Straw Bale Construction/Characteristics/Structural properties
Limits to structural strength 
Load-bearing straw-bale walls are typically used only in single-storey or occasionally double-storey structures. A dug foundation (basement) is uncommon.
An all-straw vaulted building was designed and built in Joshua Tree, California, and greatly exceeded the structural requirements for this highly active seismic zone.
Post and beam straw-bale structures have been used for buildings as large as 14,000 square feet (1,300 m²) and even for a United States Post Office, in Corrales, NM .
UK Structural Design of Loadbearing Straw Bale Buildings 
In the UK there are currently two main ways of building with straw: onsite or prefabricated. In both cases the straw is covered by an earth or lime render, note NEVER a cement render!
In the UK the recommended minimum density for a straw bale is 110kg/m^3 this is to ensure a good bond between the straw and render by improving the dimensional stability of the straw.
The below is based on the Natural Building Materials lecture series given at the University of Bath (BRE Centre for Innovative Construction Materials)
Traditional Construction 
Vertical Load Capacity
Current practise is to ignore the strength of the straw and only consider the strength of the render. Recent testing at the University of Bath has shown that the render more than any other variable affects strength and stiffness.
Consider a typical wall section for a one-storey building that uses standard two string bales laid flat (450mm) and 35mm render internally and externally. A timber base and header plate are positioned to ensure uniform load distribution.
Assume that there is sufficient composite behaviour that the render will be restrained from buckling by the straw, the wall is plumb and the load is concentric.
Area of render = 2 × 35 × 1000 = 70×10^3 mm^2 per m run of wall
So even a low strength mortar σc = 0.5 N/mm^2
Gives a theoretical allowable force, F = A × σc = 35kN per m run of wall
However it is unlikely that a wall will ever be built plumb so a practical limit of 10kN/m run is applied. Addional checks should be done if the wall is to be eccentrically loaded as this will result in unequal load share between the internal and external renders.
Lateral Load Capacity
Once again the strength of the straw is ignored and composite behaviour is assumed. Failure is taken to be when the render cracks and leaves the straw vulnerable.
Calculate the second moment of area, I = 2[b(t^3)/12 + bt(d^2)] (from parallel axis theorem)
Calculate the section modulus, z = I/y (y is distance from centroid to extreme edge)
Moment resistance of the wall is given by, M = z × σb (σb of render, ignore straw)
Rearrange M = w(l^2)/8 for w to find failure load.
Straw constructions that are one or two storeys high generally do not have racking issues providing the walls are continuous and window openings are restricted to 50% of the wall area.
The main supplier of prefabricated straw bale units in the UK is Modcell. The panels are made near to site in a flying factory, allowing the use of local straw which minimises embodied carbon due to transportation. The frame is machine cut glulam with steel corner bracing to improve racking resistance. These can be load bearing up to three storeys or used non-structurally as cladding panels.