COLUMNS & STRUTS

Submitted to:

Mr. HIMANSHU BORADE

Submitted By:

Divya Kumar Jain

Gaurav GuptaMechanical -A

CONTENTS

INTRODUCTIONDEFINITIONSHISTORY OF COLUMNS CLASSIFICATION OF COLUMNSFAILURE OF COLUMNSSIGN CONVENTIONSSTMTYPES OF STRUTSEULERS FORMULA DERIVATIONSRANKINE FORMULAEULERS FORMULA UNDER

ECCENTRIC LOADING

INTRODUCTION

COLUMNS

STRUTS

DEFINITIONS: STRUTS: A structural member ,

subjected to axial compressive force, is called a strut. These may be horizontal, inclined or even vertical.

COLUMNS : The vertical struts which are

being used in buildings and frames are more precisely called as columns.

HISTORY The use of columns has been

done from ancient times . The most ancient traces of columns have been found in Greece, few thousands of years B.C.

Later as the time proceeded the techniques of column making and materials .

In the very beginning wood was used as column material which has advanced to concrete and even Fiber Reinforced Polymer (FRP) discovered about twenty years ago.

STRUTS

STRUT AND TIE MODEL (STM)

FUNCTIONS OF STRUTS:

1. They serve as the compression chord of the truss mechanism which resists moment2. They help in the transfer shear to the supports.

TYPES OF STRUTS

a) PRISM type(having constant width)

b) BOTTLE type(width expand and contract along with length)

c) FAN type(an array of struts with varying

inclination meet at or radiate from a single node)

USES OF STRUTS

TO SUPPORT ROOFS

AS SUSPENSIONS IN AUTOMIBILES

IN MAKING FRAMESEg. LADDER

TYPES OF COLUMNSColumns are basically of two types:o LONGo SHORT / INTERMEDIATE

Slenderness ratio( Leff / r): It is the ratio of the effective

length of column to the least radius of gyration of its cross section.

Critical slenderness ratio (SRc ):

SRc corresponds to the case when the stress due to the axial load reaches the proportional limit and the critical load at the same time.

If Leff / r < SRc, the column is considered  short/intermediate.If Leff / r > SRc, the column is considered long.

Column failures

Material failure

(crushing)

Elastic buckling

(Euler)

Inelastic buckling

(combination of

buckling and

material failure)

P

P

ΔLeff

SIGN CONVENTIONS

POSITIVE BENDING

NEGATIVE BENDING

Eulers FormulaSir Leonhard Euler (1707 – 1783)

Euler Buckling (elastic buckling)

A = Cross sectional area (m2) E = Modulus of elasticity of the material (N/m2) K = Stiffness (curvature mode) factor L = Column length between pinned ends (in.) r = radius of gyration (in.)

2

2

rKL

AEPcr

A

Ir

AssumptionsThe following assumptions are

made while deriving the Euler’s Formula.

The column is initially straight & of uniform lateral dimensions.

The compressive load is exactly axial & it passes through the centroid of the column section.

The material of the column is perfectly homogenous and isotropic.

Pin joints are frictionless and fixed joints are perfectly rigid.

The weight of column itself is neglected. The column fails by buckling alone.Limit of proportionality is not exceeded.

Derivation of Euler’s formula (for different end conditions)

BIBLIOGRAPHY WEBSITES:GOOGLE BOOKSWIKIPEDIAUSTUDY

BOOKS REFERED

STRENGTH OF MATERIAL BY R.S. KHURMISTRENGTH OF MATERIAL BY R.K. RAJPUT