ppt on eccentric loading

1. ECCENTRIC LOADING of
COLUMNS
B T venkata jagadeesh
15131D1603
Given By
A seminar on

2. INTRODUCTION
• Bars are categorized as columns and beams.
• Column is geometrically looks like beam but loading is different when
compared.
• Beam takes up load perpendicularly where as column takes axial.
• Again columns divided into SHORT and LONG columns.
• Both the types differentiated by ratio of length(a) to lateral
dimensions(b).
• Long columns have more (a/b) ratio comparted to short columns.
• Short columns, generally withstand higher compressive loads.
• Long columns are used in axial load applications.
Cntd..

3. Beam Types
• Simple
• Continuous
• Cantilever
Moment
(fixed at one end)

4. Beam Types
• Fixed
Moments at each end
• Propped- Fixed at one end supported at other
• Overhang

5. Forces and Supports
Supports are translated into forces and moments in a free body diagrams.
The following are three common supports and the forces and moments used to
replace them.
Roller:
Pin
Connection:
Fixed
Support:
Fy
Fy
Fx
Fx
Fy
Mo

6. Centric loading:
The load is applied at the centroid of the cross section. The limiting
allowable stress is determined from strength (P/A) or buckling.
Eccentric loading:
The load is offset from the centroid of the cross section because of how the
beam load comes into the column. This offset introduces bending along
with axial stress.
P
𝜎 = 𝑃/𝐴
P
e
This causes Direct stress

7. e
No problem with this set
e
This set forms couple
M = P * e
P
P
P
Eccentric loading :
Combined force and couple

8. Application of Eccentric load using short column :
P
e
P
M = P * e
This causes bending stress in
addition to direct stress.

9. P
e
P
M = P * e
P
𝜎 = 𝑃/𝐴
M = P * e
Max. Bending Stress
Max. Bending Stress
Direct stress𝜎 = 𝑃/𝐴
b= M ∗ C2/I
C1C2
b= M ∗ C1/I

10. 𝜎min 𝜎max
𝛔min = P/A - M*C2/I
𝛔max = P/A + M*C1/I
Representation of stress distribution

11. ECCENTRIC LOADING ON LONG COLUMNS
=
Take sec - AQ

12. Taking sec – A Q
Algebraic sum of moments about Q be zero
We know
let
differential equation

13. EQUATION SOLVING
General solution
Boundary conditions
Put in y(max)
By solving

14. Important NOTE
Time to replace with next slide

15. Than QThan QThan Q