Solid Mechanics
Introductory Material
Mechanics
That branch of Physics that deals with the rest or motion of bodies and the phenomena of the action of forces on bodies.
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 Static Dynamic Dynamic
Mechanics
Solids Fluids
Incompressible Compressible
Static Dynamic Static Dynamic
Solid Mechanics
Structural Analysis
Soil Mechanics
Structural Design
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
= = =
= = =∑ ∑ ∑∑ ∑ ∑
Review of Statics
Review of Statics
Review of Statics
Review of Statics
Review of Statics
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
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 examples to review Statics
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?