Good Beam Diagram1

7/30/2019 Good Beam Diagram1

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9 Structures


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http://en.wikipedia.org/wiki/Image:Canary.wharf.and.dome.london.arp.jpghttp://www.diedrichsandassociates.com/images/projects/fea/steering.jpghttp://www.surrey.ac.uk/CivEng/pictures/civil/build3.jpghttp://img510.imageshack.us/


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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.

http://video.google.com/videoplay?docid=6411397054336552770&q=tacoma+bridge&total=184&start=0&num=10&so=0&type=search&plindex=9


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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

http://www.esm.psu.edu/courses/emch13d/design/animation/Fnecking.html


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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
http://en.wikipedia.org/wiki/Image:Snow_on_trees.jpg


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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.
http://www.answers.com/topic/cantileverbeam-png


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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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http://upload.wikimedia.org/wikipedia/commons/4/4a/FAE_visualization.jpg


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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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