Machine Design - 1508581959091 PDF [PDF]

Zitiervorschau

Stress 1. A steel tie rod on bridge must be withstand a pull of 6200 lbs. Find the diameter of the rod assuming a factor of safety of 4 and ultimate stress of 66,000 psi. Solution: 𝑆𝑢 = 𝜋 4

𝐹

(𝐷2 )

66,000 𝑝𝑠𝑖 4

6200

=𝜋 4

(𝐷2 )

2. If the ultimate shear strength of steel plate is 45,000 psi, what force is necessary to punch 0.9 in diameter hole in 0.5 in thick plate using a factor of safety of 3.5.

𝐹 𝐴 𝐹 𝜋𝐷𝑡

45,000𝑝𝑠𝑖 =

𝐹 𝜋(0.9)(0.5)

Solution: 𝐹 𝐴

𝑆𝑏 = =

=3

𝐿 = 3𝐷

10𝑚𝑚 � 𝑐𝑚

𝐹 𝐷𝐿 5500 𝑙𝑏𝑠 2.5(1.8)

𝐴 = 3(80) 𝐴 = 19,200 𝑚𝑚²

𝑆𝑏 = 1111.11 𝑝𝑠𝑖

= 80 𝑚𝑚

5. A cable has a length of 100 m and stretch to 5 cm when the load is applied at both ends. If the tensile stress is 50 psi, find the modulus of elasticity of the steel. Solution: =

𝐹 = 63,617 𝑙𝑏𝑠 3. A 2.5 in diameter bu 1.8 long journal bearing is to carry 5000 lb load at 320 rpm using SAE 40 lube oil at 200 °F through a single hole at 30 psi. Compute the bearing pressure.

𝑆=

𝐿 𝐷

𝑆𝐿 𝑌 50 𝑝𝑠𝑖(100𝑚)

𝐸=

Solution: 𝑆=

Solution: 𝐴 = 𝐷𝐿

𝐷 = 8𝑐𝑚 �

𝐷 = 0.691 𝑖𝑛

𝑆=

4. A journal bearing has a 8 cm diameter and length to diameter ratio of 3. Find the projected area mm².

5𝑐𝑚(

𝑚 ) 100𝑐𝑚

𝐸 = 100,000 𝑝𝑠𝑖

6. A shaft whose torque varies from 22006400 in-lbs. It has a diameter of 1.25 inches and yield stress of 63,000 psi. Find the variable component stress. Solution: 16𝑇𝑚𝑎𝑥 𝜋𝐷³ 16(6400) = 𝜋(1.35)³

𝑆𝑚𝑎𝑥 =

𝑆𝑚𝑎𝑥 = 16,688.61 𝑝𝑠𝑖 16𝑇𝑚𝑖𝑛 𝜋𝐷³ 16(2200) = 𝜋(1.25)³

𝑆𝑚𝑖𝑛 =

𝑆𝑚𝑖𝑛 = 5,736.71 𝑝𝑠𝑖

𝑆𝑚𝑎𝑥 )(𝑆𝑚𝑒𝑎𝑛 𝑆𝑚𝑖𝑛 𝑆𝑚𝑎𝑥−𝑆𝑚𝑖𝑛 2

(𝑆𝑚𝑒𝑎𝑛 = 𝑆=

𝑆𝑎 = 5475.95 𝑝𝑠𝑖

= 𝑆𝑚𝑎𝑥)

7. How many ½ inch diameter hole that can be punch in one motion of a 1/8 inch thick plate using a force of 50 tons. The ultimate stress id 53 ksi and factor of safety of 3. Solution: 𝑆𝑢 = 𝐷𝑡 =

