Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement 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%
✖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%

✖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 Ultimate Strength given Area of Tension Reinforcement [B_M]

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Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement

Formula

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

Example

`"364.5652kN*m"=0.90*("35mm²"*"250MPa"*("51.01mm"-("9.432mm"/2)))`

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Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Moment of Considered Section = 0.90*(Area of Steel Required*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2)))
B_M = 0.90*(A_{steel required}*fy_steel*(D_centroid-(a/2)))
This formula uses 5 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.
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.

STEP 1: Convert Input(s) to Base Unit

Area of Steel Required: 35 Square Millimeter --> 3.5E-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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

B_M = 364.56525

STEP 3: Convert Result to Output's Unit

364565.25 Newton Meter -->364.56525 Kilonewton Meter (Check conversion here)

FINAL ANSWER

364.56525 ≈ 364.5652 Kilonewton Meter <-- Bending Moment of Considered Section

(Calculation completed in 00.004 seconds)

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Bending Moment Capacity of Ultimate Strength given Beam Width

Go Bending Moment of Considered Section = 0.90*(Area of Steel Required*Yield Strength of Steel*Centroidal Distance of Tension Reinforcement*(1+(0.59*((Tension Reinforcement Ratio*Yield Strength of Steel))/28 Day Compressive Strength of Concrete)))

Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement

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

Distance from Extreme Compression Surface to Neutral Axis in Compression Failure

Go Neutral Axis Depth = (0.003*Effective Depth of Beam)/((Tensile Stress in Steel/Modulus of Elasticity of Steel)+0.003)

Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement Formula

What is bending moment capacity?

For an elastic design, a structure or a section considered should always have a greater bending moment capacity that the design moment so that the section will not subject to failure.

How to Calculate Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement?

Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement calculator uses Bending Moment of Considered Section = 0.90*(Area of Steel Required*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))) to calculate the Bending Moment of Considered Section, Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement formula is defined by parameters area of steel, effective depth of section, depth of equivalent rectangular stress distribution and yield strength of concrete. Bending Moment of Considered Section is denoted by B_M symbol.

How to calculate Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement using this online calculator? To use this online calculator for Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement, enter Area of Steel Required (A_{steel required}), Yield Strength of Steel (fy_steel), Centroidal Distance of Tension Reinforcement (D_centroid) & Depth of Rectangular Stress Distribution (a) and hit the calculate button. Here is how the Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement calculation can be explained with given input values -> 0.364487 = 0.90*(3.5E-05*250000000*(0.05101-(0.009432/2))).

FAQ

What is Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement?

Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement formula is defined by parameters area of steel, effective depth of section, depth of equivalent rectangular stress distribution and yield strength of concrete and is represented as B_M = 0.90*(A_{steel required}*fy_steel*(D_centroid-(a/2))) or Bending Moment of Considered Section = 0.90*(Area of Steel Required*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))). Area of steel required is the amount of steel required for resisting the shear or diagonal stress as stirrups, 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.

How to calculate Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement?

Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement formula is defined by parameters area of steel, effective depth of section, depth of equivalent rectangular stress distribution and yield strength of concrete is calculated using Bending Moment of Considered Section = 0.90*(Area of Steel Required*Yield Strength of Steel*(Centroidal Distance of Tension Reinforcement-(Depth of Rectangular Stress Distribution/2))). To calculate Bending Moment Capacity of Ultimate Strength given Area of Tension Reinforcement, you need Area of Steel Required (A_{steel required}), Yield Strength of Steel (fy_steel), Centroidal Distance of Tension Reinforcement (D_centroid) & Depth of Rectangular Stress Distribution (a). With our tool, you need to enter the respective value for Area of Steel Required, Yield Strength of Steel, Centroidal Distance of Tension Reinforcement & Depth of Rectangular Stress Distribution and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Bending Moment of Considered Section?

In this formula, Bending Moment of Considered Section uses Area of Steel Required, Yield Strength of Steel, Centroidal Distance of Tension Reinforcement & Depth of Rectangular Stress Distribution. We can use 1 other way(s) to calculate the same, which is/are as follows -

Bending Moment of Considered Section = 0.90*(Area of Steel Required*Yield Strength of Steel*Centroidal Distance of Tension Reinforcement*(1+(0.59*((Tension Reinforcement Ratio*Yield Strength of Steel))/28 Day Compressive Strength of Concrete)))

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