1. 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: shape in action

2. © MFA and DC 2007 Outline Resources: “Materials Selection in Mechanical Design”, 3 rd 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

3. © 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

4. © 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,... Standard prismatic sections

5. © MFA and DC 2007 The CES database for Architecture File Edit View Select Tools Browse SelectSearch Table: Structural sections Subset: Structural sections Structural Sections Channel + Tube + Rectangular + T-sections + Angle + I -Sections + Records for 1880 sections

6. © MFA and DC 2007 Part of a record for a structural section Material properties Price3.1-3.8 $/kg Density1650-1750 kg/m^3 Young's Modulus17-18 GPa Yield Strength195-210 MPa Pultruded GFRP Vinyl Ester (44 x 3.18) Structural properties Mass per unit length, m/l 0.562-0.837kg/m Bending Stiffness (major), E.I_max1230-1810N.m^2 Bending Stiffness (minor), E.I_min1230-1810N.m^2 Failure Moment (major), Y. Z_max647-935N.m Failure Moment (minor), Y. Z_min647-935N.m Etc. Dimensions Radius, B2.54e-003 -3.81e-003m Thickness, t0.0363-0.0389m Section properties Section Area, A3.3e-004-4.93e-004m^2 Second Moment of Area (maj.), I_max7.11e-008-1.05e-007m^4 Second Moment of Area (min.), I_min7.11e-008-1.05e-007m^4 Section Modulus (major), Z_max3.23e-006-4.68e-006m^3 Section Modulus (minor), Z_min3.23e-006-4.68e-006m^3 Etc.

7. © MFA and DC 2007 Example: selection of a beam D = beam depth B = width I = second moment of area E = Young’s modulus Z = section modulus  y = yield strength Beam Dimension Width B < 150 mm Depth D < 200 mm Function Specification Constraints Required stiffness: E I max > 10 5 N.m 2 Required strength:  y Z > 10 3 N.m F D B

8. © 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.m 2 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

9. © MFA and DC 2007 Bending Stiffness EI vs. mass per unit length Minimizing mass for given EI max 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.I max = 10 5 Nm 2 Selection box E.I max = 10 5 Nm 2

10. © MFA and DC 2007 Minimizing cost for given EI max Bending Stiffness EI vs. price per unit length E.I max = 10 5 Nm 2 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.I max = 10 5 Nm 2

11. © MFA and DC 2007 Minimizing embodied energy for given EI max E.I max = 10 5 Nm 2 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.I max = 10 5 Nm 2

12. © MFA and DC 2007 Minimizing embodied energy for given EI max Results Sawn Softwood section-(175x25x2.41) Sawn Softwood section-(200x22x2.42) Sawn Softwood section-(200x25x2.75) Sawn Softwood section-(225x22x2.72)

13. © 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

14. © MFA and DC 2007 Demo

15. © 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

16. © 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 I max > 10,000 N.m 2  Strength  y Z max > 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)

17. © MFA and DC 2007 End of Unit 10