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SOLUCIN:

PROPERTIES OF THE STEEL SHAFT (s)

Gs=80GPad 1=70mm

Allowable shear stress:s=110MPa .

IPS=

32d

1

4=2.3572106 m4 .

GsIPS=188.574103N .m

2

PROPERTIES OF THE BRASS SLEEVE (b)

Gb=40GPad2=90mm d1=70mm

Allowable shear stress:b=70MPa .

IPB=

32( d2

4d1

4 )=4.0841106m4

GsIPB=163.363103N . m

2

TORQUES IN THE COPOSITE BAR AB

TS= Tor!"e #$ the Steel sha%t AB

Tb= Tor!"e #$ the brass slee&e AB

Fro' E! (**a): TS=T( G SIps

GSIPS+GbIpb)

TS=T(0.53582) (E! +)

Tb=TTS=T(0.46418) (E! ,)

AN-LE OF T.IST OF THE COPOSITE BAR AB

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AB=TS(

L

2)

GSIPS=

TS(L

2)

G SIPS=

Tb (L

2)

GbIPb=(5.6828106 ) T (E! )

U$#/a/es:T=N .m=rad

AN-LE OF T.IST OF PART BC OF THE STEEL SHAFT

BC=T(

L

2)

GSIPS=(10.6059106 ) T (E! *)

AN-LE OF T.IST OF THE ENTIRE SHAFT ABC

=AB+BC (E!s 0 *)

=(16.2887106 ) T

U$#/a/es: 1 2 ra/ T 2 N'

a) Allowable tor!"eT

1 base/ "3o$ a$4le o% tw#st

allow=8.0=0.13963rad

=(16.2887106 ) T=0.13963 rad

T1=8.57 kN .m

b) Allowable tor!"eT

2 base/ "3o$ shear stress #$ the brass

slee&e

b=Tb(d2/2)

Ipb=70MPa

Tb=0.46418T(deeq.2)

70MPa=(0.46418T)(0.045m)4.0841106 m4

Sol"5#6$ 3ara T (E!"al toT

2 ):T

2=13.69 k N . m

5) Allowable tor!"eT

3 base/ "3o$ shear stress #$ the steel sha%t

BC

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S=T(d2/2)IPS

=110 MPa

110MPa= T(0.035m)

2.3572106m4

Sol"5#6$ 3ara T (E!"al toT

3 ):

T3=7.41 kN .m

/) a7#'"$ allowable tor!"eShear stress #$ steel 4o&er$s

Tmx=7.41kN .m