Strength of Materials I EGCE201 ?????????? 1

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Strength of Materials I EGCE201 ?????????? 1

• Instructor ??.???????? ????????? (?.??)
• ????????? 6391 ???????????????????
• E-mail egwpr_at_mahidol.ac.th
• ???????? 66(0) 2889-2138 ??? 6391
• www.egmu.net/civil/wonsiri

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Shearing Stress in Multiple Shafts
Static equilibrium must be satisfied. The vector
of all applied torques 0
TATBTCTD0
The shearing stress at any point in the shaft is
a function of the Internal torque on a plane
containing the point. The maximum Stress is
computed from
Internal torque
Radius of the shaft
The polar moment of inertia
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The shearing stress at a point on shaft through
which section 1 passes can only be defined once
the internal torque is determined.
From the free-body diagram, the internal torque
at the section
The shearing stress is given by
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The shearing stress at a point on shaft through
which section 2 passes can only be defined once
the internal torque is determined.
From the free-body diagram, the internal torque
at the section
The shearing stress is given by
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Angle of Twist in Multiple Shafts

• For this shaft sections AB, BC, and CE will each
  have different
• Internal torque (FBD)
• Polar moment of inertia
• Shear Modulus
• Length

The angle of twist of the end of a shaft
consisting of N sections is expressed as
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Relative Rotation
In some situations both ends of a shaft rotate.
The angle of twist is the angle through which one
end rotates w.r.t the other.
fixed
Both rotates
Shaft AB
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Shearing Stress on inclined planes
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Shearing Stress on inclined planes
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Statically Indeterminate Shafts

• Both ends of the shaft are built in, leading to
  two reaction torques but one has only one moment
  equilibrium equation.
• The compatibility equation is the relative
  rotation!
• See example

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Assuming a counterclockwise torque is positive,
summing moments about the axis of the shaft
results in
The total angle of twist of the shaft must be 0
since both ends are fixed.
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1.
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2.
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3.
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4.
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5.
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5. continued
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5. continued
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6.
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6. continued
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6. continued