Conference Session

Innovative Teaching Techniques in Mechanics

Collection

2006 Annual Conference & Exposition

Authors

Shanzhong (Shawn) Duan, South Dakota State University

Tagged Divisions

Mechanics

the unit vector nˆ3 .Bodies A and B are slender uniform rods with mass mA and mB , and length LA and LBrespectively. A torsional spring with the spring constant K A acts between body A and the ground.q and q are generalized coordinates. The basis vectors aˆ , bˆ , and nˆ (i = 1,2,3) are fixed on 1 2 i i ibody A, body B and the ground respectively. A force FQ is applied to point Q in the direction bˆ1 . Figure 1: A Simple Case Study – the Rigid Body Double PendulumThough the double pendulum case is simple, it contains basic features that are necessary to Page

Conference Session

What's New in Statics?

Collection

2006 Annual Conference & Exposition

Authors

Nidal Al-Masoud, Central Connecticut State University

Tagged Divisions

Mechanics

-Dimensional Equilibrium of a Particle Page 11.788.6 Figure 5: 3-Dimensional Equilibrium of a ParticleBasic vector operations moduleThis panel provides a comprehensive tool for the basic vector operations such as cross product,scalar product, unit vectors, and dot product. Figure 6 illustrates the structure of this module. Page 11.788.7 Figure 6: Vector product moduleThe cross product, also known as vector product, is an operation on coplanar vectors P and Q isdefined as 10: f f f

Conference Session

Innovative Teaching Techniques in Mechanics

Collection

2006 Annual Conference & Exposition

Authors

Ing-Chang Jong, University of Arkansas

Tagged Divisions

Mechanics

. Note that Page 11.878.4Eq. (4) is extremely useful and important in solving problems by the virtual work method!III. Relevant Fundamental ConceptsIn teaching and learning the virtual work method, it is well to recall the following relevant fun-damental concepts:̇ Work of a forceIf a force F acting on a body is constant and the displacement vector of the body from positionA1 to position A2 during the action is q, then the work U1› 2 of the force F on the body is2-6, 8,9 U1› 2 ? F © q ? FqE (5)where F is the magnitude of F and qE is the scalar component of q parallel to

Conference Session

What's New in Mechanics of Materials?

Collection

2006 Annual Conference & Exposition

Authors

Michael Hennessey, University of St. Thomas; Luke Hacker, University of St. Thomas

Tagged Divisions

Mechanics

., G. Scheuermann, J. Frey, Z. Yang, B. Hamann, K. Joy, and H. Hagen, “Tensor visualizations in computational geomechanics,” International Journal for Numerical and Analytical Methods in Page 11.502.10 Geomechanics, 2002; 26: 925-944.[7] Zhou, Y. Q.-L. Li, and S.-D. Ma, “Visualization of Geostress Tensor Along Oil Well Trajectory,” Proceedings of Computer Graphics International 2001, 3-6 July 2001, Hong Kong.[8] Zheng, X. and A. Pang, “Volume Deformation for Tensor Visualization,” IEEE Visualization 2002, Oct. 27 – Nov. 1, 2002, Boston, MA.[9] Almusallam, A. and S. E.-D. Taher, “Three-Dimensional Mohr’s Circle for Shear

Conference Session

What's New in Mechanics of Materials?

Collection

2006 Annual Conference & Exposition

Authors

Hartley T. Grandin, Worcester Polytechnic Institute; Joseph Rencis, University of Arkansas

Tagged Divisions

Mechanics

. Page 11.79.2 y L φa φ(x) φb Ta x a b T q, moment/length b x Figure 2. Material Law Formulas for a uniform shaft with end torsional couples and