Concrete is a non-uniform brittle material with low tensile strength. It consists of aggregate, cement, water and gas remaining in it. During construction and use, it is subject to changes in temperature and humidity, uneven settlement of foundation and other factors. The impact of concrete beams is prone to cracks. The existence of cracks is very harmful to the structure, so it is of great practical significance to study cracked beams. In this paper, the simply supported beam with crack is taken as the research object, and the vibration equation of the affected beam is described by the non-quality anti-rotation spring. The comparative analysis was carried out using the finite element program ANSYS calculation.
1 Theoretical calculation principle 1. 1 Bending free vibration of straight beam For a straight beam with a symmetrical plane, when the bending occurs in a plane of symmetry, the differential equation of deflection is: differentially twice, obtained: according to the principle of dc Alebert, the beam is The deflection curve at any time t can be regarded as inertial force (m 2, which can be obtained by the equation (2) to obtain the differential vibration equation of the free-form vibration of equal-section straight beams: the solution of the equation is solved by the separation variable method (3): its general solution For: S 1, 2, 3, 4) can be used to make it have a unit matrix at the origin of the coordinates. The basic solution of this structure can be used to express the vibration mode as: 1. 2 Straight beam bending free vibration with crack 2 2 Strengthening seismic capacity test The seismic calculation is an important part of seismic design and the basis for ensuring seismic capacity. For the seismic calculation of multi-storey brick houses, the bottom shear method can be used. At present, in the seismic design of multi-storey brick houses, it is a common phenomenon to not perform seismic verification, so there must be problems that are neither safe nor waste. Seismic calculation analysis shows that the strength level of the bottom mixed mortar can not be lower than M10 in the 7-storey residential brick house in the 7 degree area.
2. 3 Emphasis on seismic construction measures Reasonable seismic structural measures are the key to multi-storey brick houses/large earthquakes without falling to zero. 1) Effectively set ring beams and structural columns. Multiple earthquake damages indicate that the ring beam and the structural column can improve the shear capacity of the masonry by 10 30, and improve the deformation capacity of the masonry. It is a cost-effective measure to improve the seismic capacity of the building and mitigate the damage. The cross section of the ring beam and the reinforcement should not be too large, usually by the value required by the specification or by increasing the level. 2) Strengthen the connection measures between components. The important joints that need to be taken are: the connection of the structural column to the building and the roof, the connection of the structural column to the brick wall, the connection of the wall to the wall, the connection between the roof of the protruding roof, the connection of the rear wall, and the brickwork The connection, the bottom end connection of the construction column, the connection of the cantilever members such as the parapet wall and the cantilever member, and the like.
3) Reasonably arrange the vertical wall and the cross wall. It is preferred to adopt the structural system of cross-wall bearing or vertical and horizontal wall to bear the weight. The arrangement of the vertical and horizontal walls should be uniform and symmetrical. It should be aligned along the plane and should be continuous up and down in the vertical direction. When the vertical wall cannot be arranged, it can be handed over at the vertical and horizontal walls. A reinforced concrete structural column is added at the site, and the structural reinforcement is appropriately strengthened.
3 Conclusion Mixed structure housing is large and wide, and is an important place for human activities and life. Fully understand the hazards of neglecting seismic design, and pay attention to the seismic design of brick houses. As long as the seismic concept design and structural measures are strengthened, the mixed-structure houses are sufficiently earthquake-resistant, so that the earthquake damage of such houses can be reduced to a minimum.
Guo Jiwu. Seismic design of buildings [M]. Beijing: Higher Education Press, 1990. 1013.
Gong Sili. Architectural Seismic Design Handbook [M]. Beijing: China Building Industry Press, Shanxi Building, as shown in Figure 1, for a section of simply supported beam with n cracks, the position coordinates of n cracks are x L is the beam length. The beam is divided into n 1 segments according to the position of the crack, and the influence of the crack is described by a torsion spring. There is a mutation in the corner of the adjacent two sections. The advantage is that the cracked beam is transformed into a crack-free beam analysis.
The basic solution S is used as follows: the above equation indicates that the displacement, bending moment and shear force of the i 1 segment mode function and the i th segment mode function are continuous in the common section (x), and only one corner abrupt value c is anti-rotation The flexibility coefficient of the spring is the relative depth of the crack as a function of crack depth and height, C(0), which is the displacement, rotation angle, bending moment and shear force of the beam x = 0.
1. 3 boundary conditions of the hinged simply supported beam at both ends: (0) The determinant composed of coefficients is equal to zero, and the frequency parameter a.
2 Calculation example 0. 4. The effect of crack position and crack depth on the natural vibration frequency is shown in Fig. 2 and Fig. 3.
It can be seen from Fig. 2 and Fig. 3 that both the theoretical calculation results and the finite element analysis results show that the crack depth and crack position have a significant influence on the natural frequency of the structure. The calculation results of the two methods are basically consistent, but because the two methods are different, there is a difference in the influence trend in the calculation results. The theoretical calculation model is more sensitive to crack depth and location. Neither of these models considers the effect of opening and closing cracks during vibration.
3 Conclusion 1) Using the massless anti-rotation spring to describe the crack influence, and transform the cracked beam into a crack-free beam analysis. This analysis method is feasible. Actually, the crack position and depth in the beam have the same effect on the beam mode.
2) For the cracked beam, the theoretical calculation results are basically consistent with the calculation results of the finite element model, and have certain accuracy.
Tang Tianguo, Liu Haowu, Liu Xiaosen, et al. Application of Functional Analysis in Damage Detection and Parameter Identification of Simply Supported Beams[J] .Journal of Sichuan University (Engineering Science Edition), 2004, Gu Qiulai: Study on the Effect of Cracking on the Natural Frequency of Simply Supported Beams
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