3. (a) A steel beam in the form of a cantilever of length 4 m, designed for a structural engineering application, is req

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3 A A Steel Beam In The Form Of A Cantilever Of Length 4 M Designed For A Structural Engineering Application Is Req 1 (108.15 KiB) Viewed 16 times

3. (a) A steel beam in the form of a cantilever of length 4 m, designed for a structural engineering application, is required to carry a load of 40kN at the free end and a uniformly distributed load of 10kN/m along its length as shown in Figure 3(a). The engineer implementing the design wants to make a reasonable estimate of the vertical deflection V at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm2, I= 150 x 106 mm (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 3(b). (0) Draw an FBD (Free Body Diagram) and mark all the external forces/moments acting on the beam. What is the main difference between the two problems from a structural analysis standpoint? Describe. (ii) To re-calculate the end deflection and the reaction force R exerted by the prop using Macaulay's method, write the relevant expression for bending moment in the beam. (iii) Integrate the relevant expression to find the slope and the deflection. (iv) State clearly the boundary conditions which will lead to the determination of the integration constants in the slope-deflection expressions. Note: The constants need not be calculated but make the substitutions and indicate the terms that will be eliminated, if any. 40KN 10kN/m 40KN 10kN/m 7 17 7 4m 2m 2m R Figure 3(a) Figure 3(b)