Moment Resistance of Steel given Steel Ratio Calculator

✖Tensile Stress in Steel is the external force per unit area of the steel resulting in the stretch of the steel.ⓘ Tensile Stress in Steel [f_TS]			+10% -10%
✖Steel Ratio is defined as the ratio of steel to the beam area at which the yielding of steel happens simultaneously with the crushing of concrete.ⓘ Steel Ratio [ρ_{steel ratio}]			+10% -10%
✖Ratio of Distance between Centroids is the proportion of the distance separating two central points in a geometric or data set.ⓘ Ratio of Distance between Centroids [r]			+10% -10%
✖Width of Beam is the horizontal measurement taken perpendicular to the length of beam.ⓘ Width of Beam [W_b]			+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%

✖Moment Resistance of Steel is the ability to resist bending forces or moments without yielding or deforming excessively.ⓘ Moment Resistance of Steel given Steel Ratio [M_s]

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Formula

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Moment Resistance of Steel given Steel Ratio

Formula

`"M"_{"s"} = "f"_{"TS"}*"ρ"_{"steel ratio"}*"r"*"W"_{"b"}*("d"_{"eff"})^2`

Example

`"25.94687kN*m"="24kgf/m²"*"37.9"*"10.1"*"18mm"*("4m")^2`

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Moment Resistance of Steel given Steel Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment Resistance of Steel = Tensile Stress in Steel*Steel Ratio*Ratio of Distance between Centroids*Width of Beam*(Effective Depth of Beam)^2
M_s = f_TS*ρ_{steel ratio}*r*W_b*(d_eff)^2
This formula uses 6 Variables

Variables Used

Moment Resistance of Steel - (Measured in Newton Meter) - Moment Resistance of Steel is the ability to resist bending forces or moments without yielding or deforming excessively.
Tensile Stress in Steel - (Measured in Pascal) - Tensile Stress in Steel is the external force per unit area of the steel resulting in the stretch of the steel.
Steel Ratio - Steel Ratio is defined as the ratio of steel to the beam area at which the yielding of steel happens simultaneously with the crushing of concrete.
Ratio of Distance between Centroids - Ratio of Distance between Centroids is the proportion of the distance separating two central points in a geometric or data set.
Width of Beam - (Measured in Meter) - Width of Beam is the horizontal measurement taken perpendicular to the length of beam.
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.

STEP 1: Convert Input(s) to Base Unit

Tensile Stress in Steel: 24 Kilogram-Force per Square Meter --> 235.359599999983 Pascal (Check conversion here)
Steel Ratio: 37.9 --> No Conversion Required
Ratio of Distance between Centroids: 10.1 --> No Conversion Required
Width of Beam: 18 Millimeter --> 0.018 Meter (Check conversion here)
Effective Depth of Beam: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_s = f_TS*ρ_{steel ratio}*r*W_b*(d_eff)^2 --> 235.359599999983*37.9*10.1*0.018*(4)^2

Evaluating ... ...

M_s = 25946.8707697901

STEP 3: Convert Result to Output's Unit

25946.8707697901 Newton Meter -->25.9468707697901 Kilonewton Meter (Check conversion here)

FINAL ANSWER

25.9468707697901 ≈ 25.94687 Kilonewton Meter <-- Moment Resistance of Steel

(Calculation completed in 00.004 seconds)

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Moment Resistance of Steel given Steel Ratio

Go Moment Resistance of Steel = Tensile Stress in Steel*Steel Ratio*Ratio of Distance between Centroids*Width of Beam*(Effective Depth of Beam)^2

Stress in Steel given Cross-Sectional Reinforcing Tensile Area to Beam Area Ratio

Go Stress in Compressive Steel = Bending Moment/(Modular Ratio for Elastic Shortening*Constant j*Width of Beam*Depth of Beam^2)

Moment Resistance of Steel given Stress and Area

Go Moment Resistance of Steel = (Tensile Stress in Steel*Area of Steel required*Ratio of Distance between Centroids*Effective Depth of Beam)

Stress in Concrete

Go Stress in Concrete = 2*Bending Moment/(Constant k*Constant j*Width of Beam*Depth of Beam^2)

Stress in Steel

Go Stress in Compressive Steel = Moment in Structures/(Area of Tension Reinforcement*Constant j*Depth of Beam)

