1
Fiber? Check.
Matrix? Check.
My Shapes
My Crosssectional Areas (For Normal)
,
=
,
;
,
=
AreaCross Circle πdf circle24 df circle diameter
,
=
,
*
,
=
,
;
,
=
AreaCross Square df square df square df square2 df square length of side
,
=
,
;
=
AreaCross KeyedCircle 56πdf kcircle24 56 because 60o 16 of 360o the
,
,
=
circle df kcircle diameter
,
=
* +
; =
, =
AreaCross Plus 4t l t2 t thickness l length of one side of plus
My Surface Areas(For Shear)
,
=
*
=
;
=
,
=
AreaSurface Circle 2πr dx πdfdx df diameter dx length along longitudinal
axis
circumference * Length
,
=
;
=
,
=
AreaSurface Square 4dfdx df length of side dx length along longitudian axis
*
Sides Length
,
=

+
;
=
AreaSurface KeyedCircle πdf πdf60360 dfdx dx length along longitudian
axis
[Circumference – (Arc Length) + (Radius + Radius)]* Length
,
=(
+
)
AreaSurface Plus
4t 8l dx
+
*
Thicknesses Lengths Length
Determining Dimensions
In order to determine the values for the diameters, side lengths, thicknesses, etc (it is all arbitrary
anyway), I must set all cross sectional areas equal to each other (to have fair comparisons).
I will
choose an easy number as the cross sectional area I want to have (10
units2
).
Also because I
have more unknowns than equations, I will make
=
t l4
(for plus shape).
With this data made up,
I can now solve for the dimensions: