Put on a Black Top Hat
by Jim Antrim  1986
Unidirectional fabrics are an ideal construction material for FRP construction from an engineering standpoint: fibers can be laid directly in line with the load path, reinforcement can be optimally distributed in line with the load path, reinforcement can be optimally distributed in proportion to multidirectional load patterns, resin content is more easily reduced.From a cost and labor hour point of view there are drawbacks.Unidirectionals are usually more expensive than bidirectionals (woven roving or biaxials) because the manufacturing process required just to hold the unidirectional fibers together is inherently more expensive.Usually more layers of unidirectional need to be laid down than would bidirectional, and they are more difficult to fit to a contour.As in many of life’s decisions, economics usually wins over ideals, and the decision goes to the cheap and easy.Yet, there is a place for everything in this world: Fish belong in the sea, and unidirectionals belong on the top of a hat section.

Be it a stringer, frame, or even a lowly floor; it’s top deserves a uni.The loads in the top of a hat section are running along the length of the stiffener.Likewise, the fibers which are laid to support this load should be laid lengthwise along the top.Any fibers not parallel with the stiffener are freeloaders, excess weight.Weight is slow and weight is expensive.
The effectiveness of a unidirectional in this function is such that graphite is often cost effective.Yes, you heard it right.The black stuff, the prince of darkness, the wonder material of which high tech racing machines and spacecraft are made can actually cost less in the stringer of your production boat than good old mat and roving!
Let us examine the loading in and the makeup of a typical hat section.Most commonly, the section is used as a stiffener supporting the hull or deck shell.The general term stiffener covers beams, frames, longitudinals, stringers, girders, and floors, and any other obscure specific terms I may have forgotten.“Section” refers to a cross slice through the stiffener.The slice would look similar to a vertical slice through a stovepipe hat or Pilgrim’s hat, hence the term “hat section”.The hats’ brim is the bonding angles fastening the section to the shell plate.
Water pressure on the hull exterior exerts a bending moment on the stiffener, loading the ‘top’ of the section in tension and the bottom of the section (usually the local shell laminate) in compression.At support points, such as where the stiffener crosses a bulkhead, this loading direction is reversed.
The sides of the section carry three different loads.The primary loading is shear, induced by the opposing loads in the top and bottom faces.Secondarily, as the stiffener bends under load the differing radius of curvature between the top and bottom forces these two faces towards one another.This action loads the sides in compression vertically.Finally the sides share some longitudinal loading with the top and bottom in proportion to distance from the neutral axis.
Typically and logically a certain amount of local shell plating is considered to be part of the section.Since this “associated plating” is relatively wide and beefy by comparison to the top of the section, the neutral axis is fairly close to the hull shell, usually somewhere down around the hat band.This is a structurally inefficient solution.Because the top of the hat is further from the neutral axis, and is also smaller in area than the excessive material is required to resist those stresses.The solution is an exceptionally stiff material in the top of the section.
Unidirectional graphite has a stiffness nearly ten times that of a mat and roving laminate.Using a few layers of graphite in the top will pull the neutral axis upward, giving a better balance of loads.With balanced loading less material is required.So much less material is used that even with the high cost of graphite, overall material cost is comparable or less; and weight savings is dramatic.(All of these benefits are secondary of course to the advertising hype you can generate with a speck of graphite in your hull.)
Conceivably one could analyze the exact loadings in the section sides and make up an ideal laminate of unis with optimized fiber orientation.A nice idea, but don’t ask me to cut out and lay up those tiny pieces.Mat and roving work just fine for this purpose, as does diagonal bias material.The +/ 45 degree fiber orientation of the latter material is ideal to resist the shear loading, and does a fair job in handling the other load directions.IN addition, the material drapes well over the tight radii.
In the accompanying example we are designing a stiffener corresponding to typical loads and panel dimensions for a side longitudinal in a 4050 foot boat.For simplicity, I will assume the hull to be a solid laminate made up of alternate piles of 1 ½ oz. Mat and 24 oz. Roving.This is also the makeup of the stiffener with the exception of the graphite cap.
Neglecting the shell laminate the all mat and roving stiffener uses 4.5 ft^2 of (M&R) pairs per foot of length.This works out to a total material cost of 3.92 $/ft and a total weight of 3.10 lb/ft.
The graphite capped stiffener uses 1 ft^2 of (M&R) plus 1 ft^2 of G900 (a 9.5 oz. Graphite uni manufactured by Orcon) per foot of length.This is a total of 3.81 $/ft at a total weight of 0.83 lb/ft.The mat/roving stringer costs 3% more at a whopping 270% weight increase!In addition with far fewer layer and much less resin to mix, labor hours are bound to be less.It’s a whole new concept: GRAPHITE UNI – The boat building material for bargain shoppers!
The effectiveness of a unidirectional in this function is such that graphite is often cost effective.Yes, you heard it right.The black stuff, the prince of darkness, the wonder material of which high tech racing machines and spacecraft are made can actually cost less in the stringer of your production boat than good old mat and roving!
Let us examine the loading in and the makeup of a typical hat section.Most commonly, the section is used as a stiffener supporting the hull or deck shell.The general term stiffener covers beams, frames, longitudinals, stringers, girders, and floors, and any other obscure specific terms I may have forgotten.“Section” refers to a cross slice through the stiffener.The slice would look similar to a vertical slice through a stovepipe hat or Pilgrim’s hat, hence the term “hat section”.The hats’ brim is the bonding angles fastening the section to the shell plate.
