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

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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

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+

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 .

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+

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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

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qmax

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