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Moment Resistance in Compression Formula

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

M R = 0.5 \cdot (f ec \cdot j \cdot W b \cdot (d^{2})) \cdot (K + 2 \cdot m Elastic \cdot ρ' \cdot (1 - (\frac{D}{K \cdot d})))

M_R - Moment Resistance in Compression?f_ec - Stress in Extreme Compression Surface?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?

Moment Resistance in Compression Example

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Here is how the Moment Resistance in Compression equation looks like with Values.

Here is how the Moment Resistance in Compression equation looks like with Units.

Here is how the Moment Resistance in Compression equation looks like.

1.6661 = 0.5 \cdot (10.01 \cdot 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})))

1.6661N*m = 0.5 \cdot (10.01MPa \cdot 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})))

1.6661 = 0.5 \cdot (10.01 \cdot 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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Moment Resistance in Compression Solution

Follow our step by step solution on how to calculate Moment Resistance in Compression?

FIRST Step Consider the formula

M R = 0.5 \cdot (f ec \cdot 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

∴

M R = 0.5 \cdot (10.01MPa \cdot 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

∴

M R = 0.5 \cdot (1E+7Pa \cdot 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

∴

M R = 0.5 \cdot (1E+7 \cdot 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

∴

M R = 1.66613832N*m

LAST Step Rounding Answer

∴

M R = 1.6661N*m

Moment Resistance in Compression Formula Elements

Variables

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

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

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 Moment Resistance in Compression?

Moment Resistance in Compression evaluator uses 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)))) to evaluate the Moment Resistance in Compression, The Moment Resistance in Compression formula calculates the moment by internal forces in a beam under compressive state. Moment Resistance in Compression is denoted by M_R symbol.

How to evaluate Moment Resistance in Compression using this online evaluator? To use this online evaluator for Moment Resistance in Compression, enter Stress in Extreme Compression Surface (f_ec), 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 Moment Resistance in Compression

What is the formula to find Moment Resistance in Compression?

The formula of Moment Resistance in Compression is expressed as 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)))). Here is an example- 1.666138 = 0.5*(10010000*0.8*0.018*(0.005^2))*(0.65+2*0.6*0.6*(1-(0.00201/(0.65*0.005)))).

How to calculate Moment Resistance in Compression?

With Stress in Extreme Compression Surface (f_ec), 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 Moment Resistance in Compression using the formula - 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)))).

Can the Moment Resistance in Compression be negative?

No, the Moment Resistance in Compression, measured in Moment of Force cannot be negative.

Which unit is used to measure Moment Resistance in Compression?

Moment Resistance in Compression is usually measured using the Newton Meter[N*m] for Moment of Force. Kilonewton Meter[N*m], Millinewton Meter[N*m], Micronewton Meter[N*m] are the few other units in which Moment Resistance in Compression can be measured.

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Moment Resistance in Compression Formula

Moment Resistance in Compression Example

Moment Resistance in Compression Solution

Moment Resistance in Compression Formula Elements

Other formulas in Doubly Reinforced Rectangular Sections category

How to Evaluate Moment Resistance in Compression?

FAQs on Moment Resistance in Compression

Variable Name