New approaches to Materials Education - a course authored by Mike Ashby and David Cebon, Cambridge, UK, 2007 © MFA and DC 2007 Unit 10. Structural sections:

New approaches to Materials Education - a course authored by Mike Ashby and David Cebon, Cambridge, UK, 2007

© MFA and DC 2007© MFA and DC 2007

Unit 10. Structural sections:

shape in action

© MFA and DC 2007

Outline

Resources:

• “Materials Selection in Mechanical Design”, 3rd edition, by M.F. Ashby,

Butterworth Heinemann, Oxford, 2005, Chapters 11 and 12.

• Content and use of the database

• Structural sections and their attributes

• The CES database for Structural sections

Exercises

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Structural sections

Shape = cross section formed to a

Tube

I-section

Hollow box

All increase Second moment of area I Section modulus Z Bending stiffness E I Bending strength y Z (called YZ in the database)

When materials are loaded in bending, in torsion, or are used as slender columns, section shape becomes important

© MFA and DC 2007

Data organisation: structural sections

Universe

Structural sections

Family

• Angles

• Channels

• I-sections

• Rectangular

• T-sections

• Tubes

Material and Member

Extruded Al alloy

Pultruded GFRP

Structural steel

Softwood

Attributes

A record

Steel universal joist

• Material properties E,

• Dimensions Area A, …....

• Section props.: I, Z, K, Q ...

• Structural props.: EI, Z, ...

y

y

Standardprismatic sections

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The CES database for Architecture

File Edit View Select Tools

Browse Select Search

Table: Structural sectionsTable: Structural sections

Subset: Structural sectionsSubset: Structural sections

Structural Sections

Channel+

Tube+

Rectangular+

T-sections+

Angle+

I-Sections+Records for

1880 sections

Material propertiesPrice 3.1 - 3.8 $/kgDensity 1650 - 1750 kg/m 3̂Young's Modulus17 - 18 GPaYield Strength 195 - 210 MPa

Pultruded GFRP Vinyl Ester (44 x 3.18)

Structural propertiesMass per unit length, m/l 0.562- 0.837kg/mBending Stiffness (major), E.I_max 1230 - 1810 N.m 2̂Bending Stiffness (minor), E.I_min 1230 - 1810 N.m 2̂Failure Moment (major), Y. Z_max 647 - 935 N.mFailure Moment (minor), Y. Z_min 647 - 935 N.mEtc.

DimensionsRadius, B 2.54e-003 - 3.81e-003 mThickness, t 0.0363 - 0.0389 m

Section propertiesSection Area, A 3.3e-004 - 4.93e-004 m 2̂Second Moment of Area (maj.), I_max 7.11e-008 - 1.05e-007 m 4̂Second Moment of Area (min.), I_min 7.11e-008 - 1.05e-007 m 4̂Section Modulus (major), Z_max 3.23e-006 - 4.68e-006 m 3̂Section Modulus (minor), Z_min 3.23e-006 - 4.68e-006 m 3̂Etc.

© MFA and DC 2007

Part of a record for a structural section

Material propertiesPrice 3.1 - 3.8 $/kgDensity 1650 - 1750 kg/m^3Young's Modulus17 - 18 GPaYield Strength 195 - 210 MPa

Pultruded GFRP Vinyl Ester (44 x 3.18)

Structural propertiesMass per unit length, m/l 0.562- 0.837kg/mBending Stiffness (major), E.I_max 1230 - 1810 N.m^2Bending Stiffness (minor), E.I_min 1230 - 1810 N.m^2Failure Moment (major), Y. Z_max 647 - 935 N.mFailure Moment (minor), Y. Z_min 647 - 935 N.mEtc.

DimensionsRadius, B 2.54e-003 - 3.81e-003 mThickness, t 0.0363 - 0.0389 m

Section propertiesSection Area, A 3.3e-004 - 4.93e-004 m^2Second Moment of Area (maj.), I_max 7.11e-008 - 1.05e-007 m^4Second Moment of Area (min.), I_min 7.11e-008 - 1.05e-007 m^4Section Modulus (major), Z_max 3.23e-006 - 4.68e-006 m^3Section Modulus (minor), Z_min 3.23e-006 - 4.68e-006 m^3Etc.

