How to include Shape-Factor in MPI?
The shape factor is defined as a
dimensionless number which reflects
the efficiency of a
section, in a
given mode of loading. The factor is invariant
of the geometric scale.
How to obtain the shape factor?
Consider a
reference cross-section, for example, the area of solid circular section.
As an example, let us consider how to obtain the shape factor against bending. Second
moment of Area is defined as I
and modulus of elasticity as E, the flexural rigidity is
characterized by EI, the shape factor against bending deflection is defined as φbe =EI/ErIr
For the circular solid reference section, it is equal to 4Π I/A2, where A
is the area of crosssection.
For the same cross-sectional area, this shape factor for I
or hollow circular
cylinder could become 10 times higher than the solid cylinder.
The following table shows the Limits in Shape Efficiency corresponding to different materials
(Taken from Reference 1)
You may note that the limits are due to limitation in manufacturing process and competing failure mechanisms. |
