Monday, 29 April 2013

Re: [wanabidii] How safe is Dar‐es‐Salaam (Structures: High Rise)

 safi sana
Elias Mhegera
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Tanzania Human Rights Defenders Coalition 
Tel: 255-0754-826272
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             mhegera@gmail.com 
The only thing we have to fear is fear itself 


From: Yona Maro <oldmoshi@gmail.com>
To: wanabidii <wanabidii@googlegroups.com>
Sent: Monday, April 29, 2013 11:40 AM
Subject: [wanabidii] How safe is Dar‐es‐Salaam (Structures: High Rise)

ABOUT THE AUTHOR

Swithurn Mtimavalye Mgaya is a holder of a of Bachelor of Engineering degree in Civil Engineering from the University of Roorkee, India, (1979) with the University Medal in the Best Water Resources Project. In 1987, he was awarded a Diploma of the Imperial College of Science and Technology (London) in Public Health Engineering. He is registered with the Board of Engineers Tanzania in the Category of Professional Engineer. He is an Associate of E. M. Consultants Limited. He has written two papers, 'Causes of Foundation Failures' and 'Treatment of Industrial Waste-waters using Activated Carbon'.

ACKNOWLEDGEMENT

In mid April, 2008, I was visiting the Offices of a construction Company, N‐S (T) Ltd., adjacent the William Benjamin Mkapa Tower. I introduced myself to the Secretary, Lulu Lwoga, that I have been sent from the Board of Engineers Tanzania for an assignment. She immediately poured a number of technical challenges. One of the challenges, as she put it, "Are you sure these towers you are erecting in the City are safe? Look at this tower adjacent to us. I have been observing concrete paving tiles budging up. At one time the Contractor rectified the defects, but I am still doubtful." She concluded. I assured her that I appreciate her concern and promised to work on it.

My mind flushed back to my paper on "Causes of Foundation Failures" I wrote way back in 1979. One message kept ringing in me, "soil up‐thrust." Immediately my mind was impressed with ideas, "The effects of Global Warming." I therefore decided to let my mind be known to the Tanzanian community and the world at large. I took my idea to Jamhuri Msabila and Benedict Mukama of Engineers Registration Board who encouraged me to write a Paper on it. The Managing Director of EM Consultants Limited Eng. Mwesiga N.P. Kamulali received the idea with excitement. The referred to ideas are herein documented.

ABSTRACT

The moisture content of the soils and the levels of water table are among the important factors in the design of foundations for structures. The assumption is generally made that the conditions of the soils shall remain constant during the lifespan of the structure. The rise in sea level; however seem to be working against our basic assumption. Even small increases in sea level will threaten coastal habitats and human‐made structures and may increase the destructive power of coastal storms. Remarks have been made on the causes of Sea Level rise. It is Engineers and Scientists working in a multi‐disciplinary team who can alert and rescue the situation or at least reduce its impact. The towers mushrooming in Dar‐es‐Salaam now and other facilities are a concern of this paper.

Maziwe Island, some 8 kilometres from Pangani, Tanga, that was in 1975 had disappeared by 1992. For whatever good reasons that can be speculated for its disappearance, Dar‐es‐Salaam is very close to Tanga and the very reasons can be the cause of its disappearance.

This paper is meant to send an early warning, how to monitor our structures, how to deal with the inevitable, and the funding for the Project.

SEA LEVEL RISE

We have very little scientific researches made on global warming. Because of the many factors that affect sea level and global temperature, and the scarcity of long‐term measurements from all parts of the world, scientists are uncertain about past changes. They are even more uncertain about future changes in climate and sea level.

In 1988 the United Nations and the World Meteorological Organization created the Intergovernmental Panel on Climate Change (IPCC), a panel of more than 200 renowned earth scientists to study climate change. In 1995 it reported that the earth warmed by between 0.3 and 0.6 Celsius degrees in the past century, and that global sea level increased 1 to 2 mm per year.

The IPCC predicts that global temperature will most likely rise between 1.0 and 3.5 Celsius degrees by the year
2100. If this occurs, sea level could rise by between 15 and 95 cm by the year 2100.
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©Eng Swithurn M. Mgaya June,2008
 
The Concept of Safety of Dar-es-Salaam Structures

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Pumping

Sometimes, the change in sea level can be slow and gradual. The pumping of water or oil from the ground can lead to the gradual sinking of the ground. For example, parts of the Imperial Valley in California have dropped more than 8 m as groundwater has been withdrawn for irrigation. The withdrawal of drinking water and oil along the coast of Texas caused some of the land around Galveston Bay to drop by as much as 2.5 m over several decades. This drop in land led to the flooding of entire neighborhoods.

