CIVIL ENGINEERING
CIV ENG 4K04
Instructions:
1) The final exam is an individual effort, using McMaster standard calculator
(CASIO FX991 MS or MS Plus) only.
Also, you must not communicate with anyone else and you must self-invigilate
as per conditions given in in-person tests.
2) SAP 2000 and other software packages (e.g., Microsoft Excel) are not allowed.
3) This test includes 6 pages and 5 questions. You are responsible for ensuring
that your copy of the test is complete.
4) You will have 2.5 hours to complete the test.
5) The mark, out of a total of 50, is shown beside each question.
6) In the examiner’s opinion, all information required for the computations is
included. However, if the candidate thinks that additional information is
required, CLEARLY STATE THE ASSUMPTION AND CONTINUE WITH THE
REMAINDER OF THE QUESTION.
7) In the end, please prepare one .PDF file of your submission and you will be
given additional 30 minutes for preparation of this submission file (submit
before 3:30 pm).
8) The solutions must be submitted to the course avenue to learn site (In
AVENUE → Assessments → Assignments → (Final Exam) → Press “Add a
file” → Press Submit
9) You can make ONLY ONE submission of ONE FILE.
Page 1 of 6
Question #1 [12 Marks TOTAL – Part (a) 8, Part (b) 4]
For the beam shown in Figure 1,
a) Draw the influence line for the moment at point m.
b) Given the influence line below, determine the maximum negative shear force at point n (right of
support B) due to a uniformly distributed live load of 250 kN/m, and a uniformly distributed dead
load of 30 kN/m.
Figure 1
Page 2 of 6
Question #2 [10 Marks]
For the frame shown in Figure 2, using the method of virtual work, determine the minimum value of
the moment of inertia (I) to have a maximum horizontal displacement at point B of 100 mm. All the
members have the same moment of inertia (I) as shown in the figure and are made of steel (E =
200,000 MPa). Ignore the shear and axial deformations in your calculations.
Figure 2
Page 3 of 6
Question #3 [12 Marks]
For the frame shown in Figure 3, using the stiffness method, determine the displacements and
rotation at point B. All the members have E = 200(103) MPa, A = 4000 mm2, and I = 400(106) mm4.
Figure 3
The stiffness matrix for a frame element
The transformation matrix for a frame element
C = cos θ
S = sin θ
Fixed-end moments
Page 4 of 6
Question #4 [8 Marks]
For the frame shown in Figure 4, estimate the bending moment diagram using the portal method.
Figure 4
Page 5 of 6
Question #5 [8 Marks]
For the beam shown in Figure 5, use approximate methods to estimate the bending moment
diagram.
Figure 5
Ideal cases
IP: Inflection Point
THE END
Page 6 of 6