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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
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