Shear Forces and Bending Moments:

• A beam is a structural member, subjected to a system of external forces (involving inclined load) to generate the bending of the member in an axial plane.
• At the cross-section of the beam the shear force is explained as the unbalanced vertical force either to the right or to the left of the section.
• The bending moment at cross section of the beam is explained as the algebraic sum of moments of all of the forces acting on the beam either to the right or to the left of the section.
• All of the upward forces to the left of the section and all of the downward forces to the right of section cause positive shear force. All of the downward forces to the left of the section & all of the upward forces to the right of the section cause negative shear force.
• The BM is called to be positive, while it is acting in an anticlockwise direction to the left of the section and clockwise direction to the right of the section. The BM is called to be negative, while it is acting in clockwise direction to the left of the section & an anticlockwise direction to the right of the section.
• Whereas drawing SF and BM diagrams, all of the positive values are plotted above the base line & the negative values below it.
• The maximum BM takes place, where the SF is zero or changes sign.
• If the SF diagram line is horizontal among two points, the BM diagram is inclined. It denoted there is no load among two points. If the SF diagram is inclined among two points, the BM diagram is a parabola of second degree. It denotes that there is a uniformly distributed load among the two points. If the SF diagram is in the form of parabola of second degree among two points, the BM diagram is in the form of parabola of third degree (cubic parabola). It denote that there is a uniformly varying load among the two points.
• The point of contraflexure is a point whereas the BM is zero or changes sign.
• If a beam is subjected to a couple, the SF does not modify. But the bending moment suddenly changes in magnitude equivalent to that of the couple.
• If there is a point load or reaction, the BM does not alter at that point. But the SF suddenly modifies (either decreases or increases) in magnitude equivalent to that of point load or support reaction.
• If a beam is subjected to inclined loads, their components at right angles to the axis of components (vertical components) shall cause shear force & bending moment and their components along the axis of the beam (horizontal components) shall cause axial force or thrust in the beam.
• Whereas drawing axial forces diagram, tensile forces are taken as positive & compressive forces are taken as -ve.