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Bending Moment at Support Formula

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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. Check FAQs

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})}))

M₁ - Bending Moment at Support?Q - Total Load per Saddle?A - Distance from Tangent Line to Saddle Centre?L - Tangent to Tangent Length of Vessel?R_vessel - Vessel Radius?Depth_Head - Depth of Head?

Bending Moment at Support Example

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Here is how the Bending Moment at Support equation looks like with Values.

Here is how the Bending Moment at Support equation looks like with Units.

Here is how the Bending Moment at Support equation looks like.

1.1E+8 = 675098 \cdot 1210 \cdot ((1) - (\frac{1 - (\frac{1210}{23399}) + (\frac{{(1539)}^{2} - {(1581)}^{2}}{2 \cdot 1210 \cdot 23399})}{1 + (\frac{4}{3}) \cdot (\frac{1581}{23399})}))

1.1E+8N*mm = 675098N \cdot 1210mm \cdot ((1) - (\frac{1 - (\frac{1210mm}{23399mm}) + (\frac{{(1539mm)}^{2} - {(1581mm)}^{2}}{2 \cdot 1210mm \cdot 23399mm})}{1 + (\frac{4}{3}) \cdot (\frac{1581mm}{23399mm})}))

1.1E+8 = 675098 \cdot 1210 \cdot ((1) - (\frac{1 - (\frac{1210}{23399}) + (\frac{{(1539)}^{2} - {(1581)}^{2}}{2 \cdot 1210 \cdot 23399})}{1 + (\frac{4}{3}) \cdot (\frac{1581}{23399})}))

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Bending Moment at Support Solution

Follow our step by step solution on how to calculate Bending Moment at Support?

FIRST Step Consider the formula

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})}))

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

M 1 = 675098N \cdot 1.21m \cdot ((1) - (\frac{1 - (\frac{1.21m}{23.399m}) + (\frac{{(1.539m)}^{2} - {(1.581m)}^{2}}{2 \cdot 1.21m \cdot 23.399m})}{1 + (\frac{4}{3}) \cdot (\frac{1.581m}{23.399m})}))

Next Step Prepare to Evaluate

∴

M 1 = 675098 \cdot 1.21 \cdot ((1) - (\frac{1 - (\frac{1.21}{23.399}) + (\frac{{(1.539)}^{2} - {(1.581)}^{2}}{2 \cdot 1.21 \cdot 23.399})}{1 + (\frac{4}{3}) \cdot (\frac{1.581}{23.399})}))

Next Step Evaluate

∴

M 1 = 107993.976923982N*m

Next Step Convert to Output's Unit

∴

M 1 = 107993976.923982N*mm

LAST Step Rounding Answer

∴

M 1 = 1.1E+8N*mm

Bending Moment at Support Formula Elements

Variables

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.

Symbol: M₁

Measurement: Bending MomentUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment at Support

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

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

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

Other formulas in Saddle Support category

Go Combined Stresses at Mid Span

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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

Go Corresponding Bending Stress with Section Modulus

f wb = \frac{M w}{Z}

How to Evaluate Bending Moment at Support?

Bending Moment at Support evaluator 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 evaluate 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 evaluate Bending Moment at Support using this online evaluator? To use this online evaluator 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.

FAQs on Bending Moment at Support

What is the formula to find Bending Moment at Support?

The formula of Bending Moment at Support is expressed as 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)))). Here is an example- 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)))).

How to calculate Bending Moment at Support?

With 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) we can find Bending Moment at Support using the formula - 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)))).

Can the Bending Moment at Support be negative?

No, the Bending Moment at Support, measured in Bending Moment cannot be negative.

Which unit is used to measure Bending Moment at Support?

Bending Moment at Support 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 Support can be measured.

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Bending Moment at Support Formula

Bending Moment at Support Example

Bending Moment at Support Solution

Bending Moment at Support Formula Elements

Other formulas in Saddle Support category

How to Evaluate Bending Moment at Support?

FAQs on Bending Moment at Support

Variable Name