SFD BMD

KEY POINTS TO DRAW SFD AND BMD FOR DETERMINATE BEAMS

1. STRENGTH OF MATERIALS SFD AND BMD key points

2. SFD & BMD FOR BEAMS Types of BEAMS Types of LOADS Point loads Uniformly distributed load Uniformly varying load Couple Concept of shear force and bending moment S.F and B.M diagrams for Cantilever Simply supported including overhanging Point of contraflexure Relation between S.F., B.M and rate of loading at a section of a beam.

3. Beam - Definition Beam is the horizontal member of a structure carrying transverse loads transfer all the loads including its self-weight to the columns or walls. Transverse Load perpendicular to longitudinal axis of beam

4. https://www.youtube.com/watch?v=5K27dJqGpf8

5. Moment and Bending moment Moment: It is the product of force and perpendicular distance between line of action of the force and the point about which moment is required to be calculated. Bending Moment (BM): The moment which causes the bending effect on the beam is called Bending Moment . It is generally denoted by ‘M’ or ‘BM’.

6. Shear Force and Bending Moment Shear force at a section: The algebraic sum of the vertical forces acting on the beam either to the left or right of the section . Bending moment (BM) at section: The algebraic sum of the moments of all forces acting on the beam either to the left or right of the section

7. What the BM does to the beam

8. Shear Force and Bending Moment Diagrams SFD: The diagram which shows the variation of shear force along the length of the beam is called Shear Force Diagram (SFD). BMD: The diagram which along the length shows the variation of bending moment of the beam is called Bending Moment Diagram (BMD).

9. Sign Conversion for S.F F F F F + ve shear force - ve shear force

10. Sign Convension for B.M Sagging B.M The bending moment that tends to bend the beam to a curvature having convexity at the bottom Sagging Bending Moment is considered as positive bending moment. Convexity

11. Sign Conversion for B.M Cont … Hogging B.M Bending moment that tends to bend the beam to a curvature having convexity at the top. Hogging Bending Moment is considered as Negative Bending Moment Convexity

12. Application of SFD & BMD To know the exact placement of reinforcement in the structure to counteracts the force and moment. for shear - stirrups are used in lateral direction For bending - bars are used in longitudinal direction

13. Point of Contra flexure : It is the point on the bending moment diagram where B.M changes the sign from + ve to – ve or vice versa.

14. Important points for drawing SFD and BMD Length of S.F.D and B.M.D must be equal to the span of the beam. S.F.D is drawn below the loaded beam and B.M.D is drawn below S.F.D For Simply supported beam B.M is zero at the supports. For cantilever beam B.M will be zero at free end. Calculate S.F and B.M at all critical points If no load is present between two points, then S.F will be constant. Consider the left or right side portion of the section

15. Important points for drawing SFD and BMD Cont … Add the forces (including reaction) normal to the beam on one of the portion. (By considering sign conversion) The positive values of S.F and B.M are plotted above the base line and Negative values below the base line The S.F.D will increase or degrease suddenly i.e. by a vertical straight line at a section where there is a vertical point load. The S.F between any two vertical loads will be constant and hence the S.F.D between two vertical loads will be horizontal.

16. Relationship Between w, F, and M Rate of change of shear force is equal to rate of loading dF /dx = w Rate of change of bending moment is equal to shear force dM /dx = F