MCG 3131 - Assignment 2
Problem 1
At a point in a structural member, the stresses are represented as in the figure below. Use
Mohrs circle to determine
(a) the magnitude and orientation of the principal stresses
(b) the magnitude and orientation of the ma

MCG 3131 - Assignment 1
Problem 1
Review your notes of previous years and determine the moment of inertia of the T section
shown in the figure (a) below, around the horizontal axis passing through its centroid.
Dimensions in millimeters. Show that the pro

MCG 3131 - Tutorial
Problem 1
A full journal bearing has a shaft diameter of 80.00 mm with a unilateral tolerance of 0.01
mm. The L/D ratio is unity. The bushing has a bore diameter of 80.08 mm with a unilateral
tolerance of 0.03 mm. The SAE 30 oil supply

4I = 125664 mm4
E = 200 GPa
Reaction at A = 533 N and at B = 1667 N
a) Method 1, using superposition and beam # 10 in table A-9 at the end of the book twice, once
from each end:
yAB = (Fax/(6EIl) (l2 x2)
yc = (120021.5/(6EI3) (32 1.52) + (100011.5/(6EI3)

Answer to question 1:
a)
From table 7-9 for Sliding fit: H7/g6
(1)
For diameter of 35 mm, from table A-11 we find;
IT6: 0.016 and IT7:0.025 and
(1), (1)
From table A-12 for g: -0.009
(1)
Then for the hole:
35 mm < D < 35.025 mm
(2)
For the shaft: 35-0.016

2Shear force at section AB is 8000 cos (60) = 4000 N
Normal force at section AB is 8000 sin (60) = 6928 N
A = 20 30 = 600 mm2 = 6 10-4m2
I = 20 303 /12 = 45000 mm4
M = 4000 0.105 + 6928 0.105 = 1147 Nm
rn = h / (ln (ro / ri ) = 30 / (ln (120 / 90 ) = 104.

1
The shaft shown is supporting a rotating fan. The fan weighs 5000 N and air pressure
causes an axial load toward the right of 1000 N applied on the fan. The axial force is
supported only by bearing A. Shaft is made of UNS G10100 HR steel.
a) Neglect the

Answer to question 1:
a)
From table 7-9 for Sliding fit: H7/g6
(1)
For diameter of 35 mm, from table A-11 we find;
IT6: 0.016 and IT7:0.025 and
(1), (1)
From table A-12 for g: -0.009
(1)
Then for the hole:
35 mm < D < 35.025 mm
(2)
For the shaft: 35-0.016

1
In the figure shown a shaft with basic diameter size of 35 mm is to be attached to a gear
through a 6 mm 8 mm Key (not a standard key).
a
The shaft and the gear are supposed to have a Sliding fit, determine the limits
for the shaft and the gear.
b If th

Answer to question 2
UNS 10100HR from table A20: Sy = 180 and UTS = 320 MPa
(1)
From free body diagram y reaction at point A is found 3750 N
(3)
a)
And the maximum moment happens at the fan= 3750 0.25 = 937.5 Nm
(3)
= Mc/I = 937.5 r /(r4/4) = 1193.7/r3
(

1a)
L = L T then 0.1 = 80 23.9 10-6 T and T = 52.3C
b)
If we put numbers in shrink fit equations
= 5 10-5 = PR/Eo [(ro2 +R2)/ (ro 2 -R2) + o] + P R/Eo [(ro2 +R2)/ (-ro 2 +R2) i] =
(P0.04/72 109 ) [(0.12 +0.042)/ (0.12 -0.042) + 0.33] + (P0.04/200 109 ) [

1
When subjected to fatigue load, a part fails at reversing stress of 84.95 MPa at 1000
cycles and fails at reversing stress of 75.71 MPa when the load is applied for 10000
cycles.
a If the stress is 68 MPa how many cycles does it last?
b If this part is

1
The following figure shows state of stress at one point of a material made of steel. All the
stresses are completely reversing and they are in the same phase (becoming positive
together). The material is 45% of the time under x = 35 Kpsi, 25 percent of

1
A disk made of aluminum (E = 72 GPa, poisons ratio of = 0.33, thermal expansion
coefficient of = 23.9 10-6 /C, density = 260 kg/m3) is to be mounted on a shaft
made of steel (E = 200 GPa, poisons ratio = 0.29, thermal expansion coefficient of =
10.8 10-

MCG 3131 - Tutorial 2
Problem 1
The triangular plate cantilever beam shown below represents an idealization of a leaf
spring. Using Castiglianos method, derive an expression for the deflection of the loaded
end
Solution
The vertical plane at distance x fr

