St_Mod14_F10

St_Mod14_F10 - Module 14: Moment of Iner=a November...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Module 14: Moment of Iner=a November 19, 2010 Module Content: 1. Center of gravity, center of mass, and centroid are similar concepts which describe specific loca=ons in a body. The share similar approaches to their calcula=on. 2. Centroid of an area is par=cularly important for structural analysis, because we oXen use it to describe the cross sec=on of a beam. 3. Composite bodies are analyzed using a par=cle discre=za=on. Module Reading, Problems, and Demo: Reading: Chapter 10 Problems: Fund. Prob. 10.8, Prob. 10.38 Demo: business card bridge Homework PlaRorm: hSp://www.masteringengineering.com Course Blog: hSp://pages.shan=.virginia.edu/sta=cs2010 MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 1 Theory: Composite Bodies • composite bodies have complicated geometries which are typically built up from simpler shapes to form useful shapes for specific applica=ons • in engineering, the basic building blocks are usually circles and rectangles • in the analysis, we treat each simple shape as a par=cle MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 2 Theory: Composite Bodies • composite bodies have complicated geometries which are typically built up from simpler shapes to form useful shapes for specific applica=ons • in engineering, the basic building blocks are usually circles and rectangles • in the analysis, we treat each simple shape as a par=cle MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 2 Theory: Composite Bodies • composite bodies have complicated geometries which are typically built up from simpler shapes to form useful shapes for specific applica=ons • in engineering, the basic building blocks are usually circles and rectangles • in the analysis, we treat each simple shape as a par=cle MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 2 Theory: Composite Bodies • composite bodies have complicated geometries which are typically built up from simpler shapes to form useful shapes for specific applica=ons • in engineering, the basic building blocks are usually circles and rectangles • in the analysis, we treat each simple shape as a par=cle MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 2 Example 9.10: Composite Body (p. 473) MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) = MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) = MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) = MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) = - MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) = - MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Example 9.10: Composite Body (p. 473) MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 3 Concept: Moment of Iner=a • the moment of iner=a is mathema=cally defined as the “second moment of the area”, so called because the integral equa=on which describes it uses a quadra=c ­type equa=on as the integrand • in MAE 2310, we will examine bending stresses ­ ­these are oXen the most important stresses ac=ng on a structural member • in the deriva=on of the bending stress equa=on, a specific type of integral shows up in the denominator of the bending stress equa=on • that special integral is the moment of iner=a; note that a larger moment of iner=a results in a smaller bending stress (since it appears in the denominator) MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 4 Theory: The “Second Moment” of Area MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 5 Theory: The “Second Moment” of Area MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 5 Theory: The “Second Moment” of Area notes: • the (x,y) coordinates are defined with respect to a specific coordinate system (the “global” system) • so this means that if we use a different coordinate system...we get a different moment of iner=a • but...would those two moments of iner=a be somehow related to each other? MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 5 Theory: The Integral MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 6 Example: A Rectangular Cross Sec=on • calculate the moment of iner=a Iy around the xb axis MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 7 Example: A Rectangular Cross Sec=on, II • calculate the moment of iner=a Iy around the x’ axis MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 8 Theory: Parallel Axis Theorem • so what about the link between the moments of iner=a calculated on the two different coordinate systems? • let’s say our two coordinate system are offset from each other by distances dx and dy • then, we can reformulate the integral as: MAE 2300 Sta=cs © E. J. Berger, 2010 14 ­ 9 ...
View Full Document

This note was uploaded on 02/09/2012 for the course MAE 2300 taught by Professor Staff during the Fall '10 term at UVA.

Ask a homework question - tutors are online