CIVE2700 Cheat Sheet PDF

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Summary

Cheat sheet for midterm 1...

Description

σ

Stress:

δ

= F/A

ε

strain:

∆

=

L / Lo

σ

Young’s Modulus: E =

ε

/

ε lat

Poisson’s Ratio: v = -

ε long

/

Linear Coeff. of Thermal Expansion aL =

L / (L . T)

σ fail

FS = (

σ allow

/

)

density = r = m / V

unit weight = g = W / V

ρ

specific gravity = G =

/

ρw

Volumetric Coeff. of Thermal Expansion aV

= V / (V . T) for isotropic materials aV = 3aL

∙

Static (Dead) Loads – long term

applied and removed slowly so no vibrations

∙

random – never repeats (earthquake) recoverable deformations (springs back)

∙

usually due to gravity

↳

transient – quick impulse that decays back to resting (vehicles)

↳

∙

Plastic

∙

Proportional Limit

transition between linear and non-linear behavior

↳

∙

Ultimate Stress

↳

has little plastic deformation before failure (glass, concrete)

↳

materials: = shear stress/rate of shear strain, unit Pa.s or cP

∙

↳

↳

∙

Ductile Material

∙

Viscoelastic materials

↳

↳

stress increases during plastic deformation

↳

Rupture Stress

↳

∙

have delayed response

Creep: Long-term deformation under constant load

Toughness: energy required to fracture

Precision: measure many times and get same result

↳

↳

↳

Influence of flaws and slip planes on mechanical properties

of crystal grains influence the material behavior change grain structure

↳

compatible crystal structures

∙

host atoms in the lattice

↳

∙

∙

Interstitial atoms fit between the metal atoms

∙

∙

∙

∙

Refined grain, softened steel

reloading returns to previous peak stress

∙

∙ ↳

↳

∙

↳

∙

↳

∙ strain continues ↳ Brittle Material Viscosity: Resistance to flow (i.e. to shear force) ∙ for linear Yielding

point where specimen fractures or ruptures

Deformation depends on: Duration of load, Rate of loading, Temperature

↳

Temperature affects mechanical behavior of all materials: high temp =

↳

↳

Accuracy: close to true value; absence of

Common lattice structures: body center cubic (BCC) , face center cubic (FCC),

Grain boundaries act as crack inhibitors, increasing toughness, The size and arrangement

Smaller grains are formed by rapid cooling and increase toughness, Both heat treating and plastic strains during manufacturing

↳

∙

Can dissolve only about 6% into the host

↳

Substitutional atoms take the place of

The steel production consists of three phases:1. Reduction of iron ore to pig iron (high carbon) 2. Refining pig iron to steel 3. Forming steel into

Steel can be hardened or softened by using heat treatment. The response of steel to heat treatment depends upon its alloy composition

temperature in furnace

∙

Steel is an alloy of iron and carbon but frequently contains chromium, copper, nickel, phosphorous, etc. This is only possible if the different materials have

Must have an atomic radius less than 60% of the host metal

If the atoms are similar enough, the compounds can mix easily

∙

Bias: tendency to deviate in one direction from true value

Flaws & defects are weak spots, reducing toughness

This mainly depends on the rate of cooling of the molten metal

Alloys have one or more compounds dissolved in a metal

↳

∙

∙

periodic – repeating waveform (rotating equipment)

Production: availability and ability to fabricate material into desired shapes

Stresses develop because of different rates of thermal expansion and contraction for different materials that are connected together, use expansion joints

hexagonal close pack (HCP)

products

∙

has lots of plastic deformation before failure (structural steel, rubber)

↳

∙

∙

stretches bonds between atoms without rearranging them

transition between elastic and plastic behavior – maximum stress with full recovery

have both elastic and viscous response

Modulus of Resilience: energy required to reach yield point

Construction: ability to build the structure on site (trained work force)

∙

Elastic Limit (Yield Point)

↳

Elastic

permanent deformations when unloaded, rebound parallel to the linear portion with some remaining plastic deformation strain hardening

maximum stress on the curve (tensile or compressive strength)

A quick shock or pulse may cause little deformation, while a sustained load can cause much deformation

ductile, low temp = brittle

bias

↳ ∙

Dynamic (Live) Loads – short term shock or vibration

All solid materials deform under load

∙

atomic bonds slip past each other and rearrange

stretched bonds return, rearranged ones don’t, when reloaded, follows the rebound line and then original curve

with little or no increase in stress (after elastic limit)

