arches

I was at my friend Jolyon Gill's memorial on Tuesday. A bridge engineer of some repute. He will be missed, and the gathering of bridge engineers was a clear indication of that. The celebrant read a poem I had ot heard before and it bears repeating (thanks to Google and other fans)
THE BRIDGE BUILDER

An old man, going a lone highway,
Came at the evening cold and gray,
To a chasm, vast and deep and wide,
Through which was flowing a sullen tide.
The old man crossed in the twilight dim-
That sullen stream had no fears for him;
But he turned, when he reached the other side,
And built a bridge to span the tide.

"Old man," said a fellow pilgrim near,
"You are wasting strength in building here.
Your journey will end with the ending day;
You never again must pass this way.
You have crossed the chasm, deep and wide,
Why build you the bridge at the eventide?"

The builder lifted his old gray head.
"Good friend, in the path I have come," he said,
"There followeth after me today
A youth whose feet must pass this way.
This chasm that has been naught to me
To that fair-haired youth may a pitfall be.
He, too, must cross in the twilight dim;
Good friend, I am building the bridge for him."

-WILL ALLEN DROMGOOLE

As a member of the generation that decided that is was legitimate to charge our children for teaching them what we were given free, I find it more than a little challenging.

Book Arch

At http://bit.ly/BookArch.  The question is posed, will this book arch stand. Well, clearly it is standing. Here is a quick spreadsheet thrust model showing that it would stand at almost indefinite height at this span to thickness ratio. If the span were much greater, it would fail.

The outline obviously doesn't follow the photograph exactly. I have pasted the Photo as fill to the Plot Area in an excel graph. The model divides the arch into 20 segments and plots the thrust at each intersection and then at 150mm steps down the piers. Arches like this fail by spreading at the shoulders. THere is no way this one is absolutely symmetrical so itwill tip one way rather than failing symmetrically. The limiting case is the minimum horizontal thrust which means that the thrust goes close to the extrados at the crown and the intrados at the haunches and then slowly drifts out towards the back of the piers. If the arch and/or the pier is thinner, failure occurs at a lower height.

 

The minimum thickness at which a semicircular arch on rigid supports will stand is about span/18.