Bending Moment given Stress in Concrete

Go Bending Moment = (Stress in Concrete*Constant k*Width of Beam*Depth of Beam^2)/2

Depth of Heavy Beams and Girders

Go Depth of Beam = (Length of Span/12)+(Length of Span/10)

Depth of Roof and Floor Slabs

Go Depth of Beam = Length of Span/25

Depth of Light Beams

Go Depth of Beam = Length of Span/15

Moment Resistance of Steel given Steel Ratio Formula

Moment Resistance of Steel = Tensile Stress in Steel*Steel Ratio*Ratio of Distance between Centroids*Width of Beam*(Effective Depth of Beam)^2
M_s = f_TS*ρ_{steel ratio}*r*W_b*(d_eff)^2

What is Moment Resistance?

Moment Resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.

What is Tensile Stress?

Tensile Stress is the external force per unit area of the material resulting in the stretch of the material.

How to Calculate Moment Resistance of Steel given Steel Ratio?

Moment Resistance of Steel given Steel Ratio calculator uses Moment Resistance of Steel = Tensile Stress in Steel*Steel Ratio*Ratio of Distance between Centroids*Width of Beam*(Effective Depth of Beam)^2 to calculate the Moment Resistance of Steel, The Moment Resistance of steel given steel ratio is defined by the parameters of Tensile stress in steel, steel ratio, Distance between the Centroids of Compression and Tension and the geometry of the section. Moment Resistance of Steel is denoted by M_s symbol.

How to calculate Moment Resistance of Steel given Steel Ratio using this online calculator? To use this online calculator for Moment Resistance of Steel given Steel Ratio, enter Tensile Stress in Steel (f_TS), Steel Ratio (ρ_{steel ratio}), Ratio of Distance between Centroids (r), Width of Beam (W_b) & Effective Depth of Beam (d_eff) and hit the calculate button. Here is how the Moment Resistance of Steel given Steel Ratio calculation can be explained with given input values -> 0.02569 = 235.359599999983*37.9*10.1*0.018*(4)^2.

FAQ

What is Moment Resistance of Steel given Steel Ratio?

The Moment Resistance of steel given steel ratio is defined by the parameters of Tensile stress in steel, steel ratio, Distance between the Centroids of Compression and Tension and the geometry of the section and is represented as M_s = f_TS*ρ_{steel ratio}*r*W_b*(d_eff)^2 or Moment Resistance of Steel = Tensile Stress in Steel*Steel Ratio*Ratio of Distance between Centroids*Width of Beam*(Effective Depth of Beam)^2. Tensile Stress in Steel is the external force per unit area of the steel resulting in the stretch of the steel, Steel Ratio is defined as the ratio of steel to the beam area at which the yielding of steel happens simultaneously with the crushing of concrete, Ratio of Distance between Centroids is the proportion of the distance separating two central points in a geometric or data set, Width of Beam is the horizontal measurement taken perpendicular to the length of beam & Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.

How to calculate Moment Resistance of Steel given Steel Ratio?

The Moment Resistance of steel given steel ratio is defined by the parameters of Tensile stress in steel, steel ratio, Distance between the Centroids of Compression and Tension and the geometry of the section is calculated using Moment Resistance of Steel = Tensile Stress in Steel*Steel Ratio*Ratio of Distance between Centroids*Width of Beam*(Effective Depth of Beam)^2. To calculate Moment Resistance of Steel given Steel Ratio, you need Tensile Stress in Steel (f_TS), Steel Ratio (ρ_{steel ratio}), Ratio of Distance between Centroids (r), Width of Beam (W_b) & Effective Depth of Beam (d_eff). With our tool, you need to enter the respective value for Tensile Stress in Steel, Steel Ratio, Ratio of Distance between Centroids, Width of Beam & Effective Depth of Beam 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 Moment Resistance of Steel?

In this formula, Moment Resistance of Steel uses Tensile Stress in Steel, Steel Ratio, Ratio of Distance between Centroids, Width of Beam & Effective Depth of Beam. We can use 1 other way(s) to calculate the same, which is/are as follows -

Moment Resistance of Steel = (Tensile Stress in Steel*Area of Steel required*Ratio of Distance between Centroids*Effective Depth of Beam)

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