Bending Moment

1. Ahsanullah University of Science &Technology Presentation on: BENDING MOMENT Course No: CE-416 Course Name: Pre-stressed Concrete Lab. Course Teacher: Galib Muktadir & Sabrina Nasreen

2. Presented By- Summiaya Khatoon ID:10.01.03.122 Year:4 TH Section: C Semester:2 ND Department of Civil Engineering

3. Contents Definition of Bending Moment. Significance of Bending Moment. Sign Convention. Sagging Beam. Hogging Beam. Unit of Bending Moment. Section of Maximum Moment. Some Bending Moment Formulas. Example Problem. Solution.

4. Definition of Bending Moment A Bending Moment is the measure of the internal stress that produced by the external force or moment causing the element to bend . 4

5. Significance of Bending Moment Bending Moments are maximum at the points of maximum stress, so these points require more reinforcement to counteract the stresses. Bending moment is the main factor that decide the reinforcement detailing of a structure. 5

6. Sign Convention Bending which produces compression in top fiber and tension in bottom fiber is taken as positive bending . Also called Sagging Bending . 6

7. Sign Convention Bending which produces compression in bottom fiber and tension in top fiber is taken as Negative bending . Also called Hogging beam . 7

8. Sagging Beam Compression Tension 8

9. Sagging Beam Compression Tension 9

10. Hogging Beam Tension Compression 10

11. Unit of Bending Moment As, bending moment is the result of force and distance ,so the unit is Kip-ft or lb-ft or N-m or KN-m. 11

12. Section of Maximum Moment It can be shown mathematically, that when the shear force is zero or changes sign, the bending moment will be either a maximum or relative maximum. 12

13. Bending moment Diagram A bending moment diagram is simply a graph of bending moment plotted vertically against the distance from left. 13

14. Some Bending Moment formulas Beam Bending Moment Diagram Maximum Bending Moment p L PL w L WL^2/8 w L WL^2/2 P L PL/4 14

15. Example Problem For a simply supported beam, calculate bending moment and draw Bending moment diagram . 20N Ra 0.4 m 0.6 m Rb 15

16. Solution At first we have to calculate the reaction. From equilibrium equation,we find- Ra+Rb =20 By taking moment at point Ra, assuming clockwise direction as + ve , - Rb *1+20*0.4=0 so, Rb =8N & Ra=12N 16

17. Solution Now, shear force diagram- 12N 8N Fig: shear force diagram 17

18. Solution Finally, from shear force diagram, we can draw the bending moment diagram- 4.8 N-m Fig: Bending Moment Diagram 18

19. Thank You …