Beam Deflection Assumptions

1. Linear-elastic material behavior

response of A36 steel to bending (from the Failure, Fully-Plastic Action lab)
  

 

response of A36 steel to intermittent tension

 

response of wood to tension, with different extensometers

 

2. Homogeneous, isotropic material

by Mike Crites, Jose Soto, & Jeff Thomas, October 1997	source
Koch, P. 1972a. Utilization of the southern pines. I. The raw material. USDA Forest Service Agricultural Handbook No. 420. 733 pp.	by Jeff Thomas, 2007

 

3. Small deflection theory

span = 48 in. max. midpoint deflection = 0.7 in.	length = 36 in. max. endpoint deflection = 0.7 in.

 

The beam forms a shallow curve, i.e.

Thus,

which gives approximately 1.5% error for a slope of 0.1.

 

4. Pure bending

In other words, neglect the effect of shear deformation on the deflection

The beam actually relaxes, but we assume relaxing in negligible for long and slender beams.  If length / thickness ratio is greater than 10, then the effect of shear is less than 2 to 3% of the total deformation.

Therefore,