𝐹 𝜋𝐷𝑡

2000 𝑙𝑏𝑠 ) 𝑡𝑜𝑛 1 𝜋(52,000 𝑝𝑠𝑖)( 𝑖𝑛) 8

50 𝑡𝑜𝑛𝑠(

𝐷𝑡 = 4.897 𝑖𝑛 𝐷𝑡 𝑑 4.897 𝑖𝑛

𝑛= =

1 𝑖𝑛 2

8. Determine the minimum diameter of a taper pin for use to fix a lever to a shaft, if it is to transmit a maximum torque of 750 in-lb. The shaft diameter is 1.5 inches and has a stress of 20,000 psi. Solution: 𝐹 𝐴

𝐹 𝜋𝑆

𝐷𝑚𝑖𝑛 = 2�

𝐷 𝐹= 𝑇 2(750 𝑖𝑛−𝑙𝑏) = 1.5 𝑖𝑛

𝐹 = 1000 𝑙𝑏

1000 𝜋(20,000)

𝐷𝑚𝑖𝑛 = 2�

𝐷𝑚𝑖𝑛 = 0.252 𝑖𝑛

9. A 19 mm stud bolt is used to fastened on a 250 mm diameter cylinder head of diesel engine. If there are 10 stud bolts, determine the pressure inside the cylinder if bolt stress is 50 Mpa. Solution: 𝑆=

𝐹 𝑛𝐴

5000 =

=

𝜋(0.25𝑚)² 4

𝑃 = 2,888 𝑘𝑝𝑎

10. A column supports a compressive load of 250 Kn. Determine the outside diameter of column if inside diameter is 135 mm and compressive stress of 50 Mpa. Solution: 𝑆=

𝐹 𝐴

50 = 𝜋

𝑛 = 9 ℎ𝑜𝑙𝑒𝑠

𝑆=

𝐹 𝐴𝑐 141.76 𝐾𝑁

𝑃=

𝐹 𝜋 10( (0.019𝑚)2 ) 4

𝐹 = 141.76 𝐾𝑁

4

250,000 𝑁

(𝐷𝑜2 −1852 )

𝐷𝑜 = 201.47 𝑚𝑚

11. A steel hollow tube is used to carry a tensile load of 500 KN at a stress of 140 MPa. If outside diameter is 10 times the tube thickness of the tube. Solution: 𝐷𝑜 − 𝐷𝑖 = 2𝑡 10𝑡 − 𝐷𝑖 = 2𝑡 𝐷𝑖 = 8𝑡 𝑆=𝜋 4

𝐹

(𝐷𝑜2 −𝐷𝑖 2 )

140 = 𝜋 4

500,000 𝑁

(10𝑡 2 −8𝑡 2 )

𝑡 = 11.23 𝑚𝑚

12. A 20 mm diameter rivet is used to fastened two 25 mm thick plate. If the shearing stress of rivet is 80 Mpa, what tensile force applied each plate to shear the bolts? Solution: 𝑆=

𝐹 𝐴

𝐹 = 𝑆𝑠 𝑥 𝐴 𝜋 4

1 𝐾𝑁 ) 1000𝑁

= 80( (20 𝑚𝑚)2 )( 𝐹 = 25.13 𝐾𝑁

;is.l;Tll'lG

diameter is 80 mm. Find the inside diameter of the shaft.

1 f.

A shaft is used to transmitn2-00 KVV at 30C r-p;l hv means o; a 200 mm diameter sprncket. Deii,r-ti',ii',i'

Given: Su=350MPa

the force to the sprocket.

EC_A I U-J

T=3KN-m Do=80mnr Di=?

Given: F=? P=200KN N=300KN

Soln.

t5=6rt,

Droro.1o1=200mm

3soMP€ToMPa I= FS5

s.,,= Soln:

16TDo

P=2nTN

sarr=bs=i6;r-il4

T=Fr

D,=olDoa '

"rJ -

,.-L, E-. "\2nl'l /

4

D

t-snrccxet-

;n1;

2o"ttH tr .= -__I sprocKel I -136gI'lv 11-L'llL)f 20U,,.,,,,.,' rev'

i ru!,) l\, ,,t = t l1':

..- 'n - - ) l(,o(r,n[r'

F.o,"o.k"E-0.3OQ S.N

' 2.

nrn.'6, i;4c'

Find the diameter of a steel shaft rvlrich ra;ill be used to operate a 11"0 KW motor rotating at 5 rps ii'

torsional stress is 90 Mpa

Given: P=1OKw N=Srps

q,1" r

" 4.

nSail

i30luur)'i

Ut*

P

16TDo

16

(3 i. N -- in )(tjr'rn rrr ).