Water pressure on the hull exterior exerts a bending moment on the stiffener, loading the ‘top’ of the section in tension and the bottom of the section (usually the local shell laminate) in compression.At support points, such as where the stiffener crosses a bulkhead, this loading direction is reversed.
The sides of the section carry three different loads.The primary loading is shear, induced by the opposing loads in the top and bottom faces.Secondarily, as the stiffener bends under load the differing radius of curvature between the top and bottom forces these two faces towards one another.This action loads the sides in compression vertically.Finally the sides share some longitudinal loading with the top and bottom in proportion to distance from the neutral axis.
Typically and logically a certain amount of local shell plating is considered to be part of the section.Since this “associated plating” is relatively wide and beefy by comparison to the top of the section, the neutral axis is fairly close to the hull shell, usually somewhere down around the hat band.This is a structurally inefficient solution.Because the top of the hat is further from the neutral axis, and is also smaller in area than the excessive material is required to resist those stresses.The solution is an exceptionally stiff material in the top of the section.
Unidirectional graphite has a stiffness nearly ten times that of a mat and roving laminate.Using a few layers of graphite in the top will pull the neutral axis upward, giving a better balance of loads.With balanced loading less material is required.So much less material is used that even with the high cost of graphite, overall material cost is comparable or less; and weight savings is dramatic.(All of these benefits are secondary of course to the advertising hype you can generate with a speck of graphite in your hull.)
Conceivably one could analyze the exact loadings in the section sides and make up an ideal laminate of unis with optimized fiber orientation.A nice idea, but don’t ask me to cut out and lay up those tiny pieces.Mat and roving work just fine for this purpose, as does diagonal bias material.The +/ 45 degree fiber orientation of the latter material is ideal to resist the shear loading, and does a fair job in handling the other load directions.IN addition, the material drapes well over the tight radii.
In the accompanying example we are designing a stiffener corresponding to typical loads and panel dimensions for a side longitudinal in a 4050 foot boat.For simplicity, I will assume the hull to be a solid laminate made up of alternate piles of 1 ½ oz. Mat and 24 oz. Roving.This is also the makeup of the stiffener with the exception of the graphite cap.
Neglecting the shell laminate the all mat and roving stiffener uses 4.5 ft^2 of (M&R) pairs per foot of length.This works out to a total material cost of 3.92 $/ft and a total weight of 3.10 lb/ft.
The graphite capped stiffener uses 1 ft^2 of (M&R) plus 1 ft^2 of G900 (a 9.5 oz. Graphite uni manufactured by Orcon) per foot of length.This is a total of 3.81 $/ft at a total weight of 0.83 lb/ft.The mat/roving stringer costs 3% more at a whopping 270% weight increase!In addition with far fewer layer and much less resin to mix, labor hours are bound to be less.It’s a whole new concept: GRAPHITE UNI – The boat building material for bargain shoppers!
DESIGN PARAMETERS:
s = 4.0 ft.(supported panel width)
l = 6.5 ft. (stiffener length)
h = 5.0 ft. (water head pressure)
F.S. = 2 (factor of safety)
d = 1/100 (maximum deflection)
s = 4.0 ft.(supported panel width)
l = 6.5 ft. (stiffener length)
h = 5.0 ft. (water head pressure)
F.S. = 2 (factor of safety)
d = 1/100 (maximum deflection)
MATERIAL PROPERTIES:
(1 ½ oz. mat & 24 oz. roving) pair
t = .095 in (thickness per pair)
S = 20800 psi (failure stress) tensile and compression average
E = 1.445e6 psi (modulus)  tensile and compression average
G900 (single ply 9.5 oz. graphite uni)
t = .021 in. (thickness per ply)
S = 135000 psi (failure stress)  tensile; cap is usually in tension
E = 12.5e6 psi (modulus)  tensile
(1 ½ oz. mat & 24 oz. roving) pair
t = .095 in (thickness per pair)
S = 20800 psi (failure stress) tensile and compression average
E = 1.445e6 psi (modulus)  tensile and compression average
G900 (single ply 9.5 oz. graphite uni)
t = .021 in. (thickness per ply)
S = 135000 psi (failure stress)  tensile; cap is usually in tension
E = 12.5e6 psi (modulus)  tensile
REQUIRED STRENGTH:
M = 64*F.S.hsl^2
M = 64*2*5.0*4.0*6.5^@ = 108160 in lb
M = 64*F.S.hsl^2
M = 64*2*5.0*4.0*6.5^@ = 108160 in lb
REQUIRED STIFFNESS:
EI = (144/384) 64[100]*hsl^3[100] is deflection limit
EI = (144/384)*64*100*5.0*4.0*6.5^3 = 1.318e7 in ^2 lb
EI = (144/384) 64[100]*hsl^3[100] is deflection limit
EI = (144/384)*64*100*5.0*4.0*6.5^3 = 1.318e7 in ^2 lb
MATERIAL WEIGHT & COSTS:
G900: 2.84 $/ft^2(3 roll price)
Eglass: 1.25 $/lb(typical bulk price)
Resin: 1.25 $/lb(typical vinylester)
G900: 2.84 $/ft^2(3 roll price)
Eglass: 1.25 $/lb(typical bulk price)
Resin: 1.25 $/lb(typical vinylester)
WEIGHT (lb/ft^2)  COST ($/ft^2)  

FABRIC  Fabric  Resin  Total  Fabric  Resin  Total 
G900  0.066  0.076  0.142  2.84  0.10  2.94 
(M&R) pair  0.260  0.429  0.689  0.33  0.54  0.87 