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)))
BM = 0.90*((Asteel required-As')*fysteel*(Dcentroid-(a/2))+(As'*fysteel*(Dcentroid-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
BM = 0.90*((Asteel required-As')*fysteel*(Dcentroid-(a/2))+(As'*fysteel*(Dcentroid-d'))) --> 0.90*((3.5E-05-2E-05)*250000000*(0.05101-(0.009432/2))+(2E-05*250000000*(0.05101-0.05001)))
Evaluating ... ...
BM = 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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Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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Doubly Reinforced Rectangular Sections Calculators

Bending Moment Capacity of Rectangular Beam
​ LaTeX ​ 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
​ LaTeX ​ 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

​LaTeX ​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)))
BM = 0.90*((Asteel required-As')*fysteel*(Dcentroid-(a/2))+(As'*fysteel*(Dcentroid-d')))

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 BM 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 (Asteel required), Area of Compression Reinforcement (As'), Yield Strength of Steel (fysteel), Centroidal Distance of Tension Reinforcement (Dcentroid), 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 BM = 0.90*((Asteel required-As')*fysteel*(Dcentroid-(a/2))+(As'*fysteel*(Dcentroid-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 (Asteel required), Area of Compression Reinforcement (As'), Yield Strength of Steel (fysteel), Centroidal Distance of Tension Reinforcement (Dcentroid), 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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