[{"data":1,"prerenderedAt":28},["ShallowReactive",2],{"formula-en-circular-shaft-torsion":3},{"formula":4,"related_topics":12,"alternates":25},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},81,"circular-shaft-torsion","Stress and Angle of Twist of a Circular Shaft","φ = TL \u002F (GJp)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For a straight solid or hollow circular shaft under elastic torsion:\u003C\u002Fp>\u003Cp>$$\\tau(\\rho)=\\frac{T\\rho}{J_p},\\qquad \\tau_{\\max}=\\frac{T}{W_p}.$$\u003C\u002Fp>\u003Cp>If $T$, $G$, and $J_p$ are constant over a segment, the angle of twist is:\u003C\u002Fp>\u003Cp>$$\\varphi=\\frac{TL}{GJ_p}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$T$\u003C\u002Fstrong> — torque;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\rho$\u003C\u002Fstrong> — radial distance from the shaft axis;\u003C\u002Fli>\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>$G$\u003C\u002Fstrong> — shear modulus;\u003C\u002Fli>\u003Cli>\u003Cstrong>$L$\u003C\u002Fstrong> — segment length;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\varphi$\u003C\u002Fstrong> — angle of twist, rad.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>For a stepped shaft, the total twist is the algebraic sum $\\varphi=\\sum_i T_iL_i\u002F(G_iJ_{p,i})$.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17,21],{"id":14,"name":15,"path":16},54,"Shear and Torsion","strength-of-materials\u002Fshear-and-torsion",{"id":18,"name":19,"path":20},56,"Torsion of Solid and Hollow Circular Shafts","strength-of-materials\u002Fshear-and-torsion\u002Ftorsion-of-shafts",{"id":22,"name":23,"path":24},118,"Power Transmission by Shafts","strength-of-materials\u002Fshear-and-torsion\u002Fpower-transmission-by-shafts",{"en":26,"uk":27},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fcircular-shaft-torsion","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fcircular-shaft-torsion",1787712543223]