Question 2: How to achieve in-plane stiffness uniformity to reduce torsion caused by horizontal load? The plane layout is simple, regular and symmetrical, so that the stiffness center and centroid of the structure basically coincide, thus avoiding the torsional effect caused by the earthquake and avoiding torsional damage. The center of mass is the center of seismic force (F=-ma, a is ground acceleration), and the center of stiffness is the center of structural resistance (i.e. F=kx). If they are inconsistent, it will inevitably lead to torsional failure. The purpose of uniform vertical stiffness arrangement is to make the structure have no obvious big stiffness change in the vertical direction, that is, there is no weak layer, that is, weak layer, so as to avoid the first collapse caused by insufficient stiffness of weak layer. For example, the bottom of the structure is the most obvious weak layer, and many earthquakes are caused by the collapse of the weak layer at the bottom, which leads to the destruction of houses! Handmade original, you can continue to communicate if you have any questions!
Question 3: There are several methods to calculate the maximum seismic response of multi-degree-of-freedom elastic system.
At present, the maximum seismic response of the structure is of the greatest significance to the seismic design of the structure. There are two methods to calculate the maximum seismic response of multi-degree-of-freedom elastic system: one is the mode decomposition response spectrum method, and the other is the bottom shear method. The former is based on the concepts of mode decomposition method and seismic response spectrum, while the latter is a simplification of mode decomposition response spectrum method. 1 mode decomposition method is used to solve the maximum bottom shear force and maximum vertex displacement of the frame; As shown in figure 1, the three-story shear structure is located in the 8-degree zone (the earthquake acceleration is 0.20 g), and the first group of I sites has a structural damping ratio of 0.05. Using the response spectrum method of mode decomposition, the maximum bottom shear force and maximum vertex displacement of the structure under frequent earthquakes are calculated. Solution: The structure is a three-degree-of-freedom system, and the mass matrix and stiffness matrix are [m] = 20001.50001×103kg, [k] = 3- 1.20- 1.8 respectively. Firstly, the frequency of the natural vibration circle is calculated by the eigenvalue equation, so that B=w2600, which is [k]-W2 [m] = 5-2b-20-23-1.5b-10-1-b = 0. Namely: B3-5.5B2+7.5B-2=0. It can be obtained from the above formula: B 1 = 0.35 1, B2 = 1.6 1, B3 = 3.54. Therefore, from w=600B: w 1 = 14.5 radians/sec, w2 = 3 1. 1 radians/sec, w3 = 46. 1 radians/sec.
Question 4: Briefly describe the solution steps of the mode decomposition response spectrum method. Hello, you can use MATLAB to solve this problem.
It is realized by the library function command eig in Matlab numerical toolbox.
[ x，d] = eig(ik，im)； % ik and im are the stiffness matrix and mass matrix of the structure respectively.
d = sqrt (d)
For i = 1:% is the number of layers of the structure, that is, the prime number.
[ dl (i)，j]= min(d)；
Xgd(:，i) = x(:，j)
d(j) = max (d) + 1
End% sorts the frequency and vibration modes according to this period.
W = dl% required natural frequency
X = xgd% of the main vibration mode of the structure
For example, it may be clearer.
The characteristic parameters of three-story reinforced concrete structure are: one story to one story.
From the first floor to the third floor, the mass m of the three floors is 2 762 kg, 2 760 kg and 2 300 kg respectively.
The stiffness k is 2. 485× 104 N/m， 1。 92 1× 104 N/m， 1。 522 times respectively.
104 nm. The seismic wave adopts 200gal El Centro wave, and the sampling period is 0. 02 s ..
The natural frequency of the structure is:
W = 4。 104 1 10.490 6 14.95 1 4 。
The vibration mode matrix of the structure is:
X = - 0。 005 6 0.0 12 1 - 0.0 13 6
- 0.0 1 1 5 0.008 6 0.0 12 5
- 0.0 15 4 - 0.0 13 0 - 0.005 2
Question 5: Briefly describe the basic principles and steps of bottom shear method and mode decomposition response spectrum method. There are three calculation methods for calculating earthquake action in 15 seismic code: bottom shear method, mode decomposition response spectrum method and time history analysis method.
Applicable conditions:
(1) Structures with a height of less than 40 meters, which are dominated by shear deformation, and whose mass and stiffness are distributed uniformly along the height, and structures similar to single-point systems, can be calculated by the bottom shear method.
(2) Modal decomposition response spectrum method should be adopted for building structures other than the above structures.
(3) For the special irregular buildings, Class A buildings and high-rise buildings specified in the code, time-history analysis method should be used for supplementary calculation.
