Bending Moment Capacity of Rectangular Beam Calculator

✖Area of steel required is the amount of steel required for resisting the shear or diagonal stress as stirrups.ⓘ Area of Steel Required [A_{steel required}]			+10% -10%
✖Area of Compression Reinforcement is the amount of steel required in the compression zone.ⓘ Area of Compression Reinforcement [A_s']			+10% -10%
✖Yield Strength of Steel is the level of stress that corresponds to the yield point.ⓘ Yield Strength of Steel [fy_steel]			+10% -10%
✖The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement.ⓘ Centroidal Distance of Tension Reinforcement [D_centroid]			+10% -10%
✖Depth of Rectangular Stress Distribution is the distance from extreme fiber to rectangular stress distribution in compression zone.ⓘ Depth of Rectangular Stress Distribution [a]			+10% -10%
✖Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement.ⓘ Effective Cover [d']			+10% -10%

✖Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.ⓘ Bending Moment Capacity of Rectangular Beam [B_M]

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Formula

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Bending Moment Capacity of Rectangular Beam

Formula

`"B"_{"M"} = 0.90*(("A"_{"steel required"}-"A"_{"s'"})*"fy"_{"steel"}*("D"_{"centroid"}-("a"/2))+("A"_{"s'"}*"fy"_{"steel"}*("D"_{"centroid"}-"d'")))`

Example

`"160.7422kN*m"=0.90*(("35mm²"-"20mm²")*"250MPa"*("51.01mm"-("9.432mm"/2))+("20mm²"*"250MPa"*("51.01mm"-"50.01mm")))`

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Bending Moment Capacity of Rectangular Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Moment of Considered Section = 0.90*((Area of Steel Required-Area of Compression Reinforcement)*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))+(Area of Compression Reinforcement*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-Effective Cover)))
B_M = 0.90*((A_{steel required}-A_s')*fy_steel*(D_centroid-(a/2))+(A_s'*fy_steel*(D_centroid-d')))
This formula uses 7 Variables

Variables Used

Bending Moment of Considered Section - (Measured in Kilonewton Meter) - Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.
Area of Steel Required - (Measured in Square Meter) - Area of steel required is the amount of steel required for resisting the shear or diagonal stress as stirrups.
Area of Compression Reinforcement - (Measured in Square Meter) - Area of Compression Reinforcement is the amount of steel required in the compression zone.
Yield Strength of Steel - (Measured in Pascal) - Yield Strength of Steel is the level of stress that corresponds to the yield point.
Centroidal Distance of Tension Reinforcement - (Measured in Meter) - The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement.
Depth of Rectangular Stress Distribution - (Measured in Meter) - Depth of Rectangular Stress Distribution is the distance from extreme fiber to rectangular stress distribution in compression zone.
Effective Cover - (Measured in Meter) - Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement.

STEP 1: Convert Input(s) to Base Unit

Area of Steel Required: 35 Square Millimeter --> 3.5E-05 Square Meter (Check conversion here)
Area of Compression Reinforcement: 20 Square Millimeter --> 2E-05 Square Meter (Check conversion here)
Yield Strength of Steel: 250 Megapascal --> 250000000 Pascal (Check conversion here)
Centroidal Distance of Tension Reinforcement: 51.01 Millimeter --> 0.05101 Meter (Check conversion here)
Depth of Rectangular Stress Distribution: 9.432 Millimeter --> 0.009432 Meter (Check conversion here)
Effective Cover: 50.01 Millimeter --> 0.05001 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_M = 0.90*((A_{steel required}-A_s')*fy_steel*(D_centroid-(a/2))+(A_s'*fy_steel*(D_centroid-d'))) --> 0.90*((3.5E-05-2E-05)*250000000*(0.05101-(0.009432/2))+(2E-05*250000000*(0.05101-0.05001)))

Evaluating ... ...

