Radiation Heat Transfer

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View Factor Orientation (or View factor or shape factor) plays an important role in radiation heat transfer. View factor is defined as, "fraction of radiation leaving surface 'i' and strike 'j' ". Summation Rule (View Factor) If there is are similar surfaces 'i' and 'j' , then: Blackbody Radiation Exchange Radiation Exchange between Opaque, Diffuse, Gray surfaces in an Enclosure 1. Opaque 2. Surfaces 3. Two surface enclosure Radiation Shield It is used to protect surfaces from radiation act like a reflective surface. References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge.  Photoshoped pics  are developed.  Some pics and GIF from Google.   Videos from YouTube ( Engineering Sights ).
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Bending

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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.
  • 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).

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