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The Question. You are equipping an expedition for exploring rough terrain and you will need to take panels to fabricate bridges over obstacle you might encounter. You have to carry all of your equipment and will be interested in lightweight constructions. The width and the length of the bridge panels are fixed Your bridge panels are not to fail under a distributed load. The maximum stress for a distributed load F applied to a panel of width w, length and thickness t is max = 31F 4wt2 The elastic deflection of such a panel is 8 = 5F13 32Ewt3' where E is Young's modulus. You are given the panels' length 1 = 750 mm, the panels' width w 200 mm. the distributed load F = 160 kg (please use g=9.81 m/s²), The material data are Material Youngs modulus (GPa) Yield strength (MPa) Density(T/m³) 7.8 Sheet steel 207 220 Wood 0.7 16 90 Reinforced concrete 3 47 410 Glass fibre composite 2 48 1240 a) Failure by plastic deformation Establish a material index Mp that minimises the mass of the panel with the constraint that no plastic deformation occurs. Calculate the values for this material index for each material. The material index is defined here as having high value for low mass and conversely. At this stage, no need to convert any units from the table. The answers are acceptable with a tolerance of .1 (non-specified units).