Isostatics

Some changes in sea level, called isostatic changes, occur due to large amounts of weight being loaded or unloaded onto a region, which causes the land to sink or rise. For example, when a river delta forms, the weight of the accumulating sediments can lead to subsidence, or a sinking of the land. The Louisiana coast is sinking up to 10 mm per year due to the growing weight of the Mississippi River delta. Similarly, the removal of a large weight can cause the land to rebound. The Hudson Bay shoreline in Canada is rising out of the sea at about 10 mm per year because of the recent melting of glaciers that were weighing it down.

Eustatic

Eustatic sea level changes affect all the shorelines of the world simultaneously. During ice ages, glaciers grow, transferring water from the ocean to snow and ice on land. Such a transfer caused the eustatic sea level to fall 120 metres 21,000 years ago, when the glaciers of that ice age were at their greatest extent, and to rise back to the present elevation when most of the ice melted.

FIGURES AND FACTS Carbon Dioxide

In 1750 there were about 281 molecules of carbon dioxide per million molecules of air (abbreviated as parts per million, or ppm). Today atmospheric carbon dioxide concentrations are 368 ppm, which reflects a 31 percent increase. Atmospheric carbon dioxide concentration increases by about 1.5 ppm per year. If current predictions prove accurate, by the year 2100 carbon dioxide will reach concentrations of more than 540 to 970 ppm. At the highest estimation, this concentration would be triple the levels prior to the Industrial Revolution, the widespread replacement of human labor by machines that began in Britain in the mid‐18th century and soon spread to other parts of Europe and to the United States.

Destruction of the ozone layer is predicted to damage certain crops and to plankton and the marine food web, and an increase in carbon dioxide due to the decrease in plants and plankton.

Methane

Methane is an even more effective insulator, trapping over 20 times more heat than does the same amount of carbon dioxide. Methane is emitted during the production and transport of coal, natural gas, and oil. Methane also comes from rotting organic waste in landfills, and it is released from certain animals, especially cows, as a byproduct of digestion. Since the beginning of the Industrial Revolution in the mid‐1700s, the amount of methane in the atmosphere has more than doubled.

Nitrous Oxide

Nitrous oxide is a powerful insulating gas released primarily by burning fossil fuels and by plowing farm soils. Nitrous oxide traps about 300 times more heat than does the same amount of carbon dioxide. The concentration of nitrous oxide in the atmosphere has increased 17 percent over preindustrial levels.

