[Rhodes22-list] Cockpit Bench Seat Reinforcement - The Rest Of The Story

[Roger Pihlaja]

Lou,

I see the list already forwarded my cockpit seat reinforcement solution to
you.

Your proposed method will also stiffen the cockpit seats somewhat.  However,
what you are proposing to do may not sufficiently stiffen the seat to stop
the creaking.  I believe the creaking sound is caused when the inboard edge
of the seats deflects under load, thus causing certain structural components
to move relative to one another while pressed hard together.  For the
purposes of this discussion, let's simplify the physical situation & model
the cockpit seat as a simply supported beam, point loaded in the center.
This model is not perfect; but, it's good enough to illustrate my point.
>From structural mechanics, the deflection of our model beam is given by:

d = P * (L^3) / (16 * E * I)

Where:
d = beam deflection (inch)
P = point load in center of beam (lb)
L = unsupported beam length (inch)
E = modulus of elasticity of beam material of construction (lb/inch^2)
I = moment of inertia of beam cross sectional shape (inch^4)

In my solution, I added two structural columns per cockpit seat, equally
spaced down the length of the cockpit.  The picture link that was forwarded
to you illustrated one of those four structural columns.  Adding these
support columns had the effect of reducing L in the above equation down to
1/3 of the original length.  All else being equal, this also reduced the
deflection down to (1 / (3^3)) = 1/27 = 0.03704, or only about 3.7% of the
original deflection.  i.e. no more creaking under load!  I don't know how
much the seat would have to be stiffened in order to just eliminate the
creaking.  But, for the sake of discussion, let's assume my method provided
just enough stiffening.

In order to get a similar amount of stiffening by your proposed solution,
you are going to have to increase the product of (E * I) in the above
equation by a factor of 27X.  Now, E is a material property.  Here are some
values of E for some common materials:

Al 7075-T6: 10,400,000 lb/inch^2
1040 Steel: 30,000,000 lb/inch^2
Stainless Steel Alloy 316: 28,000,000 lb/inch^2
Nylon 6,6: 400,000 lb/inch^2
High Density Polyethylene: 200,000 lb/inch^2
Thermoset Polyester: 300,000 lb/inch^2
Epoxy: 350,000 lb/inch^2
Wood Douglas Fir parallel to grain: 1,600,000 lb/inch^2
Wood Douglas Fir perpendicular to grain: 80,000 lb/inch^2
S Glass: 10,000,000 lb/inch^2
E Glass: 10,500,000 lb/inch^2
High Modulus Graphite: 58,000,000 lb/inch^2
FRP Composite Longitudinal: 6,000,000 lb/inch^2
Epoxy/High Modulus C-Fiber Composite Longitudinal: 32,000,000 lb/inch^2

At the moment, the beam in your cockpit seat is made of some combination of
wood & FRP composite.  Since you said the wood is pretty much gone, let's be
generous & say your beam is all FRP composite at the moment.  With current
materials technology, the stiffest material you could reasonably use would
be Epoxy/C-Fiber composite.  This will improve the E value by (32,000,000 /
6,000,000) = 5.33X, leaving the rest of the stiffening to be achieved by
increasing the I value by adjusting the beam's cross sectional shape & size.

OK, you still need (27 / 5.33) = 5.06X more stiffness.  The actual beam in
the cockpit seat has a very complex cross sectional shape.  To completely
analyse the moment of inertia of this shape would require finite element
analysis using a computer.  However, for the purpose of this discusion, we
don't need to get so sophisticated.  Let's model the beam's cross section as
a rectangle of width, w = 0.5 inch and height, h = 1 inch and assume the
beam is bending about the neutral axis running down the centerline of the
beam.  From calculus, the moment of inertia of this beam is given by:

[I]now = w * (h^3) / 12 = (0.5) inch * (1.0^3) inch^3 / 12 = 0.04167 inch^4

[I]reqd = 5.06 * [I]now = 5.06 * 0.04167 =  0.2108 inch^4

Let's assume we will leave the width, w = 0.5 inch & calculate the required
height of the new Epoxy/C-Fiber beam:

(h)new = [[I]reqd * 12 / w]^0.3333 = [0.2108 * 12 / 0.5]^0.3333 = 1.72 inch

If you wish to use a beam with a round cross section; then, the required
diameter, d, would be:

[I]round = pi * (d^4) / 64

(d)reqd = [[I]reqd * 64 / pi]^0.25 = [0.2108 * 64 / 3.1416]^0.25 = 1.44 inch

So, to get the sort of stiffening required, you would have to laminate a
rectangular cross section beam of Epoxy/C-Fiber composite of about 1/2 inch
width X 1-3/4 inch height or a round beam of about 1-7/16 inch OD down the
underside for entire length of each cockpit seat.  You can't get the
required amount of stiffness using just wood for this beam.

As you can see, cutting the unsupported length of the cockpit seats by
adding structural support columns is a much simpler solution.

Good luck!

Roger Pihlaja
S/V Dynamic Equilibrium

----- Original Message -----
From: "Lou Rosenberg" <lsr3 at MAIL.nyu.edu>
To: <rhodes22-list at rhodes22.org>
Sent: Tuesday, August 24, 2004 11:07 AM
Subject: [Rhodes22-list] cockpit bench seat reinforcement


> RHODIES;
>   Seeking advice on reinforcing the cockpit seats in my R22 ( 1981) .
> The boat is now secure on is trailer in its winter home in Bklyn
> thanks to Rick Centalaonza, a boat hauler ( Coastal)
>   and some good boat yard folks in Pt Jeff and Bklyn.
>   My stb side cracks when I walk or sit  on it, but is not broken.
> The glass work underneath is brittle and the wood stiffeners are
> missing .
>   I have Casey's book on HULL & DECK repair and plan to stiffen and
> support the entire length of both benches by epoxing a dowel in the
> groove and then adding a triangular support made of pine ( since its
> not going to be seen much , teak is overkill, I believe).  The
> triangular support would need to be epoxied to the floor underneath
> the seats. I plan to space the  2 supports on each side  equally.
>
>   Has anyone had weakening of their bench seating due to damage or
> weathering and age of the glass?
>   I am wondering how the epoxied supports would react to the flexing
> of the boat later on as she is under strain.  Would it make sense to
> not epoxy the supports and just wedge them down with rubber mat under
> the wood?
>   **
>   Any advice appreciated !
>   thanks
>   Lou
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