mock exam (for practice only)course: maae 2202 a name: philip okotete mock exam (for practice only)...

NAME: Philip Okotete COURSE: MAAE 2202 A

MOCK EXAM (FOR PRACTICE ONLY)

It is most beneficial to you to write this mock midterm UNDER EXAM CONDITIONS.

This means:

• Complete the midterm in 3 hour(s). • Work on your own. • Keep your notes and textbook closed. • Attempt every question.

After the time limit, go back over your work with a different colour or on a separate piece

of paper and try to do the questions you are unsure of. Record your ideas in the

margins to remind yourself of what you were thinking when you take it up at PASS.

The purpose of this mock exam is to give you practice answering questions in a timed

setting and to help you to gauge which aspects of the course content you know well and

which are in need of further development and review. Use this mock exam as a

learning tool in preparing for the actual exam.

Please note:

• Come to the PASS workshop with your mock exam complete. During the

workshop you can work with other students to review your work.

• Often, there is not enough time to review the entire exam in the PASS workshop.

Decide which questions you most want to review – the Facilitator may ask

students to vote on which questions they want to discuss in detail.

• Facilitators do not bring copies of the mock exam to the session. Please print out

and complete the exam before you attend.

• Facilitators do not produce or distribute an answer key for mock exams.

Facilitators help students to work together to compare and assess the answers

they have. If you are not able to attend the PASS workshop, you can work alone

or with others in the class.

Good Luck writing the Mock Exam!!

Dates and locations of mock exam take-up:

Mock take-up: December 14th 2019 | 12 – 3 pm | ME 4499 Office hour/Study session: December 10th 2019 | 3 – 5 pm | CSAS front desk, 4th floor MacOdrum library



Question 1 (Multiple Choice Questions)

1) In the figure below, a rigid block rests on two wooden posts before it is loaded. What

is the value of y at which the internal force in post A is 2 times the internal force in

post B when the 50 kN force is applied?

a) 4/3 m

b) 8/3 m

c) 1/3 m

d) 3/2 m

2) The diagram below shows a gear-shaft system having torque applied to the gears.

The shaft ABC is supported by two journal bearings, while the shaft EH is supported

by the journal bearings at H. If T1 = 2 kN.m and T2 = 4 kN.m and the shaft ABC and

shaft EH have a diameter of 40 mm. What is the torque in the section ED of the shaft

system?

a) -6 kN.m

b) 2 kN.m

c) 6 kN.m

d) 8 kN.m



3) For the composite shaft subjected to axial loads shown in the figure below, which of

the following values is correct for the axial internal force in section BC?

a) 5 kip

b) 4 kip

c) 3 kip

d) 2 kip

4) Which of these is the correct transformation of the beam diagram below in order to

solve for deflection of the beam at point B using Macaulay’s step function?

Figure

(A)

(D)

(B)

(C)



5) In which of these systems is there a shear stress only?

6) For the given cantilever beam below, which of the following statements is incorrect?

a) Shear stress is zero everywhere within the beam.

b) The normal stress at point 1 is greater than the bending stress at point 2.

c) Tensile bending stress occurs at the top of the beam.

d) Normal stress is non-uniform across the cross-section of the beam

(A)

(C)

(B)

(D)



7) The diagram below shows a rigid bar attached to two steel columns. What is the

correct compatibility relationship (relationship between deflections) for the beam at A

and the beam at B if a force P is applied to the rigid bar at A.

a) ΔA = 4*ΔB

b) ΔB = 4*ΔA

c) ΔB = 5*ΔA

d) ΔA = 5*ΔB

8) Which of the following equations apply to the following shaft with a torque T being

applied at C?

a) 𝑇A = 𝑇B

b) 𝜏AB = 𝜏BC

c) 𝜏BC = 𝜏CD

d) 𝜃CB+ 𝜃BA = 𝜃CD

9) Which of the following statements is not true for a 3D stress state of a solid body?

a) The distortion of a solid body is due to shear strains

b) Shear strains do not cause the volumetric change of a solid body

c) Normal strains govern the volumetric change of a solid body

d) Volumetric change is associated with normal strains and shear strains

P



10) For 3D stress-strain relations, which of the following statements is incorrect?

a) Thermal strain of a solid body has no direction

b) The shear modulus of a material is obtained from the Young’s modulus and

Poisson’s ratio

c) The bulk modulus for hydrostatic stress state can be obtained from the Young’s

modulus and yield limit of the material

d) The volumetric strain of a solid body is zero if the Poisson’s ratio of the body

material is 0.5

11) For 3D stress state at a point, which of the following statements is incorrect?

a) Two shear stresses on each plane are always equal in magnitude.

b) Each shear stress on one plane always has a complementary shear stress

(same sign and equal magnitude) acting on the perpendicular plane.

c) Two shear stresses on each plane are always perpendicular to one another.

d) There are, in general, one normal stress and two shear stresses on each plane.

