Bending Moment at Support 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%
✖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%
✖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%

✖Bending Moment at Support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported.ⓘ Bending Moment at Support [M₁]

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Formula

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Bending Moment at Support

Formula

`"M"_{"1"} = "Q"*"A"*((1)-((1-("A"/"L")+((("R"_{"vessel"})^(2)-("Depth"_{"Head"})^(2))/(2*"A"*"L")))/(1+(4/3)*("Depth"_{"Head"}/"L"))))`

Example

`"1.1E^8N*mm"="675098N"*"1210mm"*((1)-((1-("1210mm"/"23399mm")+((("1539mm")^(2)-("1581mm")^(2))/(2*"1210mm"*"23399mm")))/(1+(4/3)*("1581mm"/"23399mm"))))`

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Download Saddle Support Formulas PDF

Bending Moment at Support Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
M₁ = Q*A*((1)-((1-(A/L)+(((R_vessel)^(2)-(Depth_Head)^(2))/(2*A*L)))/(1+(4/3)*(Depth_Head/L))))
This formula uses 6 Variables

Variables Used

Bending Moment at Support - (Measured in Newton Meter) - Bending Moment at Support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported.
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.
Distance from Tangent Line to Saddle Centre - (Measured in Meter) - 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.
Tangent to Tangent Length of Vessel - (Measured in Meter) - 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 Meter) - Vessel Radius refers to the distance from the center of a cylindrical pressure vessel to its outer surface.
Depth of Head - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Total Load per Saddle: 675098 Newton --> 675098 Newton No Conversion Required
Distance from Tangent Line to Saddle Centre: 1210 Millimeter --> 1.21 Meter (Check conversion here)
Tangent to Tangent Length of Vessel: 23399 Millimeter --> 23.399 Meter (Check conversion here)
Vessel Radius: 1539 Millimeter --> 1.539 Meter (Check conversion here)
Depth of Head: 1581 Millimeter --> 1.581 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M₁ = Q*A*((1)-((1-(A/L)+(((R_vessel)^(2)-(Depth_Head)^(2))/(2*A*L)))/(1+(4/3)*(Depth_Head/L)))) --> 675098*1.21*((1)-((1-(1.21/23.399)+(((1.539)^(2)-(1.581)^(2))/(2*1.21*23.399)))/(1+(4/3)*(1.581/23.399))))

Evaluating ... ...

M₁ = 107993.976923982

STEP 3: Convert Result to Output's Unit

107993.976923982 Newton Meter -->107993976.923982 Newton Millimeter (Check conversion here)

FINAL ANSWER

107993976.923982 ≈ 1.1E+8 Newton Millimeter <-- Bending Moment at Support

(Calculation completed in 00.004 seconds)

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< 12 Saddle Support Calculators

Bending Moment at Support

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))))

Bending Moment at Centre of Vessel Span

Go 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)

Period of Vibration at Dead Weight

Go Period of Vibration at Dead Weight = 6.35*10^(-5)*(Overall Height of Vessel/Diameter of Shell Vessel Support)^(3/2)*(Weight of Vessel with Attachments and Contents/Corroded Vessel Wall Thickness)^(1/2)

Stress due to Longitudinal Bending at Top most Fibre of Cross Section

Go Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness)

Stress due to Longitudinal Bending at Bottom most Fibre of Cross Section

Go Stress at Bottom most Fibre of Cross Section = Bending Moment at Support/(Value of k2 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness)

Stress due to Longitudinal Bending at Mid-Span

Go Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness)

Stress due to Seismic Bending Moment

Go Stress due to Seismic Bending Moment = (4*Maximum Seismic Moment)/(pi*(Mean Diameter of Skirt^(2))*Thickness of Skirt)

Combined Stresses at Topmost Fibre of Cross Section

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

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

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

Stability Coefficient of Vessel

Go Stability Coefficient of Vessel = (Bending Moment due to Minimum Weight of Vessel)/Maximum Wind Moment

Corresponding Bending Stress with Section Modulus

Go Axial Bending Stress at Base of Vessel = Maximum Wind Moment/Section Modulus of Skirt Cross Section

Bending Moment at Support Formula

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 Support?

Bending Moment at Support calculator uses 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)))) to calculate the Bending Moment at Support, Bending moment at support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported. Bending Moment at Support is denoted by M₁ symbol.

How to calculate Bending Moment at Support using this online calculator? To use this online calculator for Bending Moment at Support, enter Total Load per Saddle (Q), Distance from Tangent Line to Saddle Centre (A), Tangent to Tangent Length of Vessel (L), Vessel Radius (R_vessel) & Depth of Head (Depth_Head) and hit the calculate button. Here is how the Bending Moment at Support calculation can be explained with given input values -> 1.1E+11 = 675098*1.21*((1)-((1-(1.21/23.399)+(((1.539)^(2)-(1.581)^(2))/(2*1.21*23.399)))/(1+(4/3)*(1.581/23.399)))).

FAQ

What is Bending Moment at Support?

Bending moment at support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported and is represented as M₁ = Q*A*((1)-((1-(A/L)+(((R_vessel)^(2)-(Depth_Head)^(2))/(2*A*L)))/(1+(4/3)*(Depth_Head/L)))) or 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)))). Total Load per Saddle refers to the weight or force that is supported by each saddle in a vessel support system, 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, 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.

How to calculate Bending Moment at Support?

Bending moment at support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported is calculated using 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)))). To calculate Bending Moment at Support, you need Total Load per Saddle (Q), Distance from Tangent Line to Saddle Centre (A), Tangent to Tangent Length of Vessel (L), Vessel Radius (R_vessel) & Depth of Head (Depth_Head). With our tool, you need to enter the respective value for Total Load per Saddle, Distance from Tangent Line to Saddle Centre, Tangent to Tangent Length of Vessel, Vessel Radius & Depth of Head 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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