## 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)^(2)-(H)^(2))/(L^(2))))/(1+(4/3)*(H/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)^(2)-(H)^(2))/(L^(2))))/(1+(4/3)*(H/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)
2804177968838.14 Newton Millimeter <-- Bending Moment at Centre of Vessel Span
(Calculation completed in 00.015 seconds)
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## < 25 Vessel Supports Calculators

Maximum Combined Stress on Long Column
Maximum Combined Stress = ((Axial Compressive Load on Column/(Number of Columns*Cross Sectional Area of Column))*(1+(1/7500)*(Column Effective Length/Radius of Gyration of Column)^(2))+((Axial Compressive Load on Column*Eccentricity for Vessel Support)/(Number of Columns*Section Modulus of Column)))
Maximum Stress in Horizontal Plate fixed at Edges
Maximum Stress in Horizontal Plate fixed at Edges = 0.7*Maximum Pressure on Horizontal Plate*((Length of Horizontal Plate)^(2)/(Thickness of Horizontal Plate)^(2))*((Effective Width of Horizontal Plate)^(4)/((Length of Horizontal Plate)^(4)+(Effective Width of Horizontal Plate))^(4))
Maximum Combined Stress on Short Column
Maximum Combined Stress = ((Axial Compressive Load on Column/(Number of Columns*Cross Sectional Area of Column))+((Axial Compressive Load on Column*Eccentricity for Vessel Support)/(Number of Columns*Section Modulus of Column)))
Wind Load acting on Lower Part of Vessel
Wind Load acting on Lower Part of Vessel = Coefficient depending on Shape Factor*Coefficient Period of One Cycle of Vibration*Wind Pressure acting on Lower Part of Vessel*Height of Lower Part of Vessel*Outside Diameter of Vessel
Wind Load acting on Upper Part of Vessel
Wind Load acting on Upper Part of Vessel = Coefficient depending on Shape Factor*Coefficient Period of One Cycle of Vibration*Wind Pressure acting on Upper Part of Vessel*Height of Upper Part of Vessel*Outside Diameter of Vessel
Thickness of Bearing Plate inside Chair
Thickness of Bearing Plate inside Chair = ((6*Maximum Bending Moment in Bearing Plate)/((Width of Bearing Plate-Diameter of Bolt Hole in Bearing Plate)*Allowable Stress in Bolt Material))^(0.5)
Minimum Stress between Bearing Plate and Concrete Foundation
Stress in Bearing Plate and Concrete Foundation = (Maximum Weight of Empty Vessel/Area between Bearing Plate & Concrete Foundation)-(Maximum Seismic Moment/Section Modulus of Area A)
Compressive Stress between Bearing Plate and Concrete Foundation
Maximum Compressive Stress = (Total Weight of Vessel/Area between Bearing Plate & Concrete Foundation)+(Maximum Seismic Moment/Section Modulus of Area A)
Maximum Compressive Stress Parallel to Edge of Gusset Plate
Maximum Compressive Stress Plate = (Bending Moment of Gusset Plate/Section Modulus of Gusset Plate)*(1/cos(Gusset Plate Edge Angle))
Thickness of Base Bearing Plate
Thickness of Base Bearing Plate = Difference Outer Radius of Bearing Plate and Skirt*((3*Maximum Compressive Stress)/(Allowable Bending Stress))^(0.5)
Maximum Pressure on Horizontal Plate
Maximum Pressure on Horizontal Plate = Maximum Compressive Load on Remote Bracket/(Effective Width of Horizontal Plate*Length of Horizontal Plate)
Maximum Compressive Load on Remote Bracket = Maximum Pressure on Horizontal Plate*(Length of Horizontal Plate*Effective Width of Horizontal Plate)
Stress due to Seismic Bending Moment
Stress due to Bending Moment = (4*Maximum Seismic Moment)/(pi*(Mean Diameter of Skirt^(2))*Skirt Thickness)
Load on Each Bolt = Stress in Bearing Plate and Concrete Foundation*(Area of Contact in Bearing Plate and Foundation/Number of Bolts)
Compressive Stress due to Vertical Downward Force
Compressive Stress due to Force = Total Weight of Vessel/(pi*Mean Diameter of Skirt*Skirt Thickness)
Maximum Seismic Moment
Maximum Seismic Moment = ((2/3)*Seismic Coefficient*Total Weight of Vessel*Total Height of Vessel)
Minimum Area by Base Plate
Minimum Area provided by Base Plate = Axial Compressive Load on Column/Permissible Bearing Strength of Concrete
Maximum Compressive Stress
Maximum Compressive Stress = Stress due to Bending Moment+Compressive Stress due to Force
Maximum Compressive Load on Remote Bracket = Total Weight of Vessel/Number of Brackets
Maximum Beading Moment in Bearing Plate Inside Chair
Maximum Bending Moment in Bearing Plate = (Load on Each Bolt*Spacing Inside Chairs)/8
Maximum Tensile Stress
Maximum Tensile Stress = Stress due to Bending Moment-Compressive Stress due to Force
Cross Sectional Area of Bolt
Cross Section Area of Bolt = Load on Each Bolt/Permissible Stress for Bolt Materials
Diameter of Bolt given Cross Sectional Area
Diameter of Bolt = (Cross Sectional Area of Bolt*(4/pi))^(0.5)
Number of Bolts
Number of Bolts = (pi*Mean Diameter of Skirt)/600
Minimum Wind Pressure at Vessel
Minimum Wind Pressure = 0.05*(Maximum Wind Velocity)^(2)

## Bending Moment at Centre of Vessel Span 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)
M2 = (Q*L)/(4)*(((1+2*(((R)^(2)-(H)^(2))/(L^(2))))/(1+(4/3)*(H/L)))-(4*A)/L)

## 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), Depth of Head (H) & 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+9 = (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) .

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