Question

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Problem Statement Consider a simply supported beam with length L=1m, width w=25mm and height h. The beam has a mass m=10kg hanging from it as shown in Figure 1. The mass is located at the midpoint of the beam. Figure 1 Schematic of a simply supported beam with mass m attached to it at the midpoint. The deflection of the beam at the midpoint is given by the equation below: dmg/? 48E1 where g=9.81 m/s? is the gravitational acceleration, E is the elastic modulus of the material and / is the second moment of area given as Task The maximum acceptable deflection is 1 mm. You have three choices for the material (show in Table 1). Taking the Carbon Steel beam as a reference, what will be the relative cost of the beam if you used Aluminum or Nickel. Which one will be the cheapest? Table 1 Available materials along with their Young's modulus and relative cost. Material Young's Modulus E (GPa) Density (kg/m') Relative Cost Per kg Carbon Steel 190 7850 Aluminum 70 2700 Nickel 180 8800

Answer 1

mg mgh X6 10X9.81 x 3 - = Code pour) 30 (99) d= mgh 48E1 - 48 Expony 4E who (a allus) = 10 m since all other things are same 4x EX 0, 025) (23) Cox gid 1x1000) hit (4x EX 0.025 ) e this out of beam (Sx volume & Cont) = (B) x (Wh) x (c). PE x 0.02s xol901) PxC (989) I material TE IS Tigox1097850 0 3.39 70x10" 2700 25 3.25 Nickel 180x100 | 8800 | 20 1 77.41 So assuming cs to be a Al 3.25 = 0.9587 A cheapest 77.4 P = selative 2 = 22.83 3.39