Some pretext to introduce the topic at hand. Basically a short preamble.
What are Points of Contraflexure?
Points of contraflexure are just points of zero bending moment.
Let's consider the fixed beam example with a point load in the middle, as shown below:
Because of the shape of the shear diagram, and the fixed ends, there are moments at the fixed ends, and there is also a moment at mid-span.
Because the moments change based on the shear, at some point, the bending moment becomes zero at certain locations. These are the points of contraflexure.
Location of the Point of Contraflexure
Let's take another example considering a column with a constant shear force. The bending moment diagram will vary linearly as shown below:
The location of the point of contraflexure may vary based on the stiffness of the end connections. If the stiffness of both ends are the same, then the point of contraflexure will be located at mid-height.
However, if one end connection has higher bending stiffness than the other, the point of contraflexure wll move away from the middle. Let's take the example below.
Significance of the Point of Contraflexure
The point of contraflexure is significant for a few reasons:
- Good for locating splice joints
- Good for locating construction joints in concrete construction
- Points of contraflexure can be idealised as hinges with zero bending moment, which helps to simplify hand calculations.