Center of Gravity or mass?
Center of Gravity or mass?
(OP)
Hi Everyone
Would anybody be able to explain if bending in a section of a member, for example RC Beam, occurs about center of gravity?? To my understanding if a section is of uniform material bending will occur about centroidal axis. What about if an RC beam with different reinforcement quantities in top and bottom? what axis will bending occur about, is it centroidal, gravitational etc.???
Would anybody be able to explain if bending in a section of a member, for example RC Beam, occurs about center of gravity?? To my understanding if a section is of uniform material bending will occur about centroidal axis. What about if an RC beam with different reinforcement quantities in top and bottom? what axis will bending occur about, is it centroidal, gravitational etc.???






RE: Center of Gravity or mass?
1. IF the material is of uniform density, the "center of strength" (center of resistance to force) will be proportional to the center of mass which will be proportional to the center of gravity will be proportional to the center of volume. (You're actually using the I and S shape factors from the structural tables)
2. IF the member is NOT of uniform density and uniform strength (such as a concrete beam with rebar more heavily positioned in the bottom or top of a deep beam), you have to separate the materials and calculate each based on its distance from a convenient point of calculation.
RE: Center of Gravity or mass?
RE: Center of Gravity or mass?
RE: Center of Gravity or mass?
For a cross section of a uniform material, the only reason you'd need the center of gravity is if it were tall enough to extend into space, i.e. in a nonuniform gravity field.
RE: Center of Gravity or mass?
bending of an RC beam (as I understand it) depends on the neutral axis defined by the re-bar and the concrete in compression.
another day in paradise, or is paradise one day closer ?
RE: Center of Gravity or mass?
It is my understanding that for a RC beam, bending occurs around the elastic neutral axis until the concrete cracks. The elastic neutral axis is at the same location as the geometric neutral axis, which is the geometric centroid of the cross section.
After the concrete cracks, the neutral axis shifts upwards and an elastic analysis is required to determine the new location. For a given loading, you have to balance the compression and tension stresses to find the new neutral axis. I think the easiest way is set up a spreadsheet in excel and then use solver to iterate the neutral axis until you reach force balance.
RE: Center of Gravity or mass?
RE: Center of Gravity or mass?
but then if uniform re-bar, then using center of mass isn't incorrect (though the logic of why is important to remember).
another day in paradise, or is paradise one day closer ?
RE: Center of Gravity or mass?
The other important points are:
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Center of Gravity or mass?
RE: Center of Gravity or mass?
What do you mean by "the line about which the bending occurs"? The neutral axis is the line of zero strain, so it separates the part of the section in compression from the part in tension. That could be considered "the line about which the bending occurs", but it will usually be in a different location to the centroid of the section, which is usually the line which load eccentricity is measured from.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Center of Gravity or mass?
RE: Center of Gravity or mass?
another day in paradise, or is paradise one day closer ?
RE: Center of Gravity or mass?
I find that post rather confusing:
I don't know what the "geometric neutral axis" is. The neutral axis is the line of zero strain, and that's all it is. For a section where all stresses are linear elastic with zero nett axial force the neutral axis passes through the centroid of the transformed section, but if there is any non-linearity usually it doesn't.
For a section with combined axial load and bending you can take moments about wherever you like, as long as you use the same axis for calculating applied loads and balancing internal forces and moments. For a reinforced concrete column we usually use the centroidal axis of the concrete section, regardless of whether the section is cracked, or if the reinforcement is asymmetric. To calculate the section stresses and forces we need to find the location or the neutral axis, but that is not normally the line used for calculating applied moments.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Center of Gravity or mass?
I could have said better. Another way of saying is:
For prismatic RC beams (cross section does not change along length of beam); It does not matter what your cross sectional shape is, or how many different layers of steel you have; or even the locations of the steel. The bending will be about geometric centroid of the cross section UNTIL the concrete cracks.
The geometric centroid (aka elastic neutral axis or geometric neutral axis) is also the point of zero strain UNTIL concrete cracking occurs.
As soon as the concrete cracks (which doesn't take long); life gets more difficult and you have to an elastic analysis to find the new neutral axis.