 
The Concept of Safety of Dar-es-Salaam Structures

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Perfluorinated compounds
Perfluorinated   compounds   result   from   the   smelting   of   aluminum.   Hydrofluorocarbons   form   during   the
manufacture of many products, including the foams used in insulation, furniture, and car seats. Refrigerators built
in  some  developing  nations  still  use  chlorofluorocarbons  as  coolants.  In  addition  to  their  ability  to  retain
atmospheric heat, some of these synthetic chemicals also destroy Earth's high‐altitude ozone layer, the protective
layer of gases that shields Earth from damaging ultraviolet radiation. For most of the 20th century these chemicals
have been accumulating in the atmosphere at unprecedented rates. But since 1995, in response to regulations
enforced  by  the  Montréal  Protocol  on  Substances  that  Deplete  the  Ozone  Layer  and  its  amendments,  the
atmospheric concentrations of many of these gases are either increasing more slowly or decreasing.
Synthetic Compound Gases
Scientists are growing  concerned  about  other  gases  produced  from  manufacturing  processes  that  pose  an
environmental  risk.  In  2000  scientists  identified  a  substantial  rise  in  atmospheric  concentrations  of  a  newly
identified synthetic compound called trifluoromethyl sulfur pentafluoride. Atmospheric concentrations of this gas
are rising quickly, and although it still is extremely rare in the atmosphere, scientists are concerned because the
gas traps heat more effectively than all other known greenhouse gases. Perhaps more worrisome, scientists have
been unable to confirm the industrial source of the gas.
THE EFFECTS OF SEA LEVEL RISE
Historical
Sea‐level changes following an ice age cause profound changes in the shape of shorelines. At times of lower sea
level,  land  bridges  formed  between  Alaska  and  Asia  and  between  England  and  France.  These  land  bridges
permitted  plants  and  animals  to  migrate.  The  shorelines  of  the  world  have  retreated  from  the  edge  of  the
continental shelf to their present location as the sea level has risen. In broad coastal plains, for every meter that
sea level rises, the shoreline typically retreats about one kilometer.
Sea Cliff Erosion
In places where the rock is weak or the waves are strong, wave action can hollow out depressions in a cliff wall
that grow into sea caves. Because a headland is subject to wave action on two sides, caves dug from both sides
may eventually meet in the middle, cutting a tunnel through the headland. Further erosion will widen the tunnel,
eventually leaving behind only an overlying rock bridge called a sea arch. Continued erosion eventually causes the
arch to collapse, leaving an isolated column of rock, called a sea stack, in front of the headland.
Tectonic Uplift
The evolution of a shoreline by erosion may be interrupted by tectonic uplift, or a sudden movement of Earth's
crust, which lifts a coastal region. Once lifted above the sea, the former beaches, wave‐cut platforms, and wave‐
built terraces become a new coastal plain. The process of erosion begins again as wave action attacks the new
coastline.
The Design
I had two amazements  when I was reading between lines  B.S. 8110‐1:1997 Structural  use of concrete – Part 1
Code of Practice for design and construction:
The aim of design is the achievement of an acceptable probability that the structure being designed will perform
satisfactorily during their intended life.
The Design method recommended in this code is that of limit state design. Account should be taken of accepted
theory, experiment and experience and the need to design for durability.
 
The Concept of Safety of Dar-es-Salaam Structures

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Structural Engineering, which is

"The art of using materials That have properties which can only be estimated To build real structures that can only be approximately analyzed To withstand forces that are not accurately known So that our responsibility with respect to public safety is satisfied"

The above quoted literature brought to my attention that we need to work from first principles and that copy and paste from codes or design software should be for comparison if the assumptions made in the codes and softwares are close to ours.
Issues raised below are intended to obtain parameters we can employ in the design of a safe Dar-es-Salaam.

Dar‐es‐Salaam and The Sea Level

The relative elevation between the High Tide Level of the sea and the central business area in the City is a matter of concern. Time and again I have thought of it. I wonder if there is anybody doing the homework about the effects of Global warming. If there is none, it is time we acted. Scientists have already warned us that a small rise in sea level can be catastrophic; and maybe Maziwe Island disappearance can be Lesson One.

Dar‐es‐Salaam and Global Warming

Scientists have reported that the world has an average temperature of 15°C having warmed up by about 0.6°C for the past one century. While I do not dispute the figure, one is bound to be suspicious. Average can mean nothing when we want to deal with a particular location. I have lived in Dar‐es‐Salaam from the early 1960's and my imagination sees that the temperatures have gone up by about 10°C. We have a good number of weather stations in the country which have been recording temperature, rainfall and wind speed for some years now. It is time Engineers took their role to interpret these data to pave way to solutions of our impending issues.

Dar‐es‐Salaam and Ground Water Table

If there is rise in sea water, we would like to ascertain ourselves that the inland water table is not affected by such rise. The towers and structures we are erecting tend to block the natural draining pattern of the ground water. This may lead to the creation of patched aquifers or raise the water table in various places. Recently I watched some drilling for soil investigation at a site Science and Technology Building along Jamhuri Street. It was during an extended dry spel; and water was struck at 9.5 metres. Geology may be tricky, but simple mind would think the water table is less than that at the New Post Office and worse at the Gymkhana Grounds.

Dar‐es‐Salaam and the Acid Rain

The caves at Masaki area along the shorelines have always left me with questions unanswered. Working in Oyster‐ bay area in Dar‐es‐Salaam, during the excavation of the footings, we observed a cavity (hollow space) that extended to a distance we never measured. The area being made up mostly of lime‐stones, I suspected that there is Acid Rain effect or some kind of acid material disposal has brought the effect.

Experiences such as the one I had at Oyster‐bay are supposed to be documented to be incorporated in design as a prerequisite of the Codes of Practice. Who has the mandate to coordinate such experiences?

