Free body diagrams are crucial tools in , helping visualize all acting on an object. They simplify complex systems by isolating a body and showing external forces, making it easier to analyze and solve for unknown forces.
Understanding different types of forces and reactions is key to creating accurate free body diagrams. , friction, , and all play roles in real-world scenarios, while from maintain equilibrium in structures.
Forces
Types of Forces
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Applied forces are external forces that act on a body, causing it to move, deform, or change its state of motion
Can be represented as vectors with and (pushing a box, wind load on a building)
resist the relative motion between two surfaces in contact
Occur parallel to the surfaces and oppose the direction of motion (sliding a book across a table, tire traction on a road)
Distributed loads are forces that are spread out over an area or along a line
Represented as a force per unit area or force per unit length (snow load on a roof, water pressure on a dam)
Point loads are concentrated forces that act at a single point on a body
Represented as a single vector with magnitude and direction (a person standing on a floor, a cable pulling on a pulley)
Force Characteristics
Forces are vector quantities, having both magnitude and direction
Magnitude represents the intensity of the force, usually measured in units of Newtons (N) or pounds (lbs)
Direction indicates the line of action along which the force acts, often specified using angles or coordinate systems
Forces can be represented graphically using arrows, with the length of the arrow proportional to the magnitude and the arrowhead indicating the direction
Multiple forces acting on a body can be combined using to determine the
act at a single point and can be added directly (forces acting on a joint)
act at different points and may cause rotation or bending (forces on a beam)
Reactions
Reaction Forces
Reaction forces are forces exerted by supports or on a body to maintain equilibrium
Occur in response to applied forces and the weight of the body itself
The magnitude and direction of reaction forces depend on the type of and the forces acting on the body
A allows rotation but prevents translation, producing a force reaction (a door hinge, a truss joint)
A allows translation along a surface but prevents movement perpendicular to the surface, producing a force reaction normal to the surface (a wheel on a track, a sliding drawer)
A prevents both rotation and translation, producing both force and (a clamped beam, a bolted connection)
Moment Reactions
, also known as , are forces that occur in pairs to resist rotation
Produced by fixed supports or by constraints that prevent rotation
The magnitude of a reaction depends on the distance between the forces and the point of rotation
Calculated as the product of the force and the perpendicular distance to the point of rotation, usually measured in units of Newton-meters (N·m) or foot-pounds (ft·lbs)
The direction of a moment reaction is determined by the right-hand rule
Curl the fingers of your right hand in the direction of rotation, and your thumb points in the direction of the moment vector (counterclockwise rotation produces a positive moment, clockwise rotation produces a negative moment)
Diagram Elements
Free Body Diagrams
A (FBD) is a graphical representation of a body or system, showing all the external forces and acting on it
Used to visualize and analyze the forces acting on a body in equilibrium or in motion
To create an FBD, the body is isolated from its surroundings, and all the forces and moments are drawn as vectors
The body is typically represented as a simplified shape or a point
Forces are drawn as arrows, with the tail at the point of application and the head pointing in the direction of the force
Moments are drawn as curved arrows, indicating the direction of rotation
FBDs are essential for solving statics problems, as they help to identify the unknown forces and moments that need to be calculated
Constraints and Supports
Constraints are conditions that limit the motion or deformation of a body
Can be physical, such as supports or connections, or mathematical, such as equations of equilibrium
Supports are structural elements that provide reaction forces and moments to maintain the equilibrium of a body
Common types of supports include pinned, roller, and fixed supports
The type of support determines the number and direction of the reaction forces and moments
In an FBD, supports are typically represented by symbols that indicate the type of support and the direction of the reaction forces and moments
A pinned support is shown as a triangle, with a force reaction perpendicular to the surface
A roller support is shown as a circle, with a force reaction normal to the surface
A fixed support is shown as a triangle with a circle, with both force and moment reactions