# Example 01: Safe Uniform Load for a Beam that was Notched at the Tension Fibers at Supports

**Problem**

A 75 mm × 150 mm beam carries a uniform load *w _{o}* over the entire span of 1.2 m. Square notches 25 mm deep are provided at the bottom of the beam at the supports. Calculate the safe value of

*w*based on shear alone.

_{o}Allowable shear normal to grain = 1.85 MPa

Use the NSCP 2010 provision below:

**NSCP 2010 Section 616.4: Horizontal Shear in Notched Beams**

When rectangular-shaped girder, beams or joists are notched at points of support on the tension side, they shall meet the design requirements of that section in bending and in shear. The horizontal shear stress at such point shall be calculated by:

Where:

$d'$ = actual depth of beam at notch.

**Solution**

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$V = 0.6w_o ~ \text{kN}$

$F_v = f_v$ ← Use *F _{v}* = Allowable shear parallel to grain

$1.40 = \dfrac{3V}{2bd'}\left( \dfrac{d}{d'} \right)^2$

$1.40 = \dfrac{3(0.6w_o)}{2(75)(275)}\left( \dfrac{300}{275} \right)^2$

$w_o = 26.96 ~ \text{kN/m}$ *answer*