Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio Calculator

✖Ratio of Depth is a quantitative measure comparing the vertical extent of an object or substance to its width.ⓘ Ratio of Depth [k]			+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%
✖The Compression Reinforcement Ratio is the ratio of the area of compression steel to the area of cross-section.ⓘ Compression Reinforcement Ratio [ρ^']			+10% -10%
✖Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis.ⓘ Distance from Compression Fiber to NA [K_d]			+10% -10%
✖Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement.ⓘ Effective Cover [d']			+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%

✖Tensile to Compressive Stress Ratio is the ratio between stress in tensile steel to stress in extreme compression fiber.ⓘ Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio [fsc_ratio]

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Formula

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Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio

Formula

`"fsc"_{"ratio"} = ("k")/2*("ρ"_{"T"}-(("ρ"^{"'"}*("K"_{"d"}-"d'"))/("D"_{"centroid"}-"K"_{"d"})))`

Example

`"3.944147"=("0.61")/2*("12.9"-(("0.031"*("100.2mm"-"50.01mm"))/("51.01mm"-"100.2mm")))`

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Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
fsc_ratio = (k)/2*(ρ_T-((ρ^'*(K_d-d'))/(D_centroid-K_d)))
This formula uses 7 Variables

Variables Used

Tensile to Compressive Stress Ratio - Tensile to Compressive Stress Ratio is the ratio between stress in tensile steel to stress in extreme compression fiber.
Ratio of Depth - Ratio of Depth is a quantitative measure comparing the vertical extent of an object or substance to its width.
Tension Reinforcement Ratio - The Tension Reinforcement Ratio is the ratio between the area of tensile reinforcement to the area of cross-section.
Compression Reinforcement Ratio - The Compression Reinforcement Ratio is the ratio of the area of compression steel to the area of cross-section.
Distance from Compression Fiber to NA - (Measured in Meter) - Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis.
Effective Cover - (Measured in Meter) - Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement.
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.

STEP 1: Convert Input(s) to Base Unit

Ratio of Depth: 0.61 --> No Conversion Required
Tension Reinforcement Ratio: 12.9 --> No Conversion Required
Compression Reinforcement Ratio: 0.031 --> No Conversion Required
Distance from Compression Fiber to NA: 100.2 Millimeter --> 0.1002 Meter (Check conversion here)
Effective Cover: 50.01 Millimeter --> 0.05001 Meter (Check conversion here)
Centroidal Distance of Tension Reinforcement: 51.01 Millimeter --> 0.05101 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

fsc_ratio = (k)/2*(ρ_T-((ρ^'*(K_d-d'))/(D_centroid-K_d))) --> (0.61)/2*(12.9-((0.031*(0.1002-0.05001))/(0.05101-0.1002)))

Evaluating ... ...

fsc_ratio = 3.94414721386461

STEP 3: Convert Result to Output's Unit

3.94414721386461 --> No Conversion Required

FINAL ANSWER

3.94414721386461 ≈ 3.944147 <-- Tensile to Compressive Stress Ratio

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Structural Engineering » Concrete Structures » Behaviour in Flexure » Analysis Using Working Stress Method » Doubly Reinforced Rectangular Sections » Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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

Verified by Himanshi Sharma

Bhilai Institute of Technology (BIT), Raipur

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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 Tensile Steel to Stress in Extreme Compression Surface Ratio Formula

What are the Assumptions for Working Stress Methods?

1. Plane section remains plane before and after bending.
2. All tensile stress will be carried by tensile reinforcement.
3. The stress in steel and concrete are related by modular ratio. (Es/Ec)
4. Bond between steel and concrete is perfect with in elastic limit of steel

What is Working Stress Method?

It is a method used for the reinforced concrete design where concrete is assumed as elastic, steel and concrete act together elastically where the relation ship between loads and stresses is linear .

How to Calculate Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio?

Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio calculator uses 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))) to calculate the Tensile to Compressive Stress Ratio, The Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio formula is defined as the ratio of stress in tensile steel to stress in extreme compressive surface. It is generally used in working stress method. Tensile to Compressive Stress Ratio is denoted by fsc_ratio symbol.

How to calculate Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio using this online calculator? To use this online calculator for Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio, enter Ratio of Depth (k), Tension Reinforcement Ratio (ρ_T), Compression Reinforcement Ratio (ρ^'), Distance from Compression Fiber to NA (K_d), Effective Cover (d') & Centroidal Distance of Tension Reinforcement (D_centroid) and hit the calculate button. Here is how the Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio calculation can be explained with given input values -> 3.879489 = (0.61)/2*(12.9-((0.031*(0.1002-0.05001))/(0.05101-0.1002))).

FAQ

What is Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio?

The Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio formula is defined as the ratio of stress in tensile steel to stress in extreme compressive surface. It is generally used in working stress method and is represented as fsc_ratio = (k)/2*(ρ_T-((ρ^'*(K_d-d'))/(D_centroid-K_d))) or 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))). Ratio of Depth is a quantitative measure comparing the vertical extent of an object or substance to its width, The Tension Reinforcement Ratio is the ratio between the area of tensile reinforcement to the area of cross-section, The Compression Reinforcement Ratio is the ratio of the area of compression steel to the area of cross-section, Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis, Effective Cover is the distance from exposed surface of concrete to the centroid of main reinforcement & The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement.

How to calculate Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio?

The Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio formula is defined as the ratio of stress in tensile steel to stress in extreme compressive surface. It is generally used in working stress method is calculated using 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))). To calculate Stress in Tensile Steel to Stress in Extreme Compression Surface Ratio, you need Ratio of Depth (k), Tension Reinforcement Ratio (ρ_T), Compression Reinforcement Ratio (ρ^'), Distance from Compression Fiber to NA (K_d), Effective Cover (d') & Centroidal Distance of Tension Reinforcement (D_centroid). With our tool, you need to enter the respective value for Ratio of Depth, Tension Reinforcement Ratio, Compression Reinforcement Ratio, Distance from Compression Fiber to NA, Effective Cover & Centroidal Distance of Tension Reinforcement 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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