10.01.03.034

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AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

Name: Susmita Bhowmik

ID: 10.01.03.034

Department of Civil Engineering

Pre-stressed Concrete Lab

4 th Year; 2nd Semester

Sec : A

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BENDING MOMENT STRESS (UNIAXIAL & BIAXIAL)

STRESS

The components of the

intensity of force per

unit area- that is stress.

Bending Moment Stress

If the stress in a beam depends on the bending moment is called

bending moment stress. It is the internal stresses caused by bending

moments acting at a given distance from the neutral axis. It is also

known as flexural stress.

Bending Moment Stress (Cont.)

The formula for bending stress, σ, is as follows:

σ = My/ I M = moment acting on beam from moment

diagram (kip-in or lb-in) y = distance from neutral axis to extreme edge of

member (in) I = moment of inertia about the axis (in^4)

Bending Moment Stress (Cont.)

Recalling that

S = I/Y , the bending stress formula could be re-written as:

σ = M/S

where: S = section modulus about the axis (in³)

Types of bending moment stress

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FollowedHyperlink UNIAXIAL BENDING STRESS

BIAXIAL  BENDING STRESS

TWO TYPES OF BENDING STRESS-

Uniaxial Bending Stress

• An uniaxial bending stress system has a stress state in one direction.

• In Diagram 1 we have shown a simply supported beam loaded at the center. It deflects (or bends) under the load.

Uniaxial Bending Stress (Cont.)

Bending stress is distributed through a beam as seen in the diagram below:

Uniaxial Bending Stress (Cont.)

EXAMPLES:

A simply-supported

beam always has

tensile stresses at the

bottom of the beam

and compressive

stresses at the top of

the beam.

Uniaxial Bending Stress (Cont.)

A beam under only a

bending load will be in a

uniaxial.

Stress (force) distribution in a bent beam

EXAMPLES:

Uniaxial Bending Stress (Cont.)

Example GIVEN: A nominal 2x10 (actual dims. 1½” x 9¼”) is used as a simply-supported beam with loading as shown. The allowable bending stress is 1200 psi.

REQUIRED:

a) Determine the maximum moment on the beam.

b) Determine the maximum actual bending stress on the beam

c) Determine if the beam is acceptable based upon allowable bending stress.

Uniaxial Bending Stress (Cont.)

The maximum bending moment, Mmax, on a simply-supported, uniformly loaded beam is:

Mmax = wL2/8

or, Mmax = (140 PLF)(11') 2/8

or, Mmax = 2117.5 lb-ft

The bending stress is:

σ =M/S

=[2117.5 lb - ft(12"/ft)] / 21.39 in³

or, σ = 1187.9 PSI

Since the actual bending stress of 1187.9 PSI is less than the allowable bending stress of 1200 PSI, THE BEAM IS ACCEPTABLE.

Variation of tension and compression due to bending moment:

In biaxial bending (d), the top-left part is subjected to double compression and the bottom right part is subjected to double tension. The remaining parts are subjected to combined compression and tension.

With the shown sign convention, bending about X-axis causes compression in the top part and tension in the bottom region, whereas bending about Y-axis causes compression in the left hand part and tension in the right part.

Biaxial Bending Stress (Unsymmetric Bending)

A biaxial stress

system has a stress

state in two

direction. . It is also

known as

unsymmetrical

(skew) bending.

Biaxial bending stress(Unsymmetric Bending)

The formula of the biaxial bending stress is given by-

σx = -(Mz Y/Iz ) + (MyZ/Iy)

EXAMPLES:

The column having axial load acting in such a way that the load is eccentric about both the axes in the plane of the column then it is called biaxially loaded column.

Biaxial bending stress (Cont.)

EXAMPLES:

Schematic stress distribution of a rectangular footing under the effect of biaxial bending

together with vertical load is shown in Figure:

Biaxial bending stress (Cont.)

Loading at footing base and stress distribution

Thank You………..