Bending Moment Capacity of Ultimate Strength given Beam Width 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%
✖The Tension Reinforcement Ratio is the ratio between the area of tensile reinforcement to the area of cross-section.ⓘ Tension Reinforcement Ratio [ρ_T]			+10% -10%
✖28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.ⓘ 28 Day Compressive Strength of Concrete [f_c]			+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 Beam Width [B_M]

⎘ Copy

👎

Formula

✖

Bending Moment Capacity of Ultimate Strength given Beam Width

Formula

`"B"_{"M"} = 0.90*("A"_{"steel required"}*"fy"_{"steel"}*"D"_{"centroid"}*(1+(0.59*(("ρ"_{"T"}*"fy"_{"steel"}))/"f"_{"c"})))`

Example

`"51.35782kN*m"=0.90*("35mm²"*"250MPa"*"51.01mm"*(1+(0.59*(("12.9"*"250MPa"))/"15MPa")))`

Calculator

LaTeX

Reset

👍

Download Analysis using Limit State Method Formulas PDF PDF Image

Bending Moment Capacity of Ultimate Strength given Beam Width 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*(1+(0.59*((Tension Reinforcement Ratio*Yield Strength of Steel))/28 Day Compressive Strength of Concrete)))
B_M = 0.90*(A_{steel required}*fy_steel*D_centroid*(1+(0.59*((ρ_T*fy_steel))/f_c)))
This formula uses 6 Variables

Variables Used

Bending Moment of Considered Section - (Measured in Newton 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.
Tension Reinforcement Ratio - The Tension Reinforcement Ratio is the ratio between the area of tensile reinforcement to the area of cross-section.
28 Day Compressive Strength of Concrete - (Measured in Pascal) - 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.

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)
Tension Reinforcement Ratio: 12.9 --> No Conversion Required
28 Day Compressive Strength of Concrete: 15 Megapascal --> 15000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_M = 0.90*(A_{steel required}*fy_steel*D_centroid*(1+(0.59*((ρ_T*fy_steel))/f_c))) --> 0.90*(3.5E-05*250000000*0.05101*(1+(0.59*((12.9*250000000))/15000000)))

Evaluating ... ...

B_M = 51357.8244375

STEP 3: Convert Result to Output's Unit

51357.8244375 Newton Meter -->51.3578244375 Kilonewton Meter (Check conversion here)

FINAL ANSWER

51.3578244375 ≈ 51.35782 Kilonewton Meter <-- Bending Moment of Considered Section

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Structural Engineering » Concrete Structures » Behaviour in Flexure » Analysis using Limit State Method » Singly Reinforced Rectangular Sections » Bending Moment Capacity of Ultimate Strength given Beam Width

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

< 3 Singly Reinforced Rectangular Sections Calculators

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 Beam Width Formula

What is Bending Moment Capacity?

It is the capacity or strength possessed by the beam to resist the flexural forces acting on it. Flexure is the quality or state to be bend.

What is the Difference between Ultimate and Yield Strength?

Yield strength is defined as the maximum stress that a solid material can withstand when it is deformed within its elastic limit. Ultimate strength is defined as the maximum stress that a solid material can withstand before its failure.

How to Calculate Bending Moment Capacity of Ultimate Strength given Beam Width?

Bending Moment Capacity of Ultimate Strength given Beam Width calculator uses 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))) to calculate the Bending Moment of Considered Section, The Bending moment capacity of ultimate strength given beam width is defined as the bending moment capacity of a section,beam when the width of beam is given. Bending Moment of Considered Section is denoted by B_M symbol.

How to calculate Bending Moment Capacity of Ultimate Strength given Beam Width using this online calculator? To use this online calculator for Bending Moment Capacity of Ultimate Strength given Beam Width, enter Area of Steel Required (A_{steel required}), Yield Strength of Steel (fy_steel), Centroidal Distance of Tension Reinforcement (D_centroid), Tension Reinforcement Ratio (ρ_T) & 28 Day Compressive Strength of Concrete (f_c) and hit the calculate button. Here is how the Bending Moment Capacity of Ultimate Strength given Beam Width calculation can be explained with given input values -> 0.051348 = 0.90*(3.5E-05*250000000*0.05101*(1+(0.59*((12.9*250000000))/15000000))).

FAQ

What is Bending Moment Capacity of Ultimate Strength given Beam Width?

The Bending moment capacity of ultimate strength given beam width is defined as the bending moment capacity of a section,beam when the width of beam is given and is represented as B_M = 0.90*(A_{steel required}*fy_steel*D_centroid*(1+(0.59*((ρ_T*fy_steel))/f_c))) or 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))). 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, The Tension Reinforcement Ratio is the ratio between the area of tensile reinforcement to the area of cross-section & 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.

How to calculate Bending Moment Capacity of Ultimate Strength given Beam Width?

The Bending moment capacity of ultimate strength given beam width is defined as the bending moment capacity of a section,beam when the width of beam is given is calculated using 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))). To calculate Bending Moment Capacity of Ultimate Strength given Beam Width, you need Area of Steel Required (A_{steel required}), Yield Strength of Steel (fy_steel), Centroidal Distance of Tension Reinforcement (D_centroid), Tension Reinforcement Ratio (ρ_T) & 28 Day Compressive Strength of Concrete (f_c). With our tool, you need to enter the respective value for Area of Steel Required, Yield Strength of Steel, Centroidal Distance of Tension Reinforcement, Tension Reinforcement Ratio & 28 Day Compressive Strength of Concrete 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, Tension Reinforcement Ratio & 28 Day Compressive Strength of Concrete. 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-(Depth of Rectangular Stress Distribution/2)))

Home

FREE PDFs

🔍 Search