Properties of Fiber Glass Rods and Tubes

KQ6RH

(C) 1998, 1999, 2000

Ray Jurgens

(Up-Dated 2/25/2000)

Properties of Fiber Glass Rods and Tubes

  At this point, I have obtained all of the fiberglass materials that have been using in my antenna projects from Max Gain Systems. These materials are all listed on their web page along with size, weight, color, and price. However, if you are planning to build light weight structures more information is probably required. In particular the bending properties associated with cantilever supports. The lightest weight material is the 1/8" rod, and an 8 ft length is easily bent into a full loop. Thus, this material can only support a small amount of weight at small lengths.  The larger diameters of tubing can support increasing amounts of weight for a given deflection. The deflection information is particularly useful in predicting the total bending of a composite spreader and also for determining the amount of tension required in a guy line to re-establish specific position of the spreader.

  The tables below give bending information for each of the rods and tubes I have tested. Each size of rod or tubing will bend a specific amount when loaded depending upon the size and length. These materials will also buckle when loaded axially. I concentrated mostly in determining the properties of the materials used as cantilever beams supported rigidly on one end in a horizontal position. Under this condition, the unsupported end will deflect downward due to the gravity load along the entire length of the beam. I measured the unloaded deflection as a function of length for each size material up to and including the 3/4" tubing. I also measured the 1/8" and 1/4" solid rods in the same manner. In general, all of these materials are formed from fiberglass of uniform density and modulus of elasticity, so the bending properties are predictable with a single equation. In general, the deflection increases with the cube of length for a given size and geometry. Further loading at the unsupported end increases the deflection in proportion to the loading, i.e., the lever acts as a linear spring about the rest position. This linear behavior is exhibited so long as the deflection angle is small (less than about 15 degrees). An 8' span of the 1/8" rod material will deflect more than this angle, and the load no longer pulls perpendicular to the beam. For this reason, the smaller diameter materials are useful only in small lengths (as micro extensions). As an example, the table below shows the properties of the 1/2" tubing. Negative loading implies that the force is applied upward. Normally, I made some attempt to determine the amount of force required to bring the beam into horizontal position at the unsupported end.

grams loading at end of beam	displacement in inches	Comments
-160	0.00	Negative loading at tip
0	6.75	No loading
100	11.00	Positive loading at tip
200	16.50
300	20.50

Table 1
Deflection of 8' Cantilever Beam
0.5" OD 0.25 ID Tubing

It is clear from Table 1 that the useful range of loading is probably less than 200 grams for the 8' length. Further loading causes significant droop and such large distortions would be unable to support the wire beams in an acceptable manner. However, one way around this problem is to guy the beam into place. But, it may be more complicated to make a structure such that the beam is guyed from three or four sides. An other alternative is to deliberately bend the beam with a guy under tension from one direction such that this tension is much greater than the loading to be supported. This later procedure works well for making horizontal spreader structures for planar wire beams. The Reflected M beams pictured in that section are designed in this manner.

Table 2 below shows the deflection measurements for lengths of the 0.5" tubing for 2', 4' and 8' lengths supported horizontally and loaded at the free end. Note that some deflections were too small to measure, and some others were too large. In general the accuracy o f the deflection measurement is limited to about an 1/8 of an inch, and the gram loading is accurate to about 5%.

grams loading	2' length deflection	4' length deflection	8' length deflection
-160 (pulling up to level)			0.00
-120 (pulling up to level)		0.000
0 (unloaded)	0.000	0.375	6.75
100 (pulling down)		1.250	11.00
200		1.375	16.50
300	0.313	2.625	20.50
400		3.500
500	0.500	4.250

Table 2
Deflection of 0.5" Diameter Tubing Under Loading for Various Lengths

At this point, it is probably best to try to make some sense of these measurements so that the standard equations for beam deflection and loading can be applied. Toward this end, several things are needed, and these include the weight per unit length of the materials, their second moments of inertia, and the modulus of elasticity. We have information on most of these except the latter item which is probably constant for the material. The deflection measurements permit us to get at this number using the deflection equation for uniformly loaded beams. If we let y be the downward deflection, then the equation is

  y = w * L^4 / (8 * E * I)

where w is the weight per unit length (lbs/inch), L is the length (inches), E is the modulus of elasticity (lbs/inch^2) and I is the moment of inertia (inches^4). So, it is easy to see that we can solve for E given all the other parameters. Then, once we know E we can solve for deflections for many other cases. Table 3 is a summary of the data and resulting values of E determined for some of the smaller materials available. The value of the moment of inertia, I, can be calculated for these circular cross sections as

  I = (pi/4) * (Ro^4 - Ri^4)

where Ro is the outside radius and Ri is the inside radius (not diameters). If you use diameters in this equation, you need to divide the result by 16 to get the correct answer. The weights for these materials are located in the MGS home page, but they can be calculated quickly by multiplying the the density of the material by the cross sectional area. This gives the weight per unit length. The density of these fiber glass materials is about 6.72 x 10^-2 lbs/inch^3 or roughly 1.86 grams/cm^3. The white bicycle whip material in the table is about twice this dense (item # 3).

