notes_08b - Deflections The conjugatebeam method was...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Deflections ± The conjugate –beam method beam method was developed by Otto Mohr in 1860. ± The method is based on the similarity between the relationships for loading and shear, and shear and moment. () dV wx dx =− dM V = wxdx Mw x d ∫∫ 2 2 w ⇒= Deflections ± The previous expressions relate the internal shear and moment to the applied load. ± The slope and deflection of the elastic curve are related to the internal moment by the following expressions EI θ = 2 2 dy M = = y dx dx = Deflections ± Let’s compare expressions for shear, , and the slope, = ± What do you see? ± If you replace with the term – M/EI the expressions for shear force and slope are identical Deflections ± Let’s compare expressions for bending moment, , and the displacement, ± What do you see? ± Just as before, if you replace with the term – the expressions for bending moment and displacement are identical 2 2 = − 2 2 = Deflections ± We will use this relationship to our advantage by constructing a beam with the same length as the real beam referred to as the conjugate beam . ± The conjugate beam is loaded with the diagram, simulating the external load . Deflections w = w( ) w Real beam with applied loading. Determine the bending moment (draw the bending moment diagram) Conjugate beam where the applied loading is bending moment from the real beam Note the sign of loading w and the on the conjugate beam.
Background image of page 1

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

View Full DocumentRight Arrow Icon
± Therefore, the two theorems related to the conjugate beam method are: ± Theorem 1: The slope at a point in the real beam is equal to the shear at the corresponding point in the conjugate beam.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/17/2011 for the course CES 3102 taught by Professor Gurley during the Fall '10 term at University of Florida.

Page1 / 5

notes_08b - Deflections The conjugatebeam method was...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online