The stress components are shown in their posirve

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wice using rules for the disconRnuity funcRons to get M. No constants of integraRon needed. •  Integrate M twice to find dυ/dx and υ. Two constants of integraRon will be needed •  Apply boundary condiRons to determine the constants of integraRon. Be very careful to evaluate the disconRnuity funcRons properly. < x-a >n = 0 for x < a! •  Write a final expression for υ in terms of the disconRnuity funcRons including the values of the constants. Macaulay FuncRons •  Macaulay FuncRon DefiniRon: where n ≥ 0 •  Its integral: •  Examples: a x w0 •  C = 0 in both integraRons here. m a ax x Macaulay FuncRons a x •  Examples: 1 1 m m a ax x w0 a L x •  Construct equivalent loads that can be represented by Macaulay FuncRons! •  How? w0 w0 w0 a a x x L L a x w0 w0 P w0 w0 Singularity FuncRons w a x 0 •  For handling point forces/couples we use singularity func(ons and P M a x a x M0 a x •  Its integral: where n = -1 or n = -2 Boundary CondiRons Support Type: Pin or roller at end of beam Fixed end Boundary CondiRon: Displacement: and Moment: Displacement: and Slope: Only condiRons on displacement or slope are needed to find constants of integraRon. 16- 28) Hibbeler 4th ed The beam is subjected to the load shown. Determine the equaRon of the elasRc curve. EI is constant. 3 kip/ ft 5 kip ft 5 kip ft A B x 4 ft 8 ft 4 ft Given: applied loads, EI Find: υ(x) Plan: Use disconRnuity funcRons to find M(x) then integrate to find υ(x). 24 kip 5 kip·ft 5 kip·ft 3 kip/ ft 16- 28) Hibbeler 4th ed EnRre FBD 5 kip ft 4 ft Ay 24 kip 5 kip·ft By 5 kip·ft 4 ft Ay Load: 4 ft Ay 3 kip/ft 8 ft 5 kip·ft B y 4 ft 3 kip/ft B 4 ft 8 ft 4 ft By symmetry 5 kip·ft By x 4 ft 8 ft 5 kip ft 4 ft A 5 kip·ft 4 ft Ay 8 ft 3 kip/ft 8 ft 5 kip·ft B y 4 ft 3 kip/ft 3 kip/ ft 16- 28) Slope and DeflecRon Hibbeler 4th ed 5 kip ft 5 kip ft A B x 4 ft Boundary CondiRons: 8 ft 4 ft 3 kip/ ft 16- 28) Slope and DeflecRon Final Result Hibbeler 4th ed 5 kip ft 5 kip ft A B x 4 ft 8 ft 4 ft General State of Plane Stress •  The element below shows a general state of Plane Stress: •  Two normal stresses, sx and sy, and one shear stress txy. •  The stress components are shown in their posiRve senses. •  The components sx, sy and txy define the stress state. •  Their values are dependent on the orientaRon of the element. Rotated State of Plane Stre...
View Full 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