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Nominal Shear Strength of Concrete Formula

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The Nominal Shear Strength of Concrete is the capacity of the concrete section to resist the effects of load. Check FAQs

V c = (1.9 \cdot \sqrt{f c} + ((2500 \cdot ρ w) \cdot (\frac{V u \cdot D centroid}{B M}))) \cdot (b w \cdot D centroid)

V_c - Nominal Shear Strength of Concrete?f_c - 28 Day Compressive Strength of Concrete?ρ_w - Reinforcement Ratio of Web Section?V_u - Shear Force in considered Section?D_centroid - Centroidal Distance of Tension Reinforcement?B_M - Bending Moment of Considered Section?b_w - Width of Beam Web?

Nominal Shear Strength of Concrete Example

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Here is how the Nominal Shear Strength of Concrete equation looks like with Values.

Here is how the Nominal Shear Strength of Concrete equation looks like with Units.

Here is how the Nominal Shear Strength of Concrete equation looks like.

71.3871 = (1.9 \cdot \sqrt{15} + ((2500 \cdot 0.08) \cdot (\frac{100.1 \cdot 51.01}{49.5}))) \cdot (50.0001 \cdot 51.01)

71.3871MPa = (1.9 \cdot \sqrt{15MPa} + ((2500 \cdot 0.08) \cdot (\frac{100.1kN \cdot 51.01mm}{49.5kN*m}))) \cdot (50.0001mm \cdot 51.01mm)

71.3871 = (1.9 \cdot \sqrt{15} + ((2500 \cdot 0.08) \cdot (\frac{100.1 \cdot 51.01}{49.5}))) \cdot (50.0001 \cdot 51.01)

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Nominal Shear Strength of Concrete Solution

Follow our step by step solution on how to calculate Nominal Shear Strength of Concrete?

FIRST Step Consider the formula

V c = (1.9 \cdot \sqrt{f c} + ((2500 \cdot ρ w) \cdot (\frac{V u \cdot D centroid}{B M}))) \cdot (b w \cdot D centroid)

Next Step Substitute values of Variables

∴

V c = (1.9 \cdot \sqrt{15MPa} + ((2500 \cdot 0.08) \cdot (\frac{100.1kN \cdot 51.01mm}{49.5kN*m}))) \cdot (50.0001mm \cdot 51.01mm)

Next Step Convert Units

∴

V c = (1.9 \cdot \sqrt{1.5E+7Pa} + ((2500 \cdot 0.08) \cdot (\frac{100.1kN \cdot 51.01mm}{49.5kN*m}))) \cdot (50.0001mm \cdot 51.01mm)

Next Step Prepare to Evaluate

∴

V c = (1.9 \cdot \sqrt{1.5E+7} + ((2500 \cdot 0.08) \cdot (\frac{100.1 \cdot 51.01}{49.5}))) \cdot (50.0001 \cdot 51.01)

Next Step Evaluate

∴

V c = 71387069.3866498Pa

Next Step Convert to Output's Unit

∴

V c = 71.3870693866498MPa

LAST Step Rounding Answer

∴

V c = 71.3871MPa

Nominal Shear Strength of Concrete Formula Elements

Variables

Functions

Nominal Shear Strength of Concrete

The Nominal Shear Strength of Concrete is the capacity of the concrete section to resist the effects of load.

Symbol: V_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

28 Day Compressive Strength of Concrete

28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.

Symbol: f_c

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Reinforcement Ratio of Web Section

The Reinforcement Ratio of Web Section also called a percentage of steel is the representation of the amount of reinforcement in a concrete section.

Symbol: ρ_w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Shear Force in considered Section

Shear force in considered section is the force acting perpendicular to the longitudinal axis of the considered section, say, beam or column etc.

Symbol: V_u

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Centroidal Distance of Tension Reinforcement

The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement.

Symbol: D_centroid

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Bending Moment of Considered Section

Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.

Symbol: B_M

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Width of Beam Web

Width of Beam Web is the distance between the two external points of beam web section.

Symbol: b_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Credits

Creator Image

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Formula and 500+ more formulas!

Verifier Image

Verified by Himanshi Sharma

Bhilai Institute of Technology (BIT), Raipur

Himanshi Sharma has verified this Formula and 800+ more formulas!

Other formulas in Shear Reinforcement category

Go Ultimate Shear Capacity of Beam Section

V n = (V c + V s)

Go Nominal Shear Strength Provided by Reinforcement

V s = V n - V c

See More

How to Evaluate Nominal Shear Strength of Concrete?

Nominal Shear Strength of Concrete evaluator uses Nominal Shear Strength of Concrete = (1.9*sqrt(28 Day Compressive Strength of Concrete)+((2500*Reinforcement Ratio of Web Section)*((Shear Force in considered Section*Centroidal Distance of Tension Reinforcement)/Bending Moment of Considered Section)))*(Width of Beam Web*Centroidal Distance of Tension Reinforcement) to evaluate the Nominal Shear Strength of Concrete, The Nominal Shear Strength of Concrete is defined as the maximum value for shear strength in order to calculate the nominal strength of concrete. Nominal Shear Strength of Concrete is denoted by V_c symbol.

How to evaluate Nominal Shear Strength of Concrete using this online evaluator? To use this online evaluator for Nominal Shear Strength of Concrete, enter 28 Day Compressive Strength of Concrete (f_c), Reinforcement Ratio of Web Section (ρ_w), Shear Force in considered Section (V_u), Centroidal Distance of Tension Reinforcement (D_centroid), Bending Moment of Considered Section (B_M) & Width of Beam Web (b_w) and hit the calculate button.

FAQs on Nominal Shear Strength of Concrete

What is the formula to find Nominal Shear Strength of Concrete?

The formula of Nominal Shear Strength of Concrete is expressed as Nominal Shear Strength of Concrete = (1.9*sqrt(28 Day Compressive Strength of Concrete)+((2500*Reinforcement Ratio of Web Section)*((Shear Force in considered Section*Centroidal Distance of Tension Reinforcement)/Bending Moment of Considered Section)))*(Width of Beam Web*Centroidal Distance of Tension Reinforcement). Here is an example- 1.9E-11 = (1.9*sqrt(15000000)+((2500*0.08)*((100100*0.05101)/49500)))*(0.05000011*0.05101).

How to calculate Nominal Shear Strength of Concrete?

With 28 Day Compressive Strength of Concrete (f_c), Reinforcement Ratio of Web Section (ρ_w), Shear Force in considered Section (V_u), Centroidal Distance of Tension Reinforcement (D_centroid), Bending Moment of Considered Section (B_M) & Width of Beam Web (b_w) we can find Nominal Shear Strength of Concrete using the formula - Nominal Shear Strength of Concrete = (1.9*sqrt(28 Day Compressive Strength of Concrete)+((2500*Reinforcement Ratio of Web Section)*((Shear Force in considered Section*Centroidal Distance of Tension Reinforcement)/Bending Moment of Considered Section)))*(Width of Beam Web*Centroidal Distance of Tension Reinforcement). This formula also uses Square Root (sqrt) function(s).

Can the Nominal Shear Strength of Concrete be negative?

No, the Nominal Shear Strength of Concrete, measured in Pressure cannot be negative.

Which unit is used to measure Nominal Shear Strength of Concrete?

Nominal Shear Strength of Concrete is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Nominal Shear Strength of Concrete can be measured.

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