8/9/2019 Machine Design Midterm Sheet

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The blades of the fan in the following figure are located at point C at one end of its shaft. The steel shaft is supported at points A and B.

The blades weigh 2000 N. The modulus of elasticity of the shaft is E = 20 ! "0# $a.

a %uppose the weight of the shaft is negligible and determine the natural fre&uency of the system.

b 'f the weight of the shaft is considered( the intrinsic natural fre&uency of the shaft )without the blades* is "000 rpm.

+ind the combined natural fre&uency of the system under the effect of the weight of the shaft and the blades. (22

points)

I = d

4

/64 = 2.01110

-6

m

4

From table A-9 beam #10

Yc = (-Fa2/3EI(!"a = (-20001.2/3EI(1."1. = 0.010$ ma

%1= (&'11/'1120.= (&/1

0.= (9.$/0.010$0.= 30.12 rad/) = 2$*.* r+m

b

(1/%total12= (1/%1

2 "(1/%,t2 =(1/2$*.*2 "(1/10002 = 2*6.4 r+m or 2$.9 rad/)

The beam is made of machined A'%' "020 ,- steel and is under completely reersing bending moment /= 10 Nm. Beam has

a s&uare cross area of 0 mm by 0 mm. 't fails based on A%/E elliptic theory. The weight of the beam can be neglected. (33 points)

a* etermine the factor of safety for infinite life if the a3ial force + =0.

b* etermine the factor of safety for infinite life if the a3ial force + = 1000 N in tension. The force + is constant and not

arying.

c* etermine the factor of safety for infinite life if the a3ial force + = 1000 N in compression. The force + is constant and not

arying.

AII 1020 = 3$0 5a ad = 210 5a

e = 0. 3$0 = 190 5aI = b73/12 = 6*00 mm4

Ad 8am+l,tde= c/I = 360 1/ 6*00 = $0 5a

:a = a tb; a = 4. ad b = -0.26 t7e :a = 0.934

:b< de = 0.$0$ (7b0.= 0.$0$ (30300.= 24.24

:b = 1.24 24.24-0.10*= 0.$$e = 0.934 0.$$ 190 = 16.16 5a

a = 16.1/$0 = 1.92

b 8m,dra&e= F/A = 36000 / 900 = 40 5a

AE ell,+t,c< (8a/e2" (8m/

2= ($0/16.162" (40/2102= 1 ; = 1.$3

c ,ce m,dra&e )tre)) ,) , com+re)),o ,t ,) l,e be,& e>al to ?ero (@rom @,&re 6-2 t7e = 1.92

A large cylindrical propane tan4 is simply supported at the ends and is made of A'%' No. "00 C steel. 't has an outer diameter of " m(

length of "2 m and shell thic4ness of 5 mm. 't can be considered a thin cylinder. The internal gauge pressure is "600 7$a. The total

weight of the cylinder and its content is 80000 N which is uniformly distributed along the length of the cylinder. etermine the factor of

safety for elements located at top )A*( side )B* and bottom )C* of the cylinder( all in mid span /9/( using:

a* ;on /ises theory

b* /a3imum shear stress )Tresca* theory. (45 points)

AII 1030 B = 440 5a

8t= 5r/t = 1400000 0. / 0.00 = 140000000 5a = 140 5a8l= 5r/2t = *0 5a

From table A-9 @or beam #*

' = $0000 / 12 = 6666.6 C/m

= 'D(!-D/2; maD= D= !/2; maD= '!2/$ = 6666.6122/$ = 120000 Cm

I = (do4-d,4/64 = (14-0.994/64 = 1.934 10-3m4

8= c/I = 1200000./ 1.93410-3 = 31 5a

At to+ (A

o ,)e)