Multi-stage elastic analysis of steel frame structure with rod frame with loop spring

Through the above analysis and derivation results, the program uses FORTRAN language <11> to program the second-order elastic analysis of the planar bar structure. The general block diagram of the program is shown.

Forming the total geometric stiffness matrix to determine whether to converge the calculation unit internal force and displacement start to form the load vector to form the total first-order stiffness matrix input raw data to solve the equations output displacement and internal force calculation node force increment is iterative program flow chart calculation model verification in order to verify To calculate the correctness of the model, this paper uses the program to calculate and analyze the following example as a 12-story single-span semi-rigid joint steel frame. The steel is Q235-B and the upper 6-story column is H300×250×6×12. The section of the lower 6-story column is H500×300×6×12, all the beam sections are H350×150×6×10, and the rotational rigidity of the semi-rigid connection at both ends of the beam is kR=22430m/radkN (connected rotation according to the calculation of the connection) The stiffness is taken as kR = 1.0 × 1020 m / radkN).

The calculation model and program of this paper are used for calculation, and some results calculated by this program are compared with the calculation results of SAP and ANSYS (using beam element), and the results are shown.

From the calculation results, the following conclusions can be drawn: (1) The results calculated by the method of this paper are very close to the results of the finite element calculation, especially in the case of just connecting. Although the calculation results in this paper have some deviation from the finite element results in the semi-rigid connection, since the rigid connection simulation in this example uses a rotating spring with an initial stiffness of 1.0×10 20 m/radkN, the results are very consistent, so It is considered that the calculation model of this paper is reliable and can be used for the accurate calculation of the planar bar structure.

(2) In this example, the lateral displacement deformation of the semi-rigid connection steel frame is about 1.7 times that of the rigid connection calculation, and the effect of the second-order effect of the structure is about 1.7 times that of the rigid connection calculation. It can be seen that in the case of a planar bar structure with a semi-rigid connection, the influence of the connection semi-rigid must be taken into account when performing structural calculation and analysis, and the influence of the second-order effect of the structure should also be considered.

The effect of the connection semi-rigid on the structural performance is shown as a simplified calculation of a single-span three-story semi-rigid joint steel frame structure. The column sections are HW200×200, the beam sections are HN350×175, and both ends of the beam are semi-rigid. Connection, steel is made of Q235 steel. In order to investigate the influence of the joint rotational stiffness on the mechanical behavior of the structure, in this example, the internal force and horizontal displacement of the joint were calculated and compared by changing the magnitude of the joint rotational stiffness.

Conclusion Through the above calculation and analysis, the following conclusions can be drawn: (1) The calculation model is easy to implement by computer program, and can flexibly handle the force analysis and calculation of more complex planar bar structure. The second-order calculation results derived from the model have high precision and can be used for internal force and deformation calculation of complex planar bar structures; (2) the semi-rigid connection has a great influence on the lateral displacement of the structure.

Compared with the rigid connection, the semi-rigidity of the connection can increase the lateral displacement of the structure by more than 50%, and the degree of influence of the second-order effect of the structure will increase by more than 50% or even more. Therefore, in the calculation of this type of structure, the influence of the semi-rigidity of the connection and the second-order effect of the structure must be considered; (3) the relative linear stiffness of the connection has a great influence on the performance of the structure. The lateral value of the structure and the absolute value of the bending moment at the bottom of the column are almost linear with μ. When the μ value is greater than 8, the axial force and bending moment of the beam no longer change too much.

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