Modal decomposition response spectrum method;
Also known as standard method, it is suitable for a large number of engineering calculations. This method has two calculation methods: lateral stiffness and total stiffness.
The main difference between the lateral rigid model and the full rigid model is that the lateral rigid model adopts the simplified stiffness moment assumed by the rigid floor.
Array model. The total stiffness model is a stiffness matrix model transformed from the assumed real structural model of elastic floor.
Lateral rigid model: the simplified stiffness matrix model assumed by rigid floor is adopted to idealize the house as a spatial beam.
Columns and walls are combined into a * * * body, which is connected to the floor with infinite stiffness in the plane. No matter where the user is
There is no elastic floor, rigid floor or large space above the floor in the modeling, and the lateral rigid model without tower structure assumes each floor.
It is a rigid floor, while the multi-tower structure is assumed to be a rigid floor with one tower and one floor. Vibration of transverse rigid model.
The structural dynamic degree of freedom is relatively less, the calculation time is less, and the analysis efficiency is high, but the application scope is limited.
Full rigid model: This is a stiffness matrix model transformed from a real structural model. The overall rigid model of the structure assumes that each
The dynamic degree of freedom of each node on the non-rigid floor has two independent horizontal translation degrees of freedom, which can be elastic.
The constraint of a rigid floor can also be completely independent of all nodes on the rigid floor that are not connected to any floor.
The dynamic degree of freedom of "X" has only two independent horizontal translation degrees of freedom and one independent rotation degree of freedom.
Truly simulate structures such as elastic floors, staggered floors with large openings, conjoined, empty industrial workshops and gymnasiums.
However, there are relatively many degrees of freedom, time-consuming calculation and high storage cost.
The modal decomposition response spectrum method first calculates the natural vibration modes of the structure, and selects several vibration modes to calculate the natural vibration modes respectively.
Horizontal earthquake action: the horizontal earthquake of each vibration mode is applied to the structure to find its internal force, and finally each vibration mode is
The internal force and deformation of the structure under earthquake are obtained. Its basic principle is to use "norms"
Response spectrum, first get the "maximum" seismic force corresponding to each vibration mode, and then get the combined seismic action of the combined structure.
An important step is to find the "generalized eigenvalue" and get the first few modes and frequencies of the structure.
In this process, the program performs numerous intermediate calculations according to the laws of mechanics and mathematics, and does not output intermediate data, but only
The result value is notified to the designer.
Bottom shear method:
Equivalent base shear method According to the theory of seismic response spectrum,
The total seismic shear force at the bottom of the engineering structure is equal to the horizontal seismic action of the equivalent single point to determine the total structure.
The method of earthquake action.
A simple method for solving dynamic problems by statics approximation developed earlier and is still widely used today.
Widely used. Its basic idea is to simplify the earthquake action as the addition of inertia force on the basis of static calculation.
The research object is added, and the core is the determination of design earthquake acceleration. This method can be used in a limited range.
It reflects the dynamic characteristics of load, but it cannot reflect the dynamic characteristics of various materials and the dynamics between structures.
The force response can not reflect the dynamic coupling relationship between structures. However, the advantages of quasi-static method are also very prominent.
The physical concept is clear. Compared with the analysis method that comprehensively considers the structural dynamic interaction, the calculation method is as follows
This method is simple, the calculation workload is small, the parameters are easy to determine, rich experience is accumulated, and it is easy to popularize.
Accepted by the design engineer. However, the application scope of quasi-static method should be strictly limited: it cannot be used in earthquakes.
When the soil stiffness is obviously reduced or liquefied, it is only suitable for small design acceleration and dynamic force.
Seismic design of structures with inconspicuous force interaction. ...& gt& gt
Question 6: What is contact stiffness? Stress intensity of contact point (with special detection device)
And diamonds are 10. In other words, the hardest thing is 10.
