Beam Design Formulas with Shear and Moment Diagrams by American Forest and Paper Association.Engineers Edge structural beam bending equations.Understanding Wood: A Craftsman’s Guide to Wood Technology by Bruce Hoadley.Roark’s Formulas for Stress and Strain by Warren Young.Some references that I found useful include: The Sagulator employs established engineering formulas for calculating beam deflection. If shelf depth is doubled, deflection is cut in half.If shelf thickness is doubled, deflection is reduced to one-eighth.If shelf span is doubled, deflection is eight times greater.If shelf span is increased by one-fourth, deflection doubles.If shelf span is reduced by one-fifth, stiffness is roughly doubled (deflection is halved).The “thickness” of the edge strip will be the same direction as “depth” of the shelf, and the “width” of the strip will be the same direction as “thickness” of the shelf. An optional edging strip can be specified to stiffen the shelf. If using a hardwood ply with a composite core – veneer center plies, with relatively thick MDF outer layers under the face veneers, select MDF for the shelf material.ġ0. The melamine facing has a negligible effect on the stiffness of the shelving material.ĩ. If your melamine sheet has a different particleboard grade (M-2, M-3, etc), select that grade of particleboard in the pull-down menu. The Melamine material choice assumes M-1 grade particleboard with a melamine resin/paper facing. The shelf span parameter represents the beam span.Ĩ. Because beams are typically positioned on edge, use “thickness” to represent beam depth and “depth” to represent the thickness of the beam. This calculator can also be used to measure beam deflection. If you’re using common construction lumber, a 1 inch board is actually 3/4″ and a 2 inch board is 1-1/2″ thick.ħ. The shelf thickness value is actual thickness, not nominal. If you use fractions, just make sure to leave a space between any leading whole number and the fraction.Ħ. You can enter fractional dimensions as decimals (8.75), or as conventional fractions (8 3/4). Fine Woodworking magazines can weigh up to 40 pounds per foot.ĥ. A value of 35 pounds per running foot is used by some for library shelving. A fully loaded bookshelf weighs 20-40 pounds (9-18 kg) per running foot, or 60-120 pounds (27-54 kg) for a 3′ wide shelf. Many bookshelves have a depth of 8″ to 12″, a width of 24″ to 36″, and a thickness of 3/4″ to 1″.Ĥ. ![]() ![]() Once you have a maximum allowable sag figure in mind, you can design your shelf by tweaking the material types and dimensions. Thus, a suggested target for allowable sag is 0.02″ per foot or less.ģ. As an engineering rule of thumb, wood beams/shelves will sag an additional 50% over time beyond the initial deflection induced by the load. Expect some real-life variation from the calculated results.Ģ.The eye will notice a deflection of 1/32″ (0.03″) per running foot, or 3/32″ (0.09″) for a 3′ wide bookshelf. The deflection calculations use average wood stiffness properties of clear, straight-grained samples measured in controlled laboratory conditions (mainly from the U.S. Target sag: 0.02 in per foot (1.7 mm per m) or lessġ. Shelf Characteristicsįixed (attached to sides) Floating (not attached) You can also specify an edging strip to further stiffen the shelf. The Sagulator helps you design shelves by calculating shelf sag (deflection) given type of shelf material, shelf load, load distribution, dimensions, and method of attachment.
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