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Forces on a Beam

Forces on a Beam. F 2. S. W. F 1. F 3. Consider only this portion. Torques on a Beam. F 2. W. N. N 0. F 1. F 3. Consider only this portion. Shear at AA Plane. A. No Bending – Planes stay parallel. S. q. A. Beam Bending Tension and Compression. Compression. Tension.

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Forces on a Beam

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  1. Forces on a Beam F2 S W F1 F3 Consider only this portion

  2. Torques on a Beam F2 W N N0 F1 F3 Consider only this portion

  3. Shear at AA Plane A No Bending – Planes stay parallel S q A

  4. Beam BendingTension and Compression Compression Tension k=radius of gyration

  5. Formulae Total angle: Shear angle: Bending angle: Shear force: Bending moment:

  6. Getting the Beam Differential Equation

  7. 0 :assume constant beam geometry 0:Symmetry 0:Definition Solution

  8. Book Problem q Only shear at x=0 Beam held fixed at one end 0

  9. Book Problem – Solution Also solution to following problem: L W W Except with |x| instead of x. There is a discontinuity in q at x=0.

  10. Boundary Conditions At free ends: At points of applied force: Bend angle is continuous: Shear angle is discontinuous:

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