In the case, because the joint cannot allow the angle of rotation, so that it has a little bit moment. This is not a perfect hinge or roller, and therefore it becomes a semi-rigid joint. How do I control its structural behavior? If the flexural rigidity is quite large, the deflection shall be a very small value which is like a rigid body. Compared with the soft body, the ends of rigid body won't be warped to generate the tensional force for the back anchor bolts. I think you should be familiar the following formula of the Method of Consistent Deformation, especially the values of α and β, and I just re-write it to become a more general style. I just wanna show you "No deflection, No angle of rotation."
Actually, the rigid body is just an assumption, but you can use an H beam with high flexural rigidity to solve this problem. I mean you can choose a large size H beam, and you can reduce the deflection to a small value. In such kind of situation, the H beam can be described as a rigid body. Which size of H beam shall you choose? You have to calculate the angle of rotation for the joint, and then you can calculate the stress and strain of the back anchor bolts. The back anchor bolts may yield during the working status, but the front anchor bolts still maintain the normal working status.
When the H beam generates a deflection, the semi-rigid joint shall be warped to use the front anchor bolts as the rotational support. According to calculate the angle of rotation, I also adopt the method of consistent deformation. The external forces can be divided into several parts, and I can choose the suitable coefficients φ and ψ for following formula. After the angle of rotation has known, the next step is to calculate the stress, strain and tensional force of the back anchor bolts. Besides, the H beam is fixed on its bottom flange, so that it must generate the eccentric bending moment.
In the following formulas, the sign e, h, y and N are the eccentric distance, depth deflection, axial force of the H beam respectively. Besides, the sign dV and dH are the distance between the front and back anchor bolts and the distance between the left and right anchor bolts respectively, and the sign futa comes from the Taiwanese 2011 RC Code for the anchor bolt whose abbreviation is "a. b.".
I derive the formulas for the angles of rotation, and it can be used to control the tensional stress of the back anchor bolts. In the derived formulas, I don't need to find the critical axial force of the H beam, so that the sign k has to be calculated by the original definition, not the effective length factor. I consider the twisting moments, so that there are two angles of rotation. On the other hand, the following formulas take the SI unit system, so that you have to use N, m and rad to calculate them, especially the k formula.
In the most case, the tensional stress futa cannot control the fracture conditions for the anchor bolts. Besides, I found the bottom flange of the H beam was possible to yield during the working status, so that I must check the bending moment for the part of the H beam. However, I had known that I could not avoid the yield problem of the flange for the region of the back anchor bolts. Actually, the yield deformation is just 1mm, and the front anchor bolts are the rotational support. Hence, I can make sure the front anchor bolts won't produce the fracture results, and the H beam is just wrapped about its back end part.
I think such kind of connection should change its structural design for improving its disadvantages, and therefore the builder must choose a pair of hinge and roller components fixed on the RC girder. After the RC girder has the hinge components, the H beam can be connected with it by a pin. The couple of the anchor bolts with a small distance, and it must generate large tensional forces. Of course, this is also the reason why the bottom flange is possible to reach the yield stress. In case the angle of rotation is allowable, all of these problems can be eliminated naturally.
Reference
Actually, the rigid body is just an assumption, but you can use an H beam with high flexural rigidity to solve this problem. I mean you can choose a large size H beam, and you can reduce the deflection to a small value. In such kind of situation, the H beam can be described as a rigid body. Which size of H beam shall you choose? You have to calculate the angle of rotation for the joint, and then you can calculate the stress and strain of the back anchor bolts. The back anchor bolts may yield during the working status, but the front anchor bolts still maintain the normal working status.
When the H beam generates a deflection, the semi-rigid joint shall be warped to use the front anchor bolts as the rotational support. According to calculate the angle of rotation, I also adopt the method of consistent deformation. The external forces can be divided into several parts, and I can choose the suitable coefficients φ and ψ for following formula. After the angle of rotation has known, the next step is to calculate the stress, strain and tensional force of the back anchor bolts. Besides, the H beam is fixed on its bottom flange, so that it must generate the eccentric bending moment.
In the following formulas, the sign e, h, y and N are the eccentric distance, depth deflection, axial force of the H beam respectively. Besides, the sign dV and dH are the distance between the front and back anchor bolts and the distance between the left and right anchor bolts respectively, and the sign futa comes from the Taiwanese 2011 RC Code for the anchor bolt whose abbreviation is "a. b.".
I derive the formulas for the angles of rotation, and it can be used to control the tensional stress of the back anchor bolts. In the derived formulas, I don't need to find the critical axial force of the H beam, so that the sign k has to be calculated by the original definition, not the effective length factor. I consider the twisting moments, so that there are two angles of rotation. On the other hand, the following formulas take the SI unit system, so that you have to use N, m and rad to calculate them, especially the k formula.
In the most case, the tensional stress futa cannot control the fracture conditions for the anchor bolts. Besides, I found the bottom flange of the H beam was possible to yield during the working status, so that I must check the bending moment for the part of the H beam. However, I had known that I could not avoid the yield problem of the flange for the region of the back anchor bolts. Actually, the yield deformation is just 1mm, and the front anchor bolts are the rotational support. Hence, I can make sure the front anchor bolts won't produce the fracture results, and the H beam is just wrapped about its back end part.
I think such kind of connection should change its structural design for improving its disadvantages, and therefore the builder must choose a pair of hinge and roller components fixed on the RC girder. After the RC girder has the hinge components, the H beam can be connected with it by a pin. The couple of the anchor bolts with a small distance, and it must generate large tensional forces. Of course, this is also the reason why the bottom flange is possible to reach the yield stress. In case the angle of rotation is allowable, all of these problems can be eliminated naturally.
Reference
- J. M. Gere & S. J. Timoshenko（1972）Mechanics of Materials, D. Van Nostrand Company, Equation 11-19, Chapter 11.
