For the steel beam with Young Modulus of 200GPa, second moment of area of cross section of 5x107mm4, boundary conditions

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For The Steel Beam With Young Modulus Of 200gpa Second Moment Of Area Of Cross Section Of 5x107mm4 Boundary Conditions 1 (57.57 KiB) Viewed 34 times

For the steel beam with Young Modulus of 200GPa, second moment of area of cross section of 5x107mm4, boundary conditions, geometry, and loading as given in figure Q3, answer the following questions: a) Explain why the beam shown in Figure Q3 is statically determinate. Write equilibrium equations and find the reactions at supports A and D. (4 marks) b) Using Macaulay's method (Singular functions), write down descriptions for the bending moment, slope and deflection that covers the entire length of the beam. (5 marks) c) Identify all boundary conditions and use them to find the constants of integrations in Slope and deflection descriptions. Write down ready to use equations for bending moment, slope, and deflection as functions of position x (measured from A) along the beam. (4 marks) d) Find Maximum deflection of the beam (show that it is at x=3.98 m from A) and slope at the pinpoint A (at x=0). (7 marks) e) Find maximum bending moment along the beam (show that it is at x=3.21875 m from A) and calculate the corresponding maximum bending stress. The height of the symmetric cross section of the beam is 100 mm (ymax=50mm) (5 marks) 3m 75 KN 20 kN/m 3 m 50 kN 2m Point loads: 75kN at B, 50kN at C; Uniformly distributed load over the entire length (AD): 20kN/m; Beam segments lengths: AB=BC=3m, CD=2m Figure Q3. Beam details of geometry and loading Total: (25 marks)