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Beam Deflection for Pipe Span

 

Beam Deflection for Pipe Span formula

\(  \delta  \;=\;  \dfrac{  5 \cdot w \cdot L^4  }{ 384 \cdot E \cdot I   }  \)     (Maximum Deflection)

\(  w  \;=\;  \dfrac{  384 \cdot  \delta \cdot E \cdot I }{  5  \cdot L^4  }  \)

\(  L  \;=\;  \left( \dfrac{  384 \cdot  \delta \cdot E \cdot I }{  5  \cdot w  } \right)^{1/4} \)

\(  E  \;=\;  \dfrac{  5 \cdot w \cdot L^4  }{  384 \cdot \delta \cdot I }  \)

\(  I  \;=\;  \dfrac{  5 \cdot w \cdot L^4  }{  384 \cdot \delta \cdot E }  \)
Symbol English Metric
\( \delta \)  (Greek Symbol delta) = Maximum Deflection \(in\) \(mm\)
\( w \) = Uniform Load per Unit Length \(lbf\;/\;in\) \(N\;/\;mm\)
\( L \) = Span Length \(ft\) \(m\)
\( E \) = Young's Modulus of the Material \(lbf\;/\;in^2\) \(Pa\)
\( I \) = Area Moment of Inertia of the Beam's Cross-section \(in^4\) \(mm^4\)

The allowable pipe span between two pipe supports in piping design depends on factors like pipe material, size, wall thickness, fluid properties, and support conditions.  It’s typically calculated to ensure the pipe can withstand its own weight, the weight of the fluid, and external loads without excessive deflection or stress.  The allowable pipe span is often derived from the beam deflection formula, ensuring that the deflection does not exceed a specified limit (typically 1/360 of the span or a fixed value like 0.1 inches for piping systems).

Key Considerations
Pipe Supports  -  The type of support (simple, fixed, or guided) affects the span calculation.  Fixed supports reduce deflection but may increase stress.
Fluid Dynamics  -  For pipes carrying high-velocity fluids or subject to vibration, shorter spans may be required to avoid fatigue or resonance.
Thermal Expansion  -  Long spans may lead to excessive thermal expansion, requiring expansion loops or additional supports.
Code Requirements  -  Standards like ASME B31.1 (power piping) or B31.3 (process piping) specify maximum allowable stresses and deflection limits.
Safety Factors  -  A safety factor is often applied to account for uncertainties in loading or material properties. 

Uniform Load per Unit Length formula
 \(  w  \;=\;  w_p + w_f + w_i  \)     (Uniform Load per Unit Length)
Symbol English Metric
\( w \) = Uniform Load per Unit Length \(lbf\;/\;in\) \(N\;/\;mm\)
\( w_p \) = Pipe Weight per Unit Length \(lbm\;/\;ft\) \(Pa\)
\( w_f \) = Fluid Weight per Unit Length \(in^4\) \(mm^4\)
\( w_i \) = Insulation Weight  \(in\) \(mm\)

 

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