Stress in Extreme Compression Surface given Moment Resistance Calculator

✖Moment Resistance in Compression is the moment by internal forces in a beam under compressive state.ⓘ Moment Resistance in Compression [M_R]			+10% -10%
✖Constant j is the ratio of the distance between the centroid of compression and the centroid of tension to depth d.ⓘ Constant j [j]			+10% -10%
✖Width of Beam is the horizontal measurement taken perpendicular to the length of beam.ⓘ Width of Beam [W_b]			+10% -10%
✖The Distance to Centroid of Tensile Steel is the distance from extreme compression fiber to centroid of tension reinforcement.ⓘ Distance to Centroid of Tensile Steel [d]			+10% -10%
✖Constant k is the ratio of the depth of compression area to depth d.ⓘ Constant k [K]			+10% -10%
✖Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material.ⓘ Modular Ratio for Elastic Shortening [m_Elastic]			+10% -10%
✖The Value of ρ' is the steel ratio of compression reinforcement.ⓘ Value of ρ' [ρ']			+10% -10%
✖The Distance to Centroid of Compressive steel is the distance from extreme compression surface to the centroid of compression reinforcement.ⓘ Distance to Centroid of Compressive Steel [D]			+10% -10%

✖Stress in Extreme Compression Surface is a measure of stress at extreme compression fiber.ⓘ Stress in Extreme Compression Surface given Moment Resistance [f_ec]

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Formula

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Stress in Extreme Compression Surface given Moment Resistance

Formula

`"f"_{"ec"} = 2*"M"_{"R"}/(("j"*"W"_{"b"}*("d"^2))*("K"+2*"m"_{"Elastic"}*"ρ'")*(1-("D"/("K"*"d"))))`

Example

`"17.00547MPa"=2*"1.6N*m"/(("0.8"*"18mm"*(("5mm")^2))*("0.65"+2*"0.6"*"0.60")*(1-("2.01mm"/("0.65"*"5mm"))))`

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Stress in Extreme Compression Surface given Moment Resistance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stress in Extreme Compression Surface = 2*Moment Resistance in Compression/((Constant j*Width of Beam*(Distance to Centroid of Tensile Steel^2))*(Constant k+2*Modular Ratio for Elastic Shortening*Value of ρ')*(1-(Distance to Centroid of Compressive Steel/(Constant k*Distance to Centroid of Tensile Steel))))
f_ec = 2*M_R/((j*W_b*(d^2))*(K+2*m_Elastic*ρ')*(1-(D/(K*d))))
This formula uses 9 Variables

Variables Used

Stress in Extreme Compression Surface - (Measured in Pascal) - Stress in Extreme Compression Surface is a measure of stress at extreme compression fiber.
Moment Resistance in Compression - (Measured in Newton Meter) - Moment Resistance in Compression is the moment by internal forces in a beam under compressive state.
Constant j - Constant j is the ratio of the distance between the centroid of compression and the centroid of tension to depth d.
Width of Beam - (Measured in Meter) - Width of Beam is the horizontal measurement taken perpendicular to the length of beam.
Distance to Centroid of Tensile Steel - (Measured in Meter) - The Distance to Centroid of Tensile Steel is the distance from extreme compression fiber to centroid of tension reinforcement.
Constant k - Constant k is the ratio of the depth of compression area to depth d.
Modular Ratio for Elastic Shortening - Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material.
Value of ρ' - The Value of ρ' is the steel ratio of compression reinforcement.
Distance to Centroid of Compressive Steel - (Measured in Meter) - The Distance to Centroid of Compressive steel is the distance from extreme compression surface to the centroid of compression reinforcement.

STEP 1: Convert Input(s) to Base Unit

Moment Resistance in Compression: 1.6 Newton Meter --> 1.6 Newton Meter No Conversion Required
Constant j: 0.8 --> No Conversion Required
Width of Beam: 18 Millimeter --> 0.018 Meter (Check conversion here)
Distance to Centroid of Tensile Steel: 5 Millimeter --> 0.005 Meter (Check conversion here)
Constant k: 0.65 --> No Conversion Required
Modular Ratio for Elastic Shortening: 0.6 --> No Conversion Required
Value of ρ': 0.6 --> No Conversion Required
Distance to Centroid of Compressive Steel: 2.01 Millimeter --> 0.00201 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_ec = 2*M_R/((j*W_b*(d^2))*(K+2*m_Elastic*ρ')*(1-(D/(K*d)))) --> 2*1.6/((0.8*0.018*(0.005^2))*(0.65+2*0.6*0.6)*(1-(0.00201/(0.65*0.005))))

Evaluating ... ...

f_ec = 17005467.9119902

STEP 3: Convert Result to Output's Unit

17005467.9119902 Pascal -->17.0054679119902 Megapascal (Check conversion here)

FINAL ANSWER

17.0054679119902 ≈ 17.00547 Megapascal <-- Stress in Extreme Compression Surface

(Calculation completed in 00.004 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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NSS College of Engineering (NSSCE), Palakkad

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< 9 Doubly Reinforced Rectangular Sections Calculators

Stress in Extreme Compression Surface given Moment Resistance

Go Stress in Extreme Compression Surface = 2*Moment Resistance in Compression/((Constant j*Width of Beam*(Distance to Centroid of Tensile Steel^2))*(Constant k+2*Modular Ratio for Elastic Shortening*Value of ρ')*(1-(Distance to Centroid of Compressive Steel/(Constant k*Distance to Centroid of Tensile Steel))))

