1. CE Statics
Chapter 7 – Lecture 3

2. 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.

3. 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.

4. 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

5. 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. V M

6. 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.