CE 201 - Statics

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CE 201 - Statics

• Chapter 7 Lecture 3

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Shear and Moment Equations and Diagrams

• To design a beam, you should know the variation
  of the internal shear force ( V ) and bending
  moment ( M ) acting at each point along the axis
  of the beam.
• The variation of ( V ) and ( M ) can be known by
  the method of sections discussed earlier. In
  these cases, sections are taken at arbitrary
  distance (X) from one end rather than at one
  specific point.

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Shear and Moment Functions Discontinuities

• Change of distributed load
• Concentrated load is applied
• Couple moment is applied

That is why sections must be taken between
discontinuities.
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The normal force will not be considered because

• In most of the cases, loads are perpendicular to
  the beam
• For design purposes, the beam's resistance to
  shear and bending is more important

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Sign Convention

• Positive ( V ) is the one that causes clockwise
  rotation of the member.
• Positive ( M ) is the one that causes compression
  or pushing on the upper part of the member.

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Procedure for Analysis

• Determine the support reactive moments and forces
  by applying equilibrium equations on the entire
  beam. Resolve forces into their rectangular
  components
• Determine shear and moment functions.
• Specific sections are to be taken at
  discontinuities of loadings.
• Apply ?Fy 0 to get ( V ).
• Apply ?M 0 at the section end to get M.
• Draw shear and moment Diagrams.

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