Civil Structures

BridgesTwo types:

Simply supported beam Cantilevered beam

Innovations: From 10,000BC, primitive beam and suspension bridges to cross rivers and ravines Greeks perfected beam bridges Roman engineers design arch bridges; more stable and secure, arch did not impede

water traffic Fall of Roman Empire in 5th century; medieval arch bridges not as efficient 16th century – truss girder bridge; longer spans with safety 19th century – modern suspension bridge Bowstring girder embraced by railway engineers 20th century – first box girder used for freeways Cantilevered bridges, limited impediment to water traffic Brooklyn Bridge – first suspension bridge to use steel cables Concrete used as a building material for arch bridges Sydney Harbour Bridge completed in 1932. Cuts travel time to North Sydney Tacoma Narrows Bridge failure – leads to safer suspension bridges Sections designed to deal with wind.

Materials:Material Advantages Disadvantages

1. Timber2. Rope3. Stone

4. Bricks

5. Cast iron

6. Wrought iron

7. Steel

8. Concrete

Readily availableEasy to use; distributes load; cheapDoesn’t rot; strong in compression; availabilityDoesn’t rot; strong in compression; easily shapedStrong in compression; melt into various shapes; hollowable; considerable weight reductionUsed for cabling

Strong in tension and compression equally; cheapStrong in compression – reinforcing with steel gives strength in tension; easy to transport/shape

RotsRots/breakingHeavy; time-consuming; expensive to manufactureNot strong in tension

Rusts; have to paint; weak in tension and shear

Unreliable material due to fibrous structureRusts; quite heavy

Can crack; heavy

Stress: ƒ = P/A ƒ = stress (Pa)P = load (N)A = cross-sectional area(m2)

Strain: e = x/l e = strainx = extension (m)l = original length (m)

Shear stress: ƒs = P/A ƒs = shear stress (Pa)P = load (N)A = shear area (m2)

Terms: Elastic limit – the stress up to which the object will return to its original form Yield stress – the stress where there is a marked increase in strain without a

corresponding increase in stress Proof stress – the amount of stress necessary to bring about a certain amount of

permanent strain in a material Toughness – the ability of a material to absorb energy

Omar El Bezri Enginneering Studies1

If the shear plane runs perpendicularly across the object, the shear area will be the cross-sectional area. If, however, the shearing operation punches a hole then the shear area will be the circumference of the hole multiplied by the thickness of the material.

Hooke’s Law – “Stress is proportional to strain up to the elastic limit” (Young’s Modulus)

Young’s Modulus:E = ƒ = F/A = Fl

e x/l Ax

Factor of Safety:For ductile materials, For brittle materials,FofS = Yield stress FofS = UTS

Maximum allowable stress Maximum allowable stress

Stress/Strain diagrams:

Truss Analysis:Support Image FBD Attributes Reasons for use

Fixed Can support vertical and horizontal loads and moments

To firmly anchor a structure

Pin or hinge Can support vertical and horizontal loadsFree to rotate

To provider a non-moving support for a bridge

Roller Can only provide reactions normal to the surfaceFree to rotate

To allow side movement for expansion in a truss

Reactions at the supports:1. Draw a FBD showing all loads and dimensions2. Determine the horizontal And vertical Components of any angled forces3. Take moments around the non-roller support first to determine the reaction4. Use ΣFv and ΣFh to find the reactions at the pin support5. Find the total reaction at the pin support

Method of Joints:Using three forces:Draw a force triangle, and then use trigonometry to solve for the needed forces.Using four forces:Break all angled members up into their horizontal and vertical components, and then use

ΣFv and ΣFh to find the required forces.

Method of Sections:

Omar El Bezri Enginneering Studies2

Proportional limit

Elastic limit

Progressive yield

Ultimate tensile strength

Breaking point

Cut the truss through more than two members, that cuts through the required force. Take a moment around a point that eliminates some of the unknown forces.

Shear Force: Bending Moment:

Either start at the left and add the forces at the point loads, or draw all the external forces onto the diagram and link them with horizontal lines.

Either sum the moments about active and reactive forces, or work out the area under the SF diagram (if it has already been drawn), adding and subtracting the positive and negative values accordingly.

The neutral axis and outer fibre stresses: the upper surfaces undergo compression, while the lower surfaces undergo tension.

Bending stress:M = E = ƒb M = bending moment at section (Nm)I r y I = second moment of area (m4)

E = Young’s Modulus for the material (Pa)ƒb = My R = radius of curvature (m) I ƒb = bending stress at section (Pa)

y = section’s distance from the neutral axis (m)

Uniformly Distributed Loads (UDL): a load that is uniformly spread across a beam.

Crack Theory: The way cracks form is closely linked with the applied stress, the Young’s Modulus of the material and the strain energy present.

