MT-1620 al.2002 Unit 10 St Venant Torsion Theory Readings Rivello 81,82,84 T&G 101.104,105,106 Paul A Lagace Ph D Professor of aeronautics Astronautics and engineering systems Paul A. Lagace @2001
MIT - 16.20 Fall, 2002 Unit 10 St. Venant Torsion Theory Readings: Rivello 8.1, 8.2, 8.4 T & G 101, 104, 105, 106 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems Paul A. Lagace © 2001
MT-1620 al.2002 Ⅲ Torsion Paul A. Lagace @2001 Unit 10-p. 2
MIT - 16.20 Fall, 2002 III. Torsion Paul A. Lagace © 2001 Unit 10 - p. 2
MT-1620 Fall 2002 We have looked at basic in-plane loading. Lets now consider a second"building block of types of loading: basic torsion There are 3 basic types of behavior depending on the type of cross-section Solid cross-sections “ classical” solution technique via stress functions 2. Open, thin-walled sections Membrane Analogy Paul A. Lagace @2001 Unit 10-p. 3
MIT - 16.20 Fall, 2002 We have looked at basic in-plane loading. Let’s now consider a second “building block” of types of loading: basic torsion. There are 3 basic types of behavior depending on the type of cross-section: 1. Solid cross-sections “classical” solution technique via stress functions 2. Open, thin-walled sections Membrane Analogy Paul A. Lagace © 2001 Unit 10 - p. 3
MT-1620 al.2002 3. Closed thin-walled sections Bredt's formula In Unified you developed the basic equations based on some broad assumptions. Let's Be a bit more rigorous Explore the limitations for the various approaches Better understand how a structure "resists"torsion and the resulting deformation Learn how to model general structures by these three basic approaches Look first at Paul A. Lagace @2001 Unit 10-p. 4
MIT - 16.20 Fall, 2002 3. Closed, thin-walled sections Bredt’s Formula In Unified you developed the basic equations based on some broad assumptions. Let’s… • Be a bit more rigorous • Explore the limitations for the various approaches • Better understand how a structure “resists” torsion and the resulting deformation • Learn how to model general structures by these three basic approaches Look first at Paul A. Lagace © 2001 Unit 10 - p. 4
MT-1620 al.2002 Classical (St. Venant's)Torsion Theory Consider a long prismatic rod twisted by end torques Tin-lbs」[m-n Figure 10.1 Representation of general long prismatic rod T Length(l)>> dimensions in x and y directions g Do not consider how end torque is applied (St. Venant's principle Paul A. Lagace @2001 Unit 10-p. 5
MIT - 16.20 Fall, 2002 Classical (St. Venant’s) Torsion Theory Consider a long prismatic rod twisted by end torques: T [in - lbs] [m - n] Figure 10.1 Representation of general long prismatic rod Length (l) >> dimensions in x and y directions Do not consider how end torque is applied (St. Venant’s principle) Paul A. Lagace © 2001 Unit 10 - p. 5