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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
© MFA and DC 2007
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
© MFA and DC 2007
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
© MFA and DC 2007
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
© MFA and DC 2007
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
© MFA and DC 2007
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
© MFA and DC 2007
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
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
© MFA and DC 2007
Minimizing embodied energy for given EImax
Results Sawn Softwood section-(175x25x2.41) Sawn Softwood section-(200x22x2.42) Sawn Softwood section-(200x25x2.75) Sawn Softwood section-(225x22x2.72)
© MFA and DC 2007
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
© MFA and DC 2007
Demo
© MFA and DC 2007
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
Table: Structural sectionsTable: Structural sections
Subset: Structural sectionsSubset: Structural sections
Table: Structural sectionsTable: Structural sections
Subset: Structural sectionsSubset: Structural sections
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)
Browse Select Search
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
Browse Select Search
1. Selection data
Structural sections: Structural sectionsStructural sections: Structural sections
2. Selection Stages
Graph Limit Tree
Browse Select SearchBrowse Select Search
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
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
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