Plastic Section Modulus
The Plastic section modulus is used for materials where (irreversible) plastic behaviour is dominant. The majority of designs do not intentionally encounter this behaviour.
The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.
The plastic section modulus is then the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:
| Description | Figure | Equation | Comment |
|---|---|---|---|
| Rectangular section | |||
| For the two flanges of an I-beam with the web excluded | ,
where: =width, =thickness, are the distances from the neutral axis to the centroids of the flanges respectively. |
||
| For an I Beam including the web | |||
| For an I Beam (weak axis) | |||
| Solid Circle | |||
| Hollow Circle |
The plastic section modulus is used to calculate the plastic moment, Mp, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, Fy, by Mp=Fy*Z. Sometimes Z and S are related by defining a 'k' factor which is something of an indication of capacity beyond first yield. k=Z/S
Therefore for a rectangular section, k=1.5
Read more about this topic: Section Modulus
Famous quotes containing the words plastic and/or section:
“What a wonderful faculty is memory!—the most mysterious and inexplicable in the great riddle of life; that plastic tablet on which the Almighty registers with unerring fidelity the records of being, making it the depository of all our words, thoughts and deeds—this faithful witness against us for good or evil.”
—Susanna Moodie (1803–1885)
“... all my letters are read. I like that. I usually put something in there that I would like the staff to see. If some of the staff are lazy and choose not to read the mail, I usually write on the envelope “Legal Mail.” This way it will surely be read. It’s important that we educate everybody as we go along.”
—Jean Gump, U.S. pacifist. As quoted in The Great Divide, book 2, section 10, by Studs Terkel (1988)