[{"data":1,"prerenderedAt":24},["ShallowReactive",2],{"formula-en-beam-shear-zhuravsky":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},85,"beam-shear-zhuravsky","Beam Shear Stress — Zhuravsky Formula","τ = QS \u002F (Ib)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For transverse bending, the shear stress at a point of the cross-section is determined by the Zhuravsky formula:\u003C\u002Fp>\u003Cp>$$\\tau=\\frac{QS}{Ib}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$Q$\u003C\u002Fstrong> — shear force at the section;\u003C\u002Fli>\u003Cli>\u003Cstrong>$S$\u003C\u002Fstrong> — first moment of the cut-off part of the area about the neutral axis;\u003C\u002Fli>\u003Cli>\u003Cstrong>$I$\u003C\u002Fstrong> — second moment of area of the entire section about the neutral axis;\u003C\u002Fli>\u003Cli>\u003Cstrong>$b$\u003C\u002Fstrong> — local section width at the level where $\\tau$ is evaluated.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>At a free upper or lower boundary of a solid section, $S$ tends to zero and therefore $\\tau$ is zero. For a rectangular section, the maximum shear stress occurs at the neutral axis.\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\u002Fbeam-shear-zhuravsky","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fbeam-shear-zhuravsky",1787712543168]