In India, Taj Mahal, a tourist attractive and an architectural and Engineering masterpiece was on constant scientific monitoring. There was no trouble until a fertilizer factory was built nearby, then the marble began to be eroded. Sulphur fumes from the factory combined with rain to form acid that reacted with the marble. They factory was removed to save Taj Mahal.

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©Eng Swithurn M. Mgaya June,2008
 
The Concept of Safety of Dar-es-Salaam Structures

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Dar‐es‐Salaam and the seismic action

We are witnesses of the fact that areas which did not have the influence of seismic forces, are now; Dar‐es‐Salaam is not an exception. Buildings constructed in such areas with earthquake activity, the earth must be investigated to a considerable depth. Faults in the crust of the earth beneath the soil must obviously be avoided. Some soils may liquefy when subjected to the shock waves of a quake and become like quicksand. In such cases, either construction must be avoided altogether or the foundation must be made deep enough to reach solid material below the potentially unstable soil. Those structures which were constructed without such consideration, monitoring of the behavior of such structures is essential to ascertain safety.

Dar‐es‐Salaam and soil strata

My experience in the drilling of deep wells in Mbagala (and I hope it will represent Dar‐es‐Salaam) have revealed that there are alternating layers of sand and clay. Consideration of this is important, particularly when we want to build a tower. Certain clay soils have been found to expand 23 cm or more if subjected to long cycles of drying or wetting, thus producing powerful forces that can shear foundations and lift lightweight buildings. Some soils with high organic content may, over time, compress under the building load to a fraction of their original volume, causing the structure to settle. Other soils tend to slide under loads. Geological and hydrological data bank for Dar‐es‐Salaam is essential. Such data need to be properly investigated and well interpreted.

Dar‐es‐Salaam and Landslides

While constructing some houses in Mbezi and Kimara areas, I have encountered faults which are running for long distances. Some say that such faults run for some kilometers. Landslides may occur when water from rain sinks through the fault, seeps through cracks and pore spaces in underlying sandstone, and encounters a layer of slippery material, such as shale or clay, inclined toward the valley. The water collects along the upper surface of this layer which it softens. If the support is sufficiently weakened, a mass of earth and rock slides down along the well‐lubricated layer. Some great landslide masses move slowly and spasmodically for years, causing little destruction. An additional weight of a heavy structure on such areas may enhance or accelerate the sliding. Earthquakes and volcanic eruptions can also cause severe, fast‐moving landslides.

Dar‐es‐Salaam and Population growth

As the human population grows, more and more people live in areas exposed to natural geologic hazards, such as floods, earthquakes, tsunamis, volcanoes, and landslides. In the colonial days, construction was prohibited in the onetime swampy areas of Mikocheni, Msasani, Mwananyamala, Mbezi; to mention a few. Today they said onetime prohibited areas are the prime for construction; notwithstanding the reasons that made the areas prohibited at that time.

We need the knowledge of the geologists to try to understand these natural hazards and forecast potential geologic events, the study of the history of events as recorded in rocks and try to determine when the next eruption or earthquake will occur and also study the geologic record of climate change in order to help predict future changes. As human population grows, geologists' ability to locate fossil and mineral resources, such as oil, coal, iron, and aluminum, becomes more important. Finding and maintaining a clean water supply, and disposing safely of waste products, requires understanding the earth's systems through which they cycle.

Dar‐es‐Salaam and Materials Fatigue.

While this is not much in the Building industry, it is gradually gaining momentum now that talk of reuse of materials is gaining eminence. Reuse of steel from demolished buildings for example can be reused but the design

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©Eng Swithurn M. Mgaya June,2008
 
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engineer must consider fatigue strength, rather than elastic strength or ultimate strength, in his calculations. Even for new materials, test of their strength is of paramount importance to safeguard the safety we aim at.

Fatigue failures account for an overwhelming majority of all structural failures in cyclic devices such as engines.

Dar‐es‐Salaam and Building Materials

Structures in Dar‐es‐Salaam are basically made of cement‐sand blocks, concrete and reinforced concrete for the foundations and walls; use of concrete, steel or timber piles is rare if any. Roofs are made of reinforced concrete and timber/steel trusses covered with corrugated iron sheets and tiles. These basic materials involve aggregates, sand, water, cement, iron, timber and clay.

a. Aggregates 

Most of the Aggregates used in Dar‐es‐Salaam are basically limestone. If we have Acid rains, we can be sure the basic components of our footings to be attacked; unless it can be proven that once the aggregates are mixed with sand and cement do change the chemical composition and hence change their reaction to acid, the fact remains. 

