Bending:

It is defined as, "External loads that tends to bend any beam due to transverse loading".

• Beams  ↠  members that slender and support transverse loading acting perpendicular to their longitudinal axis.

Types of Beams:

There are three types of beams which are discussed ahead:

1. Simply Supported Beam  ↠  having two supports at either end, one is pinned and other is roller.
2. Overhanging Beam  ↠  if the end of beam extends beyond the support (having 2 supports).
3. Cantilever Beam  ↠  beam which is supported at only one end i.e. one end is fixed and other is exposed beyond the support.

Types of loading:

• Shear Force (SF)  ↠  a transverse force tends to cause shearing of beam across the section.  
• Bending Moment (BM)  ↠  due to different loading types, product of force and moment arm.

General Rules for SF and BM Diagram:

There are three rules for shear force and bending moment diagram which are given below:

1. For Point Loading:

Shear force diagram is comprising of rectangular horizontal steps while bending moment diagram contains inclined straight lines. 

2. For Uniformly Distributed Loading:

Shear force diagram is comprising of inclined straight line while bending moment diagram contains parabola. 

3. For Variable Distributed Loading:

Shear force diagram is comprising of parabola while bending moment diagram contains curve of 3rd degree. 

Important Points:

• SF and BM diagram  ↠  used to design beams and gives variation in shear force and bending moment throughout beam.
• It tells about point of max. shear force and bending moment, help us in proper placement of reinforcement material.
• BMD gives maximum or minimum value when shear force is zero.
• Point of Contra-Flexure or Inflection Point  ↠  BMD passes through zero i.e. changes from concave-up to concave-down or vice versa. 

Relationship Among Shear Force and Bending Moment:

Flexure Formula:

• Flexural or Bending Stresses  ↠  stresses caused by bending moment.

Important Points:

• Neutral axis (N.A.) is subjected to zero stresses.
• Due to deformation, longitudinal strain varies linearly from zero to maximum at outer fibers.
• Provided material should be homogeneous, linearly elastic.
• N.A. passes through centroid of cross-sectional area.
• Resultant internal moment is equal to the moment produced by normal stress distribution about N.A.

Composite Beams:

Beams that are made-up of more than one materials are called Composite Beams.

• For example: reinforced concrete beam with steel rods, bimetallic beams of wood and steel strap.
• Flexure formula is not directly applied to composite beams because developed for homogeneous beams.
• Composite beams are designed to save material, reduce size and weight.

Deflection of Beams:

It is defined as, "The deformation of a beam is usually expressed in terms of its deflection from its unloaded position".

• Deflection is measured from the neutral axis of beam to neutral axis of deformed beam.
• Path of deformed neutral surface is called Elastic Curve of the Beam.

Method to Determine Beam Deflection:

Following are the methods to determine the deflection of beam:

1. Double-Integration method
2. Area-Moment method
3. Strain -Energy method (Castigliano's Theorem)
4. Conjugate-Beam method
5. Method of Superposition

1. Double Integration Method:

It is used in solving deflection and slope of a beam at any point because we will be able to get elastic curve equation.

References:

• Material from Class Lectures + Book named Engineering Mechanics of Materials by R.C. Hibbeler (10th Edition) + my knowledge. 
• Pics and GIF from Google Images.  
• Videos from YouTube (Engineering Sights).