Maximum Ultimate Moment when Neutral Axis Lies in Web Calculator

✖Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section.ⓘ Area of Tension Reinforcement [A]			+10% -10%
✖The Tensile Steel Area for Strength is the area of tensile steel required to develop the compressive strength of overhanging flange.ⓘ Tensile Steel Area for Strength [A_st]			+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%
✖Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.ⓘ Effective Depth of Beam [d_eff]			+10% -10%
✖Equivalent Depth is the depth of equivalent rectangular compressive stress distribution.ⓘ Equivalent Depth [D_equivalent]			+10% -10%
✖Flange Thickness is the thickness of flange in a protruded ridge, lip or rim, either external or internal of a beam such as an I-beam or a T-beam.ⓘ Flange Thickness [t_f]			+10% -10%

✖Maximum Ultimate Moment is the moment acting on the beam at its maximum capacity.ⓘ Maximum Ultimate Moment when Neutral Axis Lies in Web [M_u]

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Formula

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Maximum Ultimate Moment when Neutral Axis Lies in Web

Formula

`"M"_{"u"} = 0.9*(("A"-"A"_{"st"})*"fy"_{"steel"}*("d"_{"eff"}-"D"_{"equivalent"}/2)+"A"_{"st"}*"fy"_{"steel"}*("d"_{"eff"}-"t"_{"f"}/2))`

Example

`"9E^9N*m"=0.9*(("10m²"-"0.4m²")*"250MPa"*("4m"-"25mm"/2)+"0.4m²"*"250MPa"*("4m"-"99.5mm"/2))`

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Maximum Ultimate Moment when Neutral Axis Lies in Web Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Ultimate Moment = 0.9*((Area of Tension Reinforcement-Tensile Steel Area for Strength)*Yield Strength of Steel*(Effective Depth of Beam-Equivalent Depth/2)+Tensile Steel Area for Strength*Yield Strength of Steel*(Effective Depth of Beam-Flange Thickness/2))
M_u = 0.9*((A-A_st)*fy_steel*(d_eff-D_equivalent/2)+A_st*fy_steel*(d_eff-t_f/2))
This formula uses 7 Variables

Variables Used

Maximum Ultimate Moment - (Measured in Newton Meter) - Maximum Ultimate Moment is the moment acting on the beam at its maximum capacity.
Area of Tension Reinforcement - (Measured in Square Meter) - Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section.
Tensile Steel Area for Strength - (Measured in Square Meter) - The Tensile Steel Area for Strength is the area of tensile steel required to develop the compressive strength of overhanging flange.
Yield Strength of Steel - (Measured in Pascal) - Yield Strength of Steel is the level of stress that corresponds to the yield point.
Effective Depth of Beam - (Measured in Meter) - Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.
Equivalent Depth - (Measured in Meter) - Equivalent Depth is the depth of equivalent rectangular compressive stress distribution.
Flange Thickness - (Measured in Meter) - Flange Thickness is the thickness of flange in a protruded ridge, lip or rim, either external or internal of a beam such as an I-beam or a T-beam.

STEP 1: Convert Input(s) to Base Unit

Area of Tension Reinforcement: 10 Square Meter --> 10 Square Meter No Conversion Required
Tensile Steel Area for Strength: 0.4 Square Meter --> 0.4 Square Meter No Conversion Required
Yield Strength of Steel: 250 Megapascal --> 250000000 Pascal (Check conversion here)
Effective Depth of Beam: 4 Meter --> 4 Meter No Conversion Required
Equivalent Depth: 25 Millimeter --> 0.025 Meter (Check conversion here)
Flange Thickness: 99.5 Millimeter --> 0.0995 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_u = 0.9*((A-A_st)*fy_steel*(d_eff-D_equivalent/2)+A_st*fy_steel*(d_eff-t_f/2)) --> 0.9*((10-0.4)*250000000*(4-0.025/2)+0.4*250000000*(4-0.0995/2))

Evaluating ... ...

