Ultimate Shear Strength for Welded Studs Calculator

✖Stud Diameter is the diameter of the Stud used.ⓘ Stud Diameter [d_stud]			+10% -10%
✖Modulus elasticity of concrete is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus Elasticity of Concrete [E]			+10% -10%
✖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%

✖Ultimate Shear Connector Stress is the maximum strength in shear.ⓘ Ultimate Shear Strength for Welded Studs [S_ultimate]

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Formula

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Ultimate Shear Strength for Welded Studs

Formula

`"S"_{"ultimate"} = 0.4*"d"_{"stud"}*"d"_{"stud"}*sqrt("E"*"f"_{"c"})`

Example

`"20.06622kN"=0.4*"64mm"*"64mm"*sqrt("10.0MPa"*"15MPa")`

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Ultimate Shear Strength for Welded Studs Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ultimate Shear Connector Stress = 0.4*Stud Diameter*Stud Diameter*sqrt(Modulus Elasticity of Concrete*28 Day Compressive Strength of Concrete)
S_ultimate = 0.4*d_stud*d_stud*sqrt(E*f_c)
This formula uses 1 Functions, 4 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

Ultimate Shear Connector Stress - (Measured in Newton) - Ultimate Shear Connector Stress is the maximum strength in shear.
Stud Diameter - (Measured in Meter) - Stud Diameter is the diameter of the Stud used.
Modulus Elasticity of Concrete - (Measured in Pascal) - Modulus elasticity of concrete is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
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.

STEP 1: Convert Input(s) to Base Unit

Stud Diameter: 64 Millimeter --> 0.064 Meter (Check conversion here)
Modulus Elasticity of Concrete: 10 Megapascal --> 10000000 Pascal (Check conversion here)
28 Day Compressive Strength of Concrete: 15 Megapascal --> 15000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_ultimate = 0.4*d_stud*d_stud*sqrt(E*f_c) --> 0.4*0.064*0.064*sqrt(10000000*15000000)

Evaluating ... ...

S_ultimate = 20066.2199728798

STEP 3: Convert Result to Output's Unit

20066.2199728798 Newton -->20.0662199728798 Kilonewton (Check conversion here)

FINAL ANSWER

20.0662199728798 ≈ 20.06622 Kilonewton <-- Ultimate Shear Connector Stress

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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Indian Institute of Technology (IIT), Bombay

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< 9 Ultimate Shear Strength of Connectors in Bridges Calculators

Channel Web Thickness given Ultimate Shear Connector Strength for Channels

Go Web Thickness = ((Ultimate Shear Connector Stress/(17.4*Channel Length*sqrt(28 Day Compressive Strength of Concrete)))-Average Flange Thickness)*2

Channel Length given Ultimate Shear Connector Strength for Channels

Go Channel Length = Ultimate Shear Connector Stress/(17.4*sqrt(28 Day Compressive Strength of Concrete)*(Average Flange Thickness+Web Thickness/2))

Ultimate Shear Strength for Welded Studs

Go Ultimate Shear Connector Stress = 0.4*Stud Diameter*Stud Diameter*sqrt(Modulus Elasticity of Concrete*28 Day Compressive Strength of Concrete)

Diameter of Connector given Ultimate Shear Connector Strength for Welded Studs

Go Stud Diameter = sqrt(Ultimate Shear Connector Stress/(0.4*sqrt(Modulus Elasticity of Concrete*28 Day Compressive Strength of Concrete)))

Elastic Modulus of Concrete given Ultimate Shear Connector Strength for Welded Studs

Go Modulus Elasticity of Concrete = (((Ultimate Shear Connector Stress/(0.4*Stud Diameter*Stud Diameter))^2)/28 Day Compressive Strength of Concrete)

Average Channel Flange Thickness given Ultimate Shear Connector Strength for Channels

Go Average Flange Thickness = Ultimate Shear Connector Stress/(17.4*Channel Length*((28 Day Compressive Strength of Concrete)^0.5))-Web Thickness/2

28-day Compressive Strength given Ultimate Shear Connector Strength for Welded Studs

Go 28 Day Compressive Strength of Concrete = ((Ultimate Shear Connector Stress/(0.4*Stud Diameter*Stud Diameter))^2)/Modulus Elasticity of Concrete

Ultimate Shear Connector Strength for Channels

Go Ultimate Shear Connector Stress = 17.4*Channel Length*((28 Day Compressive Strength of Concrete)^0.5)*(Average Flange Thickness+Web Thickness/2)

28-day Compressive Strength of Concrete given Ultimate Shear Connector Strength for Channels

Go 28 Day Compressive Strength of Concrete = (Ultimate Shear Connector Stress/(17.4*Channel Length*(Average Flange Thickness+Web Thickness/2)))^2