Nominal Shear Strength of Concrete Calculator

✖28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.ⓘ 28 Day Compressive Strength of Concrete [f_c]			+10% -10%
✖The Reinforcement Ratio of Web Section also called a percentage of steel is the representation of the amount of reinforcement in a concrete section.ⓘ Reinforcement Ratio of Web Section [ρ_w]			+10% -10%
✖Shear force in considered section is the force acting perpendicular to the longitudinal axis of the considered section, say, beam or column etc.ⓘ Shear Force in considered Section [V_u]			+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%
✖Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.ⓘ Bending Moment of Considered Section [B_M]			+10% -10%
✖Width of Beam Web is the distance between the two external points of beam web section.ⓘ Width of Beam Web [b_w]			+10% -10%

✖The Nominal Shear Strength of Concrete is the capacity of the concrete section to resist the effects of load.ⓘ Nominal Shear Strength of Concrete [V_c]

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Formula

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Nominal Shear Strength of Concrete

Formula

`"V"_{"c"} = (1.9*sqrt("f"_{"c"})+((2500*"ρ"_{"w"})*(("V"_{"u"}*"D"_{"centroid"})/"B"_{"M"})))*("b"_{"w"}*"D"_{"centroid"})`

Example

`"71.38707MPa"=(1.9*sqrt("15MPa")+((2500*"0.08")*(("100.1kN"*"51.01mm")/"49.5kN*m")))*("50.00011mm"*"51.01mm")`

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Download Design for Beams and Ultimate Strength for Rectangular Beams with Tension Reinforcement Formulas PDF

Nominal Shear Strength of Concrete Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V_c = (1.9*sqrt(f_c)+((2500*ρ_w)*((V_u*D_centroid)/B_M)))*(b_w*D_centroid)
This formula uses 1 Functions, 7 Variables

Functions Used

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., sqrt(Number)

Variables Used

Nominal Shear Strength of Concrete - (Measured in Pascal) - The Nominal Shear Strength of Concrete is the capacity of the concrete section to resist the effects of load.
28 Day Compressive Strength of Concrete - (Measured in Pascal) - 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it.
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.
Shear Force in considered Section - (Measured in Kilonewton) - Shear force in considered section is the force acting perpendicular to the longitudinal axis of the considered section, say, beam or column etc.
Centroidal Distance of Tension Reinforcement - (Measured in Millimeter) - The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement.
Bending Moment of Considered Section - (Measured in Kilonewton Meter) - Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section.
Width of Beam Web - (Measured in Millimeter) - Width of Beam Web is the distance between the two external points of beam web section.

STEP 1: Convert Input(s) to Base Unit

28 Day Compressive Strength of Concrete: 15 Megapascal --> 15000000 Pascal (Check conversion here)
Reinforcement Ratio of Web Section: 0.08 --> No Conversion Required
Shear Force in considered Section: 100.1 Kilonewton --> 100.1 Kilonewton No Conversion Required
Centroidal Distance of Tension Reinforcement: 51.01 Millimeter --> 51.01 Millimeter No Conversion Required
Bending Moment of Considered Section: 49.5 Kilonewton Meter --> 49.5 Kilonewton Meter No Conversion Required
Width of Beam Web: 50.00011 Millimeter --> 50.00011 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_c = (1.9*sqrt(f_c)+((2500*ρ_w)*((V_u*D_centroid)/B_M)))*(b_w*D_centroid) --> (1.9*sqrt(15000000)+((2500*0.08)*((100.1*51.01)/49.5)))*(50.00011*51.01)

Evaluating ... ...

