[{"data":1,"prerenderedAt":24},["ShallowReactive",2],{"formula-en-circular-shaft-polar-properties":3},{"formula":4,"related_topics":12,"alternates":21},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},82,"circular-shaft-polar-properties","Polar Properties of Solid and Hollow Circular Sections","Jp = πd⁴ \u002F 32","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For a solid circular section of diameter $d$:\u003C\u002Fp>\u003Cp>$$J_p=\\frac{\\pi d^4}{32},\\qquad W_p=\\frac{J_p}{d\u002F2}=\\frac{\\pi d^3}{16}.$$\u003C\u002Fp>\u003Cp>For a hollow circular section with outer diameter $D$ and inner diameter $d$:\u003C\u002Fp>\u003Cp>$$J_p=\\frac{\\pi(D^4-d^4)}{32},\\qquad W_p=\\frac{J_p}{D\u002F2}=\\frac{\\pi(D^4-d^4)}{16D}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$J_p$\u003C\u002Fstrong> — polar second moment of area;\u003C\u002Fli>\u003Cli>\u003Cstrong>$W_p$\u003C\u002Fstrong> — polar section modulus;\u003C\u002Fli>\u003Cli>\u003Cstrong>$D$, $d$\u003C\u002Fstrong> — section diameters.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The calculator below is for a solid circular section.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17],{"id":14,"name":15,"path":16},56,"Torsion of Solid and Hollow Circular Shafts","strength-of-materials\u002Fshear-and-torsion\u002Ftorsion-of-shafts",{"id":18,"name":19,"path":20},57,"Design of Helical Springs","strength-of-materials\u002Fshear-and-torsion\u002Fdesign-of-helical-springs",{"en":22,"uk":23},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fcircular-shaft-polar-properties","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fcircular-shaft-polar-properties",1787712544183]