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Assessment Task: Take Home Assessment

This assessment task must be performed individually. Answer all questions. This assessment task is work 20% of the entire unit

QUESTION 1 (5 MARKS)

Figure 1. Seepage flow problem modelled by finite element method.

For the seepage problem shown in Figure 1, use the finite element method to calculate the hydraulic heads at points P and Q. Use the following data: k1   = 0.042 mm/s, k2   = 0.61 mm/s, k3  = 0.053 mm/s  and  k4  = 0.21 mm/s, L1  = 220 mm, L2  = 51 mm, L3  = 260 mm and L4  = (36 + a) mm. The known hydraulic heads ℎc  = (184 + b) mm, ℎB  = (65 − c) mm,  ℎA  = 36 mm. The  cross-sectional  area of all the soil sections are A = 0.2 mm2 .

The following data depend on your student number

a = last 2 digits of your student number

b = last 2 digits of your student number

c = last 1 digit of your student number

QUESTION 2 (8 MARKS)

Figure 2. Assembly of three 2-node bar elements subjected to force P.

Consider the assembly of three 2-nodedbar elements shown in Figure 2. Use the finite element  method  to  determine  the  nodal  displacements.  The  node  numbers  are presented next to the filled circles. The element numbers are in brackets. The Young’s modulus  of  the  elements  is  E  = (1200 + b) KPa.  The  cross-sectional  areas  of  the elements are the same i.e., A = 0.05 m2 . The lengths of the elements are L23   = 1.8 m. The force F  = 18 KN

In your solution you must show:

1.   The element connectivity table

2.   The reduced global assembled system of equations

The following data depend on your student number

θ = (30 + last 1 digit of your student number)in degrees

α = (10 + last 1 digit of your student number)in degrees

b = last 2 digits of your student number

QUESTION 3 (7 MARKS)

Figure 1. Two beam elements subjected to distributed load q and concentrated load

P.

Figure 1 shows two beam elements subjected to distributed load q and a concentrated force  P = 120 KN.  The  flexural  rigidity  of  the  beam  elements  are  EI = 240 × 103  KNm2 . Element numbers are in brackets and node numbers are beside the filled circles. Calculate the displacements and rotation at nodes 1 and 2. The following data depends on your student number