This article will attempt to provide a clearer understanding of beam deflection formulas and their use. Simply stated these formulas show how much beams will change their shape and position under a non-destructive load. Non-destructive loads are loads that do not cause permanent change to the size and shape of the beam. All of the following use definitions and formulas from the 7th edition of Baumeister and Marks’ “Standard Handbook for Mechanical Engineers”.
Before you use any of the beam deflection formulas you must know seven things. You must first know what material is used to make the beam. You can then determine the E found in beam deflection formulas. E is the symbol that represents Young’s Modulus, a value that describes the elastic nature of a material.
Next, you need to know how much load you expect on the beam. That load is defined as ‘P’ in beam deflection formulas. Then you need to know whether that load is located at a point or distributed evenly along the beam. If the load is at a point, you need to know how far that point is from the support(s).
The location of the point load is ‘l’ in beam deflection formulas. When the load is evenly distributed ‘l’ is either at the unsupported end of the beam or in the middle of the beam that is supported at both ends. You also need to know the direction of the applied load in relation to your beam.
Now you need to know something about the shape of the cross section of your beam. All such cross sections fall into either rectangular cross sections (square or rectangular solids, square or rectangular tubes, and other shapes – ‘I’, ‘H’, ‘L’, ‘T’, etc) or rounds (circular or elliptical or oval solids or tubes).
The two geometric values ‘b’ and ‘h’ are used to define the largest continuous size of the cross section relative to the direction of your beam load ‘P’. You need to know how large are each of those values in your beam.
The value ‘b’ is the cross section size that is perpendicular to the direction of beam deflection load ‘P’. The value ‘h’ is the cross section size that lies parallel to the direction of beam deflection load ‘P’.
You will find determining the beam deflection using the Baumeister and Marks handbook will be straightforward. The various formula needed are found on pages 5-49 through 5-51 of that handbook. Other handbooks or texts use similar coding for the same values.
Simply apply the above definitions to the value symbols of whatever book you choose. Then make the beam deflection calculation with your calculator and the beam deflection formula you choose for your beam.