In the structural analysis of slender column, we normally encounter problem in determining the end-restrained condition of the column. What is the most distinct difference between pinned end restraints and hinged end restraints? What is the restrained condition as attached in the figure below?
The Apparatus is set up to test Euler's Buckling Theory, when an eccentrically
applied load is applied vertically thru the column. Since the applied force is
to the right of center, the column will become shorter, and it will curve in a bow
to the left. The mechanism itself appears to supply the lateral constraints,
to prevent lateral motions of the top or bottom of the column
The set up tests lateral, out of plane buckling of the column.
If a column is hinged, it is free to rotate about one axis ( Top, eccentric
point load ).
If the column is not hinged, it is not free to rotate ( Bottom,
the floor can not rotate, and the column also can not rotate because
the axial force is distributed over a broad surface of the entire
bottom of the column. ). It is also not fully Pinned as the column
is not socketed into the floor of the building, as a power pole would be,
or as a tree is with its roots.
I am too tired to think any more about this tonight
Looking at attached figure, it is difficult correlate the boundary conditions with any of the test book problems. Since you know buckling load from experiments, you may try to correlate this load with analytical estimated value assuming hinge/pin boundary conditions. However, you may do a numerical modeling on this column to get the buckling load....
Regards
The terms "hinged end" and "pinned end" describe exactly the same type of rotational restraint, or rather, lack of such. It is q question of preference which term you like to use. At such an end, the moment is zero unless an external moment is applied at the end. In the latter case, the whole of the applied moment is transmitted to the column end.
In an experiment in which the axial loading is applied through a knife edge, such as at the upper end of the column in the picture, the end can be considered hinged, or pinned. At the lower end of the column, you will need to know the resisting moment and corresponding rotation at that end in order to determine the rotational stiffness of that restraint (k=M/rotation (in radians)).
Dear Prof.Hellesland,
I have read many your works in slenderness limit such as "Non-slender RC columns limits for braced, end-loaded columns", "Non slender RC columns limits", "On slenderness column limits", "Lower slenderness limits for braced' end-loaded RC compression member", "Lower Slenderness Limits for Rectangular Reinforced Concrete Columns", among others. They are my bibles in my current Ph.D research. Your job's brilliant.
In the experimental test as attched in the figure, the confusion is the bottom end. In ordinary concentrically loaded column test, this end condition is considered as fixed end column as the compression itself can restrained the rotation of the column ends. However, with top end hinged (as in the case), the bottom end is not exactly fully restrained as it still can be rotated as the top end start to rotate. Can we consider the bottom end as hinged end also even under such configuration which smilar to fixed end? How can we prove that?
Regards
Dera dr.stud. Khun;
Thank you for your kind words about my research. I am glad you have found some of it useful, and appreciate your comments.
As to the restraint conditions at the base of your column, I believe (at least at this time ( ;-)) that the it may be considered fixed provided the top plane of the load cell at the base remains perfectly plane (horizontally), and that there is full contact between the bottom cross section of the column and the load cell.
Proof? To make certain, you may install a measuring device (as close to the base as possible) that allows you to check if there is a rotation theta (away from the vertical) at the column bottom. If there is no rotation, the restraint stiffness (k=M/theta) will become infinite, and thus reflecting a fixed base.
I do not think the column base can be considered hinged, unless the load cell at the base are mounted on a platform that allows rotation. And that is probably not so in your case.
Hopefully, t have not misunderstood anything. Regards, and good luck.
Dear Prof Hellesland,
I would like to check on the restraint stiffness of the column too but the tests are over. :( i think what i can do now is to conduct a theoretical investigation on pinned-pinned column and pinned-fixed column and relate the theoretical results to experimental results. Hopefully by comparison on which case is closer to experimental result, i might have some clues on the end restraint conditions. Do you think it is reliable? Thanks for your comments, they are really useful.
Looking at the diagram submitted, the Knife edge is 90 degrees,
and the top of the steel distribution plate also has a 90 degree
notch cut into it. This does not allow free rotation of the top
of the column and the steel load distribution plate. For a more
accurate assessment of the stresses and strains inside the column,
the machined notch in the distribution plate should be more than
90 degrees, while the machined knife edge should be less than
90 degrees. The 25 mm ( 1 inch ) eccentricity of the applied load
is also quite small in comparison to the diameter of the column.
How much load do you intend to apply to this column ?
In theory they have the same meaning, however you might need to check the software manual as sometimes they have different definition within the software
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