VERTICAL SHEAR IN BEAMS

Vertical shear stress distribution in beams:

Remember that shear acts normal (perpendicular) to the beam. A simply supported beam with a concentrated load in the center of so many (say 10) pounds carries the load equally to the two supports, each taking half. Therefore, the vertical shear “up” (+) at the left support is one-half 10=5, and this shear is the same along the beam until the center. At the center, the “up” shear is decreased by the load 10 to equal 5 “down” (-) on the remaining portion of the beam over to the right support. Therefore, a beam carrying a concentrated load has large total shear at the load point.

Now let’s change the concentrated load into a uniform load spread along the beam. What happens to the shear stress in the beam? The load on the supports is the same, (the reaction), but now the shear stress decreases uniformly to zero at center span, where its “sign” changes and then its magnitude increases to the support.

Therefore the shear in a uniformly loaded simple span beam is zero at mid-span, but maximum at the supports. This is more significant information for deciding where (or if) to poke holes in the beam.

(Beams are also subject to horizontal shear developed by the opposing tension and compression forces. The shear plane is located at the neutral axis. Review of this stress must be made by a design professional.)

Summary of important stuff for placing and modifying beams:

For the most part, the beams we erect are considered to be uniformly loaded and simple span, in which the middle third of the span is the most critical area for moment stress, and the outer thirds are the most critical for vertical shear stress.

Beams should not be cut on the tension side in the center third.

The web should not be cut near the supports or load points of beams carrying heavy shear.

The web may be cut through at the neutral axis at mid-span.

Sawn lumber having loose knots, check, splits, or damage should be placed so these defects do not compromise strength.

Continuous beams have moment reversal over the interior supports. That is, the top flange is in tension there. Tension also appears in the top flange at the support in cantilevered beams. Rules for making cuts or holes in beams should be recognized in these situations.

Plywood, when loaded in beam action (as in roof sheathing or flooring) must be laid so that the face grain is perpendicular (normal) to the supporting beams. This placement provides the stiffest resistance to bending. Plywood is very weak in bending across the face grain. It is a bad mistake to lay up plywood improperly.