I have a 1929 Spanish Style duplex.  I found some of the original
curtain rods in the garage.  The originals were 5/8ths inch square
solid wrought iron rods.  We had the same size wrought iron rods
manufactured for all the windows.  One of the windows requires a rod
that spans 103 inches and another window requires a 147 inch long rod.
The rods that are that long sag in the middle.  We plan on installing
a middle bracket to help support the rod.  Those particularly long
rods are also very heavy.  All of the other rods work & look great,
and curtains open and close well without the rod sagging.  The other rods
are all 67 inches long or less and are hung on a wall mounted bracket
on each end without a center bracket.

I have been told by many custom curtain rod manufacturers that hollow
rods are stonger than solid rods.  I have been told by others that
hollow rods will sag more than solid rods of the same dimensions.  3
different manufacturers of curtain rods provided this information:
Manufacturer #1 - Hollow rods of 72 inches or more require a center bracket
Manufacturer #2 - Hollow rods of 96 inches or more require a center bracket
Manufacturer #3 - Hollow rods of 100 inches or more require a center bracket

My question is:

If we stay with the current dimensions of the rods, i.e. 5/8 inch
square, which is stronger and less likely to sag, a hollow or solid
rod?

We also have a 1/2 inch rod adjacent to the 5/8 inch rod for sheer
curtains.  That 1/2 inch solid rod also sags, in fact more than the
5/8 inch rod.  Which is more likely to sag in this 1/2 inch size, a
solid or hollow rod?

I feel like a hollow rod in these two places would be a more prudent
choice, (provided it is actually stronger and less likely to sag)
because a rod that heavy could be dangerous if it every fell.  It is
also more dangerous in that taking down or putting up curatains for
cleaning, changing etc, would be much more difficult with such a heavy
rod.

I found this site that discussed this question but it mentioned pound
for pound comparative tensile strength and I need to know tensile
strength relative to like diameters.

http://www.wattflyer.com/forums/archive/index.php/t-6156.html

I am counting on being able to apply the same finish to the hollow
tubing material as we have on our solid rods, so they match all the
other rods.  I anticipate the look of the hollow rods will be slightly
different but not noticeable since all the other details will be the
same, i.e.the brackets, the finials, and the finish on the rods.  The
rods hung on brackets that are mounted to the wall about 8 feet from
the floor.

No matter what we choose vis a vis the rods, i.e. hollow or solid, we
are still planning to install a center bracket for the rods of this
length.  If weight were not an issue, is one center bracket sufficient
for a solid rod of this length or will we still have sagging even with
the center bracket...particularly for the 147 inch rod?

Hello abednega, I think I can help you with this. First of all, a
solid rod whether square or round is ALWAYS stronger than a hollow of
the same size. However, the solid rod is heavier and for the same
weight per foot you could go with a larger hollow rod that would be
stronger. Next, tensile strength has nothing to do with how much a
given rod sags. The amoumt of sag (deflection) depends only on the
"modulus of elasticity" which is the same (30,000,000 psi) for any
steel.
The amount of sag varies with the unsupported length of the rod raised
to the 4th power. So, to compare the amount of sag between two given
lengths you need to compare the two lengths raised to the 4th power.

EXAMPLE: 103 inch rod versus 147 inch rod

147^4/103^4 = 4.15

So, you would expect the 147" rod to sag 4.15 times as much as the 103" rod.

The "moment of inertia" of a shape (round or square) varies as the
diameter or side raised to the 4th power. Therefore, a larger rod is
stronger.

EXAMPLE: 1/2 diameter versus 5/8 diameter

.625^4/.5^4 = 2.44

So, a 5/8 inch diameter rod is 2.44 times as strong (in resisting sag)
as a 1/2 inch diameter rod.

As to why the three manufacturers list different lengths where center
brackets are required, I have no idea. I suspect we are not comparing
apples to apples.

You will always be better off to go with a hollow rod which is larger
diameter. The problem probably being that you are limited by the
maximum diameter you can fit in the curtain. If we knew exactly what
the curtain weighs per foot, we could calculate the sag for a given
length rod.

I believe that I have covered all the points brought up in your
question. However, if there is something I have missed please ask for
a clarification.

Good luck with your window work, Redhoss