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Bending Moment Capacity of Rectangular Beam Formula

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Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section. Check FAQs

B M = 0.90 \cdot ((A steel required - A s') \cdot fy steel \cdot (D centroid - (\frac{a}{2})) + (A s' \cdot fy steel \cdot (D centroid - d')))

B_M - Bending Moment of Considered Section?A_{steel required} - Area of Steel Required?A_s' - Area of Compression Reinforcement?fy_steel - Yield Strength of Steel?D_centroid - Centroidal Distance of Tension Reinforcement?a - Depth of Rectangular Stress Distribution?d' - Effective Cover?

Bending Moment Capacity of Rectangular Beam Example

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Here is how the Bending Moment Capacity of Rectangular Beam equation looks like with Values.

Here is how the Bending Moment Capacity of Rectangular Beam equation looks like with Units.

Here is how the Bending Moment Capacity of Rectangular Beam equation looks like.

160.7422 = 0.90 \cdot ((35 - 20) \cdot 250 \cdot (51.01 - (\frac{9.432}{2})) + (20 \cdot 250 \cdot (51.01 - 50.01)))

160.7422kN*m = 0.90 \cdot ((35mm² - 20mm²) \cdot 250MPa \cdot (51.01mm - (\frac{9.432mm}{2})) + (20mm² \cdot 250MPa \cdot (51.01mm - 50.01mm)))

160.7422 = 0.90 \cdot ((35 - 20) \cdot 250 \cdot (51.01 - (\frac{9.432}{2})) + (20 \cdot 250 \cdot (51.01 - 50.01)))

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Bending Moment Capacity of Rectangular Beam Solution

Follow our step by step solution on how to calculate Bending Moment Capacity of Rectangular Beam?

FIRST Step Consider the formula

B M = 0.90 \cdot ((A steel required - A s') \cdot fy steel \cdot (D centroid - (\frac{a}{2})) + (A s' \cdot fy steel \cdot (D centroid - d')))

Next Step Substitute values of Variables

∴

B M = 0.90 \cdot ((35mm² - 20mm²) \cdot 250MPa \cdot (51.01mm - (\frac{9.432mm}{2})) + (20mm² \cdot 250MPa \cdot (51.01mm - 50.01mm)))

Next Step Convert Units

∴

B M = 0.90 \cdot ((3.5E-5m² - 2E-5m²) \cdot 2.5E+8Pa \cdot (0.051m - (\frac{0.0094m}{2})) + (2E-5m² \cdot 2.5E+8Pa \cdot (0.051m - 0.05m)))

Next Step Prepare to Evaluate

∴

B M = 0.90 \cdot ((3.5E-5 - 2E-5) \cdot 2.5E+8 \cdot (0.051 - (\frac{0.0094}{2})) + (2E-5 \cdot 2.5E+8 \cdot (0.051 - 0.05)))

Next Step Evaluate

∴

B M = 160742.25N*m

Next Step Convert to Output's Unit

∴

B M = 160.74225kN*m

LAST Step Rounding Answer

∴

B M = 160.7422kN*m

Bending Moment Capacity of Rectangular Beam Formula Elements

Variables

Bending Moment of Considered Section

Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.

Symbol: B_M

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Bending Moment of Considered Section

Area of Steel Required

Area of steel required is the amount of steel required for resisting the shear or diagonal stress as stirrups.

Symbol: A_{steel required}

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Steel Required

Area of Compression Reinforcement

Area of Compression Reinforcement is the amount of steel required in the compression zone.

Symbol: A_s'

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Compression Reinforcement

Yield Strength of Steel

Yield Strength of Steel is the level of stress that corresponds to the yield point.

Symbol: fy_steel

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Strength of Steel

Centroidal Distance of Tension Reinforcement

The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement.

Symbol: D_centroid

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Centroidal Distance of Tension Reinforcement

Depth of Rectangular Stress Distribution

Depth of Rectangular Stress Distribution is the distance from extreme fiber to rectangular stress distribution in compression zone.

Symbol: a

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Stress Distribution

Effective Cover

Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement.

Symbol: d'

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Cover

Other formulas in Doubly Reinforced Rectangular Sections category

Go Depth of Equivalent Rectangular Compressive Stress Distribution

a = \frac{(A steel required - A s') \cdot fy steel}{f c \cdot b}

How to Evaluate Bending Moment Capacity of Rectangular Beam?

Bending Moment Capacity of Rectangular Beam evaluator 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 evaluate 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 evaluate Bending Moment Capacity of Rectangular Beam using this online evaluator? To use this online evaluator 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.

FAQs on Bending Moment Capacity of Rectangular Beam

What is the formula to find Bending Moment Capacity of Rectangular Beam?

The formula of Bending Moment Capacity of Rectangular Beam is expressed as 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))). Here is an example- 0.160787 = 0.90*((3.5E-05-2E-05)*250000000*(0.05101-(0.009432/2))+(2E-05*250000000*(0.05101-0.05001))).

How to calculate Bending Moment Capacity of Rectangular Beam?

With 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') we can find Bending Moment Capacity of Rectangular Beam using the formula - 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))).

Can the Bending Moment Capacity of Rectangular Beam be negative?

No, the Bending Moment Capacity of Rectangular Beam, measured in Moment of Force cannot be negative.

Which unit is used to measure Bending Moment Capacity of Rectangular Beam?

Bending Moment Capacity of Rectangular Beam is usually measured using the Kilonewton Meter[kN*m] for Moment of Force. Newton Meter[kN*m], Millinewton Meter[kN*m], Micronewton Meter[kN*m] are the few other units in which Bending Moment Capacity of Rectangular Beam can be measured.

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Bending Moment Capacity of Rectangular Beam Formula

Bending Moment Capacity of Rectangular Beam Example

Bending Moment Capacity of Rectangular Beam Solution

Bending Moment Capacity of Rectangular Beam Formula Elements

Other formulas in Doubly Reinforced Rectangular Sections category

How to Evaluate Bending Moment Capacity of Rectangular Beam?

FAQs on Bending Moment Capacity of Rectangular Beam

Variable Name