Concept explainers
The tapered cantilever beam AB shown in the figure has a solid circular cross section. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance v from the free end are, respectively,
in which IAis the moment of inertia at end A of the beam.
Determine the equation of the deflection curve and the deflection SAat the free end of the beam due to the load P.
The equation for the deflection curve and the deflection
Answer to Problem 9.7.8P
The equation for the deflection curve and the deflection
Explanation of Solution
Given Information:
We have,
Length of the tapered cantilever beam AB, L
Load at point A as P
Diameter at point A,
Diameter at point B,
Moment of inertia, I
The bending moment is
So, the 2nd degree diffrential equation would be,
In the above equation, taking integration on both sides :
According to boundary condition at x=L,
In above equation taking integration again,
And at 2nd Boundary conditions, x = L and v = 0.
At x = 0, then
At point A, the deflection would be below.
Conclusion:
The answers are calculated according to deflection and deflection curve.
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Chapter 9 Solutions
Mechanics of Materials - Text Only (Looseleaf)
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