A carpenter is using wood dowels to secure three wood members to form a truss. The truss will span 6 ft and must hold a snow load of 50 lb/ft². The dowels will experience a shear stress and the dowels will push against the truss member causing a bearing stress.

What is known:

• Each truss member is a 1x2 wood board (nominal size 1" x 2"). Actual dimensions are 3/4 inch by 1 1/2 inch.
• Trusses are spaced every 2 ft along the roof.
• The dowel is made from Douglas Fir wood and has a diameter of 1/2 inch.
• Wood dowel is centered on the wood truss members.

What is the shearing stress in the 1/2" dowel at the top of the wall due to the load in the top truss member? Also, what is the bearing stress in the top truss member at the top of the wall?

• First, find the load in the top truss member using basic static equilibrium.
• Use shear stress equation
       τ = V/A
• Use bearing stress equation
       σ_b = P/A_b