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The plastic section modulus can be calculated for a given cross section by: Locating the plastic neutral axis. PNA; Bringing the stress distribution to full plastic stress (constant) above and below the PNA. Summing the moments on the cross section. Finally divide the resulting moment by the yield stress to find the plastic section modulus.
Z=b·h^2/4 the plastic modulus. Since the elastic modulus of section is b·h^2/6 you can extoll 1.5 times more strength of the structure if allowed (and can) go to a plastic section behaviour. For a pipe section, that would be 1.27 times. That is the plastic modulus of a section.
Stiffness (F=Kx) is the extent to which an object resists deformation in response to an applied force. Elastic Modulus (E=Stress/Strain) is a quantity that measures an object or substance's resista...
I am designing an end plate connection. My lecture notes show its bending capacity is calculated using elastic section modulus. For class 1 I-beams, we can use its plastic section modulus. I wonder whether plates could be designed this way since it's capacity would be 50% higher. For info, I'm using Eurocode.
I am designing a freestanding steel handrail post (3'-6") spaced at 4'-0" on center maximumu. Per IBC, I am desiging this post for a point load of 200 lbs at the tip of free end. Per ASD design, can I use plastic section modulus (Z) in lieu of elastic section modulus (S)? The steel is 1" square solid ASTM A500 Grade B (Fy = 46 ksi).
The plastic section modulus is defined as the sum of all elemental areas above or below the centroid of the cross section multiplied by the distance from each of the individual elemental centroids to the centroid of the cross section as a whole.
Elastic modulus is the steel modulus based on the stress strain curve before yielding. The plastic modulus is after yielding. Plastic section modulus (Z) for various shapes are given in the steel book. I'm not sure how its' calculated. Plastic design is based on maximum strength of the steel and is covered in Chapter N of the 1989 ASD.
In plastic design, the entire section in bending is assumed to be stressed to yield, so the area in tension and the area in compression are equal. Find the centroid of each of the area above and below, multiply the area of one half by the distance between the centroids. That is the plastic section modulus.
The plastic modulus is a property related to the strength weighted area above and below the plastic neutral axis, or in other words proportional to the force carried by the section above and below the plastic neutral axis. If you have different materials it's calculation is therefore related to strength not the modulus of elasticity.
In this case the Secant Modulus and Young Modulus is equivalent. However while entering the elastic-plastic region and plastic region. As the material become incompressible, the study of the material properties requires more complex consideration such as the poison ratio changes in the region.