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Bending Moment at Centre of Vessel Span Formula

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Bending Moment at Centre of Vessel Span refers to the maximum bending moment that occurs at the midpoint of a vessel's span, which is the distance between the supports that hold up the vessel. Check FAQs

M 2 = \frac{Q \cdot L}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(R vessel)}^{2} - {(Depth Head)}^{2}}{L^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{Depth Head}{L})}) - \frac{4 \cdot A}{L})

M₂ - Bending Moment at Centre of Vessel Span?Q - Total Load per Saddle?L - Tangent to Tangent Length of Vessel?R_vessel - Vessel Radius?Depth_Head - Depth of Head?A - Distance from Tangent Line to Saddle Centre?

Bending Moment at Centre of Vessel Span Example

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Here is how the Bending Moment at Centre of Vessel Span equation looks like with Values.

Here is how the Bending Moment at Centre of Vessel Span equation looks like with Units.

Here is how the Bending Moment at Centre of Vessel Span equation looks like.

2.8E+12 = \frac{675098 \cdot 23399}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(1539)}^{2} - {(1581)}^{2}}{23399^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{1581}{23399})}) - \frac{4 \cdot 1210}{23399})

2.8E+12N*mm = \frac{675098N \cdot 23399mm}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(1539mm)}^{2} - {(1581mm)}^{2}}{{23399mm}^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{1581mm}{23399mm})}) - \frac{4 \cdot 1210mm}{23399mm})

2.8E+12 = \frac{675098 \cdot 23399}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(1539)}^{2} - {(1581)}^{2}}{23399^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{1581}{23399})}) - \frac{4 \cdot 1210}{23399})

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Bending Moment at Centre of Vessel Span Solution

Follow our step by step solution on how to calculate Bending Moment at Centre of Vessel Span?

FIRST Step Consider the formula

M 2 = \frac{Q \cdot L}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(R vessel)}^{2} - {(Depth Head)}^{2}}{L^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{Depth Head}{L})}) - \frac{4 \cdot A}{L})

Next Step Substitute values of Variables

∴

M 2 = \frac{675098N \cdot 23399mm}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(1539mm)}^{2} - {(1581mm)}^{2}}{{23399mm}^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{1581mm}{23399mm})}) - \frac{4 \cdot 1210mm}{23399mm})

Next Step Prepare to Evaluate

∴

M 2 = \frac{675098 \cdot 23399}{4} \cdot ((\frac{1 + 2 \cdot (\frac{{(1539)}^{2} - {(1581)}^{2}}{23399^{2}})}{1 + (\frac{4}{3}) \cdot (\frac{1581}{23399})}) - \frac{4 \cdot 1210}{23399})

Next Step Evaluate

∴

M 2 = 2804177968.83814N*m

Next Step Convert to Output's Unit

∴

M 2 = 2804177968838.14N*mm

LAST Step Rounding Answer

∴

M 2 = 2.8E+12N*mm

Bending Moment at Centre of Vessel Span Formula Elements

Variables

Bending Moment at Centre of Vessel Span

Bending Moment at Centre of Vessel Span refers to the maximum bending moment that occurs at the midpoint of a vessel's span, which is the distance between the supports that hold up the vessel.

Symbol: M₂

Measurement: Bending MomentUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment at Centre of Vessel Span

Total Load per Saddle

Total Load per Saddle refers to the weight or force that is supported by each saddle in a vessel support system.

Symbol: Q

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Load per Saddle

Tangent to Tangent Length of Vessel

Tangent to Tangent Length of Vessel is distance between two tangent points on the outer surface of a cylindrical pressure vessel.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Tangent to Tangent Length of Vessel

Vessel Radius

Vessel Radius refers to the distance from the center of a cylindrical pressure vessel to its outer surface.

Symbol: R_vessel

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Vessel Radius

Depth of Head

Depth of Head refers to the distance between the inside surface of the head and the point where it transitions to the cylindrical wall of the vessel.

Symbol: Depth_Head

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Head

Distance from Tangent Line to Saddle Centre

Distance from Tangent Line to Saddle Centre is the intersection point between the tangent line and the perpendicular direction to the tangent plane at the saddle centre.

