Exam (elaborations)
MECH 344 Problem Set 8-Chapter 17_Shafts-Selected Problems Concordia University
- Institution
- Concordia University ( )
MECH 344 Problem Set 8-Chapter 17_Shafts-Selected Problems Concordia University
[Show more]
Content preview
MECH 344 Problem Set 8-Chapter 17_Shafts-Selected Problems ConcordiaUniversity
SOLUTION (17.3)
Known: A simply supported steel shaft is connected to an electric motor with a
flexible coupling.
Find: Determine the value of the critical speed of rotation for the shaft.
Schematic and Given Data:
Flexible
Motor Coupling 0.25 in. dia. shaft
20 in.
Assumptions:
1. Bearing friction is negligible.
2. The bearings supporting the shafts are accurately aligned.
3. The shaft remains linearly elastic.
Analysis:
1. For the simply supported uniform load case:
w
st
wL/2 wL/2
w = A = d where = 0. 28 lb for steel
2
4 in. 3
(0. 25)2
w= (0. 28) = 0. 0137 lb
4 in.
17-4
,2. From Appendix D-2,
4
st = 5wL for a uniform load distribution
384EI
where E = 30 106 psi (Appendix C-1)
17-5
, (0. 25)4
I = d =
4
= 1. 92 10-4 in. 4 (Appendix B-1)
64 64
5(0. 0137)(20)4
st = = 4. 98 10-3 in.
384(30 10 )(1. 92 10 )
6 -4
3. Using Fig. 17.5(c), to find the shaft critical speed
5(32. 2 ft)(12 in. )
5g
nc = s2 ft
4st 4(4. 98 10 in. )
-3
nc 311 rpm ■
17-6
, SOLUTION (17.10)
Known: The dimensions of a steel shaft are given.
Find: Determine the critical speed of rotation for the steel shaft.
Schematic and Given Data:
25 mm dia.
50 kg
600 mm 600 mm
Assumptions:
1. Bearing friction is negligible.
2. The bearings supporting the shafts are accurately aligned.
3. The shaft remains linearly elastic.
4. The shaft is simply supported.
5. The mass of the shaft is negligible.
Analysis:
P
L/2
L
st
P/2 P/2
1. Using Appendix D-2, for a concentrated center load on a simply supported beam
3
we have st = PL where
48EI
E = 207 109 Pa (Appendix C-1) and
I = d (Appendix B-1)
4
64
(0. 025)4
= = 19. 2 10-9 m4
64
17-20
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller smartzone. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$18.10. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
78600 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now