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Allowable Bending Stress

 

Allowable Bending Stress Formula

\( \sigma_a \;=\;  \dfrac{ \sigma  }{ FS  }\)     (Allowable Bending Stress)

\( \sigma \;=\;  \sigma_a \cdot FS  \)

\( FS \;=\; \dfrac{ \sigma_a }{ \sigma  } \)
Symbol English Metric
\( \sigma_a \)  (Greek symbol sigma) = Allowable Bending Stress \(lbf \;/\; in^2\) \(Pa\)
\( \sigma \)  (Greek symbol sigma) = Yield Strength \(lbf \;/\; in^2\) \(Pa\)
\( FS \) = Safety Factor \(dimensionless\) \(dimensionless\)

Allowable bending stress, also called flexural stress, is the maximum stress that a structural member can withstand when subjected to bending loads without exceeding a predetermined safety margin.  It's used in structural design to ensure that beams, columns, and other flexural members can safely carry their intended loads without permanent deformation or failure.

When a beam or structural element is subjected to a load perpendicular to its longitudinal axis, it tends to bend.  This bending action creates internal stresses within the material:  Tensile stress occurs on the side of the beam that is stretched (elongated).  Compressive stress occurs on the side of the beam that is compressed (shortened).  These stresses vary linearly across the cross-section of the beam, with the maximum values occurring at the points farthest from the neutral axis (the axis where there is no bending stress).

Key Points about Allowable Bending Stress

Yield Strength  -  The minimum stress that leads to permanent deformation of the material.   It is important to note that the yield strength of a material is not a fixed value, but rather depends on various factors such as the composition, processing, and testing conditions of the material.
Ultimate Tensile Strength  -  The maximum stress a material can resist before it starts to elongate.  UTS is a mechanical property that represents the maximum stress a material can withstand before it fractures or breaks under tensile loading.  It is a measure of the material's resistance to being pulled apart or stretched.
Modulus of Elasticity  -  A measure of a material's stiffness or ability to resist deformation under an applied force.  The higher the elastic modulus, the greater the material's ability to withstand deformation without breaking or yielding.
Ductility  -  The material's ability to deform significantly before fracturing.  More ductile materials can often handle higher stresses with a larger safety factor.
Fatigue Resistance  -  The material's ability to withstand repeated loading cycles.  This is important for structures subjected to dynamic loads.
Type of Loading  -  The nature of the load (static, dynamic, impact) can influence the allowable stress.
Buckling Considerations  -  For slender beams, there's a risk of lateral-torsional buckling under bending loads, which can reduce the allowable bending stress.
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