I want to perform a structural analysis on a portal frame using a finite element solver to get a displacements and reactions for a load. The software library only accepts loads applied to node, not to the member. The node loads have 6 parameters: 3 translation (x,y,z) and 3 rotation (xx,yy,zz). My load is a uniform load of 1 kN/m along one rafter.

Is it possible to convert the uniform member load to point loads that I can apply at the nodes?

Portal frame dimensions:

• span: 10 m
• eave height: 5 m
• apex height: 6.34 m
• rafter length: 5.18 m
• roof pitch: 15°

EDIT: fixed apex height

• FWIW I've found a better library doesn't have the original restriction of only node loads - frame3dd. – Sam Sippe Dec 13 '18 at 0:00

Not being able to apply loads along the member seems like a limitation of the software (without adding more nodes). If you can only apply loads at the nodes then the proper way to do this is to get the Fixed-End Reactions of the distributed load in terms of point loads AND MOMENTS.

Basically, imagine that your member that is subjected to the DL is fully fixed at each end and get the reactions. Then you switch the sign of the reactions and these are the loads you will need to apply at the nodes.

So consider the member below. I will use SkyCiv Structural 3D software to show how this works. In red we have the DL load and in black are the reactions at the fixed ends.

So we can apply those reactions (flipping the sign) to the actual structure now as you can see below:

And we can actually use the same structural analysis software to verify that this is in fact the correct way to convert the DL to its equivalent nodal loads:

So you'll notice that the reactions and displacements are identical between the models! Any minor differences are due to rounding of the reactions which were used as the loads. However, by modelling it with point loads and moments, the shear force and bending moment diagrams will only have the correct values at the nodes (not throughout the member obviously) due to the differences between the loads. If you're only looking for displacement and reactions then it is fine to model it like this.

NOTE: The dimensions of this frame did not match yours, so these values do not apply to you - it was just a simple example. The member I used was 3m across and 1m high. The software used was SkyCiv Structural 3D. You can signup for a free account here. The free account can analyse structures with up to 5 members so your portal frame can easily be solved. Of course you won't need to worry about converting the DL to its equivalent nodal loads because the software can handle mid-member loads.

Hope that helps.

• Great example thanks. How would you calculate the moment 0.791 by hand? It's easy to see how you would calculate the 1.58kN Tx point load (3.16m * 1kN / 2) but I can't figure out how you calculate the moment. – Sam Sippe Mar 10 '16 at 3:41
• It is difficult by hand because it is a statically indeterminate problem. It's easily done using software. But if you really wanted to do it by hand then perhaps the moment distribution method will work – pauloz1890 Mar 10 '16 at 4:14
• In this case Mz = pointLoadTotal / 4; 0.79 = 3.16/4; which suggests a simple relationship however en.wikipedia.org/wiki/Fixed_end_moment gives the equation as -qL^2/12 which gives a moment of 0.832, not what we are after. The moment distribution methods are a bit beyond me. – Sam Sippe Mar 10 '16 at 4:58
• qL^2/12 only works if the beam is purely horizontal – pauloz1890 Mar 10 '16 at 5:01
• Actually, all finite element software converts from distributed loads to nodal loads internally before solving the problem. In general, the software should do it for you, not only to save you work, but also because it needs to be done in a way that is consistent with the formulation of the elements. It just happens to be the case that for most beam elements (especially "simple" formulations), the conversion is identical to finding the reactions at the end of a statically determinate beam, as described in the answer. – alephzero Mar 10 '16 at 5:22

You can apply the total force of an evenly distributed load to the centre of the member. This will be a reasonable approximation in terms of the overall distribution of load in the structure as a whole but is less useful in determining the stresses and deflections in individual members and associated joints.

However a model based on point loads should, in general, be more conservative than one with evenly distributed loads.

Having said that, the case in your example looks like something where specific building codes would need to be considered rather than ad hoc analysis.

• But if the OP's software only allows loads to be applied at the nodes, an "equivalent point load at the centre of an element" doesn't help. Whether it is a "reasonable approximation" to ignore the equivalent moments applied at the nodes is a different question (and personally I don't like making unnecessary approximations - the problem is that they may only be "reasonable approximations" except in the (unidentified) situations where they are unreasonable! – alephzero Mar 10 '16 at 5:28

If your FEM S/W can't handle distributed loads, throw it away and find something which does. It's a pain having to convert DL to NL all the time. Your software should make your life easier, not harder.

• I'm looking at a library I can automate from c# and SharpFe github.com/iainsproat/SharpFE looks like the best option so far but it doesn't have distributed loads unfortunately. Any suggestions for other libs appreciated. – Sam Sippe Mar 10 '16 at 1:18