Flexible Beams
Subject
Unlike CalQlata's Beams calculator, Beams+ has been created to determine the behaviour of flexible beams in which deflection is expected to exceed 5% of their length.
Flexible beams must be analysed using nonlinear theories that include the effect of the applied load moving closer to its support(s) as deflection increases with bending moment. Despite the modified nature of these formulas, however, in order for them to remain valid, the material must continue to obey Hooke's law.
The very large deflections that can be generated using such theories would normally result in plastic stresses in conventional beam materials (i.e. no longer obeying Hooke's law). In order for this calculator to be of practical use therefore, it is important to ensure that your beam material remains elastic at the calculated strains (bend radii).
Calculator
Beams+ includes nonlinear calculation options for a number of special loading conditions including; Cantilever, Touchdown, [bending] Stiffness, Fishing Rod and Axial Compression
The 'Cantilever' calculation option uses a refined and expanded formulation of a BernoulliEuler principle. This calculation can be used to establish the configuration of a sagging flexible beam, lifting one end off the ground or forcing a large deflection with one end anchored (see above Figure).
All other formulas used in this calculator have been developed from Castigliano's original theories for large deflections.
You can select your beam properties from CalQlata's Steel Beam Sizes or calculate them using Area Moments and Area Moments+ or you can iterate the beam’s properties until you achieve your desired reactions.
For general loading conditions you can use CalQlata’s Beams calculator to determine the reaction of beams that deflect less than 5% of their length
For help using this calculator see Technical Help
Flexible Beam Strength Calculator  Options
Cantilever
Cantilever calculates the configuration of a flexible beam fixed at one end but otherwise totally unsupported and can generate tip angles greater than 80°. Because of its incredible flexibility, ‘Cantilever’ includes a list of coordinates that can be cut & pasted into your preferred spreadsheet to generate a plot of your configuration.
You enter: 
and the flexible beam strength calculator will calculate: 


Bending moment @ B

Bend radius @ B

Distance to end A

Height to end A

Slope @ end A

plus s, x, y, and θ coordinates at 20 points along the beams deflected length

Touchdown
Touchdown calculates the potentially damaging properties of a very flexible beam, one end of which is allowed to fall onto a supporting surface significantly lower than its fixed end.
You enter: 
and the flexible beam strength calculator will calculate: 


Unsupported length

Distance to end A

Bending moment @ B

Bend radius @ B

Stiffness
Stiffness calculates the bending stiffness of a long flexible beam from the maximum deflection generated by its own weight and unsupported length.
You enter: 
and the flexible beam strength calculator will calculate: 


Bending stiffness

Maximum deflection

Bending moment (beam centre)

Bend Radius (beam centre)

Fishing Rod
Fishing rod calculates the configuration of a long slender beam with a tensile point load applied to its free end at an angle between 0 and 90 degrees.
You enter: 
and the flexible beam strength calculator will calculate: 


Beam length

Moment arm

Bending moment @ B

Bend radius @ B

Deflection @ x

Deflection @ A

Compression Beam
Compression beam calculates the configuration of a long slender beam with a compression point load applied to its guided end along with a uniformally applied lateral load.
You enter: 
and the flexible beam strength calculator will calculate: 


Reduction in length

Bending moment A

Bend radius @ A

Bending moment B

Bend radius @ B

Deflection @ A

Check minimum system requirements