Shear stress is, like any stress
measurement, a ratio
of a force
to an area
. Specifically, shear stress
occurs when a force
acts in the plane
of the surface
in question. Consider, for example, taking two 2x4
's (of lumber, that is) and lining one up on top of the other. Let them overlap
by several inches, and drill a hole
down through both board
s. Place a bolt
in the hole, and tighten a nut
on the end of the bolt
. You now should have two 2x4's lashed
together, like so:
V <--- |XXXX| | <- top piece of wood
| |XXXX| ----> V
bottom piece -> | |XXXX|
|_/_/| <- bolt
Take one end, and hand the other end to your friend. Pull. Have a tug of war. The force you're applying to either board is labeled 'V', above. Throw your friend off a cliff, and hold onto the board. Make sure he holds on to the other end as well. The bolt will now be the only thing preventing the two boards from shearing apart. If your friend weighs 200lbs. (this is 'V'), and the bolt has a cross-sectional area of 1 square inch, then the cross-sectional area of the bolt is experiencing a shear stress of 200 lbs/in2 (psi). This is because there is a 200lb. force acting in the plane of the cross-section of the bolt, which has an area of 1 in2. We're assuming that the stress is equally distributed across the surface area of the bolt. If the maximum shear stress of the bolt's material exceeds 200psi, the bolt will hold (at least, the mode of failure won't be shear stress in this plane). You did use a steel bolt, didn't you?
It is worth noting that shear stress is measured as an order 2 tensor, since it takes both a force and an area to define it, both of which are order 1 tensors (vectors). Materials are particularly susceptible to shear stress failure if they have an axis along which they're primarily composed of 'layers'. Examples include graphite and wood.
You did check the direction of the wood grain before bolting the boards together, right?