Flexural strength

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Beam under bending
stress tensile stress below, compressive stress above
(maximum in the respective edge fiber under the loading force at A or B)

The flexural strength is that tensile or compressive stress in the outer fiber of a component ( bar , plate u. Ä.) Which, when stress by a bending moment occurs, and breakage or plastic deformation leads of the component. It is one of several quantitatively specifiable strength values . ${\ displaystyle \ sigma _ {B, R}}$

exam

The flexural strength is defined as the fictitious stress that the component would have under bending stress in the event of failure if the material were to behave in a linear-elastic manner:

{\ displaystyle \ sigma _ {B, R} (x, y, z) = {\ frac {| M _ {\ eta} |} {W _ {\ eta}}}}

With

the bending stress ${\ displaystyle \ sigma _ {B}}$
the bending moment ${\ displaystyle M}$
the axial modulus ${\ displaystyle W}$

With pure bending stress , both tensile stresses ( ) and compressive stresses ( ) occur: ${\ displaystyle \ sigma> 0}$ ${\ displaystyle \ sigma <0}$

{\ displaystyle \ sigma _ {B, E} (x, y, z) = - {\ frac {M_ {z} (x) \ cdot I_ {y} (x) + M_ {y} (x) \ cdot I_ {yz} (x)} {I_ {y} (x) \ cdot I_ {z} (x) - (I_ {yz} (x)) ^ {2}}} \ cdot y + {\ frac {M_ { y} (x) \ cdot I_ {z} (x) + M_ {z} (x) \ cdot I_ {yz} (x)} {I_ {y} (x) \ cdot I_ {z} (x) - (I_ {yz} (x)) ^ {2}}} \ cdot z}

With

Coordinate x in the horizontal direction (coordinate in brackets: position specification in the component; coordinate as index: specification of the coordinate axis around which a moment acts, see below)
Y coordinate forward
Z coordinate in the vertical direction
Moments of Area of Inertia ${\ displaystyle I_ {y} (x), I_ {z} (x), I_ {yz} (x)}$

For very brittle materials corresponding flexural strength of tensile strength , since the break just occurs when the voltage on the tension reaches the tensile strength.

For metallic materials , this does not necessarily apply, for example. Is in cast iron , the bending strength 2 to 2.5 times higher than the tensile strength.

Fiber-reinforced plastics according to DIN EN ISO 14125: 2011-05

"Flexural strength: The maximum bending stress that can be borne by the test specimen during a flexural test with acceptable failure modes."

- DIN EN ISO 14125: 2011-05

Procedure A (three-point procedure)

${\ displaystyle \ sigma _ {f} = {\ frac {M_ {y}} {W}}}$ With

${\ displaystyle \ sigma _ {f}}$ the bending stress
${\ displaystyle M_ {Y} = {\ frac {F \, L} {4}}}$ the bending moment
${\ displaystyle W = {\ frac {b \, h ^ {2}} {6}}}$ the section modulus
F the force;
L is the span
h is the thickness of the specimen
b the width of the specimen

Procedure B (four-point procedure)

${\ displaystyle \ sigma _ {f} = {\ frac {M_ {y}} {W}}}$ With

${\ displaystyle \ sigma _ {f}}$ the bending stress
${\ displaystyle M_ {y} = {\ frac {F \, L} {6}}}$ the bending moment
${\ displaystyle W = {\ frac {b \, h ^ {2}} {6}}}$ the section modulus
F the force;
L is the span
h is the thickness of the specimen
b the width of the specimen

Sample values

OSB panels can achieve values of up to 22 N / mm² in the main axis and 9 to 11 N / mm² in the transverse axis.
Chipboard can reach 22 N / mm², but the values are usually lower
Blockboards show values of 20 - 55 N / mm² in the longitudinal direction, but only 11 - 30 N / mm² in the transverse direction.
Wooden boards have a flexural strength of up to 35 N / mm² in the longitudinal direction, but often only 1 N / mm² across the grain.
Multi-layer glued solid wood panels (glued wood panel , three-layer panel ...) achieve values of 15 to 35 N / mm² lengthways to the board, whereby the boards with the higher values in the longitudinal direction across the board plane often only achieve a flexural strength of 5 N / mm².
HPL laminate panels (phenol melamine resin impregnated paper webs) reach 80 N / mm².
Cementitious lightweight concrete building panel with lightweight filler -Mittellage and bilateral Deckschichtarmierung of fiberglass mesh at 12.5 mm thickness and a bending strength of 6 N / mm² and a modulus of elasticity of 4200 N / mm².

Individual evidence

↑ ^a ^b ^c ^d Lothar Issler, Hans Ruoß, Peter Häfele: Strength theory - basics . Springer-Verlag, 1995, ISBN 3-662-11739-8 , Chapter 6.3 Bending test , p. 152–156 , doi : 10.1007 / 978-3-662-11739-2 ( limited preview in Google Book search).
↑ Here is assumed a uniaxial bending in the main Achen coordinate system at doppeltsymmetrischem cross section.
↑ Herbert Mang , G Hofstetter: Strength theory. 3rd, updated Edition. Springer Verlag, Vienna / New York 2008, ISBN 978-3-211-72453-8 , 6.4 "Normal stresses", p. 156 , doi : 10.1007 / 978-3-642-40752-9 .
↑ DIN EN ISO 14125 - 2011-05 - Beuth.de . ( beuth.de [accessed on January 16, 2019]).
↑ ^a ^b ^c ^d ^e Armin Pilipp: Technology around panels & wood , November 2008, p. 45ff, Holzhandel Guth; accessed in August 2019
↑ Planning and processing - fermacell Powerpanel H²O - the wet room panel , May 2019, p. 4; In: Fermacell.de