Fahad Bin Sultan University Departement of Civil Engineering
CIVE 517: Finite Element Method
Mid-Term Exam (Fall 2019)
Oct 26, 2019
Instructor: Prof. Khaldoon Bani-Hani Time: Take Home Exam
Student Name:
Student ID:
Instructions:
1. Return the exam solution in the next lecture
2. Make any assumptions required and state them clearly.
3. Write your name on all sheets..
4. Cheating is an academic violation according to Fahad Bin Sultan University rules and
regulations, and in some cases, it may result in final dismissal from the University.
Students should not under any circumstances commit or participate in any cheating
attempt or any act that violates student code of conduct."
Question Marks
Q1 /20
Q2 /25
Q3 /20
Q4 /10
Q5 /20
Q6 /5
Total /100
Fahad Bin Sultan University Departement of Civil Engineering
CIVE 517 – Finite Element Method I Prof.. Khaldoon Bani-Hani
Midterm
Q1. For the truss shown, use the stiffness method to determine the vertical and horizontal
deflections of the loaded joint B. Assume EA is the same for each member (EA=constant).
6
A
3 5
5m
Y
3m
(-4,3)
2 2
70 kN (0,0)
B 1X
1 1
3m
4
5m
C 90 kN 3
(-4,-3)
4m 2
Q2. Consider the prismatic rod shown below. Starting from the strong form of the equilibrium
equation, i.e.,
d du
AE b 0; 0 xL
dx dx
Use the Rayleigh Ritz Principle to estimate the approximate solution of the rod shown below.
b(x)
x E, A
L = 1 m, E = 200x109 Pa, A=0.0025 m2, b(x)=10x2 kN/m.
Assume
1) A polynomial “admissible” displacement field
u (x ) a0 a1x a3x 2
2) A polynomial “admissible” displacement field
u (x ) a0 a1x a3xe x
Compare the results.
Fahad Bin Sultan University Departement of Civil Engineering
Q3. A 3-node rod element has a quadratic shape
Function matrix:
3x 2 x 2
1 L L2
4 x 4 x2
N 2
L L
x 2 x2
2
L L
For L = 1 m, E = 200x109 Pa, A=0.0025 m2, u1 = 0, u2 = 5x10-6 m and u3 = 15x10-6, find:
A) The displacement u at x = 0.25 m.
B) The strain as a function of x
C) The strain at x = 0.25 m
D) The stress at x = 0.25 m
Q4. Perform the following numerical integrations using the approximations given.
1
5x dx using 2-point Gauss-Quadrature Integration.
4
Evaluate
1
Q5. Use Sap2000E (or any available FE program) to solve the following plane truss problem.
2 4 6 8 10 12 14 16
10
1 3 5 7 9 11 13 15 17
p p p
4@10 4@10
Neglect self-weight. Force P= 10.
Top chords: A= 1.5, E=10000
Web members: A= 2.0, E=10000.
Bottom chords: A=1, E=10000.
Draw a diagram of the structure’s deformed shape.
Draw a diagram showing the axial force in each member.
Do a static force check at node 7.
Compute the reaction at node 1.
Fahad Bin Sultan University Departement of Civil Engineering
Q6. The figure on the right shows the displacement results after inputting the problem on the left.
Has all the information been entered correctly? If not, what is wrong?
