Moment of Inertia of Transformed Section given Horizontal Shear Range Solution

STEP 0: Pre-Calculation Summary
Formula Used
Moment of Inertia of Transformed Section = (Static Moment*Shear Range)/Horizontal Shear Range
Ih = (Q*Vr)/Sr
This formula uses 4 Variables
Variables Used
Moment of Inertia of Transformed Section - (Measured in Millimeter⁴) - Moment of Inertia of Transformed Section is a particularly important parameter for the analysis of beams and columns.
Static Moment - (Measured in Cubic Millimeter) - Static Moment of transformed compressive concrete area about neutral axis of transformed section.
Shear Range - (Measured in Kilonewton) - The Shear Range here is the difference between minimum and maximum shears at the point due to live load and impact.
Horizontal Shear Range - (Measured in Kilonewton per Millimeter) - The horizontal shear range at the juncture of the slab and beam at point under consideration.
STEP 1: Convert Input(s) to Base Unit
Static Moment: 10 Cubic Millimeter --> 10 Cubic Millimeter No Conversion Required
Shear Range: 80 Kilonewton --> 80 Kilonewton No Conversion Required
Horizontal Shear Range: 6.4 Kilonewton per Millimeter --> 6.4 Kilonewton per Millimeter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ih = (Q*Vr)/Sr --> (10*80)/6.4
Evaluating ... ...
Ih = 125
STEP 3: Convert Result to Output's Unit
1.25E-10 Meter⁴ -->125 Millimeter⁴ (Check conversion here)
FINAL ANSWER
125 Millimeter⁴ <-- Moment of Inertia of Transformed Section
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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12 Shear Range Calculators

Moment of Inertia of Transformed Section given Horizontal Shear Range
Go Moment of Inertia of Transformed Section = (Static Moment*Shear Range)/Horizontal Shear Range
Shear Range due to Live and Impact Load given Horizontal Shear Range
Go Shear Range = (Horizontal Shear Range*Moment of Inertia of Transformed Section)/Static Moment
Static Moment of Transformed Section given Horizontal Shear Range
Go Static Moment = (Horizontal Shear Range*Moment of Inertia of Transformed Section)/Shear Range
Horizontal Shear Range at Juncture of Slab and Beam
Go Horizontal Shear Range = (Shear Range*Static Moment)/Moment of Inertia of Transformed Section
Allowable Horizontal Shear for Welded Studs for 2 Million Cycles
Go Allowable Range of Horizontal Shear = 7.85*(Stud Diameter^2)
Allowable Horizontal Shear for Welded Studs for 100,000 Cycles
Go Allowable Range of Horizontal Shear = 13.0*(Stud Diameter^2)
Allowable Horizontal Shear for Welded Studs for 500,000 Cycles
Go Allowable Range of Horizontal Shear = 10.6*(Stud Diameter^2)
Allowable Horizontal Shear for Individual Connector for over 2 Million Cycles
Go Allowable Range of Horizontal Shear = 2.1*Length of Channel
Allowable Horizontal Shear for Individual Connector for 2 Million Cycles
Go Allowable Range of Horizontal Shear = 2.4*Length of Channel
Allowable Horizontal Shear for Welded Studs for over 2 Million Cycles
Go Allowable Range of Horizontal Shear = 5.5*(Stud Diameter^2)
Allowable Horizontal Shear for Individual Connector for 100,000 Cycles
Go Allowable Range of Horizontal Shear = 4*Length of Channel
Allowable Horizontal Shear for Individual Connector for 500,000 Cycles
Go Allowable Range of Horizontal Shear = 3*Length of Channel

Moment of Inertia of Transformed Section given Horizontal Shear Range Formula

Moment of Inertia of Transformed Section = (Static Moment*Shear Range)/Horizontal Shear Range
Ih = (Q*Vr)/Sr

What is Moment of Inertia?

The moment of inertia about any point or axis is the product of the area and the perpendicular distance between the point or axis to the center of gravity of the area. This is called the first moment of area.

What is Horizontal Shear?

In the plane, a horizontal shear (or shear parallel to the x-axis) is a function that takes a generic point with coordinates to the point; where is a fixed parameter, called the shear factor. The effect of this mapping is to displace every point horizontally by an amount proportionally to its coordinate.

How to Calculate Moment of Inertia of Transformed Section given Horizontal Shear Range?

Moment of Inertia of Transformed Section given Horizontal Shear Range calculator uses Moment of Inertia of Transformed Section = (Static Moment*Shear Range)/Horizontal Shear Range to calculate the Moment of Inertia of Transformed Section, The Moment of Inertia of Transformed Section given Horizontal Shear Range is defined as second moment of area for a composite section using modular ratio. Moment of Inertia of Transformed Section is denoted by Ih symbol.

How to calculate Moment of Inertia of Transformed Section given Horizontal Shear Range using this online calculator? To use this online calculator for Moment of Inertia of Transformed Section given Horizontal Shear Range, enter Static Moment (Q), Shear Range (Vr) & Horizontal Shear Range (Sr) and hit the calculate button. Here is how the Moment of Inertia of Transformed Section given Horizontal Shear Range calculation can be explained with given input values -> 1.3E+14 = (1E-08*80000)/6400000.

FAQ

What is Moment of Inertia of Transformed Section given Horizontal Shear Range?
The Moment of Inertia of Transformed Section given Horizontal Shear Range is defined as second moment of area for a composite section using modular ratio and is represented as Ih = (Q*Vr)/Sr or Moment of Inertia of Transformed Section = (Static Moment*Shear Range)/Horizontal Shear Range. Static Moment of transformed compressive concrete area about neutral axis of transformed section, The Shear Range here is the difference between minimum and maximum shears at the point due to live load and impact & The horizontal shear range at the juncture of the slab and beam at point under consideration.
How to calculate Moment of Inertia of Transformed Section given Horizontal Shear Range?
The Moment of Inertia of Transformed Section given Horizontal Shear Range is defined as second moment of area for a composite section using modular ratio is calculated using Moment of Inertia of Transformed Section = (Static Moment*Shear Range)/Horizontal Shear Range. To calculate Moment of Inertia of Transformed Section given Horizontal Shear Range, you need Static Moment (Q), Shear Range (Vr) & Horizontal Shear Range (Sr). With our tool, you need to enter the respective value for Static Moment, Shear Range & Horizontal Shear Range 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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