12) The figure below shows two bars pin-connected with a force P applied on the

structure at point C, and an elastic spring with a rotational stiffness of k. Which of

these statements is incorrect?

a) The horizontal reaction at A is zero

b) The vertical reaction at B is not zero

c) The vertical reaction at C is equal to P in magnitude

d) Buckling load Pcrit = 4𝑘

𝐿



13) The following simply supported beam is subjected to a point load as shown below. If

its cross-section is a rectangle, which of the following statements is incorrect?

a) The slopes at the two supports

are unequal

b) The slopes at the two supports

have opposite signs

c) The deflection of the beam at the

supports are zero

d) The maximum deflection occurs at

the loading point

14) Which of these is the Macaulay’s step function of the following beam?

15) A solid shaft and a hollow shaft are made from the same material, have the same

outer diameter and the same length. If they are subjected to the same torque load,

which of the following statements is true?

a) Solid shaft has a smaller maximum shear stress and a smaller maximum twisting angle

b) Solid shaft has a greater maximum shear stress and a greater maximum twisting angle

c) Solid shaft has greater maximum shear stress but a smaller maximum twisting angle

d) Solid shaft has a smaller maximum shear stress but a greater maximum twisting angle

a) 𝑀 = 𝑅𝐴[𝑥] − 5[𝑥]2 − 2[𝑥 − 0.5]0

b) 𝑀 = 𝑅𝐴[𝑥] − 5[𝑥]2 + 5[𝑥 − 0.5]2 − 2[𝑥 − 0.5]0

c) 𝑀 = 𝑅𝐴[𝑥] + 5[𝑥]2 − 5[𝑥 − 0.5]2 + 2[𝑥 − 0.5]0

d) 𝑀 = 𝑅𝐴[𝑥] − 5[𝑥]2 + 5[𝑥 − 0.5]2 − 2



16) A bar consists of a circular steel core surrounded by a brass tube and an aluminum

tube with rigid plates at each end, as shown below. If load P is applied on the end

plates, which statement is incorrect about the following system?

17) Strut A and B are identical except for their end constraints. A is pin-pinned and B is

fixed-free. Which of the following statements are correct?

a) Strut A can take 2 times more load than strut B

b) Strut A can take 2 times less load than strut B

c) Strut A can take 4 times more load than strut B

d) Strut A can take 4 times less load than strut B

18) Which of the following if true about buckling analysis of real struts?

a) A strut cannot fail if the applied load is less than the critical buckling load

b) Buckling or bending will occur in multiple planes

c) For rectangular beams, buckling will always occur in the plane where the 2nd

moment of are is smallest

d) A strut will buckle is the applied load is less than the critical buckling load.

a) It is a statically indeterminate system

b) The aluminum, brass, and steel components will

experience the same vertical deformation

c) The aluminum, brass, and steel components will

experience the same load.

d) The system can be solved using force equilibrium

and deformation compatibility.



(Long answer questions)

Question 2

In the structure below, member BC is made up of steel with a Young’s modulus of 150

MPa and a Poisson’s ratio of 0.3, and has a circular cross-section with a diameter of

100 mm. The load P = 10 kN.

a) Determine the internal components at point D.

b) Compute the normal stress of member BC.

c) Compute the axial deformation and the cross-sectional change in dimension for

member BC.

d) Determine the average shear stress at pin A and C. The pins are subjected to

double shear as shown, and each has a diameter of 18 mm.

D

2.5 m



Question 3

The assembly below consists of two bronze rods AB and CD of diameter 30 mm, and a

stainless-steel rod EF of diameter 40 mm, and a rigid cap G. By increasing the

temperature of the rods AB, CD and EF to 180°C from room temperature (20°C),

compute the internal force of each rod. The thermal coefficient of bronze is

α = 12 x 10-6/°C and the thermal coefficient of stainless-steel is α = 20 x 10-6/°C.



Question 4

The gear system below is made of hollow steel shafts of inner radius 20 mm and outer

radius 40 mm, and gears at B, C and D. Gear B has a radius of 150 mm, gear C has a

radius of 200 mm, and gear D has a radius of 150 mm. The steel shaft has a shear

modulus of 75 GPa.

a) Determine the angle of twist of gear D.

b) Determine the maximum shear stress in the system.



Question 5

A cantilever beam with a square cross-section with side length b is subjected to the

loading conditions as seen below. Note: 1kip = 1000 lb

a) At what distance x is the shear force maximum and at what distance x is the

bending moment maximum?

b) If the maximum allowable bending stress in the beam is 45000 psi (Pounds per

square inch), determine the value of b.

c) Using the value of b calculated in part B, determine the maximum shear stress in

the beam.

b

b

Cross-section of beam



Question 6

For the beam structure below shows a force P of 5 kN applied at point B. The beam DB

and AC are both made up of aluminum of E = 207 GPa and I = 195 mm4 with a length of

10 m. For this structure:

a) Calculate the deflection of beam AC at point B.

b) Determine the reaction force at B due to the roller support and the reaction at C

due to the pin support.

mock exam (for practice only)course: maae 2202 a name: philip okotete mock exam (for practice only)...

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