Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Document Description: Theory of Columns for Civil Engineering (CE) 2022 is part of Civil Engineering SSC JE (Technical) preparation. The notes and questions for Theory of Columns have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Theory of Columns covers topics like and Theory of Columns Example, for Civil Engineering (CE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Theory of Columns.

Introduction of Theory of Columns in English is available as part of our Civil Engineering SSC JE (Technical) for Civil Engineering (CE) & Theory of Columns in Hindi for Civil Engineering SSC JE (Technical) course. Download more important topics related with notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Civil Engineering (CE): Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
1 Crore+ students have signed up on EduRev. Have you?

Chapter 10

THEORY OF COLUMNS

Compression Member : A compression member is a structural member which is straight and subjected to two equal and opposite compressive forces applied at its ends.
Column: It is defined as a vertical member which is fixed at both the ends and subjected to an axial compressive load.Column, is a compression member that is so slender compared to its length that under gradually increasing loads, it fails by buckling at loads considerably less that those required to cause failure by crushing.  A compression member is generally considered to be a long column when its unsupported length is more than 10 times its least lateral dimension.  Column, Stanchion or post is a vertical compression member supporting floors or girders in a building.  Principal rafter is a top chord member in a roof truss.  Boom is the principal compression member in a crane.  Strut is commonly used for compression member in a roof  truss. It may either be in vertical position or in inclined position.

 

MODES  OF  FAILURE  OF  A COLUMN
Elastic instability A column subjected to axial load, may fail under the following modes: (i) Crushing (ii) Buckling (iii) Mixed mode of Buckling and Crushing.

 

Euler's Theory (Buckling failure)  Assumption of Euler's theory: (i) Axis of the column is perfectly straight  when unloaded. (ii) The line of thrust coincides exactly with the unstrained of the column. (iii) Flexural rigidity EI is uniform (iv) Material is isotropic and homogeneous. (v) The buckling value of load is assumed to obtain for all degrees of flexure. (vi) Length is assumed to be too large with respect to cross section.

 

Limitation of Euler's Formula: (i) The critical load that causes buckling depends not on strength of the material, but only on its dimensions and modulus of elasticity. This converts the strut problem from the problem of instability to a problem of stress, of which Euler's theory takes no account. (ii) In order for Euler's formula to be applicable, the critical stress p1 must not exceed the proportional limit.

 

IDEAL END CONSITION & EFFECTIVE LENGTH
Depending upon various combinations of restraints, there may be the following four cases of end condition: End condition Euler's load or critical load Equivalent length (Le)

Case 1 : Both  ends hinged

 Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Case 2 : One end fixed and other end free

Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Case 3 : Both ends fixed

 Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

PRACTICAL END CONSITION  AND EFFECTIVE LENGTH FACTORS:
As per IS : 800 - 1984, following table can be used for finding effective length: Effective length of compression members Radius of Gyration and Slenderness Ratio: 

  • The radius of gyration of a section is given by

 Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, I = Moment of Inertia A = area of section 

  • Rankine's formula The Rankine's formula is applicable for all columns  ranging form very short to very long struts.

Ranking proposed,

 Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where, Pc = fc.A= ultimate load for a strut

 Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

= Euler  crippling load for the standard case After rearranging above relations,

 Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Where,
Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

= Rankine's constant for a particular material

The document Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

Related Searches

Previous Year Questions with Solutions

,

Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

,

mock tests for examination

,

Important questions

,

pdf

,

shortcuts and tricks

,

Semester Notes

,

Summary

,

Free

,

Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

,

Theory of Columns Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

,

Exam

,

practice quizzes

,

video lectures

,

MCQs

,

study material

,

Objective type Questions

,

ppt

,

past year papers

,

Extra Questions

,

Sample Paper

,

Viva Questions

;