[{"data":1,"prerenderedAt":20},["ShallowReactive",2],{"formula-en-resultant-bending-moment":3},{"formula":4,"related_topics":12,"alternates":17},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},100,"resultant-bending-moment","Resultant Bending Moment","Mb = √(Mx² + My²)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>If mutually perpendicular bending-moment components $M_x$ and $M_y$ act simultaneously at a section, the magnitude of the resultant bending moment is:\u003C\u002Fp>\u003Cp>$$M_b=\\sqrt{M_x^2+M_y^2}.$$\u003C\u002Fp>\u003Cp>For a circular section, whose geometric properties are identical about any centroidal axis in the section plane, the maximum bending normal stress can be calculated as:\u003C\u002Fp>\u003Cp>$$|\\sigma_b|=\\frac{M_b}{W}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$M_x$, $M_y$\u003C\u002Fstrong> — bending-moment components;\u003C\u002Fli>\u003Cli>\u003Cstrong>$M_b$\u003C\u002Fstrong> — resultant bending moment;\u003C\u002Fli>\u003Cli>\u003Cstrong>$W$\u003C\u002Fstrong> — bending section modulus;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\sigma_b$\u003C\u002Fstrong> — bending normal stress.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>For noncircular sections, the orientation of the bending moment and the second moments of area about the corresponding principal axes must generally be considered explicitly.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13],{"id":14,"name":15,"path":16},68,"Combined Bending and Torsion","strength-of-materials\u002Fcombined-loading\u002Fcombined-bending-and-torsion",{"en":18,"uk":19},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fresultant-bending-moment","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fresultant-bending-moment",1787712543622]