CIEG 212 Solid Mechanics

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CIEG 212Solid Mechanics

• Introductory Material
• by
• Victor N. Kaliakin

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Mechanics

• That branch of Physics that deals with the rest
  or motion of bodies and the phenomena of the
  action of forces on bodies (recall PHYS 207).

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Mechanics
Solids
Fluids
Relatively firm or compact body neither liquid
or gaseous.
Usually classified as a gas or a liquid, the
chief distinction being density compressibility.
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Mechanics
Solids
Fluids
Rigid
Deformable
Static
Dynamic
Dynamic
Static
CIEG 211
CIEG 212
CIEG 311
CIEG 311
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Mechanics
Solids
Fluids
Incompressible
Compressible
CIEG 305
Static
Dynamic
Dynamic
Static
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Solid Mechanics
Structural Analysis (CIEG 301)
Structural Design (CIEG 302)
Soil Mechanics (CIEG 320)
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Review of Statics

• Statics is concerned with the equilibrium of
  rigid bodies that are not accelerating.
• Equilibrium equations

In two-dimensions
In three-dimensions
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Types of Bodies

• Two-Force Bodies

Forces applied at only two points along a body.

• Three-Force Bodies

Forces applied at only three points along a body.

• General Bodies

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Two-Force Bodies

• Forces applied at only two points along a body.

• Forces must lie along a line connecting the two
  points of application.

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Three-Force Bodies

• Forces applied at only three points along a body.

Forces must either be concurrent.
Or parallel
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Types of Forces

• External Forces and Moments

• Applied surface loads
• Body forces (e.g., self-weight)
• Reactions (unknown) at supports

• Internal Forces and Moments

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Applied Surface Loads
External Forces and Moments

• Caused by the direct contact of one body with the
  surface of another body.

• Concentrated forces and moment

• Distributed forces and moment

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Body Forces
External Forces and Moments

• Developed when one body exerts a force on another
  body without direct physical contact. For example,

• Force due to the earths gravitational field
  (i.e., weight)

W mg

• Electromagnetic forces

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Reactions at Supports
External Forces and Moments

• Support reactions are surface forces or moments,
  typically unknown, that develop at supports or
  points of contact between bodies.

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External Forces and Moments

• The best way in which to determine the number of
  unknown reactions at a support is to answer the
  following question

In which direction(s) is motion (i.e.,
translation or rotation) being prevented at the
support?

• If motion is indeed prevented in a particular
  direction(s), then an unknown reaction, acting
  parallel to this direction, must be present at
  the support.

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Internal Forces and Moments
Shear Force
Axial Force
Bending Moment
Remember Newtons Third Law!
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Free-Body Diagrams

• Before the equilibrium equations can be applied,
  it is essential that

1. The particular body or group of bodies be defined
   unambiguously and isolated from all other bodies.
2. All forces acting on the body be represented
   clearly completely.

• This is accomplished by means of the free-body
  diagram (FBD).

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Steps for Constructing a FBD

1. Decide which body is to be isolated.
2. Detach the chosen body from its supports and
   separate it from any other body. Sketch the
   complete external boundary of the isolated body.
3. Indicate all external forces acting on the
   isolated body at their proper positions on the
   diagram. These include known applied forces
   unknown support reactions.

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Free-Body Diagrams

• Remark when the sense of an unknown force or
  moment is not clearly apparent, no attempt should
  be made to determine it.

Instead, the sense of the force or moment should
be arbitrarily assumed the sign of the answer
will indicate whether the assumption is correct.
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Statical Determinancy

• If the number of unknown reactions is equal to
  the number of equilibrium equations, the problem
  is statically determinate.
• If the number of unknowns is greater than the
  number of equations, the problem is statically
  indeterminate.
• If the number of unknowns is less than the number
  of equations, the problem is partially
  constrained.

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• Now lets do some example problems to review
  Statics