1. Module 1 : Shear and Moment Diagrams for a Beam Dr Yan Zhuge CIV E3011 Structural Analysis
2. Shear force and bending moment diagram for beam <ul><li>The variation of shear force V and bending moment M over the length of a beam provides information necessary for the design analysis of the beam. The maximum magnitude of the bending moment is usually the primary consideration in the design and its value and position should be determined. The shear force and bending moment functions can be plotted and represented by graphs called shear force and bending moment diagrams. </li></ul>
3. Bending moment and shear force diagram 5m 15kN 5m 5kN/m 80kNm V ( kN ) M ( kNm ) 5m 15kN 5m 5kN/m 80kNm V ( kN ) M ( kNm ) 5.75 kN -9.25 kN -34.25 kN 80 kNm 108.75 kNm
4. Beam sign convention The positive directions require the distributed load to act downward on the beam; the internal shear force to cause a clockwise rotation of the beam segment on which it acts; and the internal moment to cause compression in the top fibre of the segment.
5. Procedure for analysis <ul><li>Support Reactions - to establish the reactions at the two supports </li></ul><ul><li>Shear Diagram – to establish the V and x axes and plot the known values of the shear at the two ends of the beam. The slope of the shear diagram at any point is equal to the (negative) intensity of the distributed loading. If w(x) is a curve of degree n, V(x) will be a curve of degree n+1. </li></ul>
6. Procedure for analysis (Cont.) <ul><li>Moment Diagram - establish the M and x axes and plot the known values of the moment at the ends of the beam. The slope of the moment diagram at any point is equal to the shear at the point. In particular, note that at the point where the shear is zero, and this may be a point of maximum/minimum moment. If V(x) is a curve of degree n, M(x) will be a curve of degree n+1. </li></ul>
7. Example 1 - beams 4m A C x 8m B 1kN/m 12kNm 8m 3m A C x 2m B 18kNm 3m 2m . . . 8kN 8kN D E