Bending Moment at Centre of Vessel Span Calculator

✖Total Load per Saddle refers to the weight or force that is supported by each saddle in a vessel support system.ⓘ Total Load per Saddle [Q]			+10% -10%
✖Tangent to Tangent Length of Vessel is distance between two tangent points on the outer surface of a cylindrical pressure vessel.ⓘ Tangent to Tangent Length of Vessel [L]			+10% -10%
✖Vessel Radius refers to the distance from the center of a cylindrical pressure vessel to its outer surface.ⓘ Vessel Radius [R_vessel]			+10% -10%
✖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.ⓘ Depth of Head [Depth_Head]			+10% -10%
✖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.ⓘ Distance from Tangent Line to Saddle Centre [A]			+10% -10%

✖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 [M₂]

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Bending Moment at Centre of Vessel Span Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
M₂ = (Q*L)/(4)*(((1+2*(((R_vessel)^(2)-(Depth_Head)^(2))/(L^(2))))/(1+(4/3)*(Depth_Head/L)))-(4*A)/L)
This formula uses 6 Variables

Variables Used

Bending Moment at Centre of Vessel Span - (Measured in Newton Meter) - 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.
Total Load per Saddle - (Measured in Newton) - Total Load per Saddle refers to the weight or force that is supported by each saddle in a vessel support system.
Tangent to Tangent Length of Vessel - (Measured in Millimeter) - Tangent to Tangent Length of Vessel is distance between two tangent points on the outer surface of a cylindrical pressure vessel.
Vessel Radius - (Measured in Millimeter) - Vessel Radius refers to the distance from the center of a cylindrical pressure vessel to its outer surface.
Depth of Head - (Measured in Millimeter) - 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.
Distance from Tangent Line to Saddle Centre - (Measured in Millimeter) - 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.

STEP 1: Convert Input(s) to Base Unit

Total Load per Saddle: 675098 Newton --> 675098 Newton No Conversion Required
Tangent to Tangent Length of Vessel: 23399 Millimeter --> 23399 Millimeter No Conversion Required
Vessel Radius: 1539 Millimeter --> 1539 Millimeter No Conversion Required
Depth of Head: 1581 Millimeter --> 1581 Millimeter No Conversion Required
Distance from Tangent Line to Saddle Centre: 1210 Millimeter --> 1210 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M₂ = (Q*L)/(4)*(((1+2*(((R_vessel)^(2)-(Depth_Head)^(2))/(L^(2))))/(1+(4/3)*(Depth_Head/L)))-(4*A)/L) --> (675098*23399)/(4)*(((1+2*(((1539)^(2)-(1581)^(2))/(23399^(2))))/(1+(4/3)*(1581/23399)))-(4*1210)/23399)

Evaluating ... ...

M₂ = 2804177968.83814

STEP 3: Convert Result to Output's Unit

2804177968.83814 Newton Meter -->2804177968838.14 Newton Millimeter (Check conversion here)

FINAL ANSWER

2804177968838.14 ≈ 2.8E+12 Newton Millimeter <-- Bending Moment at Centre of Vessel Span

(Calculation completed in 00.004 seconds)

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< Saddle Support Calculators

Bending Moment at Support

LaTeX Go Bending Moment at Support = Total Load per Saddle*Distance from Tangent Line to Saddle Centre*((1)-((1-(Distance from Tangent Line to Saddle Centre/Tangent to Tangent Length of Vessel)+(((Vessel Radius)^(2)-(Depth of Head)^(2))/(2*Distance from Tangent Line to Saddle Centre*Tangent to Tangent Length of Vessel)))/(1+(4/3)*(Depth of Head/Tangent to Tangent Length of Vessel))))

Combined Stresses at Topmost Fibre of Cross Section

LaTeX Go Combined Stresses Topmost Fibre Cross Section = Stress due to Internal Pressure+Stress Bending Moment at Topmost of Cross Section

Combined Stresses at Bottommost Fibre of Cross Section

LaTeX Go Combined Stresses Bottommost Fibre Cross Section = Stress due to Internal Pressure-Stress at Bottom most Fibre of Cross Section

Combined Stresses at Mid Span

LaTeX Go Combined Stresses at Mid Span = Stress due to Internal Pressure+Stress due to Longitudinal Bending at Mid-Span

Bending Moment at Centre of Vessel Span Formula

LaTeX Go

What is Design Bending Moment?

Design bending moment refers to the maximum bending moment that a structure or structural element is expected to experience under the worst anticipated loading conditions during its design life. Bending moment is a measure of the internal forces that are generated in a structure or structural element when it is subjected to a load or loads that cause it to bend. The design bending moment is determined by considering the loads that the structure is expected to experience, as well as its geometry, material properties, and other relevant factors. The design bending moment is an important parameter in the design of structures such as beams, columns, and frames, as it affects their strength and stiffness. It is usually determined through structural analysis and is used to select appropriate structural members and to verify their adequacy for the expected loads.

How to Calculate Bending Moment at Centre of Vessel Span?

Bending Moment at Centre of Vessel Span calculator 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 calculate 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 calculate Bending Moment at Centre of Vessel Span using this online calculator? To use this online calculator 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. Here is how the Bending Moment at Centre of Vessel Span calculation can be explained with given input values -> 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).

FAQ

What is 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 and is represented as M₂ = (Q*L)/(4)*(((1+2*(((R_vessel)^(2)-(Depth_Head)^(2))/(L^(2))))/(1+(4/3)*(Depth_Head/L)))-(4*A)/L) or 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). Total Load per Saddle refers to the weight or force that is supported by each saddle in a vessel support system, Tangent to Tangent Length of Vessel is distance between two tangent points on the outer surface of a cylindrical pressure vessel, Vessel Radius refers to the distance from the center of a cylindrical pressure vessel to its outer surface, 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 & 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.

How to calculate 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 is calculated using 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 calculate Bending Moment at Centre of Vessel Span, you need 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). With our tool, you need to enter the respective value for Total Load per Saddle, Tangent to Tangent Length of Vessel, Vessel Radius, Depth of Head & Distance from Tangent Line to Saddle Centre and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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