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
Warning: object could not be embedded
response of wood to tension, with different extensometers
Warning: object could not be embedded
2. Homogeneous, isotropic material
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,