6_SFD BMD all you need to know each and every one of them.pptx

engineering is loife

1. SHEAR FORCE &BENDING MOMENT DIAGRAMS At any section in a beam carrying transverse loads the shearing force is defined as the algebraic sum of the forces taken on either side of the section. Similarly, the bending moment at any section is the algebraic sum of the moments of the forces about the section, again taken on either side.

2. ORDER OF ANALYSIS of SFD & BMD Determine the reactions Section the beam before an applied load Introduce the internal equilibrant SF and BM on the section to expose them Carry out the analysis ( F = 0), ( M = 0),

3. Analysis Convention W W/2 W/2 A B C L to R tve R to L tve W/2 F AB M AB X F AB M BC X

4. Examples of SFDs & BMDs Conc Load and UDL

5. Cantilever with Conc & UDL

6. SF Sign Convention

7. BMD Sign Convection

8. Relationship between shear force Q, bending moment M and intensity of loading w Consider a beam loaded as follows

9. Relationship between shear force Q, bending moment M and intensity of loading w

10. Maximum and minimum BM The maximum or minimum B.M. occurs where dM /dx = 0 dM /dx = Q Thus where S.F. is zero B.M. is a maximum or minimum. The slope of the B.M. diagram = dM /dx = Q.

11. S.F. is positive the slope of the B.M. diagram is positive S.F. is negative the slope of the B.M. diagram is also negative.

12. Beam with point of contraflexure at X -X x x

13. Tutorial 1 B.Mmax & Position of contraflexure ?

14. Tutorial 2. A beam ABC is 9 m long and supported at B and C, 6 m apart as shown in Fig. 2. The beam carries a triangular distribution of load over the portion BC together with an applied Counter clockwise couple of moment 80 kN m at Band a u.d.1. of 10 kN /m over AB, as shown. Draw the S.F. and B.M. diagrams for the beam.

15. Tutorial 2 – Diagram

16. Tutorial 2 Solution SFD&BMD

17. Tutorial 3- SFD&BMD Position and Magnitude of BMmax ?