Masonry bearing (BS5628:1:2005) - Stress Distribution

Question

How is the stress distribution calculated in the Masonry Bearing calculation?

Answer

The load from the beam is considered to be a concentrated load applied at half the bearing length.  The stress is calculated following fundamental engineering principles in the following three ways, depending on the location of this concentrated load - when the load is eccentric the user can choose from two methods for the stress distribution Option 1 or Option 2.

1. At mid point of the spreader (i.e. spreader is same length as bearing): 
   The stress is calculated as a rectangular distribution
    
2. Eccentric  - Option 1 Triangular:
   The stress is a triangular distribution limited to 3 times the distance the concentrated load is away from the end of the wall.
    
3. Eccentric - Option 2 Similar to beam on elastic foundation:
   The stress varies along the total length of the spreader - the shape of the stress diagram (and hence the peak stress) is dependent on the eccentricity of the concentrated load.
   1. The peak stress is calculated following semi-infinite beam on elastic foundation theory. This is a general theory for calculating the deflection, bending moment and shear stress in a beam supported by an elastic continuum, commonly assumed to act as a "Winkler foundation".  Further details on this theory can be found in any good reference on elastic theory such as Warren C. Young, Roark's Formulas for Stress and Strain, Sixth Edition, McGraw-Hill, New York, 1989.
   2. See also the notes for the Masonry bearing design (EN1996) calculation, which implements a simlilar method to calculate the bearing stress.
   3. Figure 5 on pg 36 of BS 5628-1 shows the shape of the stress diagram for such an elastic distribution, but does not explicitly give its derivation.  It states the distribution of stress "...may be derived from an acceptable elastic theory"
   4. The application of beam on elastic foundation theory in the Masonry Bearing Design calculation follows the method outlined in "Structural design of masonry" 2nd Edition by Andrew Orton, published by Longman 1992.