{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 4-torsion - CHAPTER 4 TORSION TORSION Torsion...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
CHAPTER 4 TORSION
Image of page 1

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

View Full Document Right Arrow Icon
Torsion refers to the twisting of a structural member when it is loaded by moments/torques that produce rotation about the longitudinal axis of the member The problem of transmitting a torque or rotary motion from one plane to another is frequently encountered in machine design. Normally circular bars are used for such transmissions chiefly because, in these bars, a plane section before twisting remains plane after twisting. 110 TORSION TORSION
Image of page 2
Assumption to determining the relationship of the shearing stress in circular shaft subjected to torsions: the material of the shaft is homogeneous the maximum shearing stress in the shaft is within the elastic limit the twist remains uniform along the whole length of the shaft the normal cross-section of the shaft which are plane and circular before the twist remain same after the twist the straight radial line of any cross section of the shaft remain straight. the distance between any two cross section of the shaft remain the same torques are applied on planes that are perpendicular to the axis of the shaft 111
Image of page 3

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

View Full Document Right Arrow Icon
Torsional Deformation of Circular Bars Torsional Deformation of Circular Bars Consider a bar of circular cross-section twisted by couples T at the  ends. Because the bar is subjected to torsion only, it is said to be in  pure torsion. Assuming that the end B is fixed, then the torque will cause end A  to rotate through a small angle  Ф , known as the  angle of twist . Thus  the longitudinal line AB on the surface of the bar will rotate  through a small angle to position A'B 112
Image of page 4
Since the ends of the element remain planar, the shear strain is equal to angle of twist, θ . It follows that According to Hooke’s law, for linear elastic materials, shear stresses are proportional to shear strains and the constant of proportionality is the modulus of rigidity, G. Hence L r r L ' BB θ = γ θ = γ = or 113 L Gr L r G G θ = θ = γ = τ L G r θ = τ G = γ τ
Image of page 5

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

View Full Document Right Arrow Icon
Torsion Formula: Relationship between Torsion Formula: Relationship between T and T and τ τ To determine the relationship between the applied torque T and the stresses it produces, we consider equilibrium of the internal forces and the externally applied torque, T.
Image of page 6
Image of page 7
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