Two things in quick succession got me going on this. The first was the IStructE structural behaviour example for October. i will come back to that shortly.
The second was this beautiful sketch of the Mathematical Bridge in Cambridge which turned up on Twitter.
The sketch above, compared with the pictures below, looks good but actually, it illustrates how finely tuned the geometry is, earning the bridge its name.
If you look carefully at the photo, each radial goes right through three intersections of tangential members. In the sketch, they often don't quite meet.
If we start with the two each side of the centre we can see fairly well how it works. Trace from the first crossing down in each direction and you will find a straight timber running right back to the stone foundation. These straight compression members provide the stuffest path for loads and will carry most of the weight in that part of the bridge.
Move out another step and the longer strut only just reaches the very top of the stone but that's OK because the other leg is shorter and steeper and will carry more of the load.
Move out to the third radial and we find one of the supports is actually horizontal. There is a sort of goal post with inclined sides. The pic below shows the pieces and how they fit together.
When they are assembled there are suddenly a lot more crossings and its easy to see how the goal post is prevented from swaying sideways. Look at the photo above again and you will see that the radials pass outside the tangential timbers shown above. If you look a little more carefully you will see the same on the further frame. In other words, the radials go up both sides of the tangentials. The radials are actually thicker and halved at each intersection. When the two sides come together the tangentials are sandwiched between.
It really is possible to make this all work without bolts. The bottom end of those radials extends below the deck and forms a frame to stop the "arch" from tipping over sideways. The hand rails across the top tie everything together. It's a thing of beauty both to look at and to think about.
And what about the IStructE Journal?
Well, here is the question.
To me, the most important issue here is that compression and tension members are many times stiffer than bending members. There is a sense that this is acknowledged in all fours possible solutions since the big compression is in the verticals and they are shown bending but not getting shorter.
In A and D the horizontal gets shorter. It has no directly applied force. Those two can be dismissed immediately. That leaves B and C and we have to deal with the bending. With load applied to the top beam as shown it will try to sag as at C but the side columns will hold back the end rotation. B is clearly the answer.
The fact that the columns bend in an S is a secondary effect and doesn't provide a distinction between the two closest possibilities.