Moment Resistance in Compression

Go Moment Resistance in Compression = 0.5*(Stress in Extreme Compression Surface*Constant j*Width of Beam*(Distance to Centroid of Tensile Steel^2))*(Constant k+2*Modular Ratio for Elastic Shortening*Value of ρ'*(1-(Distance to Centroid of Compressive Steel/(Constant k*Distance to Centroid of Tensile Steel))))

Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio

Go Tensile to Compressive Stress Ratio = (Ratio of Depth)/2*(Tension Reinforcement Ratio-((Compression Reinforcement Ratio*(Distance from Compression Fiber to NA-Effective Cover))/(Centroidal Distance of Tension Reinforcement-Distance from Compression Fiber to NA)))

Moment Resisting Capacity of Compressive Steel given Stress

Go Moment Resistance of Compressive Steel = 2*Stress in Compressive Steel*Area of Compression Reinforcement*(Distance to Centroid of Tensile Steel-Distance to Centroid of Compressive Steel)

Moment Resistance of Tensile Steel given Area

Go Moment Resistance of Tensile Steel = (Area of Steel required)*(Tensile Stress in Steel)*(Distance between Reinforcements)

Total Compressive force on Beam Cross Section

Go Total Compression on Beam = Total Compression on Concrete+Force on Compressive Steel

Total Compression on Concrete

Go Total Compression on Beam = Force on Compressive Steel+Total Compression on Concrete

Force Acting on Compressive Steel

Go Force on Compressive Steel = Force on Tension Steel-Total Compression on Concrete

Force Acting on Tensile Steel

Go Force on Tension Steel = Total Compression on Concrete+Force on Compressive Steel

Stress in Extreme Compression Surface given Moment Resistance Formula

What is meant by Moment of Resistance?

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

How to Calculate Stress in Extreme Compression Surface given Moment Resistance?

Stress in Extreme Compression Surface given Moment Resistance calculator uses Stress in Extreme Compression Surface = 2*Moment Resistance in Compression/((Constant j*Width of Beam*(Distance to Centroid of Tensile Steel^2))*(Constant k+2*Modular Ratio for Elastic Shortening*Value of ρ')*(1-(Distance to Centroid of Compressive Steel/(Constant k*Distance to Centroid of Tensile Steel)))) to calculate the Stress in Extreme Compression Surface, The Stress in Extreme Compression Surface given Moment Resistance is defined as the stress produced in compressive state when we have a prior info of moment of resistance. Stress in Extreme Compression Surface is denoted by f_ec symbol.

How to calculate Stress in Extreme Compression Surface given Moment Resistance using this online calculator? To use this online calculator for Stress in Extreme Compression Surface given Moment Resistance, enter Moment Resistance in Compression (M_R), Constant j (j), Width of Beam (W_b), Distance to Centroid of Tensile Steel (d), Constant k (K), Modular Ratio for Elastic Shortening (m_Elastic), Value of ρ' (ρ') & Distance to Centroid of Compressive Steel (D) and hit the calculate button. Here is how the Stress in Extreme Compression Surface given Moment Resistance calculation can be explained with given input values -> 1.7E-5 = 2*1.6/((0.8*0.018*(0.005^2))*(0.65+2*0.6*0.6)*(1-(0.00201/(0.65*0.005)))).

FAQ

What is Stress in Extreme Compression Surface given Moment Resistance?

The Stress in Extreme Compression Surface given Moment Resistance is defined as the stress produced in compressive state when we have a prior info of moment of resistance and is represented as f_ec = 2*M_R/((j*W_b*(d^2))*(K+2*m_Elastic*ρ')*(1-(D/(K*d)))) or Stress in Extreme Compression Surface = 2*Moment Resistance in Compression/((Constant j*Width of Beam*(Distance to Centroid of Tensile Steel^2))*(Constant k+2*Modular Ratio for Elastic Shortening*Value of ρ')*(1-(Distance to Centroid of Compressive Steel/(Constant k*Distance to Centroid of Tensile Steel)))). Moment Resistance in Compression is the moment by internal forces in a beam under compressive state, Constant j is the ratio of the distance between the centroid of compression and the centroid of tension to depth d, Width of Beam is the horizontal measurement taken perpendicular to the length of beam, The Distance to Centroid of Tensile Steel is the distance from extreme compression fiber to centroid of tension reinforcement, Constant k is the ratio of the depth of compression area to depth d, Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material, The Value of ρ' is the steel ratio of compression reinforcement & The Distance to Centroid of Compressive steel is the distance from extreme compression surface to the centroid of compression reinforcement.

How to calculate Stress in Extreme Compression Surface given Moment Resistance?

The Stress in Extreme Compression Surface given Moment Resistance is defined as the stress produced in compressive state when we have a prior info of moment of resistance is calculated using Stress in Extreme Compression Surface = 2*Moment Resistance in Compression/((Constant j*Width of Beam*(Distance to Centroid of Tensile Steel^2))*(Constant k+2*Modular Ratio for Elastic Shortening*Value of ρ')*(1-(Distance to Centroid of Compressive Steel/(Constant k*Distance to Centroid of Tensile Steel)))). To calculate Stress in Extreme Compression Surface given Moment Resistance, you need Moment Resistance in Compression (M_R), Constant j (j), Width of Beam (W_b), Distance to Centroid of Tensile Steel (d), Constant k (K), Modular Ratio for Elastic Shortening (m_Elastic), Value of ρ' (ρ') & Distance to Centroid of Compressive Steel (D). With our tool, you need to enter the respective value for Moment Resistance in Compression, Constant j, Width of Beam, Distance to Centroid of Tensile Steel, Constant k, Modular Ratio for Elastic Shortening, Value of ρ' & Distance to Centroid of Compressive Steel 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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