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  1. MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING This is the first tutorial on bending of beams designed for anyone wishing to study it at a fairly advanced level. You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do the following. Define a beam.

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  2. A beam is a structure which has one of its dimensions much larger than the other two. The importance of beam theory in structural mechanics stems from its widespread success in practical applications. 7.1.1 Kinematic assumptions Readings: BC 5.2 Beam theory is founded on the following two key assumptions known as the Euler-Bernoulli assumptions:

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  3. Beam Rigidity (1) - Beam is bent and focused using magnets (e.g. dipole and quadrupole) - Particles have circular orbits around magnetic axis - Beam rigidity B quantifies how difficult it is to bend the beam - When B is known, it is easy to quantify bend radius and deflection - B in [T.m] - Small angular deflection B B

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  4. A beam is a structure loaded by forces acting transversely (sideways) to its length and these make the beam bend. Beams may be simply supported across a span in various ways as shown. In this module you are only required to study simply supported beams. Bending is the most severe form of stress that you can apply.

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  5. Procedure: 4th-order method. FBD of the entire beam (do not need to enforce equilibrium) Split the beam into segments. Write down the load function p(x) in each segment. If there are no distributed loads in a segment, p(x) = 0. Write down the load-deflection equation for each segment: EIv ''''( x ) = p ( x )

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  6. www.iitg.ac.in › kd › Lecture NotesBeams - IIT Guwahati

    Beams: Example Determine the external reactions for the beam Dividing the un-symmetric triangular load into two parts with resultants R 1 and R 2 acting at point A and 1m away from point A, respectively. R 1 = 0.5x1.8x2 = 1.8 kN R 2 = 0.5x1.2x2 = 1.2 kN A y A x B y R 1 R 2 0.4m ∑F x =0 A x = 1.5sin30 = 0.75 kN ∑M A =0 4.8xB y = 1.5cos30x3.6 ...

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  8. The length of a conjugate beam is always equal to the length of the actual beam. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam. A simple support for the real beam remains simple support for the conjugate beam. A fixed end for the real beam becomes free end for the conjugate beam.

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