------ri--i:r( 7{t-.,-,3

r4oJlltr1

}

q'A,r ) ; ;' 1'

Di:-OQ.e

?nl:

Whai is the speeri of $3..12 irnr shaft transmitted 75 KW if stress is nr:t to excecrl 26 Mpa. Giveii. D=63.42mi'n P=751{N .$"rr=26fu4Pa t, | -.)! rr-

Ss(torsionar)=90MPa Dsnan=?

Srrirr:

Soln:

I\:: ---? rrT

P=2rrTN

Ll

P=2nThJ D

o

P

III

tlrcr

jis

ri

nss

0.1

1c;62.;li:-'::r1!tl "11Iu9EiL; 1zo-ll-;1se.+zmm),

i'jt55erE[

"

Pt

A steel shaft transnrits 50 hp at 1400 rpm. lf allowabie stress is 500 psi, find the shaft cjiameter

nzNSs

o.et o:61161!L'r ., . f o.erozp : r----_--_._ f cl:= I--_-

111o10,!lr

Giv*n: r

(srps)t'ro;i.;r ! NSs .l\ . d-iQJ$m-rl

ii t1k,1 If r --JUr iiJ

[:J='l;{Sfl1p6 Srrr=500psi rrshfft*

3.

,/

j _

,.,-r'i-.".,".".T

. ,f rp LI- l.."...!

LLt

1.

\

'2[N'

ai

I

u.3 L06p

'r/ nSs I

-ij.-

p

, ,llar J-

_..n * ..-j6T

l\- -----';:-'-: -- / 5sft.1' \

2nN 167

Us=

,1t

A shaft has an ultirnate stress cf 3150 lrlpa zrii). i'.a. a factor of safety of 5. The tcrqui-. de ,;e li:peci bi the shaft is 3 KN-m and the diarnete r outside

i

!r=]rnTl,j

167

Ds=r,a'

o='llgi nSs-

8.

[-;-

.

J"_r"ul

r/

{

tss

ft-Iir 12in :::r -,JILIILil ' ft rlr

.t3tr01)__,_

3

o,B1C,6(5UI)P' ){

tn'

-[nn{r,n,,trtf

n)

A hollow shaft that has a 100 mm outside diameter and 80 mm inside diameter is used to transmit 100 KW at 500 rpnr. Determine the shaft stress.

Given: Do=100mm Dr=80rnnr

i

In'

P=100Kw N=600rpm

d= 2.B4in. 6. The s[raft of a motor has a le ngth of 20 times its dianreter and has a maximLrn-i twrst ':f 1 degree s when twisted at 2 KN-m torque. lf the modulus of rigidity of the slraft is 80 Gpa, find the sliaft diameter.

Su=?

Soln: P=2n"TN

\ =-_-* vs

16TDo

n[Doa-Di+)

.",s*_ re(fr)o"

Given: L=20D

e=

;(Do4-Di4)

0.B106PDo \ =-_N(Do4-Di4)

1o

G=80GPa

n Dr-

Dsnurt=?

Soln: /180\

='-

IG

-F;a

.]

W,

Ss=13.73MPa

is the polar rnoment of inertia of a solid shaft that has a torque of 1.5 KN and a stress of 25 Mpa?

What

!-6

D4G

D+G

Su=25ltfiPa

IliG

, iL 1672.2(2KN ilttotz.z'r ..J sc-:: Il----t r.tir,,,cl-

!

