Related Resources: Statics

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Engineering Statics Basics Equations and Calculators

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Static's 2D Force Components in XY Plane

Fx = F · cos θx = F · sin θy

Fy = F · sin ⁡θx = F · cos ⁡θy

F = [ Fx2 + Fy2 ]1/2

tan θx = Fy / Fx

3D Statics Components of Force

Fx = F · cos θx

Fy = F · cos ⁡θy

Fz = F · cos ⁡θz

F = [ Fx2 + Fy2 + Fz2 ]1/2

cos θx = Fx \ F

cos ⁡θy = Fy \ F

cos ⁡θz = Fz \ F

Types of Supports used in Statics Free Body Diagram

There are 5 main types of supports.

• Fixed end - This support prevents rotation, horizontal and vertical translation. By doing so it can be determined that the support will have a moment, and a horizontal and vertical force component.
• Pinned - The reaction forces for this support consist of a horizontal force and vertical force. This support does not have a moment because the support does not resist rotation.
• Roller - This support only has one reaction force which is a vertical force. This support only has one reaction force because it does not resist rotation or movement in the horizontal direction.
• Link - This support has a resultant support reaction which can consist of components vertically and horizontally.
• Rocker - Like the roller, this support also has a single reaction force which is a vertical force because is does not resist rotation and horizontal translation.

Trigonometry Cheat Sheet

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