Chapter six - Philadelphia University. Bending.pdf · 5/18/2014 1 Chapter six Laith Batarseh...

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Chapter six Chapter six

Laith Batarseh Laith Batarseh

Bending Bending

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Bending Bending

6.1. shear and moment diagrams 6.1. shear and moment diagrams

Shear and moment diagrams are important to study the bending

stresses.

To construct shear moment diagram, follow these procedures

Find the supports reactions using F.B.D and static equilibrium equations

Derive both shear and moment functions with respect to x or y axis by analyzing sections through the body

Draw shear and moment diagrams from the equations you found in the previous step

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Bending Bending

6.1. shear and moment diagrams 6.1. shear and moment diagrams

The sign conventions are opposite when the summing processes are carried out with opposite direction.

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Bending Bending

6.2. graphical method 6.2. graphical method

Regions of distributed load:

dxxwV

dxxVM

Change in moment = area under shear diagram

Change in shear = area under distributed loading

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6.2. graphical method 6.2. graphical method

FV

VVFV

0

0

0

0

MM

MxVMMM

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Bending Bending

6.3. bending deformation 6.3. bending deformation

Assumptions: 1. Plane section remains plane

2. Length of longitudinal axis remains unchanged

3. Plane section remains perpendicular to the longitudinal axis

4. In-plane distortion of section is negligible

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Bending Bending

6.3. bending deformation 6.3. bending deformation

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My

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Mc

I

My

dAyc

M

dAc

yydAyydFM

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A

AA

ZZR

max

2max

max

;

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