© MFA and DC 2007

Example: selection of a beam

D = beam depthB = widthI = second moment of areaE = Young’s modulusZ = section modulusy = yield strength

Beam

DimensionWidth B < 150 mm Depth D < 200 mm

Function

Specification

Constraints Required stiffness:E Imax > 105 N.m2

Required strength:y Z > 103 N.m

F

D

B

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Applying constraints with a Limit stage

5 15 Dimensions Minimum Maximum

Depth D m

Width B m

Section attributes

Bending Stiffness E.I N.m2

Failure Moment Y. Z N.m

0.2

0.15

100000

1000

Result : 294 sections out of 1881 meet these constraints

(a) Find lightest beam

(b) Find cheapest beam

(c) Find beam with lowest embodied energy

Objectives That meets the constraints

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Bending Stiffness EI vs.mass per unit length

Minimizing mass for given EImax

Results Extruded Aluminum Channel (130x50x1.82) Extruded Aluminum Channel (140x40x1.74) Extruded Aluminum Channel (152.4x28.6x1.75) Extruded Aluminum circular hollow (132x2.2)

E.Imax = 105 Nm2

Selection box

E.Imax = 105 Nm2

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Minimizing cost for given EImax

Bending Stiffness EI vs.price per unit length

E.Imax = 105 Nm2

Selection box

Price / length = Mass / length X Price / mass

Results Sawn Softwood section-(175x25x2.41) Sawn Softwood section-(200x22x2.42) Sawn Softwood section-(200x25x2.75) Sawn Softwood section-(225x22x2.72)

E.Imax = 105 Nm2

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Minimizing embodied energy for given EImax

E.Imax = 105 Nm2

Selection box

Embodied energy / length = Mass / length X Embodied energy / mass

Bending Stiffness EI vs.Embodied energy per unit length


E.Imax = 105 Nm2

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Minimizing embodied energy for given EImax


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The main points

It introduces the idea of choice to optimize weight, price or environmental impact

The CES Structural Sections database allows standard sections to be explored and selected to meet multiple constraints

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Demo

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Exercises: Browsing Structural sections

10.1 Find, by browsing, the records for Pultruded

Glass Vinyl Ester TUBES. What is the outer

diameter of the first tube in the list?

Answer: 0.1 m

10.2 Find, by browsing, the records for Rectangular

solid softwood Glulam beams. What is the

range of beam depths available in Glulam?

Answer: 0.18 – 0.9 m

File Edit View Select Tools

Browse Select Search Browse Select Search





Structural Sections

Channel+

Tube+

Rectangular+

T-sections+

Angle+

I-Sections+

Structural Sections

Channel+ Channel++

Tube+ Tube++

Rectangular+ Rectangular++

T-sections+ T-sections++

Angle+ Angle++

I-Sections+ I-Sections++

© MFA and DC 2007

Exercise: selecting from Structural Sections

10.3. Find the lightest section that meets the following constraints

Depth D < 60 mm

Stiffness E Imax > 10,000 N.m2

Strength y Zmax > 1000 N.m

Result

Extruded Aluminum Channel (Y.S.255MPa)-(50x50x0.79)

10.4 Now add the further constraint that the section must be an I-beam

Tree stage: I-Section

Result

Extruded Aluminum I-section (Y.S. 255MPa)-(48x44x1.1)


1. Selection data

Structural sections: Structural sectionsStructural sections: Structural sections

2. Selection Stages

Graph Limit Tree

Bending stiffness Eimax N.m^2

Failure moment YZmax N.m

etc

Dimensions

Structural

Max depth D m

Max width B m

etc

Min Max

10000

1000

0.06


1. Selection data


2. Selection Stages

Graph Limit Tree

Browse Select SearchBrowse Select Search

1. Selection data


2. Selection Stages

Graph Limit Tree



etc

Dimensions

Structural

Max depth D m

Max width B m

etc

Min Max

10000

1000

0.06



etc

Dimensions

Structural

Max depth D m

Max width B m

etc

Min Max

10000

1000

0.06

Dimensions

Structural

Max depth D m

Max width B m

etc

Min Max

10000

1000

0.06

2. Selection Stages

Graph Limit Tree

2. Selection Stages

Graph Limit Tree

I-Sections+ I-Sections++

© MFA and DC 2007

End of Unit 10

Documents

New approaches to Materials Education - a course authored by Mike Ashby and David Cebon, Cambridge, UK, 2007 © MFA and DC 2007 Unit 10. Structural sections: