = dF x ( i ) ˆ i + dFyx ( i ) ˆ j + dF z ( i ) k ˆ n ˆ = ˆ i N totalforce = dF x ( i ) A x σ ¯ = N totalforce /A x Traction: t Force per unit area at a point ( i ) ( i ) ( i ) t ( i ) = dF ( i ) = dF x ˆ i + dF y ˆ j + dF z k ˆ dA x dA x dA x dA x dF x ( i ) σ x x = (Normal Stress) dA x dF y ( i ) σ x y = (Shear Stress) dA x dF z ( i ) σ x z = (Shear Stress) dA x So: t ( i ) = σ xx ˆ i + σ xy ˆ j + σ xz k ˆ N T OT ALF ACE = σ xx dA x A x V T OT ALF ACE y = σ xu dA x A x N T OT ALF ACE z = σ xz dA x A x 3
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
To find the stresses on the y face take cut on x-z plane. z face take cut on x-y plane.
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern