Supports (Constraints)

When a support is placed on the beam, the app automatically enforces constraints on the internal system of equations that defines the problem being solved.

A virtually unlimited number of supports can be applied on the beam. Although the app does not impose a strict limit on the number of loads and supports, there are practical limitations due to your device screen size, memory, and CPU capacity.

Four different types of supports can be used. The following table summarizes each type of support as well as the constraints that characterize each one.

TypeForce (F)Moment (M)Slope (Θ)Deflection (δ)
Fixed supportsFMΘ(x) = 0δ(x) = 0
Simple supportsFM → 0continuousδ(x) = 0
Fixed hingesFM → 0discontinuousδ(x) = 0
Floating Gerber hingesF → 0M → 0discontinuouscontinuous

Setting support values

Defining supports is simpler than defining loads because supports only require a single value to be specified (i.e., their location along the beam). Supports can be placed and dragged along the beam in the same way as loads.

Fixed supports

Fixed supports can be used for cantilevers and statically-indeterminate cases.

When a fixed support is used, the app attempts to solve for the its vertical force (F) and moment (M) reactions. Fixed supports impose the following constraints on the system:

  1. The slope Θ(x) at the support location must be continuous and equal to 0.
  2. The deflection δ(x) at the support location must be continuous and equal to 0.

Simple supports

A simple support is sometimes also referred to as a pin support or a middle support. A simple supports is different from a fixed support because

When a simple support is used, the app attempts to solve for the support's vertical force (F) reaction. This type of support imposes these constraints on the system:

  1. The slope Θ(x) at the support location must be continuous.
  2. The deflection δ(x) at the support location must be continuous and equal to 0.

Fixed hinge supports

A fixed hinge support is sometimes also referred to as a hinged support. This type of support is different from a simple support because

When a fixed hinge support is used, the app attempts to solve for the support's vertical force (F) reaction. This type of support imposes this constraint on the system:

  1. The deflection δ(x) at the support location must be continuous and equal to 0.

Gerber hinge supports

A Gerber hinge support is sometimes also referred to as a floating hinge support. This type of support is different from a fixed hinge support because

When a Gerber hinge support is used, the app does not solve for a force or moment reaction on the support. This type of support only imposes a very relaxed constraint on the system:

  1. The deflection δ(x) at the support location must be continuous.
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