Understanding Plastic Behaviour

To understand the plastic behaviour of portal frames, consider the following scenarios:

A. The First Plastic Hinge forms under the Haunch.

As the first plastic hinge forms under the haunch, the value of the bending moments in the column and at the eaves in the rafter become fixed and any further increases in load will result in a drop in the bending moment diagram in the rafter with the following result:

1.The moment at the eaves remains fixed.

2.The point of contraflexure moves closer to the eaves.

3.The values of the negative moments decrease over the haunch area.

4.The values of the positive moments increase near the ridge.

The collapse mechanism is reached when further plastic hinges form near the ridge (in this scenario, plastic hinges cannot form at the upper end of the haunches since the value of the applied moment there is getting smaller with increased load).

If a collapse mechanism is not reached, then it is important to note that increasing the design loads will result in reducing the negative moments over the rafter haunch and increasing the positive moments near the ridge.

B. The First Plastic Hinge Forms at the End of the Haunch

As the first plastic hinge forms at the end of the rafter haunch, the value of the bending moment at this point remains constant.  Any further increase in load will result in a rise in the bending moment diagram over the haunch and a drop of the bending moment diagram in the rafter with the following results:

1.The moment at the end of the haunch remains fixed.

2.The point of contraflexure moves closer to the end of the haunch.

3.The values of the negative moments increase over the haunch area.

4.The values of the positive moments increase near the ridge.

5.The values of the column moments increase in line with the eaves moment.

As the values of the column moments and the values of the positive moments near the ridge are increasing simultaneously there are two possibilities:

a)The maximum positive moment near the ridge reaches a plastic value and a collapse mechanism is formed; and

b)The moment under the haunch reaches a plastic value thus forming a new plastic hinge under the haunch. As the load is increased beyond this point, the bending moment diagram along the whole length of the rafter starts to drop and the first plastic hinge that was formed at the end of the haunch disappears (this is known as a plastic hinge reversal). A collapse mechanism will only be reached when further plastic hinges form near the ridge as in the first scenario.

Once more, if a collapse mechanism is not reached, then it is important to note that increasing the design loads will result in reducing the negative moments over the haunch and increasing the positive moments near the ridge.