DOC PREVIEW
MIT 3 11 - Normal Stresses and Strains

This preview shows page 1-2-3-4 out of 12 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 12 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 12 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 12 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 12 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 12 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

LECTURE #14 :3.11 MECHANICS OF MATERIALS F03INSTRUCTOR : Professor Christine OrtizOFFICE : 13-4022 PHONE : 452-3084WWW : http://web.mit.edu/cortiz/www• Review : Beam Bending 3 : Normal Stresses and Strains• Transformations of Stress and Strain IBeam Theory 3 : Normal Stresses and Strainsyσx(y)xσy=0NAMo(+ moment)σx(max)cσx(max)Txyz●N.A.compressiontensionmpnqdθρdxefyMoMoFlexure formula : where : normal stress in x-directioninternal bending momenty = vertical distance from NA axis(see Gere Chapter 12, Appendix D, p 321)I = moment of inertia of cross-sectoxxoMyIMσσ=−==()[]()[]maxmaxmaxmaxmaxmaxmaxional area()for rectangular beams : 2(),"flexural modulus"oxooxxMx yIhyMx yMyEI EIEIσεε=−==− =−=Beam Theory (Cont'd) : Shear Stresses and StrainsyzNA22 Derivation in Gere Section 5.8 : (rectangular cross section)24where : shear stress shear forceh = height of cross sectional areay= distance from NA (rectangular cross sectxyxyxyVhyIVτττ=− −==max3ion)2cross sectional areaVAA=−=ττττxy(y)x2-D (Plane) Stress Stateyzxy•Ox•Oττττxyσσσσxσσσσyττττxyσσσσxσσσσy00000xxyyx yσττσττττyxxy•Oxy•Ox’y’Given A State of Plane Stress, What Is The Equivalent Stress State On An Element Rotated By An Arbitrary Angle, θθθθ + CCWxy•Ox’y’xy•Ox’y’θθσxAoτxyAoσyAotanθτyxAotanθσx’ Ao/cosθτx’y’ Ao/cosθyxy•Ox’y’θθσxAoτxyAoσyAotanθτyxAotanθσx’ Ao/cosθτx’y’ Ao/cosθ''''''(1) tan tan(2) tan tanxyxyx x yxy x yxσστ θτ θττσσθθ=+ +=+ −yVariation of Stresses With θθθθSTRESS TRANSFORMATION EQUATIONSxy xyx' xyxy xyy' xyxyx'y' xy()cos(2)sin(2 )22()cos(2)(sin(2 )22()sin(2)cos(2 )2σσ σσ θστθσσ σσ θστθσσ θττθ+−+−−=+ +=− −=− +Variation of Stresses With θθθθFor σσσσY=0.2σσσσx, ττττxy=0.8σσσσxxy xyx' xyxy xyy' xyxyx'y' xy()cos(2)sin(2 )22()cos(2)(sin(2 )22()sin(2)cos(2 )2σσ σσ θστθσσ σσ θστθσσ θττθ+−+−−=+ +=− −=− +Principal Stresses and Anglesxy xyx' xyxy xyy' xyxyx'y' xy()cos(2)sin(2 )22()cos(2)(sin(2 )22()sin(2)cos(2 )2σσ σσ θστθσσ σσ θστθσσ θττθ+−+−−=+ +=− −=− +-100100 100 200 300TAN(2θP)2θPPrincipal Stresses and


View Full Document

MIT 3 11 - Normal Stresses and Strains

Documents in this Course
Load more
Download Normal Stresses and Strains
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Normal Stresses and Strains and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Normal Stresses and Strains 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?