T=1.SKN

11ti7Z.?'l

--

rrr)

-t ^L-)=

o

m

Given:

rrdaG ' rr ' 583,61TL _ 5B3.6lT(20D)

----

0c0mm)

tls6lifl- i

\:l--(__l

* ^-

1

TL

32TL -130-

t-,-

oom mt-'mln r!9i99)r,.

rr-

:##tTr

TL "(#) ^_ =

*'-'-)

roe(roo \ sec -/'r:

*

wrao\-[/-__ rL _ tG

o.g

Soln: 167

'

b'= iF , nda

D= 66.33mm

32

1

A lrollow shaft developed a lorque of 5 KirJ ani.i shaft stress is 40 Mpa. lf cutsicie ciianreter of :iri:ft is 1C|0 mm, determine the shaft innei'cliarne ,;ei'.

,=*((#i).J= 't ('ot )' 32 \rrss./

/

Given: T=5KN-m S.=40MPa Do=100nrm Di=?

J=32[;l;:g/ &

\vs=-- 16'f Do

J= 2.02x t0-6mma

-Di4)

Given: ds63;1=2in

G=83x 1.06KPa D,=* /1too,nm)4

o

ri\

force tangent to L foot diameter pulley is 5 KN and is mounted on a 2 inches shaft. Determine the torsional deflection if G= B3xl"06 Kpa.

1U, A

Soln. n(Do4

,

,-- r, / ro / r.srN-m\' I . mm-/ I \ /

-

1 6 (

s KN

- rn) ( 1 o o m m

+0--llnl''

Tr(_

1

(ry.]'I)

N

,-A

Uprrlley-

I

SL

lt

F=5KN

)

Soin: DEZT!6zL mm

F=2rT[!

T=Fr

rrt( -=) r=sKN(-s#ry

Giiren:

(} -/)|

rJS-

T=761.96N-m

D.1,31=2irl

@=f!=

T=24000in-lb N=120rpnr

IG

D4G

!!jf _ L D4G

9=

(f^I^.

584(761.e6N-m)

161'

fr){a:i"ro,'H) 3= o 8o47m

'

uq_-

f

u

11. What is the minimum diameter r:i a steel shafl which will be used to operate a .14 i(l,l.m torqLr,? and will llot twist more than 3" in a length of 5 rrl? ( G = 83x1C6 Kpa )

Given: D=? T=14KN-m

16

t4. V/hat

(24000 in - tb)

il(2in):r

TIO.'

S"= 1s278.s7.ltl;

the diameter of iine shaft that transmit L50 K\,V at 150 rps? is

Gii,rn: Line shait P=i 50Kvr F:=,201 07

N=15rps Ni=900rpin

O=3o

L=6m

G=83x 106KPa

Soln: D3N

P-_

Soln:

s

3.5

[=

\7-^_5B4TL D4G

o I-saaTL-

!oG L/^-.;r"*1***-rr,16ra

shaft iras 50 mrn diarrleter is running at 300 rp;n" What is tlie r:ower thai coulrj be delivr:r by

1"5. ,,'\ l"i^rain

I-s1'B3x1o.r*)

{\m./

o

the

D= 118.45mm

12. A solid shaft 5 m long is stresseiJ to 60 Mpa r,viier: twisted through 4'. Find the shaft dianreter if G ., 683 Gpa.

slra

it.

Cii';en.

(Main) D=50nrm=1.97in t'l=300rpirr Pr=?

Given: L=5rn S=60MPa

Soin:

D3N (t.97in)r(:00r'pirr) n r=: .80 B0 p=ZS.60.Lp

O=4o

a

D=? G=83GPa

16. A 2 inches Ciameier rnain shaft running at 600 rpm

Soln: r6T rtdr

is ntounted by a 12 inciies diameter pulley and is

o-lL= lrylr=Y@=r.r5]:;! D,IG

JG

1r4.67sL

oc

o

I t 4.67

|- (,0

1...

iir lD'

DG

1,

5,,,,1.'J"'02','"'11 ttl'

il..-.fl--'

iir []'

Q= 103.62nttlt 13. Compute the nraximum unit shear in a 2 irrclie-c diameter steel shafting that transrriits 2;!,1100 ir:"i'r of torque at 120 rprn.

then connected tr: the siraft of driven machine mounted by a 40 ir,che s ciianleter puiley by means of beit. The belt ,:ffir:ierrcy is 90%. Find the diameter of the shoi-t shaft G!ven: i'lr=6gOtOtn

Dr=12in [r3r=2

D2=461n

e=90%

f{=550rpnr S.=? D.=35mm

Dsnort=?

