Lecture 16 – Equilibrium of beams (cont.)

Instructor: Prof. Marcial Gonzalez

Spring, 2021ME 323 – Mechanics of Materials

Reading assignment: 5.1—5.4

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Last modified: 1/14/21 7:18:29 PM

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Beam theory (@ ME 323)- Geometry of the solid body:

straight, slender member with constant cross sectionthat is design to supporttransverse loads.

- Kinematic assumptions: Bernoulli-Euler Beam Theory (Lecture 14)Timoshenko Beam Theory, etc.

- Material behavior: isotropic linear elastic material; small deformations.

- Equilibrium:1) relate stress distribution (normal and shear stress) with

internal resultants (only shear and bending moment)

2) find deformed configuration

Equilibrium of beams

Longitudinal Planeof Symmetry

Longitudinal Axis

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Sign Convention

Example 19 (last lecture):Draw shear force and bending moment diagrams

Shear and bending diagrams

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Equilibrium relationships- Shear force and bending

moments diagrams

Equilibrium of beams

Change in shear force from x1 to x2 is equal to the area under the load curve from 1 to 2

Change in bending moment from x1 to x2 is equal to the area under shear force curve from 1 to 2

Equilibrium relationships- Sign convention!

Equilibrium of beams

These are all positive external loads and couples

Note: become familiar with sign convention for external loads and for internal reactions.6

= |

= |

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Shear and bending diagrams- Graphical features

Equilibrium of beams

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Shear and bending diagrams- Graphical features

Equilibrium of beams

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Example 20:Determine and

Shear and bending diagrams

Any questions?

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Equilibrium of beams