3869x

001552

Dipl.-Ing. (BA) Sandy Matula

2019-01-02

Cross-Section Design of a Two-Span Beam

The cross-section class of a two-span beam will be designed in the following text. In addition, the necessary cross-section designs will be performed. The global stability failure will be excluded due to sufficient stabilizing measures.

System, Loading, Internal Forces

Beam Section HEA 240, S355

Cross-Section Class Design

The area of the inner support of the two-span beam governs for designing the cross-section class and performing the cross-section design.

Design for the web (ψ = -1)
[1] Table 5.2, cross-section parts supported on two sides

\begin{array}{l} c = 230 - 2 \cdot (12 21) = 164 mm \\ vorh c / t_{w} = \frac{164}{7, 5} = 21, 87 \\ grenz c / t_{w} = 72 \cdot ε = 72 \cdot 0, 81 = 58, 32 > 21, 87 \end{array}

Formula 1

The web thus fulfills the requirements of cross-section class 1.

Design for the bottom chord (ψ = 1)
[1] Table 5.2, cross-section parts supported on one side

\begin{array}{l} c = \frac{240 - (7, 5 2 \cdot 21)}{2} = 95, 3 mm \\ vorh c / t_{f} = \frac{95, 3}{12} = 7, 94 > 9 \cdot ε = 7, 29 \\ grenz c / t_{f} = 10 \cdot ε = 10 \cdot 0, 81 = 8, 10 > 7, 94 \end{array}

Formula 2

The chords thus fulfill the requirements of cross-section class 2. The cross-section has to be assigned to cross-section class 2, because the class of the cross-section part that is evaluated as the most unfavorable will govern for the entire cross-section.

Shear Buckling of Web

A check must be performed to learn if the shear buckling of the web has to be evaluated, regardless of the assignment of the cross-section class according to 6.2.6, Section (6) in [1]. The value η in Equation 6.22 in [1] is applied with 1.20.

\frac{h_{w}}{t_{w}} = \frac{230 - 2 \cdot 12}{7, 5} = 27, 47 < grenz \frac{h_{w}}{t_{w}} = 72 \cdot \frac{ε}{η} = 72 \cdot \frac{0, 81}{1, 20} = 48, 6

Formula 3

According to EN 1993-1-5, Section 5, no shear buckling design is required.

Shear Designs

The cross-section design is carried out for a cross-section of class 2. Above the inner support, the beam is subjected to bending and shear force; at the location of the maximum sagging moment, only to bending. The influence of the M-V interaction is checked before determining the ultimate limit state of the structure. If V_Ed is not more than 0.5 ⋅ V_pl,Rd, reducing the moment resistance according to [1] Section 6.2.8 (2) is not required.

\begin{array}{l} V_{pl, z, Rd} = A_{Vz} \cdot τ_{Rd} = 25, 18 \cdot \frac{35, 5}{\sqrt{3} \cdot 1, 0} = 516, 09 kN \\ \frac{V_{z, Ed}}{V_{pl, z, Rd}} = \frac{130, 96}{516, 09} = 0, 254 < 0, 5 \end{array}

Formula 4

It is not necessary to reduce the moment resistance.

The following design has to be fulfilled for the design value of the acting bending moments M_Ed:

\frac{M_{Ed}}{M_{c, Rd}} \leq 1, 0

Formula 5

The design value of the bending stress of a cross-section, loaded with uniaxial bending, is determined as follows for cross-sections of class 2:

\begin{array}{l} M_{c, Rd} = M_{pl, Rd} = \frac{W_{pl} \cdot f_{y}}{γ_{M 0}} \\ M_{c, Rd} = M_{pl, Rd} = \frac{2 \cdot S_{y} \cdot f_{y}}{γ_{M 0}} = \frac{2 \cdot 372, 3 \cdot 35, 5}{1, 0} = 264, 33 kNm \\ \frac{M_{Ed}}{M_{c, Rd}} = \frac{155, 76}{264, 33} = 0, 59 \leq 1, 0 \end{array}

Formula 6

Author

Ms. Matula provides technical support for our customers.

Links

Structural Analysis Software for Steel Structures

References

European Committee for Standardization (CEN). (2010). Eurocode 3: Design of Steel Structures – Part 1‑1: General Rules and Rules for Buildings, EN 1993‑1‑1:2010‑12. Berlin: Beuth Verlag GmbH.
Kuhlmann, U.; Feldmann, M.; Lindner, J.; Müller, C.; & Stroetmann, R. (2014). Eurocode 3 - Bemessung und Konstruktion von Stahlbauten – Band 1: Allgemeine Regeln und Hochbau – DIN EN 1993-1-1 mit Nationalem Anhang – Kommentar und Beispiele. Berlin: Beuth.
Albert, A. (2018). Schneider – Bautabellen für Ingenieure mit Berechnungshinweisen und Beispielen (23rd ed.). Cologne: Bundesanzeiger.

;