Sign convention of shear force, moments and torsion

1. Sign convention of shear force and moments

signconv
Figure 1. Sign conventions for moments

2. Shear force

  • Sign convention

    • The shear force in end 1 is consistent with the external load

    • The shear force in end 2 is multiplied with -1

3. Example

  • Cantilever beam

  • Global axis and local axis are equal

4. F > 0 , line end 1 in origo

  • Shear force in z-direction < 0

  • Moment about y-axis > 0

fpos1
  • Note: The shear force in end 2 is multiplied with -1 and presented as result

fpos2

fpos3

fpos4

5. F < 0 , line end 1 in origo

  • Shear force in z-direction > 0

  • Moment about y-axis < 0

fneg

fneg2

6. F > 0, line end 2 in origo

  • Shear force in z-direction > 0

  • Moment about y-axis > 0

fposend2 1
fposend2 2
fposend2 3

7. F < 0 line end 2 in origo

  • Shear force in z-direction < 0

  • Moment about y-axis < 0

fnegend2 1
fnegend2 2

8. Torsion

  • Right hand rule

9. M > 0

  • Apply moment M about x-axis, M > 0

  • Torsional moment > 0

mpos

mposplot

10. M < 0

  • Apply moment M about x-axis, M < 0

  • Torsional moment < 0

mneg

mnegplot