Bredt's formula

Starting point for the derivation of Bredt's formulas

The Bredt's formulas are a fundamental part of the strength of materials . They form a basis for the calculation of shear stresses and deformations in components with closed, thin-walled hollow cross-sections under pure torsional stress . Subsequently, thus can also Torsionswiderstände and thrust midpoints calculated.

The formulas originally come from Rudolf Bredt , who published them in the VDI Journal in 1896 .

1. Bredt's formula

${\ displaystyle T = {\ frac {M_ {T}} {2 \ cdot A_ {m}}}}$

${\ displaystyle T = \ tau \ cdot t \}$	: Shear flow (constant) in [N / mm], with the shear stress in [N / mm²] and the wall thickness t in [mm] ${\ displaystyle \ tau}$
${\ displaystyle M_ {T} \}$	: Torsional moment in [Nm]
${\ displaystyle A_ {m} \; = \; {\ frac {1} {2}} \ oint {p (s) \; ds}}$	: area enclosed by the cross-sectional center line in [mm²]

2. Bredt's formula (specific twist angle)

${\ displaystyle {\ frac {d \ vartheta} {dx}} = {\ frac {\ oint {\ tau (s) \; ds}} {2 \; G \ cdot A_ {m}}}}$

${\ displaystyle \ vartheta}$	: Twisting (twisting)
${\ displaystyle x}$	: Run coordinate along the member axis in [mm]
${\ displaystyle \ tau (s) = {\ frac {T} {t (s)}}}$	: Shear stress
${\ displaystyle G}$	: Shear modulus in [N / mm²]

Torsion resistance (St. Venant's twist resistance)

The Bredt formula can be used to determine the torsional resistance (i.e. the torsional area moment of the 2nd degree ) of closed thin-walled profiles:

{\ displaystyle I_ {T} = {\ frac {M_ {T} \ cdot l} {G \ cdot \ vartheta}} = {\ frac {4 \ cdot A_ {m} ^ {2}} {\ oint {\ frac {ds} {t (s)}}}}}

with the length of the component in [mm]. ${\ displaystyle l}$

This formula is often referred to as the second Bredt formula.

swell

^ Rudolf Bredt ( Memento from September 5, 2007 in the Internet Archive )

Web links

Construction dictionary online - Bredtsche formulas
HTWG Konstanz, lecture Technical Mechanics (PDF file; 140 kB)

literature

Karl-Eugen Kurrer : History of Structural Analysis. In Search of Balance , Ernst and Son, Berlin 2016, pp. 556f and 573f, ISBN 978-3-433-03134-6 .

[1] Rudolf Bredt ( Memento from September 5, 2007 in the Internet Archive )