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fpjeepy

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- Thread starter fpjeepy
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In summary, the tip should be designed to handle the load, the thickness at the base should be calculated, and the thickness at the other points should be calculated and tested.

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fpjeepy

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- #2

jrmichler

Mentor

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A beam designed for constant bending stress will have the maximum flexibility for a given stress. It also has the minimum weight for a given maximum stress and for a solid prismatic beam. So here is what I recommend:

1) Design the tip to handle your load. A theoretical analysis of a simple cantilever beam will tell you that zero bending stress at the tip requires zero thickness. A slightly more sophisticated analysis will calculate a minimum thickness to handle the shear stress. A little testing will tell you how thick the tip has to be in order to stand up to the real loads without breaking out little pieces. This is a case where a few simple tests are better than 1000 calculations.

2) Assume a load and an allowable stress, then calculate the thickness at the base. Use those same numbers to calculate thickness at the 20%, 40%, 60%, and 80% (distance from base to tip) points. Connect those points with either straight lines or a smooth curve, whichever is easier. The real world difference is minimal.

3) Test it. If too flexible or weak, redesign with the same load and a lower allowable stress. Note that only the longitudinal plies in plywood contribute to strength and stiffness, while the cross plies are dead weight spacers.

Hint: Do the calculations in a spreadsheet, so that changing the allowable stress can be done by changing only one number.

- #3

A simplified tapered cantilever beam is a type of beam that has a varying cross-sectional area along its length, with one end fixed and the other end free to move. This type of beam is commonly used in engineering and structural analysis.

A simplified tapered cantilever beam has a varying cross-sectional area, while a regular cantilever beam has a constant cross-sectional area. This change in cross-sectional area affects the beam's stiffness and deflection, making it more complex to analyze.

There are several generalizations that can be made for a simplified tapered cantilever beam, including the assumption of linearly varying cross-sectional area, constant material properties, and small deflections. These generalizations allow for simplified calculations and analysis of the beam's behavior.

The generalizations for a simplified tapered cantilever beam are commonly used in engineering and structural design to determine the maximum stress and deflection of a beam under various loading conditions. They also help in selecting the appropriate cross-sectional dimensions for a beam to meet specific design requirements.

While simplified tapered cantilever beam generalizations are useful for quick and simplified analysis, they do have limitations. These generalizations do not account for non-linear material behavior, large deflections, or complex loading conditions. Therefore, they should be used with caution and validated with more advanced analysis methods for more accurate results.

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