CIEG 212Solid Mechanics

Introductory Materialby

Victor N. Kaliakin

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).

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.

Mechanics

Solids Fluids

Rigid Deformable

Static StaticDynamic Dynamic

CIEG 211 CIEG 212CIEG 212CIEG 311 CIEG 311

Mechanics

Solids Fluids

Incompressible Compressible

Static DynamicStaticDynamic

CIEG 305CIEG 305

Solid Mechanics

Structural Analysis

(CIEG 301)

Soil Mechanics

(CIEG 320)

Structural Design

(CIEG 302)

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

Types of Bodies

• Two-Force BodiesForces applied at only two points along a body.

• Three-Force BodiesForces applied at only three points along a body.

• General Bodies

Two-Force Bodies

• Forces applied at only two points along a body.

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

Three-Force Bodies

• Forces applied at only three points along a body.

Forces must either be concurrent.

Or parallel

Types of Forces

• External Forces and Moments• Applied surface loads

• Body forces (e.g., self-weight)

• Reactions (unknown) at supports

• Internal Forces and Moments

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

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

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

• 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

Internal Forces and Moments

Axial Force

Shear Force

Bending Moment

Remember Newton’s Third Law!

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.

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.

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.

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.

Now let’s do some example problems to review Statics