This document discusses shear force and bending moment diagrams for beams. It provides the following key points: 1) Shear force and bending moment diagrams show the variation of shear force V and bending moment M over the length of a beam, which is necessary for design analysis. 2) The maximum bending moment is the primary consideration in design, and its value and position must be determined. 3) The procedure for drawing shear force and bending moment diagrams involves first calculating support reactions, then plotting the shear diagram with slope equal to loading, and finally the moment diagram with slope equal to shear.

1. Module 1 : Shear and Moment Diagrams for a Beam Dr Yan Zhuge CIV E3011 Structural Analysis

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.

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