Answer Happy

A fixed end 1-beam (Figs. 1 & 2 below, Case 14, Table A-9, Textbook) is to be loaded with a concentrated load P at the center of the beam, as shown below. Assume it can be fabricated from 1 of the following 3 materials: 1020 HR steel ($0.30/1b) Find other necessary parameters from Textbook or online source 7075 Aluminum ($2.00/b) Find other necessary parameters from Textbook or online source Carbon Reinforced Composite, assume isotropic properties ($15.00/b) Find other necessary parameters from Textbook or online source E (p Width (in) weight density Length (15) Steel Aluminum Composite ? 3.00E+07 1.00E+07 1.50E+07 See I beam Properties below 0.283 0094 180 180 Figure 1 Fixed end beam with center load Lis beam length E is elastic modulus of the material I is 2nd area moment of inertia (given in Fig. 3 below) 0.074 180 Load The beam is to be an I-Beam section, Fig. 3 below, 5 10 x 35, 15 feet long (180 inches). The maximum deflection is given by: You=PL³/192E1 (Fig. 2 below, Case 14, Table A-9, Textbook), where P is center load
14 Fixed supports-center load 1. -1/2 1 t Ri= R₁ - M₁-M₂- Vis --Vic- MAS (4-1) Mac= The maximum stress o is given by Mc/I, where FX YARET(4-M) You FP 19211 Figure 2 Shear and Moment Diagrams for Fixed End Beam FI (continued) M is the maximum moment (Fig. 2 above, Table A-9, Textbook) c is one half beam height I is 2nd area moment of inertia, (Fig. 3 below) Using an Excel spreadsheet keeping the beam geometry the same, find the maximum permissible center load "p" for each material considering the following cases in your analysis (increase the center load by 2000 l increments on spreadsheet): 1. Maximum deflection considerations (You loss of function deflection is 0.5 inch, therefore maximum allowable deflection is 0.25 inch with a factor of safety, n = 2)) 2. Maximum stress considerations (o shall not exceed S,/2 of the material with a strength factor of safety, n = 2) 3. Minimum cost considerations (which material can handle the highest load at minimum cost?) 4. Minimum weight considerations (which material has the lightest weight and is able to handle maximum load?)