Transcript Statics Lecture

Statics
Using 2 index cards:
Create a structure or system of structures that
will elevate two textbooks at least 1.5cm off your
desk
Statics
Kentucky & Indiana Bridge
Chicago
What is Statics?
Branch of Mechanics that deals with
objects/materials that are stationary or in
uniform motion. Forces are balanced.
Examples:
1. A book lying on a table (statics)
2. Water being held behind a dam (hydrostatics)
Dynamics
Dynamics is the branch of Mechanics that deals
with objects/materials that are accelerating due
to an imbalance of forces.
Examples:
1. A rollercoaster executing a loop (dynamics)
2. Flow of water from a hose (hydrodynamics)
Now on to the point…
Statics
Newton’s 3 Laws of Motion:
1. A body at rest will stay at rest, a body in motion will stay
in motion, unless acted upon by an external force
This is the condition for static equilibrium
In other words…the net force acting upon a body is
Zero
Newton’s 3 Laws of Motion:
2. Force is proportional to mass times acceleration:
F = ma
If in static equilibrium, the net force acting upon a body is
Zero
What does this tell us about the acceleration of the body?
It is Zero
Newton’s 3 Laws of Motion:
3. Action/Reaction
Statics
Two conditions for static equilibrium:
1.
Since Force is a vector, this implies
Individually.
Two conditions for static equilibrium:
1.
Two conditions for static equilibrium:
Why isn’t
sufficient?
Two conditions for static equilibrium:
2. About any point on an object,
Moment M (or torque t) is a scalar quantity that
describes the amount of “twist” at a point.
M = (magnitude of force perpendicular to moment arm) * (length
of moment arm) = (magnitude of force) * (perpendicular
distance from point to force)
Two conditions for static equilibrium:
MP = F * x
MP = Fy * x
F
F
P
P
x
x
M = (magnitude of force perpendicular to moment arm) * (length
of moment arm) = (magnitude of force) * (perpendicular
distance from point to force)
Moment Examples:
1. Tension test apparatus – unknown and reaction forces?
2.
If a beam supported at its endpoints is given a load F at its
midpoint, what are the supporting forces at the endpoints?
Ra
Rb
Find sum of moments about a or b.
Watch your signs – identify positive
Moment Examples:
3.
An “L” lever is pinned at the center P and holds load F at the
end of its shorter leg. What force is required at Q to hold the
load? What is the force on the pin at P holding the lever?
What is your method for solving this problem? Remember,
Trusses
Trusses: A practical and economic solution to many structural
engineering challenges
Simple truss – consists of tension and compression members
held together by hinge or pin joints
Rigid truss – will not collapse
Trusses
Joints:
Pin or Hinge (fixed)
Trusses
Supports:
Pin or Hinge (fixed) – 2 unknowns
Reaction in x-direction
Reaction in y-direction
Rax
Ray
Trusses
Supports:
Roller - 1 unknown
Reaction in y-direction only
Ray
Assumptions to analyze simple truss:
1.
2.
3.
4.
Joints are assumed to be frictionless, so forces can only be
transmitted in the direction of the members.
Members are assumed to be massless.
Loads can be applied only at joints (or nodes).
Members are assumed to be perfectly rigid.
1.
2.
2 conditions for static equilibrium:
Sum of forces at each joint (or node) = 0
Moment about any joint (or node) = 0
Start with Entire Truss Equilibrium Equations
Truss Analysis Example Problems:
1. A force F is applied to the following equilateral truss.
Determine the force in each member of the truss shown
and state which members are in compression and which
are in tension.
Truss Analysis Example Problems:
2. Using the method of joints, determine the force in each
member of the truss shown. Assume equilateral
triangles.
Static determinacy and stability:
Statically Determinant:
All unknown reactions and forces in members can be
determined by the methods of statics – all equilibrium
equations can be satisfied.
m = 2j – r (Simple Truss)
Static Stability:
The truss is rigid – it will not collapse.
Conditions of static determinacy and stability of trusses:
Materials Lab Connections:
• Tensile Strength = Force / Area
• Compression is Proportional to 1 / R4
Problem Sheet solutions due Monday