An Alternative Shear Formula in Non-Principal Coordinates

Abstract

An alternative formula is presented to compute shear stresses in non-principal coordinates of arbitrary cross-sections for linear elastic, prismatic beams. In contrast to the formula traditionally used in textbooks for non-principal coordinates, the new formula avoids lengthy computations with the first and second moments of area. The trade-off is that the normal stresses must be computed before the shear stresses; however, since in practical situations both normal stresses and shear stresses need to be known, this is not considered a general disadvantage of the proposed formula. Whereas the traditional formula takes different formats for principal and non-principal coordinates, the new formula is valid in any coordinate system. Thus, simplicity is gained.

Keywords

shear formula prismatic beams beam theory thin-walled structures

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References

Wang

C.-C.

, ‘Some vector formulas for the bending and shearing of prismatic beams with arbitrary cross sections’, Thin-Walled Structures, 21 (1995), 175–190.

Barber

J. R.

, Intermediate Mechanics of Materials (McGraw-Hill, Singapore, 2001).

Hartsuijker

, Stresses, Strains, Displacements (Academic Services, Schoonhoven, 2001) (in Dutch).