Soln:

t

Pou

6-_

Soln:

Pin €P;n=F6,u1

p::ri1p=:

D:tN,. u /^\ rout= li- (e/ =-

Porl=54hp

(z;:l1r,oorprrr;

--: (ll.Yt,)

i'_-

I

-,i,

roz.

il.ar {1

6s 0

oc

-:;)

(#;)

(1

0m)

r:!x:n] rit I n

0,{18

11-7 a176KN -rn r * -rJa

LJ*-:-nlln

N1D1=N2D2

^,-

(600rp:n)( I2in) (40in)

_

'

180r'm

hJz=

i,'

T

161'-=

(\

3B

--5

-

t

N

o

-

{

-rr)rn) n(35titltt)3tttrtt1

18orl)rn

@ sE:-14.-9Al*Ea

D= 2.25in

1"7. A L.5" diameter shr:rt shaft is used to

transm't 44.4

hp. Determine the shaft speed.

o| ---D'N 3B

20. A circular saw blaclc has a circular speed of 25 m/sec and 500 n-rm dianreter is driven by a belt that has a sleep af 7%. Find the required speed of dri,ren shaft if speeci ratio is 3.

3BD ._ :rB{44.41r1))

!\r_ iY-

"1s:

o;ii_l

'16(I252:iB.BN J-

nd3

n3 /3BPour /3s(s4l!t,) lJ t-

{

nrin

z

T=125238.8hl-mrn

D3N

l.--

4?27q_i!-ry:'r1

n'r'N

2

tJivtil

-.:

(l.5in)3 D3 N=499.91rpm ' N:B.33rps :18. A 3" diameter solicJ shaft is dr:sirecj

ir-

t.

rc -A SEC

D=500rirm Seli sliP=:/!6

tc replace

n I --ai-

I\j

a

hollow shaft having 4" outsiCe cliameier. Corisicer the strength to be the sanre, deterrnine the: inside diameter of hollcw shaft.

|

1-Jl\2

Cn!n't. uu[ Nl D2

N2

D1

UL

D1

$oln; SH=Ssotic

16T_ l6TDo_ ad3 n(Do+-Di+; 1Do b, = D"--D,, Doa

D;=

-

V=n'D2l{2

Di4= DoD3

{/ffi - rfiD3 : i&nr'l - (,tid(3}n)3

. 1A

--J

D2=3D1=$(500rnm) Da='l50Cri:rn

A motor is used to drlrye a ceritrifugal pump thai dischargcs 3000 li/nrin ai a lreacj of 10 rn. tlre purnp efficierrcy is 58% anC runriing at 5S0 rprn. Find the torsionar stress of slraft if shaft Cianreter

35 rnm.

Given:

v=3000* L=10m e=0.68

s

Di=i.Si[ 23".

i!r.:Nz:9I4-93fplr

Arr 800ntni diame'cer circulai" saw blade is driven hy a ili00 rpin mctor vrith gear speed ratio of 1.g.

find tire peripheral speed cf the blade. !s

Giyen: it1='l$Qff1p:n D=800min i\^t,-. \)uiit. Ni---..

1800rprn , ^ N2

Given:

Nz=1000rpm V5h6g=TT D N

vs136g=8.

z

=

L=1Oft n (B 0 0 ri i nr ) (_1]I-1

25( r oo o) (io

r

t;',;) ;'; :

Soln:

ll-

L:

3

r--

B.95VD"

(')=(D)=

g

2

\8,95./

'/u,ro"=137'5lL

22. A machine shaft is supported on bearings ll, ri apart is to transmit 190 KVV at 300 rpm v,rliiic subjected to bending load of 500 kg at the cerrter. lf shearing stresses 40 MPa, determine the shaft diameter.

