Problem
A 75 mm × 150 mm beam carries a uniform load wo 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 wo based on shear alone.
Allowable shear parallel to grain = 1.40 MPa
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:
$f_v = \dfrac{3V}{2bd'}\left( \dfrac{d}{d'} \right)^2$
Where:
$d$ = total depth of beam.
$d'$ = actual depth of beam at notch.
Solution
