BENDING MOMENT AND SHEAR FORCE

Bending moment on a transverse section of a beam is the algebraic sum of the moment of all the forces on the right side or on the left side of the transverse section.

A shear force on a transverse section is the algebraic sum of all the on the right side or on the left side of the transverse section.

SHEAR FORCE AND BENDING MOMENT DIAGRAMS

A bending moment (BM) diagram for a structural member is a diagram which shows the values of the bending moment at various sections of the structure.

A shear force diagram is a diagram which shows the value of the shear force on a various section of the structure.

Before drawing the shear force and bending moment it diagrams, we must know the different types of beams and different types of the load acting on the beams.

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Types of beams:

1. Simply supported beam

2. Cantilever Beam

3. Continuous Beam

4. Overhanging beam

5. Double over hanging beam

6. Fixed beams

Types of loads:

1. Concentrated load or point load

2. Uniformly Distributed Load (UDL)

3. Uniformly Varying Load (UVL)

Sign conventions

· The shear force at a section will be considered positive when the resultant of the forces to the left to the section is upwards, or to the right of the section is downwards Similarly the shear force at a section will be considered negative if the resultant of the forces to the left of the section is downwards, or to the right of the section is upwards.

· The bending moment at a section is considered positive if the bending moment at that section is such that it tends to bend the beam to a curvature having concavity to the top similarly bending moment at a section is considered as negative if the curvature having convexity to the top.

Sagging moment and Hogging moment

The moment causing a portion of the beam to be bent into concave shape on its top surface is known as the sagging moment.

The moment causing a portion of the beam to be bent into convex shape on its top is known as the lagging moment.

Procedure for drawing shear force(SF) and bending moment(BM) diagram

The following steps should be followed for drawing SF and BM

1. Determining the reaction forces and moment using equilibrium equations.

2. Determine shear force at all the salient points such as supports, the point of application of a load or another point of intersecting.

3. Draw the shear force diagram and locate the sections at which the shear force changes the sign.

4. Find the magnitude of bending moment at all salient points and find the value of maximum bending moment where shear force is zero.

5. Locate the points of contraflexure if any.

Note: point of contraflexure is a section at which change in sign of bending moment occurs.

BENDING MOMENT AND SHEAR FORCE