混凝土开裂状态下梁、肋梁、板梁的变形和挠度计算

技术文章

有限元软件 RFEM 及其附加模块 RF-CONCRETE 提供了多种用于计算板梁开裂状态下(state II)的变形与挠度计算方法。本篇技术包括重点阐述其计算方法 (C) 和在有限元软件中的建模方法(M)。本文阐述说明的计算和建模方法不仅仅受限于板梁计算而且还可以推广使用到其他类似结构体系的设计与计算。

Calculation Methods of Deformation/Deflection Analysis

C1: Analytical Calculation - Member
The calculation method according to EN 1992‑1‑1, Section 7.4.3 [1], allows for a simplified approximation of the deformation in cracked state. Using this method, the deformation is determined on an extracted member structure. The connected structural elements, such as surfaces, for example, are not considered in the calculation.

C2: Analytical Calculation - Surface
The RF-CONCRETE Deflect add-on module determines the deformations in the cracked state by using a method based on the analytical calculation method according to EN 1992‑1‑1, Section 7.4.3 [1]. In this case, linear-elastic material properties are applied to the reinforcing steel and concrete until the tension strength is reached. If the tension strength of the concrete is exceeded, damage development occurs. The analysed structure must consist entirely of surfaces. This calculation method is suitable for surfaces subjected to bending.

C3: Nonlinear Calculation - Member
This is a physically nonlinear method, which considers the crack formation and the accompanying redistribution of internal forces in the deformation analysis. The analysed structure must be a pure member structure.

C4: Nonlinear Calculation - Surface
This is a physically nonlinear method, which considers the crack formation and the accompanying redistribution of internal forces in the deformation analysis. The analysed structure must consist entirely of surfaces. In this method, a two-dimensional surface model is internally expanded via the height. For this, the steel cross-section is divided into a defined number of steel and concrete layers. For further information, see the manual RF-CONCRETE Surfaces, Chapter 2.8.2 [2].

C5: Nonlinear Calculation - Combined Structure
In theory, structures consisting of both surfaces and members can be analysed using the stiffness export. RF-CONCRETE Members and RF-CONCRETE Surfaces provide the option to export the stiffness determined in the cracked state to RFEM in a load case or a load combination. The calculation is started in one of the two modules, the stiffness is exported to RFEM, and the other module performs the nonlinear calculation once again to consider the exported stiffness. It should be noted that the interaction between the surface and the member element might not be considered in a single export of the stiffness.

Modelling Options

The available calculation methods can be combined with various modelling approaches in the modelling or they can be linked to them. This will be explained below, using an example of a simply supported beam with a T-section.

Figure 01 - M1: Member Structure in Rendered View

M1: Beam Structure
The structure is modelled as a pure member structure. A possible modelling option is to detach the individual components from the entire structure and analyse them separately, or to create the structure from members only.

M2: Combined Structure of Member and Surface Elements
T-beam chords are modelled as a surface element and the web as a member element. This is a typical model when using members of the Rib type. The member type of a rib can only be used for the analytical calculation (C1). For the nonlinear calculation method (C3), the rib must be converted into an eccentric beam member since it has no actual stiffness in the model.

Figure 02 - M2: Combined Structure Made of Surface and Member Elements

M3: Folded Plate Structure with Vertically Arranged Web
The structure is modelled as a pure folded plate structure without any member elements. In the case of modelling the structure as a surface model, you can attribute the cross-section of the T-beam to a structural line, which defines the position and the orientation of the surfaces. Thus, the web would be modelled as a vertical surface, which is orthogonal to the surfaces of the chord.

Figure 03 - M3: Folded Plate Structure with Vertically Arranged Web

M4: Folded Plate Structure with Horizontally Arranged Web
As in the case of M3, the model consists entirely of surfaces. Both the chords and the web are modelled as a surface with eccentricity arranged horizontally to the centroidal axis. The surface forming the web has a thickness corresponding to the overall height of the structure.

Figure 04 - M4: Folded Plate Structure with Horizontally Arranged Web

General Information About Modelling in Add-on Modules
Basically, the calculation of the deformation in cracked state requires a definition of an existing reinforcement in the structure which is as close as possible to the actually designed reinforcement or case coincides with it, at best. In RF-CONCRETE Members, it is possible to adjust the existing reinforcement and save it as a template (see RF-CONCRETE Members, Chapter 3.6 [3]). In RF-CONCRETE Surfaces, you can define the amount of the existing reinforcement manually or for each element, surface by surface (see RF-CONCRETE Surfaces, Chapter 3.4.3 [2]).

Combination of Methods for Determining Deformation and Modelling

Depending on the modelling, only certain methods are suitable for the deformation analysis. The following table shows the possible combinations.

Figure 05 - Combination of Modelling Options and Calculation Methods for Deformation Analysis

*1) If using a Rib member type in M2, it is possible to perform the analytical calculation C1. In the case of eccentric members, a part of the surface would be neglected when using C1.

*2) It should be noted that the C2 method is designed for structural components predominantly subjected to bending.

Reference

[1]  Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings; EN 1992‑1‑1:2004 + AC:2010
[2]  Manual RF-/CONCRETE Surfaces. (2017). Tiefenbach: Dlubal Software. Download.
[3]  Manual RF-/CONCRETE Members. (2011). Tiefenbach: Dlubal Software. Download.

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结构设计与有限元­分析软件(FEA)可以用于建立平面与空间结构模型,适用于由杆件、面、板、墙、折板、膜、壳、实体以及接触单元等的建模与分析计算。

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钢筋混凝土杆件和面设计(板、墙、折板和壳)

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