↳

Relieves internal stresses & strains introduced by mechanical working

∙

↳

Common heat treatments: Annealing: Heating metal to austenite & slowly cooling it to room

Improves ductility & toughness; Normalizing: Similar to, but not the same as annealing, Difference in temp. &

rate of cooling, Heat well above critical temp & then cool slowly in still air, Removes coarse grain structure & produces uniform fine grain; Hardening: Slowly heating metal to form austenite, Quenched (cooled rapidly) by plunging into water, oil, or brine, Hardens (strains) the steel, Must be followed by tempering; Tempering: Uniform heating below critical temperature followed by air cooling, Increases ductility & toughness of steel, but reduces strength & hardness, Usually done after hardening through quenching → relieve internal strains that might cause cracking

↳

General corrosion uniform corrosion process

↳

↳

Slow cooling → coarse grained steel

↳

Rapid cooling → fine grained steel

Pitting corrosion non-uniform, highly localized → pits

↳

↳

Fine-grained materials: higher strengths, more uniform in structure, smoother surfaces

Galvanic corrosion two metals of different electrochemical potential in contact

↳

Stress corrosion under stress,

↳ ↳ ↳ ↳ ↳ Corrosion-resistant steels combination of alloying elements ↳ Steel grades: Grade refers to the strength of the steel ∙ chemical composition ∙ strength level ∙ methods of manufacture ∙ methods of identification ∙ identified by a number and a letter ∙ Number → yield point in MPa ∙ Letter → characteristics of the 6 types of steel available ∙ For example, 350W → yield point of 350 MPa, weldable steel ↳ Flat rolled products – plates, flat bars, sheets and strips ↳ Sections – rolled shapes, rolled bar-size shapes and hollow structural sections ↳ Bolts (used for connections) ↳ Welding electrodes (rods of wire used to produce welds) ↳ Aggregates can be defined as a combination of distinct parts gathered into a mass or a whole ↳ Shape: angular, rounded, flaky, or elongated ↳ Flaky and elongated are bad because of easy breakage and difficulty compacting in thin asphalt layers ↳ High friction (angular, rough) for strength & stability of asphalt ↳ Low friction (rounded, smooth) for workability of concrete ↳ Texture and angularity – fractured faces, Visual inspection to determine the percent of aggregates with: no fractured faces, one fractured face, more than one fractured face ↳ Traditional: Maximum aggregate size – the largest sieve size that allows all the aggregates to pass; Nominal maximum aggregate size the Superpave: Maximum aggregate size – one sieve size larger than the nominal maximum aggregate size; Nominal maximum aggregate size one sieve larger than the first sieve to retain more first sieve to retain some aggregate, generally less than 10% ↳ than 10% of the aggregate ↳ #4 sieve four openings/linear inch ↳ Weight of a given volume of graded aggregate that has been compacted -> bulk density ↳ Bulk unit weight is the weight of aggregate required to fill a “unit” volume. ↳ Uniform (or one-sized) ∙ all particles of same size ∙ largest volume of voids ∙ paste requirement is highest ↳ Continuous ∙ combination of many sizes ∙ minimizes volume of voids ∙ preferred for efficient use of paste ↳ Gap ∙ missing one or more particle sizes ↳ Maximum aggregate size ∙ Smallest sieve opening through which entire sample passes ↳ Nominal maximum size ∙ Smallest sieve opening through which most (90-95%) of the sample passes ∙ Grading requirements are based on nominal maximum size ↳ Isotopes are atoms that have the same number of protons and electrons but different numbers of neutrons ↳ The maximum number of electrons in a shell is equal to 2n where n is the principal quantum number of the shell ↳ The orbital path of electrons is defined by four parameters: The principal quantum number or shell designation, the crystal flaws have a major influence • impurities • voids ↳ Primary Bond: forms when atoms interchange or share electrons in order to fill the outer subshell designation, the number of energy states of the subshell, the spin of the electron. ↳ (valence) shells like noble gases. Stronger than the Secondary Bond ↳ Secondary Bond: forms from an imbalanced electric charge among atomic arrangements. ↳ Metals- metallic bonds between atoms with 1, 2, or 3 valence electrons - steel, iron, aluminum, etc. ↳ Inorganic Solids - covalent and ionic bonds between atoms with 5, 6, or 7 valence electrons; Ceramics – portland cement concrete, bricks, diamond, glass, aggregates (rock) ↳ Organic Solids - long molecules of covalent hydrogen-carbon molecules with secondary bonds between chains, hydrocarbons, asphalt, plastics, wood ↳ Refining Pig Iron and Scrap to Steel: Remove excess carbon and other impurities by oxidation in another furnace ∙ Basic oxygen furnace – 300 tons in 25 minutes Electric arc – electric arc melts steel – lots of energy Deoxidize with aluminum, ferrosilicon, manganese, etc. Killed Steel: completely deoxidized Forming Steel into Products ↳ ∙ ∙ ∙ ∙ Cast into ingots (large blocks that must be re-melted and reshaped) ∙ Continuous shapes ↳ Steel is an alloy of iron and carbon ∙ Higher carbon: steel is harder & more brittle ∙ Modulus of Elasticity is the same for all Cast iron: high (>2%) carbon brittle three (same atomic bonds) ∙ ∙ High carbon steel: medium (0.8%-2%) carbon brittle ∙ Structural steel: low (0.15%-0.27%) carbon ductile ↳ Fine aggregate less ¼ inches: too small for induvidual inspection ↳ Coarse aggregate material retained on a sieve with 4.75 mm openings ↳ Fine aggregate material passing a sieve with 4.75 mm openings ↳ Important for proportioning concrete: negative free moisture – aggregates will absorb water, positive free moisture – aggregates will release water ↳ The maximum aggregate size should be less than the narrowest dimension between forms & reinforcement, between reinforcing bars, or the depth of slab localized, process much faster

