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9 Structures
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9.1 Youngs modulus
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In selecting the materials for a componentit is essential to know how the materialbehaves under various loads.
The strength of a material depends on its
ability to sustain a load without unduedeformation or a failure.
Tensile testing, in which a specimen is
loaded until destruction, is one of the mostimportant materials property tests.
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9.1 Youngs modulus
stress and strain
Used for the description of the elastic properties(STIFFNESS) of structural elements like: Wires
Rods Columns
Beams
being under the influence of forces.
Young's modulus can be used to predictthe elongation orcompression of an object as long as the stress is less than theyield strength of the material.
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Definitions Young's Modulus is a ratio of the stress to the
strain. Symbol E ; Units: [N/m2]
Stressis force (load) per unit area acting on a body or system
Symbols; Units: [N/m2]
Strainis the ratio of a change in dimension to the original
value of that dimension. Symbol e; Units: [-]
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An elastic material returns to its original length (or shape) when any load isremoved.
Aplastic material distorts easily but does not break.
Youngsmodulusprovidesquantitativedata relating tothe relationshipof strength andstiffness instructures.
Beyond theyield point, thematerialundergoes
plasticdeformation
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There are three typical definitions of
tensile strength
Yield strength: the stress atwhich material strain changesfrom elastic deformation toplastic deformation, causing itto deform permanently.
Ultimate strength: themaximum stress a material can
withstand.
Breaking (Rupture)strength: the stresscoordinate on the stress-straincurve at the point of rupture.
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Assignment
Draw a stress / strain diagram for a brittlematerial
Draw a stress / strain diagram for a plasticmaterial
Draw a stress / strain diagram for an elasticmaterial
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Stress / Strain diagrams by
categories
A = Elastic
B = Yield Point/ Elastic limit
C = Failure point
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Examples of Stress Strain diagrams
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Typical tensile strengths
MaterialYield strength
(MPa)Ultimate strength
(MPa)Density(g/cm)
Structural steel 250 400 7.8
Spider silk 1150 1200Kevlar 3620 1.44
Carbon nanotube 62000 1.34
Pine wood 40Concrete 3
Assignment: rewrite the table with SI units
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HW: Due Tuesday 02/10/2007
A tensile strength specimen has a diameter of 11.3 mm and a gaugelength of five times the diameter. In a tensile test to destruction,the following results were obtained:
1. Plot a load extension graph.
2. Calculate the Youngs modulus for the sample
Load
[kN]
2 4 6 8 10 12 14 16 18 20 22 24
Extension
[m]
1.6 3.3 5.0 6.6 8.0 10.0 11.5 13.5 18.0 25.0 36.0 57.0
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9.2 Forces
Force is an action which may cause rotation,deformation, or an increase in pressure for the body itacts upon.
Forces applied to a component of a structure are calledstructural loads.
CW: what is the load
acting upon wrist, arms,
spinal cord, leg, sole?
Handout: Defining terms
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Loads
Dead
Live
Environmental Static
Dynamic
Combination
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External loads
This involves loads wherephysical contact is made
This is when an object is
attached to a lift (ie.Helicopter) and the weightof the object adds to the
helicopters. This involvesloads where physical contactis made
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Body load
Is a load without physical contact, eg a structures own
weight.
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Mass and Weight
Mass is "How much matter is in an object".Weight is a vector force that is the measure of
Mass in relation to gravity. It is simply the mass
of an object multiplied by the acceleration ofgravity.
Mass is measured in SI units, in Kilograms (kg)Weight is measured in Newtons (N). A Newton
is literally (kilograms * meters)/(seconds2)
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Relationships of external loads to internal forces and
the concept of the balance of equilibrium of forces
within a structure.
A structure works byinterpreting how externalloads give rise to internal
forces within the structuralmembers.
A static structure is inequilibrium, otherwise itwould move, ie the forcesacting upon it are equal insize and opposite in
direction.
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Tensile and compressive forces and how
they affect equilibrium within a structure
Tensile loads tend toextend or stretch astructural member.
Compressive loads tendto compress or shorten astructural member.
Tensile and compressiveforces must balance ifthe structure is to
maintain equilibrium.
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Calculate a tensile or compressive
strain given values of force and area.
The simple equation that is required with thisgiven information is: Stress = Force/Area.
The unit of stress is measured in N/m2Assignment CW:
Find the strain in a tug-o-war rope which resists a
load of 700N and is 15mm in diameter
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Calculate a tensile or compressive strain given
values of the original dimension and the change in
dimension.
Strain = Extension/Original Length
Strain has no unit because it is a ratio between
two numerical valuesAssignment CW:
A steel wire 6mm diameter and 8m long extends
5mm under a pull of 3.6kN. Calculate the strain inthe wire.
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Evaluate the importance of forces in
a design context.
HW Due: 12/11/07
Write one paragraph
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The main problem that arises is if the failure to support specific forcewill fail. If we apply forces, will the failure to support the tension,compression, shear, bending, torsion or elastic instability occur?
