FreitagC

Principles of Engineering

Statics

Statics - The study of objects in a state of equilibrium
Applied Forces + Reaction Forces = 0

Arches

Arch bridge - a bridge that uses long span arches for support”

Suspension

Suspension bridge - “a bridge having a road or deck hung from a pair of steel cables, each carried by two towers, one at each bank

Beam bridge / Truss Bridge - A bridge whose main structural element consists of a beam set across two or more vertical supporting members.

Forms a series of triangles - very stable!
Trusses form the skeleton Shape of a structure
Trusses carry and transfer loads

Cable-Stayed

Cable-stayed bridge - A bridge in which the deck is supported on either side of a central tower or towers by cables. Unlike a suspension bridge, the cables that hold the deck attach directly to the tower, rather than hanging from a larger cable running between the towers.

Strength of Shapes

Triangles	Arches	Dome

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Newton's Laws

1st Law: An object at rest will remain at rest or an object in motion will remain in a straight line with constant velocity if the net force acting in the object is zero.

2nd Law: An object on which force is exerted will move in the direction of net force and the acceleration will be proportional to the net force.

3rd Law: Every action has an opposite and equal reaction

Mechanical Forces

Compression Tension Bending Torsion Shearing

Equilibrium - A state of balance due to the equal action of opposing forces in a structure

Law of equilibrium: From Newton's first law of motion, we can establish the law of equilibrium. There may be a number of forces acting on a body, if there are no net forces or moments , then the body is in equilibrium.

Static Equilibrium - Sum of the Forces & Moments = Zero

∑ F=0 ∑ M=0

The forces here are canceling each other out. It is in a state of static equilibrium
∑ F=0 ∑ M=0

Vectors - A quantity that must be described by both magnitude and direction; answers the questions “how much?” and “which way?” Examples: velocity, Force.

Scalar - A quantity that can be described by magnitude only; answers the question “how much?” Examples: mass, time.is simply a number, a magnitude alone.

Force: Force is action of one body on another. It is a vector.   A force has a magnitude, a direction and a point of application.

                       Force= mass * acceleration (from Newton's 2nd law)

Rectangular components of a force: A force can be resolved into its component forces in the same way as we resolve a resultant of two forces. P = Force

Vector Calculations - SOH CAH TOA

Py= P Sin, Px= P cos

Free Body Diagrams
Introduction to Free Body Diagrams

Free Body Diagram - A sketch of an object (body) of interest with all the surrounding objects stripped away and all of the forces acting on the object (body) shown.

Free Body Diagrams

Reaction Forces - Reactions are passive forces that are induced at the supports of a structure.

SOH CAH TOA

Pythagorean Theorem: c²= a² + b²

®SFX = 0
SFY = 0

SFY = 0

               RCy + Ray = 2300

                              RCy(30) = 2300 (18)

               RCy = 2300 (18) / 30

               RCy =

               RCy =

               Ray = 2300 – Rcy

               Ray =

Ray =

SFX = 0; RAx = 0 (there is no horizontal component force)

Moments / Torque - The tendency to rotate about a point determined by the product of a force multiplied by the distance from this force to this point. Moment = Force x Distance

Moment = Force x Distance

Formula:
Moment = Force x Distance
M₁ = M₂