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# CES Mechanics I Lecture 6

RWTH Aachen University, Bachelor program in Computational Engineering Science

Topics:

• Free-body diagrams. 1.4
• Support reactions.
• Elvis and Nixon.
• Coplanar equillibrium equations. 3.1.4, 3.2.2

Corresponding Gross et al. Statik chapters are shown in red.

Key techniques:

• Drawing free-body diagrams:
• sketching the body without supports,
• drawing applied forces, including distributed loads through centroid of the load volume/area and weight through CG,
• drawing reactions at supports, assuming a sense (direction),
• labeling angles and dimensions.
• Choosing an independent set of equilibrium equations.
• Choosing equilibrium equations that will involve least computation.
• Recognizing statically-determinate and statically-indeterminate problems.

ConcepTests (RWTH only):

Admissible equilibrium equation sets for general coplanar force systems:

• Two force equations and one moment equation:

\sum F_{x^\prime} = 0, \sum F_{y^\prime} = 0, \sum M_A = 0; avoid x^\prime \parallel y^\prime

• Two moment equations and one force equation:

\sum M_A = 0, \sum M_B = 0, \sum F_{x^\prime} = 0; avoid x^\prime \perp AB

• Three moment equations:

\sum M_A = 0, \sum M_B = 0, \sum M_C = 0; avoid A, B, C colinear

The following two cases (concurrent and parallel) involve subsets of the general equations, and they are listed here for completeness only.

Admissible equilibrium equation sets for concurrent coplanar force systems (moment equation about point of intersection O is trivially satisfied):

• Two force equations:

\sum F_{x^\prime} = 0, \sum F_{y^\prime} = 0; avoid x^\prime \parallel y^\prime

• Two moment equations:

\sum M_A = 0, \sum M_B = 0; avoid A, B, O colinear

• One force and one moment equation:

\sum F_{x^\prime} = 0, \sum M_A = 0; avoid x^\prime \perp OA

Admissible equilibrium equation sets for parallel coplanar force systems (force balance in the direction x perpendicular to all forces trivially satisfied):

• One force and one moment equation:

\sum F_{y^\prime} = 0, \sum M_A = 0; avoid x \parallel y^\prime

• Two moment equations:

\sum M_A = 0, \sum M_B = 0; avoid x \perp AB

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