### SHEAR STRESS IN WOOD AND STEEL BEAMS

**1**Shear at neutral axis of rectangular beam (maximum stress),

**Note:**this is the same formula derived for maximum shear stress before

**2**Shear stress at the bottom of rectangular beam. Note that y= 0 since the centroid of the area above the shear plane (bottom) coincides with the neutral axis of the entire section. Thus Q= Ay = (bd/2) 0 = 0, hence

v = V 0/(I b) = 0 = fv, thus

fv = 0

**Note:**this confirms an intuitive interpretation that suggests zero stress since no fibers below the beam could resist shear

**3**Shear stress at top of rectangular beam. Note A = 0b = 0 since the depth of the shear area above the top of the beam is zero. Thus

Q = Ay = 0 d/2 = 0, hence v = V 0/(I b) = 0 = fv, thus

fv = 0

Note: this, too, confirms an intuitive interpretation that suggests zero stress since no fibers above the beam top could resist shear.

**Shear stress distribution over a rectangular section is parabolic as implied by the formula Q=b(d^2)/8 derived above.**

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**5**Shear stress in a steel beam is minimal in the flanges and parabolic over the web.

The formula v = VQ/(I b) results in a small stress in the flanges since the width b of flanges is much greater than the web thickness. However, for convenience, shear stress in steel beams is computed as “average” by the simplified formula:

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