The figure shows a torsion bar OA fixed at O, simply supported at A, and connected to a cantilever AB. The spring rate of the torsion bar is kT, in newton-meters per radian, and that of the cantilever is kl, in newtons per meter. What is the overall spring rate based on the deflection y at point B?
The overall spring rate based on the deflection
Answer to Problem 1P
The overall spring rate based on the deflection
Explanation of Solution
Write the expression for the stiffness of the torsion bar.
Here, the torsional stiffness of the bar is
Write the expression of the torque on the torsional bar.
Here, the length of the bat is
Since the force
Substitute
Write the expression for stiffness of the cantilever portion AB.
Here, the lateral stiffness of the bar is
Write the expression for net deflection of a combined system.
Here, total deflection is
The net defection of the combined system is the combination of the torsional deflection and lateral deflection.
Write the equation of net deflection of the combined system.
Conclusion:
Substitute the value of
Substitute
Thus, the overall spring rate based on the deflection
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Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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