by In the previous article, if the displacement at one end is zero in the plane structure, no matter how much the displacement at the other end is, according to the current definition, the torsional displacement ratio can only be 2.0.
It is also very simple to break through the limit of torsional displacement ratio, that is, consider the directionality of torsional displacement.
In plane torsion, the whole plane moves around the torsion center, and the displacement value and direction of each point are different.
The direction is perpendicular to the line between the point and the torsion center, and the displacement direction of both ends of the structure is opposite.
If a section perpendicular to the translational direction is made through the torsion center, the superposition of translational displacement and torsional displacement on this section is a little like the stress distribution of the section when the prestressed beam is bent, and also a little like the base reaction when the natural foundation is subjected to eccentric vertical load.
+There are three kinds of superposition results: trapezoid, single triangle and double triangle.
The example described in the provisions of the Code refers to the first case, and the torsional displacement ratio of 2.0 is the second case; In the third case, if the torsion ratio can be calculated, it will be greater than 2.0.
Interestingly, if the translational displacement approaches zero, the average value of displacement at both ends will also approach zero, and the torsional displacement ratio will tend to infinity.
Obviously, the existence of infinite torsional displacement ratio will confuse engineers.
We understand from the 2.0 limit value of “Yuegao”, that is, the maximum torsional displacement cannot be greater than the translational displacement, and the superimposed displacement graph can only reach a triangle, and there can be no crooked bow tie.
The occurrence of a skewed bow tie means that the translational and torsional superimposed displacements at both ends of the structure are in the opposite direction.
The average value of the two values is mathematically computable, but what is its engineering significance? Of course, the limit value of “Yuegao” for 2.0 is only “inappropriate”.
The torsional displacement is the plane torsional angle multiplied by the torsional radius.
If the radius is large enough, the final product of the torsional angle is not small, and it may be larger than the translational displacement.
Lao Yang guessed that the original intention of “Yue Gao” was to give up the limit value of torsional displacement ratio and put forward the limit value of torsional angle, 0.0005rad, which seems to be a very small value.
To make a simple estimation, the floor height is 5500, and the displacement between the lower layers of the frame structure under the horizontal seismic action is controlled by 1/550, which is 10mm.
Under the condition of a torsion radius of 20 meters, the end point torsion displacement can reach 10mm, which means that the plane scale of the structure will be limited within 40 meters, which is a little small.
The origin of 0.0005rad, “Yue Gao” is explained from the compression angle of the frame column.
The article notes that when the torsion angle is not greater than 0.001 rad, the compression bearing capacity of the frame column will not be affected.
Here is a concept that the old goat didn’t understand.
The plane torsion of the structure is shown as a whole movement.
At each point, it is still translational.
The torsion angle that affects the frame column as a component should be the torsion angle between the upper and lower floors (both ends) of the vertical component.
Is this the same as the plane torsion angle of the structure? The torsion angle related to the torsion displacement ratio, including the formula used in the “Guangdong Gao” article description, is a plane angle.
Just like the earth and a group of brothers are rotating while circling the sun, the two corners determine the spring, summer, autumn and winter, and the other determines the meridian.
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