#	Outside Dia	Inside Dia	Length	y displacement	I	w	E
	(inches)	(inches)	(feet)	(inches)	(inches^4)	(lbs / inch)	(lbs/inch^2)
1	0.125	0.00	2.00	0.750	1.50x10^-5	8.33x10^-4	3.07x10^6
2 black	0.250	0.00	4.00	2.375	2.44x10^-4	3.23x10^-3	3.69x10^6
3 white	0.250	0.00	4.00	1.750	2.44x10^-4	6.43x10^-3	1.00x10^7
4	0.375	9/64	4.00	1.250	1.89x10^-3	6.72x10^-3	3.02x10^6
5	0.500	9/64	8.00	6.750	3.69x10^-3	8.72x10^-3	3.71x10^6
6	0.500	9/64	4.00	0.375	3.69x10^-3	8.72x10^-3	3.70x10^6
7	0.750	0.500	8.00	3.750	1.59x10^-2	1.56x10^-2	2.78x10^6

Table 3
Determination of Modulus of Elasticity from Deflection Measurements

Notice that the value of E is around 3x10^6 psi for all of the black fiber glass samples, but there is some variation that may indicate slight differences in the material. However, using a value near 3x10^6 will provide a good first estimate for engineering purposes, and the variation in the table can be used as an estimate of the expected variance. Note that the white bicycle whip material is very different. It is twice a dense as the other materials in the table and has a modulus of elasticity that is 3 times as high (about equal to that of aluminum) as the other samples. The E values for the fiber glass are about 1/10 as large as structural steel (for perspective).

The tables that follow are measurements of loading applied to the ends of the horizontal cantilevers. So as long as the displacements are small, the beams respond as linear springs so that the displacement about the quiescent displacement is proportional to the applied load. So we can assume that y = K*W where W is the applied load. The spring constant, K, can be derived from the moment diagram of the loading, however, it may be adequate to know the dependence on the length of the beam is as K ~ L^3/(E*I), so the spring is very stiff for short lengths and gets loose rapidly as the length of the beam increases. So, y ~ L^3 * W / (E * I), and you can find the constant of proportionality for the data in the tables so that you can use W in what ever units you like. Also, note, the 0.5" tubing is given in Table 2 and is not repeated here.

L length in feet	W grams weight applied	Displacement inches
2	0	0.75
2	50	10.00

Table 4
Displacement for 1/8" Diameter Solid Fiber Glass Rod

Table 5
Displacements for 1/4" Solid Black Fiber Glass

Table 6
Displacements for 1/4" Solid White "Fiber Glass ?"

Table 7
Displacements for 3/8" Fiber Glass Tubes

Table 8
Displacements for 3/4" Fiber Glass Tubes

These tables are useful in determining the displacements of the beams when loading is applied and can be useful for estimating deflections when the supports are at differing angles, such as 45 degrees. In general, one should consider the wire load carefully, and choose materials strong enough to carry the load without serious distortion to the structure. The structures can be made more stable by using nylon monofilament guy lines, however, buckling, and other problems might appear if the guys or wires are too tight. Since the displacements depend upon the length cubed when loads are applied at the tips, the total displacement of compound or telescoping sections can be estimated from the tables above. More information on these topics will be added from time to time.

 I have recently spent some time testing kevlar thread in place of the monofilament nylon fish line. This material is very strong and hardly stretches at all. However, this very property can also be a problem in getting the loading distributed equally in the various guy lines. This also means that the lengths must be measured and cut very exactly, and one must know exactly what length to cut. In systems with multiple guy lines, tension on one line affects the others, i.e., all parts of the structural system are coupled. Since these systems present considerable computational difficulty, you can save a lot of grief by including a small turnbuckle in each line. This allows individual adjustment of the tensions. The turnbuckles should be placed at the ends of the guys at the most stable point (for example the guy post). Alternatively, separate guy tie rings can be used for each guy set allowing adjustment of individual guy sets. This second method usually is lighter in weight. You should take care that each guy set is made with identical lengths even though the actual lengths can depart slightly from those calculated.

 The 1/8" material is useful for short extenders for either the 1/4" or 3/8" tubes. I found that terminal lugs can be crimped on to the 1/8" inch rods and grommets inserted to provide a wire guide. The wires can be secured in proper location using a 4" piece of #18 copper wire twisted around the lug and then to either side of the wire.

1/8" Extenders with Crimp Lugs

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