Mechanics

what is it?

mechanics - the study of forces and their effects

source: EM Program at UIUC

 

rigid body mechanics (Classical mechanics)

• Statics - the study of bodies in equilibrium (zero acceleration)
• Dynamics - the study of the accelerated motion of bodies

deformable body mechanics (Mechanics of materials)

• determine the stresses, strains, and displacements in structures due to various loadings
• understand the mechanical behavior of structures (up to the loads that cause failure)

fluid mechanics

 

solving mechanics problems

problem format and homework suggestions

evaluating student work

6. simply going through the motions
4. rarely analyzes engineering problems clearly and precisely
3. emerging engineering skills
2. clear, precise, and well-reasoned, though with occasional lapses into weak reasoning
1. often analyzes engineering problems clearly and precisely, formulates information accurately, distinguishes the relevant from the irrelevant, and recognizes key questionable assumptions

 

statics

A rigid body is a collection of particles that remain at fixed distances from each other at all times and under all conditions of loading. 

The rigid-body concept represents an idealization of the true situation, since all real bodies will change shape to a certain extent when they are subjected to a system of forces. When it is assumed that the body is rigid (free of deformation), the material properties of the body are not required for the analysis of forces and their effects on the body.

 
free-body diagram - drawing of an object and the external forces acting on it

1. Select the object to be isolated.
2. Redraw the object isolated from its surroundings.  Show relevant dimensions and angles.
3. Draw all external forces acting on the object, including gravity.
4. Choose a coordinate system.

force - the action of one body on another ... spatial energy potential?
 

Concentrated Force		Force Distributed Over a Line		Force Distributed Over an Area

 

mechanics of materials

formula sheet

stress has pressure units (psi or Pa)

pressurex pressure metrics contact points beam compression beam flexure pin and roller cantilever   source: Jeff Thomas, April 2000

source: Measurements Group Inc.

 stresses typically cannot be added and subtracted like scalars

 the MoM formulas have many limitations...

Length	Metals		Bone	Muscle		Wood
0.000000000000001 m	sub-atomic		sub-atomic	sub-atomic		sub-atomic
0.000000000001 m
		atomic, crystallographic, monomeric
0.000000001 m			collagen molecule	tropo-collagen, micro-fibril
	microstructure					protofibrils
			hydroxyapatite, collagen fibril	fibril	sub-fibril	microfibrils, cellulose fibers, laminated cell walls
0.000001 m			collagen fiber
			lamellae	fibroblasts		cell diameter
			Haversian osteon		fascicle
0.001 m		macrostructure				cell length
			organ	organ		growth rings
1 m			organ system	organ system		trunk

...but serve as a good starting point for understanding how force is transmitted through an object