Database

0008-B-Curved support

The example was created by

Dr.-Ing. Casimir Katz, Dr.-Ing. Roland Sauer, M.Eng. Walter Rustler

and published on 10.11.2017 on

published. You can find it at https://evadat.com/en/bsp/0008/.

It was qualified on 11.05.2018.

Developed by Dr.-Ing. Casimir Katz, Dr.-Ing. Roland Sauer, M.Eng. Walter Rustler

Published on: 10.11.2017 | Qualified on: 11.05.2018

EN This title was machine-translated by DeepL.

B0Classification

ClassB · Numerical verification example
Structural system typeBar structure (general)
MechanicsStatics - second-order theory
Material lawElastic
MaterialGeneral
Verification formatDetermination of internal forces

B1Problem description

This section was machine-translated by DeepL.

A cantilever support with a tapered cross-section is subjected to an axial load with an imperfection, as well as other forces and a temperature difference. (Fig. B1-1) The forces and moments according to second-order theory are calculated for various cross-sectional models.

Tab. B1-1: Model parameters and load
Model properties	Loading
E = 21 MN/cm² αT = 1.2 × 10⁻⁵ 1/K l = 12 m, l* = 4 m Ψo = 1/200, where w = -48 mm	γ = 78.5 kN/m³, γg = 1.35 V = 500 kN qE = 6 kN/m, qA = 10 kN/m ΔT = _{T_right} – T__left = –25° H = 20 kN, H* = 10 kN

Tab. B1-2: Cross-sectional dimensions of the polygonal cross-section
Position	h[mm]	s[mm]	b[mm]	t[mm]	A[cm²]	Iy[cm⁴]
E * A	220 320 520	12 12 12	200 267 400	20 20 20	101.60 140.27 217.60	8609.9 26,230.7 111112.6

Tab. B1-3: Cross-sectional dimensions of the thin-walled cross-section with area compensation
Position	h[mm]	s [mm]	b[mm]	t[mm]	A[cm²]	Iy[cm⁴]
E * A	220 320 520	12 12 12	194.0 260.7 394.0	20 20 20	101.60 140.27 217.60	8,560.0 26,160.3 111,000.0

Eine Kragstütze mit einem gevouteten Querschnittsverlauf wird unter Normalkraft mit einer Imperfektion sowie weiteren Kräften und einem Temperaturunterschiede belastet. (Abb. B1-1) Die Kräfte und Momente nach Theorie II. Ordnung werden für verschiedene Modellierungen des Querschnitts berechnet.

Tab. B1-1: Modellparameter und Belastung
Modell-Eigenschaften	Belastung
E = 21 MN/cm² αT = 1.2 x 10^-5 1/K l = 12 m, l* = 4 m Ψ_o = 1/200, w^o=-48 mm	γ = 78.5 kN/m³, γ_g = 1.35 V = 500 kN q_E = 6kN/m, q_A = 10 kN/m ΔT = T_right - T_left = -25° H = 20 kN, H* = 10 kN

Tab. B1-2: Querschnittswerte des polygonalen Querschnitts
Position	h[mm]	s[mm]	b[mm]	t[mm]	A[cm²]	Iy[cm⁴]
E * A	220 320 520	12 12 12	200 267 400	20 20 20	101.60 140.27 217.60	8609.9 26230.7 111112.6

Tab. B1-3: Querschnittswerte des dünnwandigen Querschnitts mit Flächenausgleich
Position	h[mm]	s[mm]	b[mm]	t[mm]	A[cm²]	Iy[cm⁴]
E * A	220 320 520	12 12 12	194.0 260.7 394.0	20 20 20	101.60 140.27 217.60	8560.0 26160.3 111000.0

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B5References

[1] Rubin, H.: Ein einheitliches, geschlossenes Konzept zur Berechnung von Stäben mit stetig veränderlichem Querschnitt nach Theorie I. und II. Ordnung. In: Bauingenieur 66, 1991.
[2] Gruttmann, F.; Sauer, R.; Wagner, W.: A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections. In: Computer Methods in Applied Mechanics and Engineering 160, 1998.

Editors

Dr.-Ing. Casimir Katz SOFiSTiK AG (Garching, Germany)

–

Creator

Dr.-Ing. Casimir Katz SOFiSTiK AG (Garching, Germany)

SOFiSTiK FEA (2018-0) SOFiSTiK AG

Editor 1

Dr.-Ing. Roland Sauer RIB Software GmbH (Stuttgart, Germany)

TRIMAS (V18.0 01022018) RIB Software GmbH

Editor 2

M.Eng. Walter Rustler Dlubal Software GmbH (Tiefenbach, Germany)

RFEM (5.13.01) Dlubal Software GmbH

Editor 3

Dr.-Ing. Casimir Katz Creator, Editor 1

SOFiSTiK AG (Garching, Germany)

Software used: SOFiSTiK FEA (2018-0) SOFiSTiK AG

Dr.-Ing. Roland Sauer Editor 2

RIB Software GmbH (Stuttgart, Germany)

Software used: TRIMAS (V18.0 01022018) RIB Software GmbH

M.Eng. Walter Rustler Editor 3

Dlubal Software GmbH (Tiefenbach, Germany)

Software used: RFEM (5.13.01) Dlubal Software GmbH