V_c = 71387069.3866498

STEP 3: Convert Result to Output's Unit

71387069.3866498 Pascal -->71.3870693866498 Megapascal (Check conversion here)

FINAL ANSWER

71.3870693866498 ≈ 71.38707 Megapascal <-- Nominal Shear Strength of Concrete

(Calculation completed in 00.020 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Bhilai Institute of Technology (BIT), Raipur

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< 12 Shear Reinforcement Calculators

Nominal Shear Strength of Concrete

Go 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)

Stirrup Area given Stirrup Spacing in Practical Design

Go Stirrup Area = (Stirrup Spacing)*(Design of Shear Stress-(2*Capacity Reduction Factor*sqrt(28 Day Compressive Strength of Concrete)*Effective Depth of Beam*Breadth of Web))/(Capacity Reduction Factor*Yield Strength of Reinforcement*Effective Depth of Beam)

Stirrup Spacing for Practical Design

Go Stirrup Spacing = (Stirrup Area*Capacity Reduction Factor*Yield Strength of Steel*Effective Depth of Beam)/((Design of Shear Stress)-((2*Capacity Reduction Factor)*sqrt(28 Day Compressive Strength of Concrete)*Breadth of Web*Effective Depth of Beam))

Stirrups area for Inclined Stirrups

Go Stirrup Area = (Strength of Shear Reinforcement*Stirrup Spacing)/((sin(Angle at which Stirrup is inclined)+cos(Angle at which Stirrup is inclined))*Yield Strength of Reinforcement*Effective Depth of Beam)

Area of Steel Required in Vertical Stirrups

Go Area of Steel required = (Nominal Shear Strength by Reinforcement*Stirrup Spacing)/(Yield Strength of Steel*Centroidal Distance of Tension Reinforcement)

Stirrup Area given Support Angle

Go Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined)

Nominal Reinforcement Shear Strength for Stirrup Area with Support Angle

Go Nominal Shear Strength by Reinforcement = Stirrup Area*Yield Strength of Steel*sin(Angle at which Stirrup is inclined)

Bar Diameter given Development Length for Hooked Bar

Go Bar Diameter = ((Development Length)*(sqrt(28 Day Compressive Strength of Concrete)))/1200

Development Length for Hooked Bar

Go Development Length = (1200*Bar Diameter)/sqrt(28 Day Compressive Strength of Concrete)

Ultimate Shear Capacity of Beam Section

Go Ultimate Shear Capacity = (Nominal Shear Strength of Concrete+Nominal Shear Strength by Reinforcement)

Nominal Shear Strength Provided by Reinforcement

Go Nominal Shear Strength by Reinforcement = Ultimate Shear Capacity-Nominal Shear Strength of Concrete

28 Day Concrete Compressive Strength given Development Length for Hooked Bar

Go 28 Day Compressive Strength of Concrete = ((1200*Bar Diameter)/(Development Length))^2

Nominal Shear Strength of Concrete Formula

Why is it important to Calculate the Shear Strength of Concrete?

If in case the shear force acting on the section is greater than the nominal strength of concrete, Vc, then extra shear reinforcement must be given, as stirrups.

How to Calculate Nominal Shear Strength of Concrete?

Nominal Shear Strength of Concrete calculator 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 calculate 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 calculate Nominal Shear Strength of Concrete using this online calculator? To use this online calculator 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. Here is how the Nominal Shear Strength of Concrete calculation can be explained with given input values -> 1.9E-11 = (1.9*sqrt(15000000)+((2500*0.08)*((100100*0.05101)/49500)))*(0.05000011*0.05101).

FAQ

What is 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 and is represented as V_c = (1.9*sqrt(f_c)+((2500*ρ_w)*((V_u*D_centroid)/B_M)))*(b_w*D_centroid) or 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). 28 Day Compressive Strength of Concrete is defined as the strength of the concrete after 28 days of using it, The Reinforcement Ratio of Web Section also called a percentage of steel is the representation of the amount of reinforcement in a concrete section, Shear force in considered section is the force acting perpendicular to the longitudinal axis of the considered section, say, beam or column etc, The Centroidal Distance of Tension Reinforcement is the distance measured from external fiber to centroid of tension reinforcement, Bending Moment of Considered Section is defined as the sum of moment of all forces acting on one side of the beam or section & Width of Beam Web is the distance between the two external points of beam web section.

How to calculate 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 is calculated using 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 calculate Nominal Shear Strength of Concrete, you need 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). With our tool, you need to enter the respective value for 28 Day Compressive Strength of Concrete, Reinforcement Ratio of Web Section, Shear Force in considered Section, Centroidal Distance of Tension Reinforcement, Bending Moment of Considered Section & Width of Beam Web 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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