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CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible...

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Solid Mechanics Introductory Material
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Page 1: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Solid Mechanics

Introductory Material

Page 2: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Mechanics

That branch of Physics that deals with the rest or motion of bodies and the phenomena of the action of forces on bodies.

Page 3: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Mechanics

Solids Fluids

Usually classified as a gas or a liquid, the chief distinction

being density & compressibility.

Relatively firm or compact body;

neither liquid or gaseous.

Page 4: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Mechanics

Solids Fluids

Rigid Deformable

Static Static Dynamic Dynamic

Page 5: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Mechanics

Solids Fluids

Incompressible Compressible

Static Dynamic Static Dynamic

Page 6: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Solid Mechanics

Structural Analysis

Soil Mechanics

Structural Design

Page 7: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Review of Statics • Statics is concerned with the equilibrium of

rigid bodies that are not accelerating. • Equilibrium equations:

In two-dimensions:

In three-dimensions:

0, 0, 0x y zF F M= = =∑ ∑ ∑

0, 0, 0,

0, 0, 0x y z

x y z

F F F

M M M

= = =

= = =∑ ∑ ∑∑ ∑ ∑

Page 8: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Review of Statics

Page 9: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Review of Statics

Page 10: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Review of Statics

Page 11: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Review of Statics

Page 12: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Review of Statics

Page 13: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

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

Page 14: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Two-Force Bodies

• Forces applied at only two points along a body.

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

Page 15: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Three-Force Bodies

• Forces applied at only three points along a body.

Forces must either be concurrent.

Or parallel

Page 16: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Types of Forces

• External Forces and Moments

• Applied surface loads

• Body forces (e.g., self-weight)

• Reactions (unknown) at supports

• Internal Forces and Moments

Page 17: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Applied Surface Loads

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

• Concentrated forces and moment

• Distributed forces and moment

External Forces and Moments

Page 18: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Body Forces

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

• Force due to the earth’s gravitational field (i.e., weight)

W = mg

• Electromagnetic forces

External Forces and Moments

Page 19: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Reactions at Supports

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

External Forces and Moments

Page 20: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

• 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.

External Forces and Moments

Page 21: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Internal Forces and Moments

Axial Force

Shear Force

Bending Moment

Remember Newton’s Third Law!

Page 22: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Free-Body Diagrams • Before the equilibrium equations can be

applied, it is essential that

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

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.

Page 23: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

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.

Page 24: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

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.

Page 25: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

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.

Page 26: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

Now let’s do some examples to review Statics

Page 27: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 28: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 29: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 30: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 31: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 32: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 33: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

The figure shows a typical hydraulic digger for making trenches. The bucket is exerting a force of 20 kN horizontally to the right at J on the ground. (a) Neglecting the weight of the members and the bucket, determine, choosing a suitable free-body diagram in each case: (i) The force in ram GF. (ii) The force in ram CD. (ii) The force in ram AC. (b) If the total volume of metal in the members is 0.1 m3, and they are made of steel of density 7800 kg m-3, is the weight of the members likely to be negligible? Which of the above answers for the forces in the rams is likely to be most in error due to this simplification?

Page 34: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 35: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil
Page 36: CIEG 212: Solid Mechanics · Static Dynamic . Mechanics . Solids . Fluids Incompressible Compressible . Static Dynamic . Static . Dynamic . Solid Mechanics . Structural Analysis Soil

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