Statically Indeterminate

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Statically Indeterminate
Objective
To determine the internal torque and the
associated shear stress for statically
indeterminate problems.
Find,

1. Reaction at A and B.
2. Internal torque at segment AC and CB.
3. Stress at AC and CB.

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Statically Indeterminate
Equation of equilibrium.
Where TA and TB are reactions at supports.
Equation of equilibrium.
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Compatibility Equations
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Example
The solid steel shaft as shown in figure has a
diameter of 20 mm. If it is subject to the two
torques, determine the reactions at the fixed
support A and B.
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Solution
Equation of equilibrium.
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Compatibility
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Example
The shaft as shown in figure is made from a
steel tube, which is bonded to a brass core. If a
torque of T 250 Nm is applied at its end, plot
the shear-stress distribution along a radial line
of its cross-sectional area. Take Gst 80 GPa,
Gbr 36 GPa.
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Solution
Equilibrium.
Compatibility.
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Solving Eqs. 1 and 2, we get
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The enD