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\_ | Explain the following terms with at-least one example: i. Round off error li. Accuracy iii. Precision iv. Significant digits Truncation error 2 | An I 1-m beam is subjected to a load, and the shear force follows the equation Vx) = 5 + 0.25x? where Vis the shear force and x is length in distance along the beam. We know that Y= dd/dx, and Mis the bending moment. Integration yields the relationship. M= M,+ i Vay Jo If Mo is zero and x = 11, calculate Musing multiple-application Simpson’s | rule using I-m increment. /3"4 Develop finite element formulation for a one dimensional 2 noded torsional shaft element. Where A = Cross-sectional area, J= Polar Moment of Inertia, E = Young’s modulus, @ = shear rotation of shaft, z= Poisson’s ratio and x = distance measured along the shaft’s length. If the shaft is rigidly fixed (@ = 0) at one end, using finite-element method calculation rotation of shaft at free end. Take D (shaft diameter) = 0.2 m, E = 200 GPa, Z = 10 m, and 7= 2500 N/m. uw 4 | The concentration of pollutant bacteria c in a lake decreases according to the equation: 6 = T5e7!! 4 20970078 Determine the time required for the bacteria concentration to be reduced to 15 using the Newton-Raphson method with an initial guess of ¢ = 6 and a stopping criterion of 0.5%. Check your result. 5 | The following equation can be used to compute the oxygen level c (mg/L) in a river downstream from a sewage discharge: le = 10 — 20(e°81* — 69) where x is the distance downstream in kilometers. (a) Determine the distance downstream where the oxygen level first falls to a reading of 5 mg/L. (Hint: It is within 2 km of the discharge.) Determine your answer to a 1% error. Note that levels of oxygen below 5 mg/L are generally harmful to gamefish such as trout and salmon. (b) Determine the distance downstream at which the oxygen is ata minimum, What is the concentration at that location? 6 | The shear stresses, in kilopascals (kPa), of nine specimens taken at various depths in a clay stratum are listed below. Estimate the shear stress at a depth of 4.5m. Scanned by CamScanner 
