[{"data":1,"prerenderedAt":24},["ShallowReactive",2],{"formula-en-bending-navier-stress":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},84,"bending-navier-stress","Normal Stress in Simple Bending — Navier Formula","σ = M \u002F W","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For simple bending of a beam within the linear-elastic model, normal stress varies linearly with distance from the neutral axis:\u003C\u002Fp>\u003Cp>$$\\sigma_x(y)=-\\frac{My}{I}.$$\u003C\u002Fp>\u003Cp>The maximum absolute stress at an extreme fiber is:\u003C\u002Fp>\u003Cp>$$|\\sigma_{\\max}|=\\frac{|M|y_{\\max}}{I}=\\frac{|M|}{W},\\qquad W=\\frac{I}{y_{\\max}}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$M$\u003C\u002Fstrong> — bending moment;\u003C\u002Fli>\u003Cli>\u003Cstrong>$I$\u003C\u002Fstrong> — second moment of area about the neutral axis;\u003C\u002Fli>\u003Cli>\u003Cstrong>$y$\u003C\u002Fstrong> — distance from the neutral axis;\u003C\u002Fli>\u003Cli>\u003Cstrong>$y_{\\max}$\u003C\u002Fstrong> — distance to the relevant extreme fiber;\u003C\u002Fli>\u003Cli>\u003Cstrong>$W$\u003C\u002Fstrong> — section modulus.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The sign of $\\sigma_x$ depends on the sign convention for $M$ and $y$; one side of the section is in tension and the other in compression.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17],{"id":14,"name":15,"path":16},61,"Stresses in Bending","strength-of-materials\u002Fbending\u002Fstresses-in-bending",{"id":18,"name":19,"path":20},58,"Bending","strength-of-materials\u002Fbending",{"en":22,"uk":23},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fbending-navier-stress","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fbending-navier-stress",1787712543160]