# STRENGTH OF MATERIAL : SFD-BMD

By Deepanshu Rastogi|Updated : March 25th, 2021

## Shear Force and Bending Moment Diagrams

Beam is one of the most important structural components.Beams are usually long, straight, prismatic members and always subjected 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) of a beam 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 as 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) Simply 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 has a tendency to slide the surface, it acts parallel to surface.

Bending Moment

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

Only for distributed and concentrated load not for 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 equation  ,we can write

From equation ,we can write

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 i.e.,

Statically Indeterminate Beam

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

You can avail Online Classroom Program for all AE & JE Exams:

## Online Classroom Program for AE & JE Exams (12+ Structured LIVE Courses and 160+ Mock Tests)

If you are preparing for ESE/ GATE or other PSU Exams (Civil Engineering), then avail Online Classroom Program for ESE and GATE CE:

## Online Classroom Program for ESE/GATE CE(20+ Courses and 180+ Mock Tests)

You can avail of BYJU'S Exam Prep Test Series specially designed for all AE & JE Exams:

## BYJU'S Exam Prep Test Series AE & JE (160+ Mock Tests)

You can avail of BYJU'S Exam Prep Test Series specially designed for all Civil Engineering Exams:

## BYJU'S Exam Prep Test Series ESE/GATE CE (180+ Mock Tests)

Thanks

Sahi Prep Hai To Life Set Hai.