M_u = 8968522500

STEP 3: Convert Result to Output's Unit

8968522500 Newton Meter --> No Conversion Required

FINAL ANSWER

8968522500 ≈ 9E+9 Newton Meter <-- Maximum Ultimate Moment

(Calculation completed in 00.020 seconds)

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Indian Institute of Information Technology (IIIT), Bhopal

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NSS College of Engineering (NSSCE), Palakkad

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Maximum Ultimate Moment when Neutral Axis Lies in Web

Go Maximum Ultimate Moment = 0.9*((Area of Tension Reinforcement-Tensile Steel Area for Strength)*Yield Strength of Steel*(Effective Depth of Beam-Equivalent Depth/2)+Tensile Steel Area for Strength*Yield Strength of Steel*(Effective Depth of Beam-Flange Thickness/2))

Value of Omega if Neutral Axis is in Flange

Go Value of Omega = Distance from Compression Fiber to NA*Constant β1/(1.18*Effective Depth of Beam)

Distance when Neutral Axis Lies in Flange

Go Distance from Compression Fiber to NA = (1.18*Value of Omega*Effective Depth of Beam)/Constant β1

Depth when Neutral Axis is in Flange

Go Effective Depth of Beam = Distance from Compression Fiber to NA*Constant β1/(1.18*Value of Omega)

Maximum Ultimate Moment when Neutral Axis Lies in Web Formula

What is Ultimate Moment Capacity?

The ultimate moment capacity is the moment acting on the beam at its capacity. The estimated nominal moment capacity should be multiplied by the strength reduction factors to give the design ultimate moment capacity of the beam. This can be represented using the symbol Mu .

How to Calculate Maximum Ultimate Moment when Neutral Axis Lies in Web?

Maximum Ultimate Moment when Neutral Axis Lies in Web calculator uses Maximum Ultimate Moment = 0.9*((Area of Tension Reinforcement-Tensile Steel Area for Strength)*Yield Strength of Steel*(Effective Depth of Beam-Equivalent Depth/2)+Tensile Steel Area for Strength*Yield Strength of Steel*(Effective Depth of Beam-Flange Thickness/2)) to calculate the Maximum Ultimate Moment, The Maximum Ultimate Moment when Neutral Axis Lies in Web formula calculates the moment acting on the beam on its maximum capacity. Maximum Ultimate Moment is denoted by M_u symbol.

How to calculate Maximum Ultimate Moment when Neutral Axis Lies in Web using this online calculator? To use this online calculator for Maximum Ultimate Moment when Neutral Axis Lies in Web, enter Area of Tension Reinforcement (A), Tensile Steel Area for Strength (A_st), Yield Strength of Steel (fy_steel), Effective Depth of Beam (d_eff), Equivalent Depth (D_equivalent) & Flange Thickness (t_f) and hit the calculate button. Here is how the Maximum Ultimate Moment when Neutral Axis Lies in Web calculation can be explained with given input values -> 9E+9 = 0.9*((10-0.4)*250000000*(4-0.025/2)+0.4*250000000*(4-0.0995/2)).

FAQ

What is Maximum Ultimate Moment when Neutral Axis Lies in Web?

The Maximum Ultimate Moment when Neutral Axis Lies in Web formula calculates the moment acting on the beam on its maximum capacity and is represented as M_u = 0.9*((A-A_st)*fy_steel*(d_eff-D_equivalent/2)+A_st*fy_steel*(d_eff-t_f/2)) or Maximum Ultimate Moment = 0.9*((Area of Tension Reinforcement-Tensile Steel Area for Strength)*Yield Strength of Steel*(Effective Depth of Beam-Equivalent Depth/2)+Tensile Steel Area for Strength*Yield Strength of Steel*(Effective Depth of Beam-Flange Thickness/2)). Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section, The Tensile Steel Area for Strength is the area of tensile steel required to develop the compressive strength of overhanging flange, Yield Strength of Steel is the level of stress that corresponds to the yield point, Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber, Equivalent Depth is the depth of equivalent rectangular compressive stress distribution & Flange Thickness is the thickness of flange in a protruded ridge, lip or rim, either external or internal of a beam such as an I-beam or a T-beam.

How to calculate Maximum Ultimate Moment when Neutral Axis Lies in Web?

The Maximum Ultimate Moment when Neutral Axis Lies in Web formula calculates the moment acting on the beam on its maximum capacity is calculated using Maximum Ultimate Moment = 0.9*((Area of Tension Reinforcement-Tensile Steel Area for Strength)*Yield Strength of Steel*(Effective Depth of Beam-Equivalent Depth/2)+Tensile Steel Area for Strength*Yield Strength of Steel*(Effective Depth of Beam-Flange Thickness/2)). To calculate Maximum Ultimate Moment when Neutral Axis Lies in Web, you need Area of Tension Reinforcement (A), Tensile Steel Area for Strength (A_st), Yield Strength of Steel (fy_steel), Effective Depth of Beam (d_eff), Equivalent Depth (D_equivalent) & Flange Thickness (t_f). With our tool, you need to enter the respective value for Area of Tension Reinforcement, Tensile Steel Area for Strength, Yield Strength of Steel, Effective Depth of Beam, Equivalent Depth & Flange Thickness 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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