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Weld Polar Area Area Momen Momentt of Inert Inertia ia Calculat Calculation ion for for Weldin Welding g Joint Joint
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Determining the Moment of Inertia Equation for Rectrangular Fillet Weld
Weld design calculation, as discussed in the previous weld sizing article, article , requires determining the moment of inertia equations of the whole fillet weld. We will discuss the steps required for calculating the area moment of inertia as well as the polar moment of inertia for the welding joint of joint of the previous article which has a rectangular shaped joint like below:
Determining Determining Moment of Inertia Equation E xample
Where, a = 150 mm b = 100 mm
Little theory: The area or the second moment of inertia of a planer cross section of a beam define the beam’s ability to withstand the bending and torsional shear stress. The area moment of inertia of a composite section can be calculated by adding/subtracting adding/subtracting the sub-areas. The area moment of inertia about Z axis of a planer area laid in XY plane is called polar moment of inertia (Jz). The polar moment of inertia (Jz) can be found by adding the area moment of inertia about the X axis (Ix) and that about the Y axis (Iy) or Jz=Ix+Iy. Jz=Ix+Iy .
Steps for calculating the area and polar moment of inertia equations of the above fillet weld joint: The area moment of inertia about the X and the Y axis are calculated by subtracting the second moment of inertia values of the inner rectangular area from that of the outer rectangular area. Finally, the polar or torsional torsional moment moment of inertia (Jz ) is calculated by summing up the Ix and Iy.
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Weld Polar Area Moment of Inertia Calculation for Welding Joint
Step-1: Calculating Ix: Ix = (Ix of the outer rectangle) – (Ix of the inner rectangle) = [a*b3 /12] – [(a-2)*(b-2)3 /12]
Putting, a=150 and b=100
Ix = 12500000 – 11608034.66 = 891965.34 mm 3
Step-2: Calculating Iy: Iy = (Iy of the outer rectangle) – (Iy of the inner rectangle) = [b*a3 /12] – [(b-2)*(a-2)3 /12]
Putting, a=150 and b=100
Ix = 28125000 – 26474634.66 =1650365.34 mm 3
Step-3: Calculating Jz:
Jz = Ix + Iy = 891965.34 + 1650365.34 = 2542330.68 mm 3
About Shibashis Ghosh Shibashis is a mechanical design engineer by profession and writer/blogger by passion. He has worked in various design projects in automobile, power plant an d heavy e arth moving equipment domain since 2005. In his spare time apart from maintaining this blog, he enjoy investing time building his first RC plane Read More>> Find more about me on:
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Weld Polar Area Moment of Inertia Calculation for Welding Joint
February 24, 2013 at 8:22 pm (UTC 5.5) Shouldn’t the units be in mm^4?? (mm)^3 * mm = mm^4
2. MechGuru
February 25, 2013 at 7:45 pm (UTC 5.5) You are right, the units should be mm^4 instead of mm^3. Thanks for pointing it out, i will correct it soon.
3. Janco Viljoen
August 5, 2013 at 12:16 am (UTC 5.5) is it allowed to add different section of moment of inertia of fillet weld.
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Weld Polar Area Moment of Inertia Calculation for Welding Joint
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