Steel structure design method and limit state of structure

1. Functional requirements of the structure

The basic problems to be solved by the building structure are to meet the requirements of various predetermined functions.

The functions that the structure should meet during the specified design life:

(1) It can withstand various effects that may occur during normal construction and normal use;

(2) Good working performance in normal use;

(3) It has sufficient durability under normal maintenance;

(4) The necessary overall stability can be maintained when and after the occurrence of accidents (such as earthquakes, fires, explosions, impacts, etc.) specified by the design.

The above-mentioned "various effects" refer to various causes such as internal force or deformation of the structure, such as concentrated load or distributed load applied to the structure, and causes of external deformation or constrained deformation of the structure, such as earthquake, foundation settlement, temperature. Change, etc.

2. Reliability of the structure

The ability of a structure to perform a predetermined function under specified conditions for a specified period of time is referred to as the reliability of the structure. Structural reliability is a quantitative description of structural reliability, that is, the probability that a structure will perform a predetermined function under specified conditions within a specified time. The requirement for structural reliability is related to the length of the design base period of the structure. The design base period is long and the reliability requirement is high, and vice versa. The design period for a typical building is 50 years.

The limit state of the structure

A part of the entire structure or structure that exceeds a certain state cannot meet a certain functional requirement of the design specification, and the specific state is called the limit state of the function. The limit state is essentially a boundary between structural reliability and unreliability, so it can also be called a "boundary state". Clear limits or limits should be specified for various limit states of the structure.

China's "Steel Structure Design Code" (hereinafter referred to as GB50017 specification or specification) stipulates that the load-bearing structure should be designed according to the following two types of limit states:

(1) The ultimate state of load carrying capacity includes: strength failure of components and joints, fatigue damage and unsuitable for continued bearing due to excessive deformation, structural and structural loss of stability, structural transformation into maneuvering system and structural overturning.

(2) The normal use limit state includes: local damage (including concrete cracks in the combined structure) that affects the normal use or durability of the structure, members, and non-structural members.

Compared with the normal use limit state, the former may cause personal injury and a large amount of property loss, so the probability of occurrence should be low, while the latter is less harmful to life, so the probability of allowing it can be higher, but Still should pay enough attention.

4. Probability limit state design principle

Let the limit state of the structure be described by the following limit state equation:

Where Z = g(.) - the functional function of the structure;

Xi(i=1,2,...n)—the basic variables that affect the reliability of a structure or component, refer to various functions and material properties, geometric parameters, etc.; when structural reliability analysis is used, The effect and structural resistance are the basic variables of the synthesis; the basic variables can be considered as independent variables.

When there are only two basic variables, the action effect S and the structural resistance R, the functional function of the structure can be expressed as:

Since both R and S are random variables, the function Z is also a random variable. There are three possible states for the function function Z:

The fixed value design method considers that R and S are both deterministic variables. The structure is absolutely safe by designing Z ≥ 0 and giving a certain safety factor. This is not the case. Due to the randomness of Z, structural failures are still known.

The failure probability of a structure or component can be expressed as:

Let the probability statistics of R and S obey the normal distribution, and calculate their average values ​​μR, μS and standard deviation σR, σS respectively, then the function function also obeys the normal distribution, and its mean and standard deviation are respectively

Figure 1.3.1 shows the probability density curve for a normal distribution of function functions. The shaded area from -∞ to 0 in the figure indicates the probability of Z < 0, that is, the probability of failure, which is obtained by the integral method. As can be seen from Figure 1.3.1, there is the following relationship between the mean and standard deviation of Z in the probability density curve of a normal distribution:

When the statistical values ​​of R and S are not normally distributed, the reliability indicators of structural members should be calculated by substituting the mean and standard deviation of their equivalent normal distributions into the formula (1.3.9). When the function function Z is a nonlinear function, this function can be developed into a Taylor series and its linear term is used to calculate β.

The reliability indicators used in the design of structural members can be determined based on the reliability analysis of existing structural members (so-called calibration method), taking into account the use of experience and economic factors. China's "Standard for the Reliability of Building Structure Design" (GB50068) stipulates that the reliability index of the ultimate state of the bearing capacity of structural members shall not be less than the provisions of Table 1.3.2. The various components of the steel structure are designed according to the steel structure design specification. After calibration analysis, the β value is about 3.2, and the steel structure is generally ductile failure, so the overall safety level is two.

V. Design expression

1 bearing capacity limit state expression

For ease of application and in a form that is familiar to people for a long time, the formula (1.3.9) can be transformed as follows:

The left and right of the formula (1.3.10) are the design checkpoint coordinates S* and R* of S and R respectively, which can be written as:

The Unified Standard for Reliability Design of Building Structures (GB50068) stipulates the design expressions for the limit states of structural members. The relevant load representative values, material performance standard values, geometric parameter standard values, and each shall be used according to the design requirements of various limit states. The expression of the partial coefficient and the like.

The action partial coefficient γF (including the load partial coefficient γG, γQ) and the structural component resistance partial coefficient γR should be based on the statistical parameters and probability distribution types of the basic variables in the structural function function, and the structural member reliability indicators specified in Table 1.3.2. , through calculation and analysis, and considering engineering experience.

Considering that there are often more than one type of variable load applied to the structure, it is impossible for these loads to reach their respective maximum values ​​at the same time. Therefore, the combined coefficient sum of the loads is also determined according to the combined load effect distribution. The structural importance factor should be determined according to the safety level of the structural members, the design life, and considering the engineering experience.

According to the functional requirements of the structure, when designing the ultimate state of the bearing capacity, the basic combination of action effects should be considered. The necessary fashion should consider the accidental combination of action effects (considering the combination of accidents such as fire, explosion, impact, earthquake, etc.).

(1) Basic combination

Under the basic combination of load (action) effects, the formula (1.3.11) can be transformed into an equivalent limit state formula expressed as a basic variable standard value, a partial coefficient and a combination coefficient, and expressed in the form of stress. The basic combination of load effects is determined by the most unfavorable value in the following design expression:

For general racks and frame structures, simplified calculations can be used:

Combination controlled by variable load effects:

The combination controlled by the permanent load effect is still calculated according to equation (1.3.13).

In the formula (1.3.12) and (1.3.13), except for the first variable load combined value coefficient ψc1 floor cover (such as the instrument shop warehouse, metalworking workshop, tire factory preparation workshop, grain processing workshop, etc.) ) or the roof (the gray area of ​​the house near the blast furnace) must be controlled by the formula (1.3.13) to take γG=1.35. Other heavy-duty roofs with large concrete roof panels and very special circumstances are possible by the formula (1.3). .13) Control design.

(2) Accidental combination

For accidental combinations, the limit state design expression should be determined according to the following principles: the representative value of the accidental action is not multiplied by the sub-coefficient; the variable load that occurs at the same time as the accidental action should be based on the observation data and engineering experience to adopt the appropriate representative value. The design expression and various coefficients shall be in accordance with the specifications of the special specification.

2 normal use limit state expression

For the normal use limit state, according to the requirements of the building structure reliability design uniform standard, the standard combination of load, the frequency combination and the quasi-permanent combination are respectively designed, and the design such as deformation does not exceed the corresponding specified limit.

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