1. A cantilever tube has an unsupported length L = 350.0 mm, an outside diameter of 45mm and an inside diameter of 35mm.
It is made of an aluminum alloy.
By how much will the end deflect under and end-load of 500 N?
Use data from CES for the (mean) value of Young’s modulus of aluminum alloys, the equation for the elastic deflection of a cantilever and for the second moment of a tube.
Submission requires:- expressions and data used, calculation and solution clearly identified.
2. Use a Young’s Modulus-Density (E-Ï) chart normalized to wrought aluminium alloys WAA to find
(a) any metals that are both higher modulus and less dense than WAA and
(b) materials (not just metals) that are both higher modulus and less dense than WAA
Submission requires:- brief explanation of selection methodology, normalised properties chart(s), results table (10marks)
3. Use an E-Ïchart to identify materials with both 50GPa< E < 100 GPa and E 1/2 /Ï > 0.003 (GPa)1/2/(kg/m3).
Remember that, on taking logs, the index M = E 1/2 / Ïbecomes Log ( E ) = 2Log (Ï)+ 2Log (M )
Submission requires:- brief explanation of selection methodology, properties chart(s), results table. (25 marks)
4. In strength-limited applications, deflection is acceptable provided the component does not fail; strength is the active constraint.
Derive the material index for selecting materials for a beam of length L, specified strength and minimum weight. For simplicity, assume the beam to have a solid square cross-section t x t. You will need the equation for the failure load of a beam.
Constraints Length L is specified
Beam must support a bending load F without yield
Objective Minimize the mass of the beam
Free variables Cross-section area, A
Choice of material
Submission requires:- Collection of appropriate expressions, derivation and final clear statement of MI (25 marks)
5. Show your material index of Q4 on an appropriate properties chart, selecting the 5 materials with the highest MI.
Submission requires:- Appropriate properties chart with selection line, results table. (10marks)
6. Choose a material from Q5 suitable for producing a light and strong tubular framework- eg space frame, roll cage
By appropriate use of sensible data- size, dimensions, thicknesses, select a sequence of processes which include shaping, joining (if necessary) and surface finishing for the product.
Submission requires:- Process selection stages with clear and substantiated constraints and suggested processes