Question 7: How to correctly calculate the plasticity of floor slab and its economic analysis Abstract: Rigid floor slab hypothesis is a unique concept in building structure analysis. Its introduction can make the calculation concept clear and the calculation method simple, and the results can be used in engineering design. At present, it is the main parameter affecting the overall analysis in various design and calculation software. A correct understanding of its specification basis and mechanical principle is helpful for designers to design rationally. 1 Foreword The assumption of rigid floor is one of the important parameters in general information, and it is a parameter group that affects the analysis of the whole building structure, and its change directly affects the rationality of the whole calculation result. Due to the differences of programmers in computing theory and understanding of specifications, the total amount of information in each program will be different, that is, different versions of the same program are also different. Therefore, when using the program, we should be familiar with and understand the programming principles and instructions, correctly understand the specification basis and mechanical concepts of each parameter, analyze the specification requirements, mechanical principles and engineering experience, and make reasonable selection. According to the requirements of the code, the computer results should be reasonable and effective after analysis and judgment before they can be used in engineering design. 2. Assumptions of floor stiffness 2. 1 Floor is the main horizontal component, with a large number and a wide range. On the one hand, it bears vertical load and transmits it to vertical members such as columns and walls. On the other hand, when it is subjected to horizontal load (wind, earthquake, etc.). ), which also passes its functionality to vertical components. Therefore, it is not only an important stress component, but also an important force transmission component. Because there are both in-plane stiffness and out-of-plane stiffness in the floor slab, it has an important influence on the overall stiffness of the structure and the internal force of vertical and other horizontal members in structural analysis, that is, the stiffness of the floor slab directly affects the analysis results (internal force, deformation and reinforcement) of the overall structure and related members (including the floor slab itself). Therefore, the reasonable assumption of floor stiffness has become the main calculation principle of structural analysis. With the increasing complexity of architectural functions and the diversification of architectural modeling, the architectural structure is becoming more and more complex. Under this influence, seeking reasonable simplification and assumption of floor stiffness to meet the requirements of engineering design is a topic that designers pay attention to and think about, and it is also one of the reasons why various programs are constantly revised and improved, and concise, efficient and reliable calculation methods are introduced. 2.2 The assumption of rigid floor means that the in-plane stiffness of the floor is infinite and the out-of-plane stiffness is zero. This is a unique concept that can make the concept of structural calculation clear and simple. The structure has only three common degrees of freedom in each layer, namely two translational degrees of freedom dx and dy and one torsional degree of freedom θz around the vertical axis, and each node in this layer has only three independent degrees of freedom. The efficiency of computer calculation is greatly improved, and the application scope of the program is more and more extensive. Assuming that the out-of-plane stiffness of the rigid floor is zero, the contribution of the effective flange of the floor beam to the out-of-plane stiffness is ignored, which makes the total stiffness of the structure smaller, the period longer, and the attracted earthquake action smaller and unsafe. Therefore, the code stipulates that the out-of-plane stiffness of the floor is indirectly considered by the increase coefficient of beam stiffness. Therefore, in the calculation of internal force and displacement, the beam stiffness of cast-in-place floor slab and assembled integral floor slab adopts the increase coefficient of 1.3-2.0 to consider the increase effect of flange. Through the above treatment, the floor of most projects in current design can meet the assumption of rigid floor, and the calculation and analysis based on this can be used in engineering design. 2.3 Elastic Floor Assumption For complex floors, such as irregular floors, long and narrow circular floors, large opening floors, multi-towers, slab-column structures, thick slab transfer floor structures, etc. The deformation in the floor will greatly change the displacement and internal force of each lateral member in the floor, especially the displacement and internal force of the member with small lateral stiffness will increase. If the rigid floor assumption is still used for calculation and analysis, the calculation results will be untrue and the reliability of the results cannot be guaranteed, so flexibility must be adopted. The assumption of elastic floor fully considers the weakening and unevenness of in-plane stiffness of the floor, and the actual in-plane and out-of-plane stiffness of the floor is used for calculation and analysis, and the results are more in line with the calculation model of the structure. In SATWE, there are three kinds of elastic floors: elastic plate 6, elastic floor 3 and elastic membrane assumption floor. (1) Elastic floor 6 uses shell elements to calculate the internal and external stiffness of the floor, aiming at the slab-column structure and slab-column shear wall structure. The calculation results will reduce the reinforcement of beams, which is unsafe and not suitable for beam-slab structures. (2) The elastic plate 3 adopts the method of infinite in-plane stiffness and real out-of-plane stiffness of the floor, and is calculated by thick plate bending element, which is suitable for the analysis and calculation of thick plate transfer floor structure. (3) Elastic membrane, the above two assumptions are correct for frame, shear wall, frame-shear wall and frame ... >; & gt
Question 8: Ask a structural engineer: What aspects of earthquake action should be considered in structural design? The significance of seismic design of building structures is to ensure that buildings can withstand the influence of earthquake action. Especially after Wenchuan earthquake and Zhouqu earthquake, it has become a particularly important link to consider the seismic design and strictly abide by the seismic code in architectural design, because it is related to the safety of people's lives and property. ...
675980741-2010-1-2210: 49-education/science > In architecture, earthquake action is usually calculated by mode decomposition response spectrum method. Firstly, the finite element method is used to calculate each mode and natural vibration period of the structure, then the seismic influence coefficient and participation coefficient of each mode are calculated, and then the J-order mode I particle is calculated. ...