What do you understand by plane stress, plane strain

Reference no: EM133684498

Finite Element Analysis

ASSIGNMENT - Plane Elasticity or modelling with 2D elements.

Question 1. What do you understand by plane stress, plane strain and axisymmetric problems? Give an example for each type showing the details of the structure, loading and boundary conditions.

Question 2. A reinforced concrete wall (or a deep beam) shown in the figure below is used to transfer a downward ultimate load of 600 kN/m. This wall is supported by two 400 mm x 400mm RC columns. Using Strand7's plane stress elements model this wall to determine the maximum deflection and maximum bending stresses (in compression and tension). Convergence is to be established and Richardson's extrapolation scheme is to be used, if necessary. Use modulus of elasticity of concrete Ec = 30GPa and Poisson ratio = 0.20.

463_Reinforced concrete wall.jpg

Note: Model the 400 x 400 columns as line (or fixed) supports for the deep beam.

Question 3. Re-analyze the beam shown above, using beam elements in Stand 7, and determine the maximum deflection and bending stresses in both compression and tension. Compare the results with those obtained from Q2, and comment. (You may use center to center beam span of 5 m and fixed point supports at ends)

Question 4. Electrical and mechanical service penetrations are required and therefore two 400 square holes are to be made at appropriate locations. By inspecting the stress contours or stress distribution (not at or near the supports), determine appropriate locations. Justify your choice of locations keeping in mind that stresses and deflections must not change significantly. You may justify your answer by comparing three options and you are required to use the number of elements obtained in Q2. (i.e. do not perform a convergence study for this question).

Question 5. A concrete dam having the cross-section shown below is proposed for a hydropower plant facility.
Model this dam using plane strain elements in Strand 7 and determine the following:

1083_Reinforced concrete wall1.jpg

Tip deflection.
Maximum stresses.
Note. You can either carry out a convergence study or use a reasonable number of elements to model the dam cross-section using your engineering judgement. Please note that coarse meshes do not give correct answers.

Reference no: EM133684498

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