Crevice corrosion accelerated by moisture & contaminants in crevices

ground, immersed in water

2

Protective coatings: paint, epoxy coating

Galvanic protection Zn coating

Cathodic protection structures below

W SS D=W s +W p

W S = Bone dry – dried in oven to constant mass W m = Air dry – moisture condition state undefined W OD = weight at oven dry W AGG = weight of aggregate in stockpiled conditions

W m− W s Ws W SSD−W s Ws

Moisture content: M =

Absorption: A =

W AD W WET

x100

x100 (%)

weight of material volume of material x unit weoght of water density of particles(solid volume) Apparent Specific Gravity: ASG = density of water W OD = W OD−W SW W OD −W SW = ( V solid + V impermeable voids ¿ γ w density of particles(solid volume+ pore volume ) BSG = density of water W SS D−W SW = ( V solid + V impermeable voids +V permeable voids ¿ γ w W OD W SSD BSG = BSG = W SSD−W SW W SSD−W SW A Bulk dry sp. Gr. = B+S−C S Bulk SSD Sp. Gr. = B+S−C 1 Blended specific gravity: G = P1 P2 P 3 + + +… G1 G2 G3 SSD

W SSD−W OD W OD W SSD−W AD Effective Absorption: EA = W SSD W WET −W SSD Surface Moisture: SM = W SSD Absorption Capacity: AC =

Specific Gravity (Relative Density): SG =

OD

= weight of submerged sample

A = dry weight B = weight of the pycnometer filled with water C = weight of the pycnometer filled with aggregate and water D = saturated surface – dry weight of the sample

= weight at wet conditions

x100

W AGG−W OD W OD

= Moist – moisture condition state undefined

W SW

= weight at air dry

Percent free moisture = M - A Moisture Content: MC =

Wm

= saturated surface dry – moisture

condition state undefined

x100 (%)

x100 (%)

x100 (%)

A B + A −C S− A (100) Absorption (%) = A volume of pores Porosity = total volume of particle Apparent Sp. Gr. =

Void content = total volume – solid volume of particles

V solid

(%) =

V solid V

x 100 =

W /γ solid W /γ bulk

γ bulk x 100 BSG OD x γ w (BSGOD x γ w)−γ bulk Void content (%) = BSG OD x γ w

x 100 =

γ bulk γ solid

x 100 =

x 100

Fitness Modulus: FM =

Σ (cumulative % by mass retained on each sieve) 100 Σ Ri 100 Ri = cumulative percent retained on sieve sequence *range of 2.3 - 3.1 for fine aggregate types larger FM being coarser aggregate G= Composite SG G1, G2, G3 = SG of fractions 1,2, and 3 P1, P2, P3= decimal fractions by weight of aggregate 1,2,and 3 in the blend where the total is 1.00 Sand Equivalency Test: SE =

hsand

/

hclay

x 100

=...