10.13 A cantilever beam is loaded with force P at its free end to produce a deflection APL/3EI. The beam has a circular cross section, I r'/4. Develop a figure of merit for selecting a material that minimizes the weight of a beam for a given stiffness (PI), By using the following material properties, select the best material (a) on the basis of performance and (b) on the basis of cost and performance. %3D %3D E Material GNM2 ksi P, Mgm Approx. Cost, $/ton (1980) Steel 200 29 x 10' 7.8 450 Wood 9-16 1.7 x 10' 0.4-0.8 450 Concrete 50 7.3 x 10' 2.4-2.8 300 Aluminum 69 10 x 10 2.7 2,000 Carbon-fiber- 70-200 15 x 10' 1.5-1.6 200,000 reinforced plastic (CFRP)

Problem 2 A simply supported timber beam has a span of 6 m long and carries a uniformly distributed load of 28 KN/m over its entire span. This load already includes an allowance for beam weight. The timber is 80% stress grade Apitong. The allowable deflection is of the span. The properties of the Apitong are given. 240 i. E = 7.31 x10³ Mpa = 1.73 Mpa Which of the following gives the smallest dimension of the beam such that the allowable shear stress is not exceeded. a. 220 mm x 440 mm b. 150 mm x 300 mm C. 200 mm x 400 mm

12. Assume a uniformly load simply support beam with a rectangular cross section. The width of the beam is fixed by other design considerations. Determine the ratio between the difference in depth required for an aluminum beam compared to a steel beam in order to obtain the same maximum deflection. MOE aluminum can be taken as 10,000 ksi, for steel as 30,000 ksi. The maximum deflection for the beam is 5wl*/384EI Factoring the deflection equations we can conclude that for equal deflection Eala = Esls where subscripts a and s represent values for aluminum and steel. The depth of must be times the depth of the

For the simple truss shown in the picture the students are required to determine a combination of values for the cross-sectional area of the truss members and the angle 0 that will allow the structure to be both safe for example, the axial stresses developing within the truss elements are less than the yield stress fy = 500MPA and cheep, provide that the cost of the material is cost = 1.1£/kgr. Assume that the density of the material is 8100 kgr/m³. It is noted that the structural analysis has been already carried out for and the analytical relations expressing the internal forces have been provided in the picture. P=2000 KN cost Ray -Reye %½. taco Kw PEA Tel PAB EA Ray E,A lon Pazo Ray/ Ray Sime Pascose + Pac -> Parea -Pao coso Paca Ray coe Ray cose Sino