# statics

Statics is concerned with the analysis of loads (force and torque, or “moment”) on physical systems in static equilibrium – either at rest, or its center of mass moves at constant velocity.

Statics is the branch of mechanics that deals with the analysis of structures to determine the supports needed to carry predetermined loads. Statics is a basic course for most engineers, but is particularly important in the fields of civil engineering, structural engineering, and architecture.

Statics is the engineering application of a branch of physics called Mechanics. It describes bodies which are acted upon by balanced forces and torques so that they remain at rest or in uniform motion. In statics, the bodies being studied are in equilibrium. The equilibrium conditions are very similar in the planar, or two-dimensional, and the three-dimensional rigid body statics. These are that the vector sum of all forces acting upon the body must be zero; and the resultant of all torques about any point must be zero. Thus it is necessary to understand the vector sums of forces and torques. For example, a civil engineer would have used Statics extensively in the design of the Golden Gate Bridge in 1937.

Topics covered in typical statics courses include static equilibrium, centers of gravity, analysis of trusses, frames and machines, internal normal and shearing forces, bending moments, and torque, shear and bending moment diagrams, relations between distributed load, shear, and bending moment, friction, distributed forces, and area moments of inertia.

• Forces and Particle Equilibrium, Components of a force, Lines of action
• Moment of a Force and of a Couple; Resultants, Cross products, Moments, couples, moments about a line, Equivalent systems
• Analysis of General Equilibrium Problems, Free-body diagrams, Fundamental applications of equilibrium equations, Interacting bodies or parts of a structure
• Structural Applications and Distributed Loads, Plane trusses, Space trusses, Systems containing multiforce members
• Centroids and Center of Gravity, Centroids, Method of composite parts
• Friction
• Forces, Rectangular Components, Particle Equilibrium
• Forces in space, 3D Equilibrium
• Vector operations
• Couples, Equivalent Systems
• 2D, 3D Rigid Body Equilibrium, 2-Force Bodies
• Trusses, Method of Joints , Method of Sections,
• Frames, Machines
• Friction, Wedges and Belts
• Moment of Inertia

Weight and balance
A balanced-arm lamp, sometimes called a floating arm lamp, is a lamp with an adjustable folding arm which is constructed so that the force due to gravity is always counteracted by springs, regardless of the position of the arms of the lamp. Many lamp brands (such as the Anglepoise, originator of the concept) as well as other devices, such as drawing boards, use this principle.

• Ask – Having an adjustable desk lamp is important for many reasons. Being able to change the direction to light different things on a works surface is one use. Changing the amount of light for fine, close work and then lighting a broader area with less intense light. How will the lamp be used? How can the light be adjusted to cover a broad area or just brightly light a small area?
• Imagine – How can the light be moved around? What would keep it from tipping over?
• Design, Build* – How long do the arms need to be to light the whole desk? How much counter-weight is required? How are the springs attached to the arms?
• Improve – How can the light swivel?

That’s engineering

• Bending – Combination of forces that causes one part of a material to be in compression and another part to be in tension.
• Compression – Force that squeezes material together.
• Design Process – Identify the problem and brainstorm, design, build, test, evaluate, share, redesign, and rebuild.
• Load-Bearing Members – To support or strengthen a roof, bridge, or other elevated structure with a network of beams and bars.
• Neutral Axis – An imaginary plane that runs through the middle of a material under bending at which zero stress is experienced.
• Tension – Force that pulls material apart.
• Truss – Support something with a structure.

Engineering ideas

• Mechanics, Force, Torque, Moment, System, Newton’s First Law, Velocity, Mass, Gravity, Friction, Stress, Equilibrium, Civil engineering, Structural engineering, Architecture

Do It
Challenges for you to work on…

• Popsicle stick tower crane – static equilibrium where forces and torques are balanced in a well-designed engineering structure
• Forces and Graphing – explore forces acting on an object, graph experimental data, introduce the algebra concepts of slope and intercept of a line
• Paper Cup Walk With paper cups and cardboard, create a platform that can support their weight. This activity teaches about weight distribution.
• Weight and balance – One of the first things that every new pilot learns is weight and balance. This has everything to do with a plane’s center of gravity which affects how the plane will fly. If the weight in an airplane isn’t within the limits of the plane’s design, it will not fly safely or predictably. Learn more about airplanes, center of gravity, weigh and balance, and effects on aerodynamics.