Eiruvin 1:3

The beam across an alley’s entrance must be wide enough to support half a brick of three handbreadths (about 4.5 inches). It is sufficient if the beam is a tefach wide (about 3 inches – only 2/3 the width of the brick) because the brick can overhang on either side.

Eiruvin 1:4

The beam must be both wide enough and strong enough to support the half-brick of three handbreadths; Rabbi Yehuda says it must be wide enough but it need not be strong enough.