MAAE 3202 Mid Term Assignement 2012

Department of Mechanical & Aerospace EngineeringCarleton University

MAAE3202 Mechanics of Solids IIMid-Term Assignment November 7. 2012

Read the following instructions carefully:1. Answer all the questions in the space provided and staple this cover page together with

the answer sheets for submission.

2. Your submission of the answers for marking is optional. However, marks obtained in this assignment will be added to your Final Examination marks as bonus. The maximum total bonus marks is 15.

3. All questions carry equal marks.

4. You are strongly encouraged to complete this assignment by yourself. If it helps to promote learning from one another, you may work as a group of no more than 3 students. All students in the group must be identified (see Item 7 below) and each must still submit individual answer sheets, albeit with the same answers. All students in a group will receive the same marks.

5. Students are reminded of the academic integrity standards as stated in the University Calendar. Those found in violation of these standards will be penalised accordingly.

6. The deadline for the assignment is: Noon, November 8. 2012 SHARP. It is to be submitted into the drop box located near the general office of the Department of Mechanical & Aerospace Engineering (between rooms ME3135 and ME3144).

7. Please mark an “X” in one of the boxes below, and write your name(s) and student number(s) in the appropriate column. Please initial beside your name.

Individual ❏ Group ❏Name Student # Name Student #

______________________________ 1) __________________________

Section A ❏ B ❏ 2) __________________________

Submitted by: 3) __________________________

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Question 1

A beam fixed at both ends is 2m long and is loaded with a vertical load P at the mid-span along his length. It’s thin-walled cross-section is shown in Figure 1 which has a uniform thickness of 3mm. The shear modulus of the steel is 79GPa.

a) If the twist of the member is must not exceed 5˚, what is the maximal permissible load P that can be applied.

b) Determine the maximum shear stress due to the twist of the section.c) Indicate in Figure 1. where the maximum shear stress due to bending of the beam occurs.

r

P

MAAE3202 Mechanics of Solids II Mid-Term Assignment

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Question 2

A cantilever beam made of steel has a constant cross-section of uniform thickness as shown in Figure 2. The beam is loaded with a set of point loads acting through the centroid of the section and in planes parallel to the cross-section as indicated in Figure 2.

a) Determine the principle axes of the cross-section using Mohr’s circle.b) Determine the moment vector components along the principle directions.c) Determine the orientation of the neutral axis.d) Determine the maximum compressive and tensile stresses in the cross-section.


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3 kN

5 kN

7 kN

1m

1m

400 mm

300 mm

100 mm

100 mm

y

z

Figure 2


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Question 3

A piping system expansion loop consisting of a series of 90˚ bends is fabricated of pipe of constant size as shown in Figure 3. The symmetric expansion loop is subjected to a temperature difference ΔT. The overall length of the loop is L and the thermal expansion of tubing material is α.Determine for each end of the loop the restring bending moment M and force N induced by the temperature change.

r= 0.5mR=1ma=0.5m


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r

R

aa

r

NM

N

M

Figure 3


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MAAE 3202 Mid Term Assignement 2012

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