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Stress in Extreme Compression Surface given Moment Resistance Formula

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Stress in Extreme Compression Surface is a measure of stress at extreme compression fiber. Check FAQs

f ec = 2 \cdot \frac{M R}{(j \cdot W b \cdot (d^{2})) \cdot (K + 2 \cdot m Elastic \cdot ρ') \cdot (1 - (\frac{D}{K \cdot d}))}

f_ec - Stress in Extreme Compression Surface?M_R - Moment Resistance in Compression?j - Constant j?W_b - Width of Beam?d - Distance to Centroid of Tensile Steel?K - Constant k?m_Elastic - Modular Ratio for Elastic Shortening?ρ' - Value of ρ'?D - Distance to Centroid of Compressive Steel?

Stress in Extreme Compression Surface given Moment Resistance Example

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Here is how the Stress in Extreme Compression Surface given Moment Resistance equation looks like with Values.

Here is how the Stress in Extreme Compression Surface given Moment Resistance equation looks like with Units.

Here is how the Stress in Extreme Compression Surface given Moment Resistance equation looks like.

17.0055 = 2 \cdot \frac{1.6}{(0.8 \cdot 18 \cdot (5^{2})) \cdot (0.65 + 2 \cdot 0.6 \cdot 0.6) \cdot (1 - (\frac{2.01}{0.65 \cdot 5}))}

17.0055MPa = 2 \cdot \frac{1.6N*m}{(0.8 \cdot 18mm \cdot ({5mm}^{2})) \cdot (0.65 + 2 \cdot 0.6 \cdot 0.6) \cdot (1 - (\frac{2.01mm}{0.65 \cdot 5mm}))}

17.0055 = 2 \cdot \frac{1.6}{(0.8 \cdot 18 \cdot (5^{2})) \cdot (0.65 + 2 \cdot 0.6 \cdot 0.6) \cdot (1 - (\frac{2.01}{0.65 \cdot 5}))}

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Stress in Extreme Compression Surface given Moment Resistance Solution

Follow our step by step solution on how to calculate Stress in Extreme Compression Surface given Moment Resistance?

FIRST Step Consider the formula

f ec = 2 \cdot \frac{M R}{(j \cdot W b \cdot (d^{2})) \cdot (K + 2 \cdot m Elastic \cdot ρ') \cdot (1 - (\frac{D}{K \cdot d}))}

Next Step Substitute values of Variables

∴

f ec = 2 \cdot \frac{1.6N*m}{(0.8 \cdot 18mm \cdot ({5mm}^{2})) \cdot (0.65 + 2 \cdot 0.6 \cdot 0.6) \cdot (1 - (\frac{2.01mm}{0.65 \cdot 5mm}))}

Next Step Convert Units

∴

f ec = 2 \cdot \frac{1.6N*m}{(0.8 \cdot 0.018m \cdot ({0.005m}^{2})) \cdot (0.65 + 2 \cdot 0.6 \cdot 0.6) \cdot (1 - (\frac{0.002m}{0.65 \cdot 0.005m}))}

Next Step Prepare to Evaluate

∴

f ec = 2 \cdot \frac{1.6}{(0.8 \cdot 0.018 \cdot ({0.005}^{2})) \cdot (0.65 + 2 \cdot 0.6 \cdot 0.6) \cdot (1 - (\frac{0.002}{0.65 \cdot 0.005}))}

Next Step Evaluate

∴

f ec = 17005467.9119902Pa

Next Step Convert to Output's Unit

∴

f ec = 17.0054679119902MPa

LAST Step Rounding Answer

∴

f ec = 17.0055MPa

Stress in Extreme Compression Surface given Moment Resistance Formula Elements

Variables

Stress in Extreme Compression Surface

Stress in Extreme Compression Surface is a measure of stress at extreme compression fiber.

Symbol: f_ec

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress in Extreme Compression Surface

Moment Resistance in Compression

Moment Resistance in Compression is the moment by internal forces in a beam under compressive state.

Symbol: M_R

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Moment Resistance in Compression

Constant j

Constant j is the ratio of the distance between the centroid of compression and the centroid of tension to depth d.

Symbol: j

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Constant j

Width of Beam

Width of Beam is the horizontal measurement taken perpendicular to the length of beam.

Symbol: W_b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Beam

Distance to Centroid of Tensile Steel

The Distance to Centroid of Tensile Steel is the distance from extreme compression fiber to centroid of tension reinforcement.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance to Centroid of Tensile Steel

Constant k

Constant k is the ratio of the depth of compression area to depth d.

Symbol: K

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Constant k

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.

Symbol: m_Elastic

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Modular Ratio for Elastic Shortening

Value of ρ'

The Value of ρ' is the steel ratio of compression reinforcement.

Symbol: ρ'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of ρ'

Distance to Centroid of Compressive Steel

The Distance to Centroid of Compressive steel is the distance from extreme compression surface to the centroid of compression reinforcement.

Symbol: D

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance to Centroid of Compressive Steel

Other formulas in Doubly Reinforced Rectangular Sections category

Go Total Compressive force on Beam Cross Section

C b = C c + C s'

Go Total Compression on Concrete

C b = C s' + C c

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

Stress in Extreme Compression Surface given Moment Resistance evaluator 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 evaluate 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 evaluate Stress in Extreme Compression Surface given Moment Resistance using this online evaluator? To use this online evaluator 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.

FAQs on Stress in Extreme Compression Surface given Moment Resistance

What is the formula to find Stress in Extreme Compression Surface given Moment Resistance?

The formula of Stress in Extreme Compression Surface given Moment Resistance is expressed as 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)))). Here is an example- 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)))).

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

With 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) we can find Stress in Extreme Compression Surface given Moment Resistance using the formula - 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)))).

Can the Stress in Extreme Compression Surface given Moment Resistance be negative?

No, the Stress in Extreme Compression Surface given Moment Resistance, measured in Pressure cannot be negative.

Which unit is used to measure Stress in Extreme Compression Surface given Moment Resistance?

Stress in Extreme Compression Surface given Moment Resistance is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Stress in Extreme Compression Surface given Moment Resistance can be measured.

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Stress in Extreme Compression Surface given Moment Resistance Formula

Stress in Extreme Compression Surface given Moment Resistance Example

Stress in Extreme Compression Surface given Moment Resistance Solution

Stress in Extreme Compression Surface given Moment Resistance Formula Elements

Other formulas in Doubly Reinforced Rectangular Sections category

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

FAQs on Stress in Extreme Compression Surface given Moment Resistance

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