B_M = 160.74225

STEP 3: Convert Result to Output's Unit

160742.25 Newton Meter -->160.74225 Kilonewton Meter (Check conversion here)

FINAL ANSWER

160.74225 ≈ 160.7422 Kilonewton Meter <-- Bending Moment of Considered Section

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Structural Engineering » Concrete Structures » Behaviour in Flexure » Analysis using Limit State Method » Doubly Reinforced Rectangular Sections » Bending Moment Capacity of Rectangular Beam

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Bending Moment Capacity of Rectangular Beam

Go Bending Moment of Considered Section = 0.90*((Area of Steel Required-Area of Compression Reinforcement)*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))+(Area of Compression Reinforcement*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-Effective Cover)))

Depth of Equivalent Rectangular Compressive Stress Distribution

Go Depth of Rectangular Stress Distribution = ((Area of Steel Required-Area of Compression Reinforcement)*Yield Strength of Steel)/(28 Day Compressive Strength of Concrete*Beam Width)

Bending Moment Capacity of Rectangular Beam Formula

What is Bending Moment Capacity of Beam?

The Moment capacity is maximum Bending Moment that can be resisted by an element before it fails in bending. since rectangular beams are subjected to flexural loads and bending, it is important to calculate its capacity to resist the failure.

How to Calculate Bending Moment Capacity of Rectangular Beam?

Bending Moment Capacity of Rectangular Beam calculator uses Bending Moment of Considered Section = 0.90*((Area of Steel Required-Area of Compression Reinforcement)*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))+(Area of Compression Reinforcement*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-Effective Cover))) to calculate the Bending Moment of Considered Section, The Bending moment capacity of rectangular beam is defined as the parameters area of tension reinforcement,area of compression reinforcement,yield strength of steel,effective depth of section,and depth of equivalent rectangular stress distribution. Bending Moment of Considered Section is denoted by B_M symbol.

How to calculate Bending Moment Capacity of Rectangular Beam using this online calculator? To use this online calculator for Bending Moment Capacity of Rectangular Beam, enter Area of Steel Required (A_{steel required}), Area of Compression Reinforcement (A_s'), Yield Strength of Steel (fy_steel), Centroidal Distance of Tension Reinforcement (D_centroid), Depth of Rectangular Stress Distribution (a) & Effective Cover (d') and hit the calculate button. Here is how the Bending Moment Capacity of Rectangular Beam calculation can be explained with given input values -> 0.160787 = 0.90*((3.5E-05-2E-05)*250000000*(0.05101-(0.009432/2))+(2E-05*250000000*(0.05101-0.05001))).

FAQ

What is Bending Moment Capacity of Rectangular Beam?

The Bending moment capacity of rectangular beam is defined as the parameters area of tension reinforcement,area of compression reinforcement,yield strength of steel,effective depth of section,and depth of equivalent rectangular stress distribution and is represented as B_M = 0.90*((A_{steel required}-A_s')*fy_steel*(D_centroid-(a/2))+(A_s'*fy_steel*(D_centroid-d'))) or Bending Moment of Considered Section = 0.90*((Area of Steel Required-Area of Compression Reinforcement)*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))+(Area of Compression Reinforcement*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-Effective Cover))). Area of steel required is the amount of steel required for resisting the shear or diagonal stress as stirrups, Area of Compression Reinforcement is the amount of steel required in the compression zone, Yield Strength of Steel is the level of stress that corresponds to the yield point, The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement, Depth of Rectangular Stress Distribution is the distance from extreme fiber to rectangular stress distribution in compression zone & Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement.

How to calculate Bending Moment Capacity of Rectangular Beam?

The Bending moment capacity of rectangular beam is defined as the parameters area of tension reinforcement,area of compression reinforcement,yield strength of steel,effective depth of section,and depth of equivalent rectangular stress distribution is calculated using Bending Moment of Considered Section = 0.90*((Area of Steel Required-Area of Compression Reinforcement)*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))+(Area of Compression Reinforcement*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-Effective Cover))). To calculate Bending Moment Capacity of Rectangular Beam, you need Area of Steel Required (A_{steel required}), Area of Compression Reinforcement (A_s'), Yield Strength of Steel (fy_steel), Centroidal Distance of Tension Reinforcement (D_centroid), Depth of Rectangular Stress Distribution (a) & Effective Cover (d'). With our tool, you need to enter the respective value for Area of Steel Required, Area of Compression Reinforcement, Yield Strength of Steel, Centroidal Distance of Tension Reinforcement, Depth of Rectangular Stress Distribution & Effective Cover 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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