I'm having difficulties with calculating the distribution of forces and moments in a statically determinate structure shown below.

enter image description here

I'm especially confused about the arc part. Will there be only bending moments, or should we expect torque as well? Any help with approaching this problem is appreciated!


1 Answer 1


When you want to determine the internal reactions to a structure (in a example such as this), then the best course of action is

  1. to isolate the structure of interest by creating section around the part.

enter image description here

  1. The next step is to draw the internal forces on the points where the section (blue bubble) intersects with the structure. Please notice, that in this example (by habit more than anything else), I am using a convenience reference system which uses direction
  • dir 1: normal to the section (for tensile/compressive forces)
  • dir 2: perpendicular to the axial direction on the plane of the image
  • dir 3: perpendicular to the axial direction and to the plane of the image (Z-axis).

enter image description here

In this part of the example I am only plotting (for simplicity):

  • $\color{blue}{N}$: the axial force (which is normal to the section)
  • $\color{green}{Q_2}$: the shear force perpendicular to the axial force
  • $\color{red}{M_3}$: the bending moment around the z-axis (perpendicular to the image plane).

In the section presented above, the last two (namely $\color{green}{Q_2}$ and $\color{red}{M_3}$) are zero.

However, as you gathered there are 3 other internal forces (for the 3D case), namely:

  • $\color{green}{Q_3}$: the shear force with direction (parallel to the Z -axis)
  • $\color{red}{M_t}=\color{red}{M_1}$: the torsional moment
  • $\color{red}{M_2}$: a bending moment in the direction of $Q_2$.

enter image description here

are there torsional moments?

Yes in this example, at different points you will have different moments and forces.

Apart from bending moments you will also find torsional moment on the straight beam on the support and partially on the curved part of the structure.


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