Given:

n_ /10/fV "- \&es/

u

D= 1 .18tn

ft shaft is running at 260 rpm. what that this shaft could safely deliver?

25. A 12

L=1 nr P=1 90Kw

Given: L=1Zft N=260rpm

N=300rprn m=500k9 @ center S.=40lJPa

Soln:

33

(nrt1; o= (a)' \8.95,/ = \

dsnan=?

8.95 ,/

D='1.5525in Soln:

P=2nTN I l-

P:

T= 6.0479KN-m FL

^r- 4+-

,

(sootg)1?Irfi1g;1t:,t

tvt-

M=1.22625KN-m 16 Ds=;E J@iF

d-

76.

3

nd3

\ .rft-t+

r"l

-I

(Q22625)z + (6.0479)2)l'1 * d=t -zii-r -' nl 40r-l \

o

nn.ri

mm',/

d =92.28mm

23. A L00 mm diameter shaft is; subjected to a toitli:r: of 6 KN-m, a.nd bending moment of 2.5 KN-m. fir,ii

the nrax berrding stress developed. Soln:

S,= S,=

q/M'+

r" (M +

fi2srKNmf + (6ri(Fl"ti

"r-**), o Ss=45.84MPa

24. A shaft has a length of L0 ft. find the diameter the shaft that could safely deliver.

r/

ci

t

(*) = z6ctr?tm(+:':)' p=3.37hp

lli=

Pi"essu,"e Vessei

1.

ll0m

l- = 12m

Deterrlrne ll-ie itrl-c: rilir i i:l"ess'..1 r"s r-;f cvlindr"ical

talx

5 = 50 l\4pa

:rCi[t n-iin ]ntei-n,:l

i*l

diarletei', 70 r'nnr l.hicli ar,ci 3 l: lengthi rf sl.resses limiled to lr+ri

!{uticns: p

=Tl,

= 9.ti1 KN/m'z(12rn)

iVlpa.

= 117.72 Kpa q,- PDL

l') G

ive n:

2t

Di = 500nrm

(1't7.72)(10) r-^ ,^? ---at

5UX1U- =

t = 20mm

o

L-Jllt

S =,

140 Mpa

lqi-ulla!. ^ t)Di Lt_

140x1-03 =

P=

. 2.

t = 1l_.772_nm

a'

/) (o.s) 2(o o2)

Determine the safe wall thickness of a 50 inches steel tank with internai pressure of B Mpa. The ultimate stress is 295 Mpa. The factor of safety to use is 3.

11200 Kpir Given: Di = 50m

P--1-1-J-Miza

Determrnt Llre btrrstin!i :,:eat;l pressLrre rrf ;r stee! shell with diameter of ZiJ ir-rches arrci macie 5/1ti sieel plate.

Pi

=BMpa

5u = 296 Mpa r:i'

FS=3 'i-

-?

L -i

Solution:

G ive n. ra: a/l:-^ i)i .1 \J lll

-

(+ JL _

t = 5y'1t-r in e = 809'o S = 63,00i1 psi

.9u

Pi =?

.tr,:

PiDI ')t

P Di ZL

Solution:

c PiDi

2e6xLA3 8x1036Sr:in)1""$;)

J_

4.t.e

321

l'(?,o)

63,000=,/s7,+\ 'l

\-tcJ (-i) 8;

39.37

c I = 3150!_ 3.

A r,vater tank 1C rn x l-2

t=0.0515ffix-.itn

cornpletely fiiled with water. Determine the minirrrunr thickiress of the plate i1'stress is Ilmiierj 1.c ::ril MPa. Give n:

s

t-n is

5.

in

t=2.03inr

]-he interrral p-.res:;r:i-c ci a 4OtJ rnnt irrside diamet€r r:i'iii-rilncaltank is 10 ivipa and thir:l