In 2010, I found several books about the joint of semi-rigid frame in China, but I hadn't seen the real case of it among the structural components. Recently, my company assigned me a small project to calculate the joints for the fixed crane of building construction. There is an H beam placed on a RC girder, and its bottom flange is fixed by several anchor bolts.
What's the different between the semi-rigid joint and the rigid joint in structural analysis? The rigid joint is a fixed end, but the semi-rigid joint is described by a hinge with a spring. Of course, you must know how to calculate the semi-rigid joint in the structural theory, but I think you may not know how to measure the spring stiffness. When you use the computer program, you need to input the boundary conditions and the relative data.
The spring stiffness becomes a key, but I think the easier approach is to guess the ratio compared with the rigid joint. Let's see the stiffness formula in the general form for the joint of semi-rigid frame:
Assume the H beam size is RH300x300x10x15, and I can find its moment of inertia is 20,200cm^4 in the Taiwanese LSD Handbook. However, the real case is fixed on the bottom flange of the H beam, so that I have to correct the moment of inertia for its new shape. What's its new shape? The new shape is a flat-rolled steel whose size is B300xH15, and I can calculate its moment of inertia is 8.4375cm^4.
In case you wanna get a more conservative value, you can add some web to calculate its moment of inertia. I think the length of 1/6 flange width is suitable as the added web section. Hence, the new shape is like the English character T, but the moment of inertia is still very small. Why do I choose the ratio 1/6? Actually, I just read ANSI/AISC 360-10 2012, and it adopts more than 1/2 web depth as a T shape steel calculation. However, the web depths are too long for the Taiwanese BH steel sections, so that I choose the 1/6 "flange" width as the web depth. In this case, the web depth of T shape steel is 50mm, and I can calculate its moment of inertia is 66.3854cm^4. I think the T shape steel is more reasonable, and the ratio of the moment of inertia is about 0.32864%.
This is a simple calculation, and the moment of inertia should be larger actually. Besides, the coefficient α of stiffness is different from the rigid joint, and therefore the stiffness cannot be calculated by my simple way accurately. I think you have understand what my point is, and I just wanna tell you that the reaction moment is smaller than what you think.
What's the different between the semi-rigid joint and the rigid joint in structural analysis? The rigid joint is a fixed end, but the semi-rigid joint is described by a hinge with a spring. Of course, you must know how to calculate the semi-rigid joint in the structural theory, but I think you may not know how to measure the spring stiffness. When you use the computer program, you need to input the boundary conditions and the relative data.
The spring stiffness becomes a key, but I think the easier approach is to guess the ratio compared with the rigid joint. Let's see the stiffness formula in the general form for the joint of semi-rigid frame:
Assume the H beam size is RH300x300x10x15, and I can find its moment of inertia is 20,200cm^4 in the Taiwanese LSD Handbook. However, the real case is fixed on the bottom flange of the H beam, so that I have to correct the moment of inertia for its new shape. What's its new shape? The new shape is a flat-rolled steel whose size is B300xH15, and I can calculate its moment of inertia is 8.4375cm^4.
In case you wanna get a more conservative value, you can add some web to calculate its moment of inertia. I think the length of 1/6 flange width is suitable as the added web section. Hence, the new shape is like the English character T, but the moment of inertia is still very small. Why do I choose the ratio 1/6? Actually, I just read ANSI/AISC 360-10 2012, and it adopts more than 1/2 web depth as a T shape steel calculation. However, the web depths are too long for the Taiwanese BH steel sections, so that I choose the 1/6 "flange" width as the web depth. In this case, the web depth of T shape steel is 50mm, and I can calculate its moment of inertia is 66.3854cm^4. I think the T shape steel is more reasonable, and the ratio of the moment of inertia is about 0.32864%.
This is a simple calculation, and the moment of inertia should be larger actually. Besides, the coefficient α of stiffness is different from the rigid joint, and therefore the stiffness cannot be calculated by my simple way accurately. I think you have understand what my point is, and I just wanna tell you that the reaction moment is smaller than what you think.
