PPT - Beam on Elastic Foundation - Civil Engineering (CE) PDF Download

 Page 1


BEAMS ON ELASTIC 
FOUNDATION
Page 2


BEAMS ON ELASTIC 
FOUNDATION
INTRODUCTION
• Beneath the foundation soil mass is considered as
identical, independent, closely spaced, linearly elastic
springs which is known as Winkler foundation.
• Bending of beams on an elastic foundation is
developed on the assumption that the reaction forces of
the foundation are proportional at every point to the
deflection of the beam at that point .
• One of the most important deficiencies of the Winkler
model is that a displacement discontinuity appears
between the loaded and the unloaded part of the
foundation surface. In reality, the soil surface does not
show any discontinuity.
Page 3


BEAMS ON ELASTIC 
FOUNDATION
INTRODUCTION
• Beneath the foundation soil mass is considered as
identical, independent, closely spaced, linearly elastic
springs which is known as Winkler foundation.
• Bending of beams on an elastic foundation is
developed on the assumption that the reaction forces of
the foundation are proportional at every point to the
deflection of the beam at that point .
• One of the most important deficiencies of the Winkler
model is that a displacement discontinuity appears
between the loaded and the unloaded part of the
foundation surface. In reality, the soil surface does not
show any discontinuity.
Classification of beams:
The beams on elastic foundation can be           
classified into three types 
• Short beams for which ß?? = 0.6
• Medium beams or semi-infinite beams for which 
0.6< ßL < 5
• Long beams or infinite beams ß?? = 5
L= length of the beam 
Page 4


BEAMS ON ELASTIC 
FOUNDATION
INTRODUCTION
• Beneath the foundation soil mass is considered as
identical, independent, closely spaced, linearly elastic
springs which is known as Winkler foundation.
• Bending of beams on an elastic foundation is
developed on the assumption that the reaction forces of
the foundation are proportional at every point to the
deflection of the beam at that point .
• One of the most important deficiencies of the Winkler
model is that a displacement discontinuity appears
between the loaded and the unloaded part of the
foundation surface. In reality, the soil surface does not
show any discontinuity.
Classification of beams:
The beams on elastic foundation can be           
classified into three types 
• Short beams for which ß?? = 0.6
• Medium beams or semi-infinite beams for which 
0.6< ßL < 5
• Long beams or infinite beams ß?? = 5
L= length of the beam 
Infinite beam subjected to point load
• As we know  ,   EI
d
2
y
d?? 2
= - M
EI
d
3
y
d?? 3
= - V
EI
d
4
y
d?? 4
= - q
Page 5


BEAMS ON ELASTIC 
FOUNDATION
INTRODUCTION
• Beneath the foundation soil mass is considered as
identical, independent, closely spaced, linearly elastic
springs which is known as Winkler foundation.
• Bending of beams on an elastic foundation is
developed on the assumption that the reaction forces of
the foundation are proportional at every point to the
deflection of the beam at that point .
• One of the most important deficiencies of the Winkler
model is that a displacement discontinuity appears
between the loaded and the unloaded part of the
foundation surface. In reality, the soil surface does not
show any discontinuity.
Classification of beams:
The beams on elastic foundation can be           
classified into three types 
• Short beams for which ß?? = 0.6
• Medium beams or semi-infinite beams for which 
0.6< ßL < 5
• Long beams or infinite beams ß?? = 5
L= length of the beam 
Infinite beam subjected to point load
• As we know  ,   EI
d
2
y
d?? 2
= - M
EI
d
3
y
d?? 3
= - V
EI
d
4
y
d?? 4
= - q
• Where the distributed reaction force q  is 
positive when acting upward
• For linearly elastic foundation, the distributed 
force q is linearly proportional to the deflection 
y . Thus,
q = ky
k = bk
0
Where k is the elastic coefficient, k
0
is the elastic 
foundation modulus, and b  is the width of the 
foundation.