# Strength of Materials - Shear Force and Bending Moment Diagrams Complete Study Notes

By Sidharth Jain|Updated : February 14th, 2022

Complete coverage of the APPSC AE Exam syllabus is a very important aspect for any competitive examination but before that important subjects and their concept must be covered thoroughly. In this article, we are going to discuss the Shear Force and Bending Moment Diagrams topic which is very useful for APPSC AE Exams.

## Shear Force and Bending Moment Diagrams

The beam is one of the most important structural components. Beams are usually long, straight, prismatic members and always subject forces perpendicular to the axis of the beam.

• A Shear Force Diagram (SFD) indicates how a force applied perpendicular to the axis (i.e., parallel to cross-section) is transmitted along the length of that beam.
• A Bending Moment Diagram (BMD) will show how the applied loads to a beam create a moment variation along the length of the beam.

Types of Supports (a) Roller Support – resists vertical forces only.

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

• Hinge and roller supports are called simple supports

(c) Fixed support or built-in end

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

Types of beams: Beams are classified based on the type of supports: (1) supported beam: A beam with two simple supports

(2) Cantilever beam: Beam fixed at one end and free at other

(3) Overhanging beam

(4) Continuous beam: More than two supports

Shear Force

Shear force tends to slide the surface; it acts parallel to the surface.

Bending Moment

Any moment produced by forces acting on the beam must be balanced by an equal opposite moment produced by internal forces acting in the beam at the section. This moment is called the bending moment.

Only for distributed and concentrated load, not for a couple.

• The necessary internal forces to keep the segment of the beam in equilibrium are

Differential equations of equilibrium

Sign Conventions :

So the differential equations would be:

From the equation  , we can write.

From the equation , we can write.

Statically Determinate Beam

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

Statically Indeterminate Beam

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

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