Recently, structural Engineers prescribe ratio M20 (1:1½:3) of concrete for reinforced structures. I'll be surprised if contractors do attain such strengths, particularly using limestone aggregates. I've had some sad experiences on the matter. 

b Sand: 

Illustrated with an experience should send the message home. Working at a site at Yombo Vituka I ordered sand for the works. With all the good aggregate‐cement‐sand‐cement‐water mix and workmanship concrete took a long time to set. After removal of formwork, it was as if I used blinding concrete. On follow up, I learnt that the sand supply collected the sand from a quarry near an ocean. The sand tested salty, but tested too late. 

When Engineers instruct to make trial mixes of concrete before commencement of work, some contractors think the Engineers are demanding too much. A quarry used 10 or 20 years ago fairly well can prove to be unfit today, considering the many environmental changes taking place. 

c. Cement:

I was taught of the various classifications of cement while in School. For 20 years in the field, I used Portland cement, but never queried if this class of cement was right for those particular conditions. It was in 1999 at the then Kahama Mines when the Project Manager yelled "No Twiga Cement is to be used here" meaning ordinary Portland Cement, when my mind started pondering about the specifications and the conformity criteria for Ordinary cements. It was then that I seriously went through Code of Practice BS 197‐ Cement.

There is a theoretical understanding or an assumption that a bag of cement weighs 50 kilogrammes; you are witnesses that this is not usually the case. Bags of cement weigh sometimes as low as 40 kilogrammes. This has a serious impact on the strength of the structure under construction due to such an assumption

d. Steel:

Temperatures and salty humidity of Dar‐es‐Salaam are favourable conditions for corrosion particularly for areas close to the sea or beach areas. Protection of reinforcing steel from the reach of the moisture in the atmosphere requires a properly vibrated concrete, provision of damp‐proof courses, plastering and paints.

Exposed steel can be painted using aluminium, zinc etc. with the right under‐coat.

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©Eng Swithurn M. Mgaya June,2008
 
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e. Timber:

Timber is perceived as a rustic material and is sometimes used in public parks, on private property, or in other situations in which a natural or historic appearance is desirable. The strength and durability of timber are quite limited compared to those of steel and concrete. Therefore, timber is suitable only for short spans that carry minimal traffic loads, even in this case treatment is essential.

PROPOSED ACTION

Just pointing out the impending risks arising from our own actions without coming out with at least a proposed action to get solutions is to create frustration. These proposed actions may leave a lot to be desired, but at least somebody may be willing to fill the gap; for which you are welcome.

1. Measurement of Movement of Structures 

Measurement of vertical and horizontal movement of our structures, particularly of our flourishing towers, results of which shall enable us to send an alarm or take action before worse comes to worse. This will also give us an experience for the further development of other towers or structures. 

2. Measurements of High Sea Levels and Land Levels 

Measurements of the relative levels between the High Sea Levels and the Land levels, including seeking experiences of countries which have already faced flooding catastrophes. This can alert us how long it will take for the sea level to top our banks and prepare by protection or face the inevitable, whichever will be cheaper. 

3. Drilling of Observation Wells 

To monitor the the rise or fall of ground water table, we need to drill observation wells and install monitoring equipment. 

While drilling results of the samples taken shall enable to know the depth and the type of various strata. The results may help us to know some of the behavior of structures. 

Physical and chemical properties of water from these wells recorded shall be an indicator of the pollution of underground water. 

4. Access to Temperature, Rainfall and Wind Records 

Tanzania is privileged to have Weather Stations almost nationwide, with records, if preserved, dating back to the 1950s. These records need to be interpreted in Scientific and Engineering terms. This, I am sure can come out with results that will assist to preserve the Earth's environment in a state that supports life. 

5. Measurement of Seismic Action 

Tanzania is among the countries of the world where volcano is still active. I don't need any reference for I am witness to that fact. The rift valley crossing our country should make us suspicious. I don't know if there is any statutory body assigned with the duty of watching and recording the behavior of volcanic actions in our country 

6. Study of Broad Coastal Plains 

Since measurement of the increase of sea level can be difficult to measure directly, the use of broad coastal plains can do the homework. Since rise of water level by one metre can go to a kilometer away, mathematically this is easy. 