Symbol: A

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Tangent Line to Saddle Centre

Other formulas in Saddle Support category

Go Combined Stresses at Mid Span

f cs3 = f cs1 + f 3

Go Bending Moment at Support

M 1 = Q \cdot A \cdot ((1) - (\frac{1 - (\frac{A}{L}) + (\frac{{(R vessel)}^{2} - {(Depth Head)}^{2}}{2 \cdot A \cdot L})}{1 + (\frac{4}{3}) \cdot (\frac{Depth Head}{L})}))

Go Combined Stresses at Bottommost Fibre of Cross Section

f cs2 = f cs1 - f 2

Go Combined Stresses at Topmost Fibre of Cross Section

f 1cs = f cs1 + f 1

How to Evaluate Bending Moment at Centre of Vessel Span?

Bending Moment at Centre of Vessel Span evaluator uses Bending Moment at Centre of Vessel Span = (Total Load per Saddle*Tangent to Tangent Length of Vessel)/(4)*(((1+2*(((Vessel Radius)^(2)-(Depth of Head)^(2))/(Tangent to Tangent Length of Vessel^(2))))/(1+(4/3)*(Depth of Head/Tangent to Tangent Length of Vessel)))-(4*Distance from Tangent Line to Saddle Centre)/Tangent to Tangent Length of Vessel) to evaluate the Bending Moment at Centre of Vessel Span, Bending Moment at Centre of Vessel Span refers to the maximum bending moment that occurs at the midpoint of a vessel's span, which is the distance between the supports that hold up the vessel. Bending Moment at Centre of Vessel Span is denoted by M₂ symbol.

How to evaluate Bending Moment at Centre of Vessel Span using this online evaluator? To use this online evaluator for Bending Moment at Centre of Vessel Span, enter Total Load per Saddle (Q), Tangent to Tangent Length of Vessel (L), Vessel Radius (R_vessel), Depth of Head (Depth_Head) & Distance from Tangent Line to Saddle Centre (A) and hit the calculate button.

FAQs on Bending Moment at Centre of Vessel Span

What is the formula to find Bending Moment at Centre of Vessel Span?

The formula of Bending Moment at Centre of Vessel Span is expressed as Bending Moment at Centre of Vessel Span = (Total Load per Saddle*Tangent to Tangent Length of Vessel)/(4)*(((1+2*(((Vessel Radius)^(2)-(Depth of Head)^(2))/(Tangent to Tangent Length of Vessel^(2))))/(1+(4/3)*(Depth of Head/Tangent to Tangent Length of Vessel)))-(4*Distance from Tangent Line to Saddle Centre)/Tangent to Tangent Length of Vessel). Here is an example- 2.8E+15 = (675098*23.399)/(4)*(((1+2*(((1.539)^(2)-(1.581)^(2))/(23.399^(2))))/(1+(4/3)*(1.581/23.399)))-(4*1.21)/23.399).

How to calculate Bending Moment at Centre of Vessel Span?

With Total Load per Saddle (Q), Tangent to Tangent Length of Vessel (L), Vessel Radius (R_vessel), Depth of Head (Depth_Head) & Distance from Tangent Line to Saddle Centre (A) we can find Bending Moment at Centre of Vessel Span using the formula - Bending Moment at Centre of Vessel Span = (Total Load per Saddle*Tangent to Tangent Length of Vessel)/(4)*(((1+2*(((Vessel Radius)^(2)-(Depth of Head)^(2))/(Tangent to Tangent Length of Vessel^(2))))/(1+(4/3)*(Depth of Head/Tangent to Tangent Length of Vessel)))-(4*Distance from Tangent Line to Saddle Centre)/Tangent to Tangent Length of Vessel).

Can the Bending Moment at Centre of Vessel Span be negative?

No, the Bending Moment at Centre of Vessel Span, measured in Bending Moment cannot be negative.

Which unit is used to measure Bending Moment at Centre of Vessel Span?

Bending Moment at Centre of Vessel Span is usually measured using the Newton Millimeter[N*mm] for Bending Moment. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Bending Moment at Centre of Vessel Span can be measured.

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Bending Moment at Centre of Vessel Span Formula

Bending Moment at Centre of Vessel Span Example

Bending Moment at Centre of Vessel Span Solution

Bending Moment at Centre of Vessel Span Formula Elements

Other formulas in Saddle Support category

How to Evaluate Bending Moment at Centre of Vessel Span?

FAQs on Bending Moment at Centre of Vessel Span

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