Transcription of Shear Stress
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Shear StressDue to the presence of the Shear force in beam and the fact thattxy=tyxa horizontal Shear force exists in the beam that tend to forcethe beam fibers to Shear in BeamsThe horizontal Shear per unit length is given byq=VQIwhereV=the Shear force at that section;Q=the first moment ofthe portion of the area (above the horizontal line where the Shear isbeing calculated) about the neutral axis; andI=moment of inertia ofthe cross-sectional area of the beam. The quantityqis also known astheshear Shear Stress Across the WidthAverage Shear Stress across the width is defined astave=VQItwheret=width of the section at that horizontal line. For a narrowrectangular beam witht=b h/4, the Shear Stress varies across thewidth by less than80% Transverse Shear StressFor a narrow rectangular section we can work with the equationt=VQItto calculate Shear Stress at any vertical point in the crosssection.
The nails have F nail = 400 N. If q all is the allowable shear per unit length and s is the spacing between the nails then F nail = q alls) q all = F nail s = 400 N 0.05 m = 8⇥103 N/m Hence, q all = VmaxQ I) Vmax = q allI Q = (8⇥103 N/m)·(14.36⇥106 m4) 102⇥10 6 m3 = 1.126 kN
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