This document discusses the concept of kern in pre-stressed concrete design. The kern is the region where compressive loads can be applied without causing tensile stresses. It is widely used in designing pre-stressed beams, footings, and dams. The document shows how the location of a compressive force (C) relative to the kern affects the stress distribution - forces within the kern cause only compression, while those outside can cause tension as well. Examples are given for beam and footing sections, explaining how kern limits the maximum compressive load before tension occurs.

1. Presented by
Md. Raihanual Islam Dulal
Student ID: 09.01.03.072
Department of Civil Engineering
AUST, Dhaka

2. CE 416
Pre-stressed Concrete Lab.
Course Teachers:
Lecturer Mr. Galib Muktadir Ratul
Lecturer Ms. Sabreena Nasrin
Department of Civil Engineering
Ahsanullah University of science and Technology

3. KERN
The kern of a section is the region in which compressive point load
may be applied without producing any tensile stress on the cross
section.
Kern
B
L
The kern concept is widely used in the design of pre-stressed
concrete beams, footings and concrete dams.

4. Some cross Section & its Kern

8. KERN in Beam Section
The inner zone of any cross section is called the central kern,
Figure-(a). A compressive force applied within the kern will cause
only compressive stresses on the cross section. When the force is
applied at the point (limit) of the kern, the stress on the opposite
(remote ) fiber will be zero, Figure-(b). A compressive force applied
outside the kern will cause tensile stresses as well as compressive
stresses, Figure-(c). The upper and lower limits of the central kern
are called at and ab.

9. Figure: Central kern

10. KERN in Pre-Stressed Concrete Section
Relationship between Stress Distribution & the location of C, according to the elastic theory
Kt
Kb
If C outside
the
kern,
some tension
will be exist .
c.g.c
C
T
+
(a)C below bottom kern point
Kt
Kb
c.g.c
C
T
(b)C at bottom kern point
+
If C at bottom
kern point stress
distribution will
be
triangular
with Zero stress
at the top fiber.

11. Kt
c.g.c
Kb
C
+
T
If
C falls
within
the
kern,
the
enter section
will be under
compression
(c)C within kern point
Kt
Kb
c.g.c
C
T
(d)C at c.g.c
+
If C at c.g.c.,
stress will be
uniform over
the
entire
concrete
section

12. Kt
C
c.g.c
+
Kb
T
If C at top kern
point
stress
distribution will
be triangular with
Zero stress at the
bottom fiber.
(e)C at top kern point
Kt
C
c.g.c
+
Kb
T
(f)C above top kern point
-
If C outside the
kern,
some
tension will be
exist .

13. KERN in Footing Section
Figure: Cross section of a footing section

14. Case (a)
Case (b)
Case (c)

15. For case (a) and (b) Resultant load is within KERN (
qa
For case (c) Resultant load is beyond KERN (
qmax
qa
x
)
)