Sign issue with the skew bending formula

In summary, the conversation discusses an issue with the sign minus in the skew bending formula for stress generated by bending moments. The confusion arises due to the superposition principle and the sign convention used for the axes and bending moment vector. The bending moment vector is taken to be in the first quadrant between the X and Y principal axes, resulting in opposite signs in the z direction.
  • #1
Amaelle
310
54
Good day !
I have an issue with the sign minus inside the skew bending (unsymmetric) formula
First we all know that the stress generated by the bending moment is the following:
flexural formula.jpg


and then after we have the formula
unsymmetric bending.png


I really don't understand why we don t have the sign minus in all the formula, because of the superposition principle? I'm really confused regarding that point
Many thanks in advance
 

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  • #2
I am not certain of the topic ... I assume it is the beam that's asymmetric rather than the bending. E.g. as at http://courses.washington.edu/me354a/Unsym.pdf.
What looks like the same equation appears there on page 3. In that case it arises from the sign convention that happens to have been used for the axes and the bending moment. The bending moment vector is taken to be in the first quadrant between the X and Y principal axes. The cross product of that with the axis vectors will be into the page for one axis and out of the page for the other, i.e. opposite signs in the z direction.
 
  • Like
Likes Amaelle
  • #3
thanks a lot!
 

What is the skew bending formula and why is it important in the field of science?

The skew bending formula is a mathematical equation used to calculate the bending stress in a beam that is subjected to an off-center or eccentric load. It is important in science because it helps engineers and researchers understand the behavior of structures under different loading conditions, which is crucial for designing safe and efficient structures.

What is the sign issue with the skew bending formula and how does it affect the accuracy of calculations?

The sign issue with the skew bending formula arises when the sign convention used to determine the direction of the bending stress is not consistent with the actual direction of the stress. This can lead to incorrect calculations and affect the accuracy of results.

How can the sign issue with the skew bending formula be resolved?

The sign issue with the skew bending formula can be resolved by carefully defining the sign convention and consistently using it throughout the calculation process. It is also important to consider the direction of the bending stress and adjust the sign accordingly.

What are some common sources of the sign issue with the skew bending formula?

The sign issue with the skew bending formula can arise from various sources, such as incorrect application of the sign convention, misinterpretation of the direction of the bending stress, or using the wrong formula for a specific loading condition. It can also occur due to human error or typos in calculations.

How can the accuracy of calculations using the skew bending formula be improved?

To improve the accuracy of calculations using the skew bending formula, it is important to carefully follow the sign convention, double-check all input values and calculations, and use the correct formula for the specific loading condition. It is also recommended to use computer software or spreadsheets for complex calculations to minimize human error.

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