# Presentation: 514938

## Bookends and Buckling Insurance

- Hans Jostlein
- September 12, 2006 , 2006

## Overview

- Thermal expansion
- One Bookend Case
- Gravity amplification
- Two Bookend Case
- Block leaning
- Block buckling
- Gap Filling Schemes
- Forces on the Bookends
- Foam Installation, Foam Uniformity
- “Insurance” scheme against block buckling

- Page

## Thermal expansion     One Bookend Case

- Blocks sit on building floor, which does not expand
- Tops are glued together with connector boards
- PVC expands with a TCE = 73 ppm/C

- Detector top expands by 4.8 cm for a 10 C rise

- Page

## Thermal expansion – Gravity amplification:

- As blocks lean,
- CG moves and makes them lean more
- Result: additional leaning of 0.7 cm – small !

- Page

## Thermal expansion Two Bookend Case 

- Page

## Thermal expansion --Forces 

- Forces act near the top connector board
- We assume that 12 inches, twice the board height, contribute
- Webs act as springs
- One block has a spring constant of  5 x 10^8  N/m
- We assume unyielding bookends
- A 10 C temperature rise produces a force of  26 ton
- Force acts on the top of the bookends
- Stress  in the connector boards is  only 8 psi
- Stress in the horizontal webs is 159 psi
- Compare to Ang Lee’s note 957,
-       which states that these webs can take 500 psi
-      with a safety factor of 4.4 against buckling

- Page

## Block leaning 

- A  block may not be exactly vertical
- If the top is 1 inch off vertical, the leaning force is 390 # force
- If all blocks lean by 1 inch, the total force is 8 tons
- This is not a problem by itself, but may promote buckling

- Page

## Block buckling

- Block Buckling
- Gap Filling Schemes
- Forces on the Bookends
- Foam Installation, Foam Uniformity
- “Insurance” scheme against block buckling

- Page

## Buckling Stability

- Ang Lee has concluded, in DocDB note  # 826,
- that  the NOVA structure will have a safety factor
- of only 2.1  against block buckling
- if the modulus of PVC falls to 150 ksi due to creep
- We have no firm lower bound on the 20 year creep modulus for our PVC.
- We may not be able to get a usable firm lower limit
- by the time we need to decide structural parameters.

- Page

## Buckling Forces

- We estimate buckling forces for a simple model:
- Blocks are simply connected at top and bottom, free in between
- Blocks have constant curvature when buckling
- If we define
- H = full block height
- B = bowing distance at half height
- We find that the CG height changes as
- Delta = (4/3) * b^2 / H
- The bowing force is  f = (4/3) * 2 * b/H  * m * g
- For a block that bows 1⁄2” at mid-height, the force is 2070 # force.
- If all blocks bow the same way, the total force is 43 ton,
- acting at mid-height on one  bookend

- Page

## Buckling Remedies                       - - Thicker Extrusion Walls

- Ang LEE suggests in note # 826
- that the buckling safety factor would increase
- to  4.4 (at a PVC modulus of 150 ksi)
- If the horizontal extrusions were to have the same thick wall
-  (4.5 mm sheath, 3 mm webs)
- As the vertical extrusions.
- _A few problems :_
- More inert detector mass
- More PVC  hence more cost
- Adhesive stresses grow from 175 psi to 230 psi

- Page

## Buckling Remedies  - - Gap Filling

- Ang LEE suggests in note # 957, and Vic Guarino in note # 1050,
- to fill the block expansion gaps after a few years
- Gap filling can stop cell swelling and block buckling.
- _However, a few comments are in order:_
-  cell swelling is _not_ a problem, as per Ang Lee’s note # 957
- Filling the gaps will eventually transmit the full hydrostatic pressure to both bookends.
- The force is 3100 tons, applied at 1/3 detector height (5 m)

- Page

## Gap Filling Issues

- Gaps could be filled with epoxy, with granular materials, or with foam.
- Epoxy and granular materials will create a layer of inert material
- of unknown thickness,  which may be undesirable in the detector
- Epoxy is expensive,
- while granular materials (e.g. walnut shells) can be cheap.
- Granular materials are “easy” to install.
- Foam is low density and stiff enough to resist 20 psi.
- It is, however, very difficult to install in the narrow gaps between blocks.
- It can also leave large voids and have uneven compliance.

- Page

## The Proposed Solution:  Air Bags

- Page

## Air Bags

- Bag Sizes:
- Bags might be horizontal, full width,  perhaps 1 m high each.
- They would have a welded seam across the middle,
- to allow separate control for left and right,
- in case a block buckles unevenly.

- Bags would be installed while the block is horizontal on the blockraiser,
- with “carpet tape” (double-sticky), along their top edges.

- They would have filler tube assemblies (a’ la Pool Toy) welded to each end.
- The filler tubes will be connected to a 1⁄4 “ OD plastic tube bundle
- that runs along both sides of the detector.

- Since there is no air flow (except for leaks) the small tubes will be adequate

- Page

## Air Bag Properties

- The pressure is very low,  e.g. 1/3 IWP for a 1⁄2” buckling
- Bags are made from Polyethylene or other weldable material
- PE is rated (as per ASTM D 1998 - 97 for storage tanks) at a 600 psi design stress
- This supports  14 psi in a half inch gap
- I have tested a 6 mil wall PE bag to 20 psi in a 1⁄2” gap

- Page

## Air Bag Supply System

- Page

## Monitoring the Buckling

- Buckling will occur extremely slowly, if it happens at all.
- Gaps will be visible from the walkways on both sides.
- Simple devices such as plumb bobs may be used.
- Monthly monitoring will be adequate.
- Alternatively, distance sensors, either capacitive or inductive,
- can be installed at low cost across each gap.

- Page

## Air Pressure Calculation

- Buckling forces for each block superimpose linearly.
- All forces must be transmitted back to the bookend
- on the convex side of the buckled block.
- It is easy to calculate the set of air pressures needed
- to either resist the buckling forces or to
- reverse the buckling over time.

- Page

## Conclusions

- We  have looked at the total NOVA Far Detector as a Structural  Unit.
- Thermal expansion with just one bookend will cause modest leaning and no instability.
- Thermal expansion with two bookends will cause acceptable forces on the bookends.
- Filling the gaps causes huge forces on the bookends and will be difficult to do.
- We propose to install air bags in the gaps,
- which can be inflated (to very low pressures) later if and when block buckling should occur.

- Page