As designers, we must remember that the forces have to be distributed
evenly over the whole area. The limitations of the bending and torsionequations must also be taken into account. In deriving the bendingequation it was assumed that each cross-section of the beam issymmetrical about the plane in which the loads are applied.
Further complications arise when a component carries two or more
types of loading simultaneously. This would result in the fracture in thematerials. Among other things, the designer has to specify the material from which
each component is made. Many materials are not equally strong intension and compression and the designer must therefore consider both
tensile and compressive stresses. Concrete, for example, has little strength in tension and steel rods offer
little resistance to compression. But if the steel rods are embedded in aconcrete beam near the tension face, the bending moments are resistedby tension in the steel and compression in the concrete.
There is a body load and an external load that acts upon buildings thusreinforced concrete is used.
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Class work: Norman Example 8.1 and Assignment 2 p 402Handout pp 370-375
1. List the types of equilibrium.
2. List the types of structures.
3. Describe a monocoque structure.
4. Outline the differences between concentrated and
distributed forces.5. What other terms are used to name dead and live
loads?
6. Define a vector.7. Define coplanar forces.
8. Define concurrent forces.
9. State the principle of concurrency.
9 3 Th t th d tiff f
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9.3 The strength and stiffness of
structures
D fl ti l ti
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Deflection - elasticmovement or sinkingof a loaded structural
member, particularly ofthe mid-span of abeam.
Stiffness -The ratio ofa steady force acting ona deformable elasticmedium to the resulting
displacement.
Stiffness = Load
Deflection
Unit [N/m}
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External load
If an external loadis applied to somepart of a structure,
that part will bedeflected to someextent, depending
on the size of theload and thestiffness of the
structure.
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Beam
A beamis a bar, body or
structure, with one dimensionlarge compared with the otherdimensions, whose function isto carry lateral loads
(perpendicular to the largedimension) and bendingmovements.
Many beams are horizontaland the loads they carry areweights acting verticallydownwards.
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Bending moment
A bendingmoment exists in astructural element
when a moment isapplied to theelement so that
the elementbends.
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Computer model of a beam under load
Moment about a pivot
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Moment about a pivot The load distance from the
pivot is called the moment aboutthe pivot. The distance betweenthe load and the pivot is calledthe moment arm.
The moment arm is theperpendicular distance FROM the
force's line of application TO theaxis of rotationMoment = Force * Moment Arm
Unit [N*m]
CW:Lift weightsCalculate the moment of a 40 kg wallshelve acting at a distance of 20 cm from
its fixing to the wall.
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Class work
Consider a trap door held by a piece of string,BC.
Pand Qare forces.
The trap door is hinged
about point O.
Write the formula: Moment ofPabout O
Moment ofQabout O
Calculate Q when the door is 20 kg and the angle OBQis 30 degrees.
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Factor of safety
It is the designers responsibility to ensure that everycomponent of a structure can withstand the forcesacting on it.
The first step is to decide on a safe stress for the
material of the component. This is usually called theworking stress and it is obtained by dividing thefailure stress by a factor called the factor of safety.
The failure stress is obtained by experiment. If failureis taken to mean the onset of permanent strain thenthe yield point is used. In some circumstances failureis considered to be fracture and the ultimate strength
is taken as the failure stress.
Factor of safety
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Factor of safety
Factor of safety = Design Load
Normal maximum load
The value of the factor of safety will depend upon
the type of loading to be expected. If the structure
carries only static loadsa low value such as two
may be used. If there are suddenly applied orimpact loads a higher value must be taken.
Factors of safety for steel structures will vary from
about 3 for static loads to about 15 for impactloads or 20 where fluctuating loads may cause
fatigue failure.
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CW: Due Monday 19/11/2007
Evaluate the importance of strength andstiffness in a design context.
Write 1 paragraph
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9.4 Beams Beams are structural
members that aresubject to loads actingnormallyto theirlongitudinal axis.
The loads create shear
stresses and bendingmoments and causethe beam to bend orflex.
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Cantilever beam
Cantilever
beams are rigidlysupported at oneend with theother end free.
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Computer model
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Single shear stress:Class Work
23 kN
23 kN
Pin in single shear
Single shear stressA load of 23 kN is attempting to shear a
12 mm rivet holding a brake pad/backing
plate assembly together.Calculate
the shear
stress
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Class work
Describe how beams are designed to transferforces and distribute loads through the beams.
Finite element analysis
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Finite element analysis
Finite element analysis
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Finite element analysis
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HW: Due Tuesday 27/11/06
Produce a timeline with the historicaldevelopment of the materials used tomanufacture beams. Include examples!
Format: A4 page with five or more entries.
Read HANDOUT
Properties of
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Properties of
different sectionsCW
List the crosssections that arestiff for both loads.List the cross
sections that areweak for bothloads.Outline the
benefits of usingthis sectionalshapes.Handout
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