09.01.03.072
description
Transcript of 09.01.03.072
Presentation onKERN
Presented by
Md. Raihanual Islam Dulal
Student ID: 09.01.03.072
Department of Civil Engineering
AUST, Dhaka
CE 416 Pre-stressed Concrete Lab.
Course Teachers: Lecturer Mr. Galib Muktadir RatulLecturer Ms. Sabreena Nasrin
Department of Civil EngineeringAhsanullah University of science and Technology
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.
The kern concept is widely used in the design of pre-stressed concrete beams, footings and concrete dams.
B
L
Kern
Some cross Section & its Kern
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.
Figure: Central kern
Kt
Kb
c.g.c
CT
Kt
Kb
c.g.c
CT
(a)C below bottom kern point
(b)C at bottom kern point
If C at bottom kern point stress distribution will be triangular with Zero stress at the top fiber.
If C outside the kern, some tension will be exist .
Relationship between Stress Distribution & the location of C, according to the elastic theory
+
-
+
KERN in Pre-Stressed Concrete Section
Kt
Kb
c.g.cC
T
Kt
Kb
c.g.c
C
T
(c)C within kern point
(d)C at c.g.c
If C falls within the kern, the enter section will be under compression
If C at c.g.c., stress will be uniform over the entire concrete section
+
+
Kt
Kb
c.g.c
T
C
Kt
Kb
c.g.c
T
C
(e)C at top kern point
(f)C above top kern point
If C at top kern point stress distribution will be triangular with Zero stress at the bottom fiber.
If C outside the kern, some tension will be exist .
+
+
-
KERN in Footing Section
Figure: Cross section of a footing section
Case (a) Case (b) Case (c)
For case (a) and (b) Resultant load is within KERN
For case (c) Resultant load is beyond KERN
( )
( )
qmax
x
qa
qa