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1) The Concept of Cantilever Beam Analysis
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2) Example
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3) Tutorial & Comparison of Results
2. Cantilever Beam
In this lecture, We will learn about the concepts, principles, and behaviour of cantilever beams. Besides this, we will learn how to calculate the internal forces at any location of the beam. And then, we will compare the results like SFD, BMD and deflection, of the cantilever beam having different loading conditions using midas Civil.
Chapter 1) The concept of cantilever beam analysis
- Introduction to cantilever beam.
- Find the internal forces at any location of the beam.
Chapter 2) Example
- Modelling, boundary condition setting, applying load using Midas Civil.
- Analysis and compare the results for the cantilever beam having different loading conditions.
Chapter 3) Comparison of results
- Comparison of Deflection, shear forces, and moment in members.
Summary
Cantilever beams are statically determinate beams like simple beams, but the suport conditions are different.
In the cantilever beam, one end is constrained in both movement and rotation direction, and the other end has no restraints in any direction.
In the cantilever beam, one end is constrained in both movement and rotation direction, and the other end has no restraints in any direction.
Force equilibrium condition applied
→ Calculate the reaction force on the cantilever
→ It is possible to calculate the sectional force generated at any position (cross section) inside the member
In order to explain the relationship between deflection-deflection angle-curvature in a cantilever beam, let's take the case where a constant moment acts on a simple beam with a span of ℓ as shown in the figure below and a cantilever beam with a span of ℓ/2 as an example.
Since the moment is constant, the curvature is constant as long as the modulus of elasticity and the size of the cross section do not change.
Central deflection in simple beam = deflection at free end of cantilever beam
End deflection angle = angle of deflection at the free end of the cantilever beam
This is because the curvature, that is, the area of the hatched portion of M/EIy is the same.
The angle of deflection is the area of the shaded area, and the deflection corresponds to the moment of the area of the shaded area.
For convenience, the sign indicating the direction of the deflection and deflection.
The fact that the deformation values of the simple beam and the cantilever beam are the same can be seen from the deformation shape.
Deformation shape of the right part from the center of simple beam = Deformation shape of cantilever beam
This is because the slope of the tangent to the deflection at the center of the simple beam is zero (0), so this part shows the same effect as the fixed end.
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