Structural Analysis of a Beam

The process used for determining the adequacy of a wood, steel, or even a concrete beam is essentially the same. Once a beam has been selected the method is as follows:

·         Determine the loads

·         Calculate the stresses

·         Check the allowable stresses against the actual stresses.

Determine the Loads
The first step in the structural analysis of a beam is determining the amount of load, or weight the beam is going to support.  There are two major categories of loads:

Live Loads – A live load is a type of load that is temporarily placed on a structure (i.e. loads from snow, wind, vehicles, etc.).  The magnitude of live loads will be defined or referenced in a local building code.

Dead Loads – are loads permanently attached to a structure (i.e. loads from building materials, furniture, etc.).  Sometimes the weights of materials are exactly known and can be added together to determine the total dead load.  More often the dead load is assumed and given an approximate weight.

Calculating the Stresses
There are two types of stresses that are typically calculated when performing a beam design: bending stress and shear stress.  A more complete definition of both bending stress and shear stress can be found here.  In order to calculate the bending and shear stresses it will be first necessary to calculate the maximum bending moment and maximum shear that occurs in the beam.

The maximum moment and shear will most likely occur at different locations, and the process used to determine their value will be defined in a separate article.  The other two pieces of information needed to determine the stresses will be the section modulus and cross sectional area of the beam being used.  The section modulus and cross sectional area can be calculated, or in most cases can be looked up in tables (like in the National Design Specification (NDS) for wood beams, or the AISC Steel Manual for steel beams).  Once all the information has been tabulated the following equations can be used to determine the nominal maximum bending stress and nominal maximum shear stress:

Compare Actual Stresses against Allowable Stresses
In most cases the allowable stresses are tabulated in a design manual of some sorts (like in the NDS for wood, or the AISC Steel Manual for steel).  Once the allowable stresses have been located determining the adequacy of a beam is simply a matter of comparing the actual stresses to the allowable stresses.  So, a beam is adequate if the following is true:

Other Considerations
One major consideration not discussed in this article is that of deflection, or sag in the beam.  A beam might be strong enough structurally, but might deflect so much that it effects the actual performance of the beam.  Deflection is a calculation that is very important and will be addressed in a separate article.

Another consideration when doing any kind of beam design is that of using structural design software.  There are several different engineering design software packages available for beams, columns, or foundation design.  StruCalc, Enercalc, Risa, and BeamChek are a few examples of those structural design software packages.