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Career Interviews Small Group Communication B8 class < 30 min (or option) Advertise for your profession (and get a free tee shirt) Contact if interested
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Area Moments of InertiaDefinition & Composite Area
ENGR B36 - StaticsPat Aderhold11/26/2014
News & Notes
News & Notes• Career Pathways @BC Interviews
Small Group Communication B8 class < 30 min (or email option)
• Advertise for your profession(and get a free tee shirt)
Contact kathryn.ramsey@email.bakersfieldcollege.edu if interested
News & Notes• Summer undergraduate research @ UPenn
http://www.seas.upenn.edu/sunfest/
• NASA Comm. Coll. Aeorspace Scholarshttp://ncas.aerospacescholars.org/
• ASCE Young Members Form: Game Night December 5, 5:30pm Location TBD Contact asce.ssj.ymf@gmail.com for more info
Today’s Agenda
• First half of class: Area Moments of Inertia
• Second half of class Questions to prep for Exam #3 Questions about Group Design Project Notes:• BYO Wine Bottle or use mine• Read carefully, object must be unstable when unloaded
Significance• Not immediately intuitive• Consider three common mechanics scenarios
Fluid pressure Bending moment on beam Torsional loading on beam
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 442
Learn it / use it because it’s helpful
SignificanceAll three scenarios share common principle
Moment caused by fluid pressure
Total bending moment
Total moment about longitudinal axis
DefinitionRefer to as “moment of inertia”
Analogous to inertial forces in rotating bodies More appropriate name second moment of area
(First moment = “moment”)
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 442
Practice Problem A/3
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 450
Radius of Gyration• Some area “A” with a moment of inertia Iy
• What if you... Smush the area into tiny strip? Place a distance ky from the y-axis?
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 443-444
Radius of Gyration• Calculate Iy
• And what did that do exactly?.... Just a property of the given area It has its uses (stability of columns, behavior of polymer chains)
Parallel Axis Theorem• Scoot area from axis to new location• Find moment of inertia about new location?
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 444
Parallel Axis Theorem(Proof in text)• Find moment of A about its centroid (“ Iy ”)
• Take distance to centroidal axis (“dy”)
• Remember! Must be parallel axis Must pass through centroid
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 444-445
Practice Problem A/12
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 451
NOTE: Remember Table D/3 p. 497-498
Complex Shapes• Moment of inertia is integration
(adding up many differential parts)• Works with finite pieces too
(comparable to composite centroids)
Practice Problem A/35
Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 459
Other Considerations• Other relationships in text
I for rectangular and polar Radius of gyration rectangular and polar
• Simple tools developed today... but can be used for virtually any
shape
For Exam #3• Can fill out a note card
Up to 4” x 6” One side only Bring to me for approval on Wednesday
• Three problems Distributed loading / shear & moment diagrams Buoyancy Friction
Review
For Next Class• Practice Problems 6/63 & 6/66• Think of questions and review problems
Exam #3 on Monday!
Group Design Project due next Wednesday!
Open Time
• Ask individual questions on HW
• Work on group design project
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