Strength of Materials : Shear Force and Bending Moment Diagrams

A Beam is defined as a structural member subjected to transverse shear loads during its functionality. Due to those transverse shear loads, beams are subjected to variable shear force and variable bending moment.

Shear force at a cross section of beam is the sum of all the vertical forces either at the left side or at the right side of that cross section.

Bending moment at a cross section of beam is the sum of all the moments either at the left side or at the right side of that cross section.

Types of Rigid Supports

• Simple Supports
  • Roller Support
  • Hinge Support (or) Pin Support
• Fixed Supports
  • Clamped Supports (or) Built-in Supports

(a) Roller Support – resists vertical forces only

(b) Hinge support or pin connection – resists horizontal and vertical forces

(c) Fixed support or built-in end

Note: The distance between two supports is known as “span”.

Types of Beams

Statically Determinate Beam

A beam is said to be statically determinate if all its reaction components can be calculated by applying three conditions of static equilibrium.

Statically Indeterminate Beam

When the number of unknown reaction components exceeds the static conditions of equilibrium, the beam is said to be statically indeterminate.

TYPES OF LOAD

The following are the important types of load acting on a beam,

1. Concentrated or point load,
2. Uniformly distributed load, and
3. Uniformly varying load.

(i) Concentrated or Point Load: load act at a point.

 (ii) Uniformly Distributed Load: load spread over a beam, rate of loading w is uniform along the length.

(iii) Uniformly Varying Load: load spread over a beam, rate of loading varies from point to point along the beam.

SIGN CONVENTIONS FOR SHEAR FORCE AND BENDING MOMENT

Shear force: If moving from left to right, then take all upward forces as positive and downward as negative.

Or if the shear force tries to rotate the element clockwise then it is takes as positive & if the shear force tries to rotate the element anticlockwise then it is takes as negative.

Bending moment: If moving from left to right, take clockwise moment as positive and anticlockwise as negative.

Or if forces are forming sagging moment then it is taken as positive and if forces are forming hogging moment then it is taken as negative.

RELATIONS BETWEEN LOAD, SHEAR FORCE AND BENDING MOMENT

  RELATIONS BETWEEN LOAD, SHEAR FORCE AND BENDING MOMENT

  The rate of change of shear force is equal to the rate of loading.

  The rate of change of bending moment is equal to the shear force at the section.       

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