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Class #24. Beams Shear and Bending Moment Diagrams Calculus Development Statics Spring 2006 Dr. Pickett. Shear and Bending Moment Diagrams. Long and Slender beam It lies in a plane Is loaded only in that plane Have only 3 equilibrium equations. If a whole beam is in equilibrium.

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### Class #24

Beams

Shear and Bending Moment Diagrams

Calculus Development

Statics

Spring 2006

Dr. Pickett

Shear and Bending Moment Diagrams
• Long and Slender beam
• It lies in a plane
• Is loaded only in that plane
• Have only 3 equilibrium equations
Steps for V and BM diagrams

1.Draw FBD

2.Obtain reactions:

SM (@left support) to obtain reaction at right;

SM (@Right support) to obtain reaction at left;

Check SFy = 0

3. Cut a section ;

Obtain internal P,V,M at cut section ;

SM, SFy, SFx

4. Record, draw internal P, V, M on both sides of cut sections ;

- magnitude

- units

- direction on both sides of cut

If a whole beam is in equilibrium then part of the beam is also in equilibrium
• Draw a free body diagram
• Slope of shear ( V ) diagram @ X equals

value of load diagram @ X

• Integrating across the length of the beam
• Not valid if concentrated load between x1 and x2.
• The change in shear ( ΔV ) from

equals the area under the load

diagram from

As very very small
• Slope of the moment ( M ) diagram @ X equals

the value of the shear ( V ) diagram @ X

• Integrating across the length of the beam

Yes valid with concentrated load between x1 and x2

Not valid if a couple is applied between x1 and x2.

• The change in moment from equals the area under the shear diagram from
BEAM END CONDITIONS

Pin-Roller Pin

Fixed-Free

Fixed-?

Problems
• Draw the shear and bending moment diagrams of the following problems: (B & J 5th)

7.20,7.22

7.20 contd
• AREA UNDER V DIAGRAM

FROM

TO

MOMENT

7.22 contd

V(x) = -wx

M(x) = -wx2/2