The Monolithic™ Dome
It is the most disaster resistant building that can be built at a reasonable price without going underground or into a mountain.
A wind of 70 miles per hour blowing against a 30 foot tall flat walled building in open flat terrain will exert a pressure of 22 pounds per square foot (see sidebars). If the wind speed is increased to 300 miles per hour the pressure is increased to 404 pounds per square foot (psf). Wind speed of 300 MPH is considered maximum for a tornado. It is far greater than that of a hurricane.
Cars can be parked on 100 psf. The side pressure on the building could equal the weight of cars piled 4 high. No normal building can withstand that much pressure. Many Monolithic Domes are buried up to 30 feet deep. They must withstand pressures up to 1 ton per square foot (2000 psf)].
Against tornado pressure a Monolithic™ Dome 100 feet in diameter, 35 feet tall would still have a safety margin of nearly 1½ times its minimum design strength. In other words, the stress created by the 300 mile per hour wind would increase the compressive pressure in the concrete shell to 1,098 psi. The shell is allowed 2,394 psi using design strengths of 4,000 psi.
The fact is, the Monolithic™ Dome is not flat and therefore never could the maximum air pressure against it of 404 pounds per square foot be realized. Neither is the concrete only 4,000 psi. It is always much greater. The margin of safety is probably more like three or four.
Concrete Dome Wind Analysis
Commercial building 30 feet high in exposure C (most severe exposure in open flat terrain). Using design wind pressure from UBC 1985 Edition, section 2311.d, of 70 MPH. V = 300 MPH.
p = Ce Cq Qs I
I = 1.0 (Commercial Building)
Qs = 13psf (pressure from wind)
Ce = 1.3 (building height 30 ft. – exposure C)
Cq = 1.3 (method 2)
Therefore p = (1.3) (1.3) (1.3psf) (1.0) = 22psf
Assume same building and same exposure but with wind speed of 300 mph.
Preference: Finte, Mark, Handbook of Concrete Engineering; Nan Nostrand Reinhold, 1974.
p = 1/2 Cs Ca Cg P Vh2 (H/h)2/alpha
Assume everything is constant except the wind speed.
p = C Vh2 = 22psf for V = 70 mph (example 1).
Therefore C = (22) / (70)2 = 0.00449
Then p = (0.00449) Vh2 for V = 300 mph; p = 404psf
The maximum concrete stress in dome 100 feet in diameter by 35 feet high with p = 400psf is 1,098psi compression. From the “Concrete Dome Seismic Analysis” example we see the allowable stress is significantly higher at 2,394 psi.
The forces caused by wind and earthquake on a concrete dome generally do not control the design. Domes are very strong and durable and in a realistic situation would probably still be standing when all conventional structures had failed.
The Monolithic™ Dome at Port Arthur, Texas has now been hit by three hurricanes. A hurricane does not exert enough pressure on a dome to be even noticed. As shown above the dome can very easily withstand the stresses of a tornado.
However, debris carried by a tornado could cut the surface membrane. If the debris contained a large timber or metal object, it might be possible if conditions were just right to put a puncture into the dome. But the puncture would be very local and would certainly never cause serious collapse of the dome. Possibly damage to the doors or windows may occur if there was a rapid decompression caused by the tornado.
|70 mph||22 psf|
|100 mph||50 psf|
|150 mph *||100 psf|
|300 mph * *||404 psf|
|* Force 5 hurricane (worst)|
|* * Force 5 tornado (worst)|
The most likely natural disaster a Monolithic™ Dome may encounter is an earthquake. The worst areas in the United States are listed as seismic zone 4. From analysis (see “Concrete Dome Wind Analysis” illustration) it is easy to see that earthquake forces do not even approach the design strength the Monolithic™ Dome is built to withstand under normal every day usage. It would take an external force many times as large as the earthquake to approach the design strength of the concrete itself.
Concrete Dome Seismic Analysis
See Above Illustration
N < a > = – apk1 cos < b >
N < ab > = – apk2 sin < b >
N < b > = – apk3 cos < b >
Seismic Force (UBC 1985 Edition)
V= ZSICKW (Formula for the total design lateral force)
Z= 1.0 Zone IV (Seismic Zone Factor)
I= 1.5 (Importance Factor = Hospital)
K= 2.0 (Unusual building such as Dome — conservative)
Therefore: V = (1.0) (1.5) (0.14) (2.0) W = 0.420W — Note: V = 0.14W for normal shear wall building!
V = (0.420) (100) = 42.0 psf (pounds/square foot) — one square foot of shell 8” thick weighs 100 lbs. The value of p = V = 42.0 psf.
For demonstration purposes assume p = 60 psf. This represents earthquake forces in excess of the most sever code requirement by a factor of 1.4.
Maximum stress due to N < b > is -64.8 psi; N < a > is -70.6 psi. Maximum bending moment is 909.3 lbs – ft/ft.
For a vertical live load of 40 psf in addition to the dead load of the shell the following stresses and moment are obtained. Maximum stress due to N < a > = -82.5psi; N < b > = -70.7 psi or .146.5 psi. The maximum bending moment is 1,588.0 lbs-ft/ft.
The maximum allowable compressive force in the concrete is: fc = 1.33 (0.45) (4000psi) = -2.394psi. This is many times greater than the -70.6psi needed.
The forces caused by a major earthquake are considerably less than normal provided for when a dome is designed for nominal vertical loads.
Nuclear fallout is another disaster consideration. It is interesting to note that the only structure left standing near ground zero at Hiroshima was the concrete skeleton of a dome. Certainly the Monolithic™ Dome would be superior to most buildings if a nuclear fallout condition occurred. Rain would tend to wash the radiation off the building much better than conventional buildings.
Generally the Monolithic™ Dome is quite tall. Radiation strengths are inversely proportional to the square of the distance from the source. The roof of the Monolithic™ Dome would hold the radiation further from the occupants than many other structures. Also concrete itself is a good absorber of radiation. The concrete Monolithic™ Dome would greatly reduce the effects of fallout on the occupants.
It is interesting to note that German thin shell structures stood up to allied bombing in the second world war better than most other structures. When a bomb would hit a thin shell it would either bounce off their tough resilient exterior or it would puncture a hole through.
Since there are no single components that carry large loads, there is nothing that can be knocked down like a beam or a column. Therefore repair was a simple patch to cover the hole that was made when the bomb would go through.
Note: Dr. Arnold Wilson, retired professor of Civil Engineering at Brigham Young University and Senior Consulting Engineer for Monolithic, is a recognized expert on thin shell concrete construction. Thin shell is the generic name for a Monolithic™ Dome.