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Aims : Aims : After this session is over you will be After this session is over you will be able to: able to: Apply analytical methods to the Apply analytical methods to the management and production of management and production of construction, civil engineering or construction, civil engineering or building services installation building services installation processes and operations processes and operations Objectives: To be able to Determine amounts of materials Determine amounts of materials removed from excavations and the removed from excavations and the amounts of equipment required amounts of equipment required Compare the effectiveness and Compare the effectiveness and efficiency of solutions to construction efficiency of solutions to construction situations . situations .

Trapezium Rule Practical Substructure And Excavation Presentation1

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Page 1: Trapezium Rule Practical  Substructure And Excavation Presentation1

Aims :Aims :After this session is over you will be able to:After this session is over you will be able to:

• Apply analytical methods to the management and Apply analytical methods to the management and production of construction, civil engineering or building production of construction, civil engineering or building services installation processes and operationsservices installation processes and operations

Objectives: To be able to •Determine amounts of materials removed from Determine amounts of materials removed from excavations and the amounts of equipment required excavations and the amounts of equipment required

•Compare the effectiveness and efficiency of solutions to Compare the effectiveness and efficiency of solutions to construction situations .construction situations .

Page 2: Trapezium Rule Practical  Substructure And Excavation Presentation1

Why is excavation important ?

The first considerations when excavating must be ….

Page 3: Trapezium Rule Practical  Substructure And Excavation Presentation1

First - Excavation Hazards…

The greatest risk… Cave-ins

Other hazards include:..

Asphyxiation due to lack of… oxygen

Inhalation of… toxic materials

Moving machinery can cause… a collapse

Accidental severing of… utility lines

Fire

Page 4: Trapezium Rule Practical  Substructure And Excavation Presentation1

Injury and Death

Excavating is one of the most hazardous construction operations

Most accidents occur in trenches 5-15 feet deep

There is usually no warning before a cave-in

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Definitions•Excavation – a man-made cut, cavity, trench, or depression formed by earth removal.

Trench – a narrow excavation. The depth is greater than the width, but not wider than 15 feet.

Shield - a structure able to withstand a cave-in and protect employees

Shoring - a structure that supports the sides of an excavation and protects against cave-ins

Sloping - a technique that employs a specific angle of incline on the sides of the excavation. The angle varies based on assessment of impacting site factors.

Page 6: Trapezium Rule Practical  Substructure And Excavation Presentation1

Summary

The greatest risk in an excavation is a cave-in.

Employees can be protected through sloping, shielding, and shoring the excavation.

A competent person is responsible to inspect the excavation.

Other excavation hazards include water accumulation, oxygen deficiency, toxic fumes, falls, and mobile equipment.

Page 7: Trapezium Rule Practical  Substructure And Excavation Presentation1

Steps to be followed during substructure construction

Step 1 - Green field siteThis is the starting point for the excavation, the first stage is to remove the topsoil and state whether it is being kept or removed from site. The topsoil is excavated in isolation, as it is valuable.

Where shall we dump the topsoil ?

Page 8: Trapezium Rule Practical  Substructure And Excavation Presentation1

Step 2 - Removal of top soilTopsoil is measured per metre squared as the depth to be excavated is given in the item description in the Bill of Quantities.

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Step 3 Trench excavationThis is the first use for the centre line measurement, which is multiplied by the breadth and depth of the trench to give the volume of material to be excavated

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Step 4 Earthwork SupportSupport to the sides of the excavation is required to prevent collapse. Note that two depths are required, one for the outer side of the trench and one for the inner side of the trench.

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Step 5 Concrete FoundationsThe centre line is again used in this item. The quantity of concrete required is measured by volume and Centre Line x Breadth x Depth is calculated

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Step 6 Brickwork wallingBrickwork walling in substructure billing is measured to the DPC level. The centre line is used but will need adjustment if the wall thickness changes between inner and outer leafs i.e. half brick and one brick thick.

Page 13: Trapezium Rule Practical  Substructure And Excavation Presentation1

Step 7 Backfill to trenchBackfill is measured in two stages; the first is the quantity at either side of the brick walling by subtracting from the excavated material quantity the material for concrete foundations and brickwork. The second is at the outer leaf top soil level, a new centre line can be calculated for the backfill at this area.

Page 14: Trapezium Rule Practical  Substructure And Excavation Presentation1

For any excavation with sloping sides is there an easy way to calculate the perhaps thousands of tonnes of materials which needs to be removed …

Trenches with sloping sides are trapezoidal in shape…

Then we need to calculate the area of a trapezium…

Lets see how we calculate the area of a …

Page 15: Trapezium Rule Practical  Substructure And Excavation Presentation1

The Area Of A Trapezium.A Trapezium is any closed shape which has two sides that are parallel and two sides that are not parallel.

Page 16: Trapezium Rule Practical  Substructure And Excavation Presentation1

The formula to calculate the area of a trapezium like the red one shown, is in the yellow box below it.Write the formula down :

a

b

h

Area = ½ h ( a + b )

Get a pen and paper and lets try a few…

Page 17: Trapezium Rule Practical  Substructure And Excavation Presentation1

What Goes In The Box ? To find the area of the shapes below Use the formula :

(1)

20cm

13cm

10cm

2.7m5.4m4.9m

(2)

165cm2

19.85m2 (to 2 d.p)

Area = ½ h ( a + b )

Page 18: Trapezium Rule Practical  Substructure And Excavation Presentation1

Example 1 Calculate the area of the trapezium below :

16cm

11cm

13cm

Solution ( Using the formula).

Area = ½ h ( a + b )

a = 16 b =11 h = 13

Area = ½ x 13 x ( 16 + 11 )

Area = ½ x 13 x 27

Area = 175.5cm2

Page 19: Trapezium Rule Practical  Substructure And Excavation Presentation1

Now for the practical use of the Trapezium formula

Now Use the trapezium formula to calculate the volume of the material excavated on the following page.

Note something happens to the material when it is excavated…This can have an impact on the cost of transporting it.

OK lets go,analyse the text on the next page and set your work out methodically….

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Tutors note 1

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clue-State

Clue change

Tutors note 3

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Tutors note 4

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Now for another practical use of the Trapezium formula

Now Use the trapezium formula to calculate the volume of the wall on the following page.

Then calculate the weight of the brickwork.

Hint:- The dimensions shown are in mm…first divide all dimensions by 1000 to get your units in metres.

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