vilas nikam- mechanics of structure-column
TRANSCRIPT
![Page 1: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/1.jpg)
A POWERPOINT PRESEMTATION
ON COLUMN
PRESENTED BY
Prof V N NIKAM(Lecturer)
[email protected] Sandip Institute of Polytechnic
Nashik
![Page 2: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/2.jpg)
6. COLUMNSImportant definition
➲ Column: A vertical member of a structure use to sup-port axial compressive load called as column.
➲ Strut:inclined structural member subjected to axial compressive load called as strut.
➲ Buckling: The bending action of column is called as buckling.
➲ Radius of Gyration (k):k = √(I/A)k = radius of gyrationI = Moment of InertiaA = Cross sectional area of column section
Important definition➲ Column: A vertical member of a structure use to sup-
port axial compressive load called as column.➲ Strut:inclined structural member subjected to axial
compressive load called as strut.➲ Buckling: The bending action of column is called as
buckling.➲ Radius of Gyration (k):
k = √(I/A)k = radius of gyrationI = Moment of InertiaA = Cross sectional area of column section
![Page 3: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/3.jpg)
➲ Effective length of column: The length of column which deflects or bends as if it is hinged at its ends is called as effective length.
![Page 4: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/4.jpg)
Effective length for various end condition
![Page 5: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/5.jpg)
Classification of column
➲ Short Column➲ Medium Column➲ Long Column
![Page 6: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/6.jpg)
Short Column
➲ Column fails in crushing only.➲ In design of short column, compressive stress are con-
sidered and bending stress are neglected.➲ Slenderness ratio (λ) < 30
![Page 7: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/7.jpg)
Medium size column
➲ A column fails in crushing and bending both direct stresses as well as bending stresses are developed.
➲ For medium column, 30< λ < 100
![Page 8: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/8.jpg)
Long column
➲ Long column fails only in bending or buckling.
➲ Slenderness ratio for long column is very large.
➲ In design of long column bending stress are considered and direct stresses are neglected.
➲ For long column λ > 100
![Page 9: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/9.jpg)
Failure of column
a) Failure by crushingShort column fails in compression only due to crushing.Let A = cross sectional area of column.
PC = crushing load σc = Crushing stress PS = Safe load on column Crushing load PC = бC . A
![Page 10: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/10.jpg)
.b) Failure by buckling or bending➲ Before crushing, at a certain load column start
bending called as buckling load or critical load or crippling load.It may be calculated by a) Euler's formulab) Rankine's Formula
![Page 11: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/11.jpg)
![Page 12: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/12.jpg)
Euler's Theory of column➲ Euler's theory is applicable for only long column.➲ He had considered bending stress only and compressive stress
are completely neglected.Assumption in Euler's column theory.1. The material of column is perfectly homogenous and isotropic.2. The column is initially straight and of uniform lateral dimen-sions.3. The load on column is exactly axial.4. The column is long and fails due to bending or buckling only.5. The self weight of column is neglected.6. The column is stressed upto limit proportionality.
![Page 13: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/13.jpg)
Euler's FormulaEuler's buckling load or crippling load is given by
PE = Euler's buckling load.
E = Modulus of elasticity of column material
I = minimum moment of inertia of column section
Le = Effective length of column.
![Page 14: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/14.jpg)
Also Crushing stress
Euler's formula is applicable when λ > 80
![Page 15: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/15.jpg)
Factor of safety
➲ Factor of safety for mild steel and cast iron is taken as 3 and 5 respectively.
➲ Safe Load
![Page 16: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/16.jpg)
Strength of columnLoad carrying capacity of column is called as strength of column. It is given by
![Page 17: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/17.jpg)
Rankine's formula
Rankine had derived formula for long column as follows.
➲ Where
➲ PR = Rankine's Crippling loadLe = Effective length of columnk = Minimum radius of gyrationσc or fc = Ultimate crushing stressA = Area of cross sectiona or α = Rankine's constant
![Page 18: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/18.jpg)
Value of crushing stress for and Rank-ine's constant for different material
SR NO Material σc = Crushing stress in N/mm2
A = Rankine's constant
1 Timber 50 1/750
2 Wrought Iron 250 1/9000
3 Mild steel 325 1/7500
4 Cast Iron 550 1/1600
![Page 19: vilas Nikam- Mechanics of structure-Column](https://reader031.vdocuments.site/reader031/viewer/2022012322/5a6e75907f8b9a7a488b45c5/html5/thumbnails/19.jpg)
Thank you !!!!!!!!!!!!!!!!!!!