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### Som 2

1. 1. CHAPTER 2 SHEAR FORCE & BENDING MOMENT Faculty Name : MISSAM RAZA Dept. MECH LJ Polytechnic
2. 2. Shear force & bending moment Basic definitions 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’. Faculty Name : MISSAM RAZA Dept. MECH LJ Polytechnic
3. 3. Shear force & bending moment Sign convection Faculty Name Dept. LJ Polytechnic Sign Convention for shear force F F F F + ve shear force - ve shear force MISSAM RAZA Dept. MECH LJ Polytechnic
4. 4. Shear force & bending moment Sign convection Faculty Name Dept. LJ Polytechnic Sign convention for bending moments: The bending moment is considered as Sagging Bending Moment if it tends to bend the beam to a curvature having convexity at the bottom as shown in the Fig. given below. Sagging Bending Moment is considered as positive bending moment. Fig. Sagging bending moment [Positive bending moment ] Convexity
5. 5. Shear force & bending moment Sign convection Faculty Name Dept. LJ Polytechnic  Similarly the bending moment is considered as hogging bending moment if it tends to bend the beam to a curvature having convexity at the top as shown in the Fig. given below. Hogging Bending Moment is considered as Negative Bending Moment. Fig. Hogging bending moment [Negative bending moment ]
6. 6. Shear force & bending moment Point of contrafluxure Faculty Name Dept. LJ Polytechnic Point of Contra flexure [Inflection point]:  It is the point on the bending moment diagram where bending moment changes the sign from positive to negative or vice versa.  It is also called ‘Inflection point’. At the point of inflection point or contra flexure the bending moment is zero.
7. 7. Shear force & bending moment Variation of SF & BM graphs Faculty Name Dept. LJ Polytechnic  Variation of Shear force and bending moments for various standard loads are as shown in the following Table Type of load SFD/BMD Between point loads OR for no load region Uniformly distributed load Uniformly varying load Shear Force Diagram Horizontal line Inclined line Two-degree curve (Parabola) Bending Moment Diagram Inclined line Two-degree curve (Parabola) Three-degree curve (Cubic- parabola) Table: Variation of Shear force and bending moments
8. 8. Shear force & bending moment SF & BM calculations Faculty Name Dept. LJ Polytechnic  Sections for Shear Force and Bending Moment Calculations: Shear force and bending moments are to be calculated at various sections of the beam to draw shear force and bending moment diagrams.  These sections are generally considered on the beam where the magnitude of shear force and bending moments are changing abruptly.
9. 9.  Therefore these sections for the calculation of shear forces include sections on either side of point load, uniformly distributed load or uniformly varying load where the magnitude of shear force changes abruptly.  The sections for the calculation of bending moment include position of point loads, either side of uniformly distributed load, uniformly varying load and couple Shear force & bending moment SF & BM calculations Faculty Name Dept. LJ Polytechnic
10. 10. Shear force & bending moment Common relationships Faculty Name Dept. LJ Polytechnic Load 0 Constant Linear Shear Constant Linear Parabolic Moment Linear Parabolic Cubic
11. 11. Shear force & bending moment Common relationships Faculty Name Dept. LJ Polytechnic Load 0 0 Constant Shear Constant Constant Linear Moment Linear Linear Parabolic M