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©Eng Swithurn M. Mgaya June,2008
 
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7. Identify and Demarcate Quarry Sites 

We like to standardize things and this should include standard quarry sites and standard borrow pits. Working in a Road project in Kisarawe, I doubted the material from the assigned borrow‐pit, but I my Supervisor told that the site had been explored by a respected Consultancy firm and therefore had no need to doubt. We employed all professionalism in the construction and all tests gave excellent results – raised the certificate and we were promptly paid. The first rain and all the road was a deposit of mud. 

8. Set up Habitat Laws 

As pointed out earlier, as the human population grows, more and more people live in areas exposed to natural hazards, and when worse comes to worse they ask what does the government do to help. When they moved into such habitats they did not consult the government. 

During colonial days, some areas in Dar‐es‐Salaam were prohibited for habitation. As if all colonialists did was bad, their departure found senior and enlightened people occupying the very areas. The houses designed drain waste water and sewerage to septic tanks and soak‐pits, which are unsuitable for such water‐logged areas; and end up making their way out as surface disposed sewerage. Don't ask who designed the disposal system – they copied and pasted without due consideration of the geology or land formation of the area. 

Unless we come up with strict habitat laws, we shall move from having environmental pollution to environmental contamination. 

9. Measurement of Soil Erosion and Deposition on Sea 

Isostatic changes which we have described earlier like that of Mississippi river are caused by deposition of silt at its delta. With all the news of erosion we hear or read, one wonders how much our deltas affected and what is the impact of such deposits. Can you think of the river at Salender bridge depositing silt so much so the entrance to the ocean is blocked. Thanks to the campaign to protect Mangrove trees, which tend to further reduce the velocity of the river and deposit continues. I shall not be surprised that one day Jangwani is a lake. We therefore need to take measurements and study the effect of soil erosion and deposition at the sea and take remedial measures. 

10. Setting up Tanzanian Codes of Practice 

Rome was not built in a day, but it requires somebody to start. We can do it. I don't remember exactly which country, but do remember to have read a code of Practice of a very small country in Asia which had developed its Codes or rules or policy of Practice. Papers of Engineers submitted for discussion and the deliberations; research papers presented by Students from Engineering institution and others can be a starting point to collect the relevant requirements. 

FUNDING 
Somebody once said, 'It is easier said than done'. Where do we get the funds for this commitment? 

1. Arrangements can be made by Engineers in practice to come up with the challenges, take them to the Engineering Institutions of Higher Learning for students to make a research for the same, with an incentive for the paper that will present practical solutions to the challenges. 

2. The Local Government is collecting property tax for all the Building in Dar‐es‐Salaam, at least an agreed upon portion can be located for this purpose. 
3. All Engineers, Consulting firms and Contractors shall be obliged to contribute towards the fund. 
4. The Central Government's contribution 
5. Consultancy Services offered by the Office. 

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©Eng Swithurn M. Mgaya June,2008
 
The Concept of Safety of Dar-es-Salaam Structures

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REQUIREMENT

To start this Office an initial of 1,000,000US$ shall be required the first year and 750,000US$ the following year. For the first year, the monies shall be used for:

Setting an Office 

Purchase of working gadgets 

Research and Exploration Fees 

Travelling and expenses 

Salaries for Administrative Staff 

Preparation of Reports 

SUMMARY 

Environmental issues and safety are gaining an upper hand in the Building industry worldwide. We want a safe life and safety for the investments. The issues at hand need to be settled – we cannot afford to let it go, for it means our own undoing. When you are using materials that have properties which can only be estimated to build structures that can only be approximately analyzed to withstand forces that are not accurately known so that our responsibility with respect to public safety is satisfied; an account should be taken of accepted theory, experiment and experience. 

CONCLUSION 

Issues discussed impact everybody. A multi‐disciplinary team of Engineers and Scientists are required to work on the issues raised; to alert and rescue the situation or at least reduce its impact. It is cheaper to demolish a multi‐ million tower at will after evacuating everything and everybody, rather than let it fail without warning and loose the tower, property and human life, the price of which you cannot calculate. 


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