MCG 3131 - Tutorial 5
Problem 1
Estimate the critical speed of rotation for the steel shaft shown below.
Solution
1
2
3
Problem 2
(Note: it is important to read section 17.3 in Juvinall and Marshek 5 th edition before doing
this problem, since some materi

MCG 3131 - Tutorial 3
Problem 1
Background: The failure locus represents the envelope of all the safe stresses for a
particular theory. This is typically done in 2-D, in the A B plane, where A and B are the
two non-zero principal stresses. In this plane,

MCG 3131 - Tutorial 4
Problem 1
A solid round bar, 25 mm in diameter, has a groove 2.5-mm deep with a 2.5-mm radius
machined into it. The bar is made of AISI 1020 normalized steel and is subjected to a purely
reversing torque of 130 N. m.
(a)
Estimate the

MCG 3131 - Tutorial 1
Problem 1
Consider the rectangular beam below, of Youngs modulus E and second moment of area I.
Draw a free-body diagram of the beam. Write the equilibrium equations for the whole beam
to find reactions. Write the local equilibrium e

1
The rectangular beam shown is under the axial force Fx and shear forces Fy and Fz and
torsion load Tx as shown in the following figure. Neglect any stress concentration. The
beam has ultimate strength of Sut = 600 MPa and yield strength of Sy = 350 MPa.

Answer 2:
I = r4/4 = 306794 mm4 and E = 210 GPa
FA = 3000 N, FB = 5000 N
q = 3000<x>-1 8000<x-0.75>0 +8000<x-1.75>0
V = 3000<x>0 8000<x-0.75>1 +8000<x-1.75>1
M = 3000<x>1 4000<x-0.75>2 +4000<x-1.75>2
EI dy/dx = 1500<x>2 4000/3 <x-0.75>3 +4000/3 <x-1.75>3

1
Determine the state of stress at a point M at radius r = 100 mm at section AB on the
curved beam. The beam has a rectangular cross section of 20 mm 30 mm. (22
points)
8000 N
R 120 mm
R 105 mm
R 90 mm
A
M
B
60

1
In the following figure the beam is simply supported at the ends and is made of steel. The
uniform load of w = 8000 N/m is applied at part of the beam as shown. The beam has
circular cross sections of D = 50 mm.
a Find the deflection at midspan (middle

MCG 3131 - Tutorial
Problem 1
A full journal bearing has a shaft diameter of 80.00 mm with a unilateral tolerance of 0.01
mm. The L/D ratio is unity. The bushing has a bore diameter of 80.08 mm with a unilateral
tolerance of 0.03 mm. The SAE 30 oil supply

MCG3145 Summer 2009
University of Ottawa
Ch.12: Yield and Fracture Criteria
1
MCG3145 Summer 2009
University of Ottawa
12.1: Introduction
The previous chapters related the applied load to the internal stresses in a material
The Subsequent Chapters will lo

Grid Analysis
Making a Decision By Weighing Up Different Factors
Also known as Decision Matrix Analysis, Pugh Matrix Analysis, and Multi-Attribute Utility Theory
(MAUT)
Imagine that your boss has put you in charge of taking on a new outsourced IT supplier

Guidelines for Engineering and Laboratory Reports
This document gives a guide for the format of engineering reports in general and the MCG
4340 formal lab reports in particular.
1. General Requirements
The report is to be typed on one side of standard 8 x

Ball and Roller Bearings
2200/E
Cat.No.
NTN corporation
Warranty
NTN warrants, to the original purchaser only, that the delivered product which is the subject of this sale (a) will conform
to drawings and specifications mutually established in writing as

MCG3145
ADVANCED STRENGTH OF MATERIALS
1
Topic 9
- Energy and virtual work
- Classical energy methods
2
Introduction (17.1)
Based on the concept already discussed in preceding chapters, the
Internal Strain Energy = External Work
Most effective procedure f

Gearing
Topics:
Spur, bevel, helical and worm gears
Kinematics
Force analysis
Bending and contact stress analyses
1
Spur gears
Angular velocity ratio:
p np
rg
g ng
rp
Pitch-line velocity: V rp p rg g
Juvinall and Marshek
For conjugate gear-tooth act

Rolling-element bearings
Juvinall and Marshek
1
Different series
Juvinall and Marshek
Frictional properties
Rolling-element bearings can have less
frictional resistance than high grade partial
journal bearings operating with flooded
lubrication systems. T