Question 1:

Q1 Figure 1 shows a steel beam used in one of the floors of a chemical plant. Using the method of superposition calculate the reactions at the each of the supports and the fixed end moments.

Draw Bending Moment (BM) and shear force diagram for the beam AB. (Standard formulas of general loading cases are provided in the study desk)

Q2 Using the stiffness method, determine the reactions at the supports and the fixed end moment of the steel beam shown in Figure 1. Show the stiffness matrices for each member and the assembled global stiffness matrix.

Use a convenient method for the solution such as inverse matrices or use of simultaneous equations. E (Steel) is 200 GPa and Beam section details can be found in the One Steel product catalogue. (An extract of one steel catalogue will be posted on the study desk)

Q3 Perform a structural analysis using Creo3.0 simulate for the Steel beam as shown in Figure 1. Tabulate manual calculations and FEA results. Compare your FEA results with the calculated values of Q2.1 and Q2.2. You need to show beam's BM & SF plots, the beam's stress/strain plots and a deflection plot.

Question 2:

Q1. Write a short note (not more than half A4 page) on your understanding on St. Venant's Principal for your engineering design analysis.

Q2. Perform an FE analysis on Creo 3.0 Simulate for the axially loaded 8 mm thick aluminium plate shown in Figure 2. You need to simplify the problem using the symmetry and create a coarse mesh first and then refine the mesh appropriately. A picture of the refined mesh and necessary details must be provided. Also you also need to show X-Y 2D plane plots and through thickness stress/strain plots whenever necessary.

(a) Plane Stress Case:

Estimate the "Stress Concentration Factor" Kt at stress raisers areas identified by letter A and B. Estimate the principal stress (Max) and strain (Max) and local stress/strain (X & Y) at C, the centre of the plate. Using the X & Y components of the strain , manually calculate X,Y stress components and Z strain component using generalized "Hooks Law". Show all necessary steps of manual calculations, (2D plane stress) X & Y stress/strain plots and Max principle stress/strain plots.

(b) Plane Strain Case:

Estimate the "Stress Concentration Factor" Kt at stress raisers areas identified by letter A and B. Estimate the principal stress (Max) and strain (Max) and local stress/strain (X & Y) at C, the centre of the plate. Using the X & Y components of the strain , manually calculate X,Y and Z stress components using generalized "Hooks Law". Show all necessary all necessary steps of manual calculations, (2D plane strain) X & Y stress/strain plots and Max principle stress/strain plots.

Q3. Perform a 3D analysis on Creo 3.0 Simulate for the axially loaded 8 mm thick aluminium plate shown in Figure 2:

(c) Estimate the "Stress Concentration Factor" Kt at stress raisers areas identified by letter A and B. Estimate the principal stress (Max) and strain (Max) and local stress/strain (X,Y & Z) at C, the centre of the plate. Tabulate Kt for cases a to c and comment on appropriate analysis for the axially loaded 8 mm thick aluminium plate. Show all necessary (3D analysis) X, Y & Z stress/strain plots and Max principle stress/strain plots.

Question 3:

Figure 3 shows a conceptual model of a connecting rod which was prepared for an initial stress/strain analysis. The maximum normal operational pressure acting on the Gudgeon pin at the power stroke was estimated as 20MPa. The material of the connecting rod is steel alloy 42CrMo4 (E=198 GPa, Poisson ratio =0.3, Ult. Strength 800 MPa - 1000 MPa, Coef. of Expansion=17.3 x 10E-6 /0C)
(a) Create a suitable model to analyse the structural performances of the connecting rod at the maximum load application. You need to show, force applications, constraints and the refined model with the mesh using appropriate graphical representations.
(b) Perform a 3D Static analysis and show surface stress/strain plots and the stress/strain plots through the sections planes indicated by dotted lines.

You need to create a coarse mesh first and a then refine the mesh appropriately. A picture of the refined mesh and necessary details must be provided. Also you also need to show X-Y 2D plane plots and through thickness stress/strain plots whenever necessary. You are required to use symmetry for FEA modelling, as appropriate.

Question 4:

Clearly explain by point form the procedure to calculate the reactions at the supports , the fixed end moment and the mid- span deflections of beam segments AC, CD and DB of steel beam shown in Figure 1 of Q1, using the stiffness method. You need to show sketches wherever necessary.