Strain Energy:SE = ½ ƒe SE = strain energy / unit volume (J/m3)

ƒ = stress (Pa)e = strain

Critical crack length:Lg = 2WE Lg = critical crack length (m) Πƒ2 W = work of fracture for each surface (J/m2)

E = Young’s Modulus (Pa)ƒ = average tensile stress (Pa)

Omar El Bezri Enginneering Studies3

Neutral axis of the beam

To prevent cracks in a metallic material, we weld the material together. In polymeric materials, it may be possible to use adhesives, or replace the item altogether. In ceramic materials, replacement is often the only option.We can eliminate cracks from forming by creating an object with no corners, or placing interfaces within an object. These are areas within a material, weaker than the surrounding area, that run perpendicularly to the expected growth of cracks. When the crack reaches this interface, it is blocked from passing it.

Engineering materials:

Testing of materials:Non-destructive tests include:

o X-ray testing – used to determine if small cavities are presento Dye penetrant – used to find small cracks in the surface by placing a dye on

the surface and examining the surface under UV lighto Ultrasonic – ultrasonic pulses are used to determine if cavities are present

Destructive tests include:o Tensile – used to determine the tensile strength of materials. Test piece is

stretched and load and extension are recordedo Compressive – used to determine the compressive strength of materials. Test

piece is compressed and load and deformation are recordedo Transverse – used to determine a materials performance when undergoing

bending and shearo Torsion – done to see how a material will cope with twisting forces (couples)

Ceramics:o Stone – weak in tension, strong in compression, low in toughness (brittle)o Glass – made from silica, soda, and lime. It is a very viscous liquid.

Toughened glass is heated, then the outer surfaces are cooled quickly to place them in compression – this makes the glass a lot stronger

o Cement – a ceramic material formed by complex reactions when alumina, soda and lime are reacted. Cement is a ceramic material while concrete is a composite that partly consists of cement. When cement is mixed with water, it produces a silicate gel, which creates heat, so needs to be hosed down. Cement and concrete also do not reach full strength for many years.

Composites:o Timber – consists of pored (hardwood) and non-pored (softwood). Pored

timbers come from flowering plants (angiosperms) and non-pored timbers come from the pines and conifers (gymnosperms). Has an excellent strength to weight ratio, and reasonable performance in bending, and a relatively high Young’s Modulus. It is susceptible to attacks by weather and pests.

o Mortar – used between bricks in buildings. Contains Portland cement, sand and lime in the ratio 3:2:1.

o Concrete – consists of cement, sand and aggregate (usually gravel). Cost is reduced by the aggregate, because less cement is required. Offers far greater strength than cement and is cheaper. Consists of 4 parts aggregate to 2 parts sand to 1 part cement. Reinforced concrete can be made in one of two ways:

Pre-stressed concrete is created when stressed cables are placed through the wet concrete – when it dries, these are released, placing the concrete in compression and increasing its strength.

Post-stressed concrete is formed when concrete is cast with tubes running through the material – after setting and curing, wires are pulled through the tubes and anchored in tension, increasing the strength of the concrete.

Omar El Bezri Enginneering Studies4

Concrete also gets “concrete cancer” – when the reinforcing steel corrodes it expands, which causes the concrete to crack. To alleviate this, the concrete is vibrated into position, to reduce porosity.

o Asphalt – Widely used for road surfaces. It is tough and crack-resistant due to the exposed aggregate. It can deal with slight movements in the road surface better than concrete, because of its toughness.

o Laminates – materials that consist of varying materials sandwiched together. Some of these include:

Plywood – consists of layers of timber with the grain arranged at 90o to each successive layer

Laminated glass – two layers of glass are passed through rollers that compress a vinyl sheet lying between them. The result is a shatter-proof glass

Bimetallic strips – one metal will have a different thermal expansion rate to the other so as it heats up it will deflect from its neutral position. Used for thermostats and protection circuits in gas systems

o Geotextiles – woven polymers or ceramic fibres used for a variety of purposes. Used to stabilize road surfaces and stop drains from getting clogged

Corrosion: the chemical deterioration of a material. Metallic corrosion involves the breakdown of metals or metallic alloys, and is basically the reverse of the refining process.

o Oxidisation occurs when a metal loses electrons, and it occurs at the anode. Reduction is when a metal gains electrons, and it occurs at the cathode. An easy way to remember this: OILRIG (Oxidisation is loss, reduction is gain).

o Dry corrosion occurs through chemical reactions of metals or alloys with gases in furnaces at high temperatures. Wet corrosion occurs when a metal is placed into a fluid, usually an electrolyte.

Uniform attack – if a metal is placed in a liquid, some parts will become anodic while others will become cathodic. The locations of the anode and cathode will continually change, resulting in uniform corrosion.

Galvanic attack: Galvanic corrosion occurs when dissimilar metals are placed

together in the presence of a corroding environment Concentration cells occur where there is a difference in

concentration of the electrolyte, for example where the liquid has been settled for a period of time

Stress cells are the result of high residual stress in parts of a metal object – these areas become anodic while the lower stress areas become cathodic.

o Some protective methods are used to stop corrosion, including painting, and galvanizing, or dipping the steel pieces in molten zinc which creates a protective layer.

Orthogonal Drawing:Developments:

A development is when a shape is laid out flat with any fold lines shown. They can be simple, such as a cube, or can be more difficult – for these we use development by triangulation.

Omar El Bezri Enginneering Studies5

Omar El Bezri Enginneering Studies6