# Strength of a welded steel gate with vertical bars vs. crossed diagonal bars

Looking for some hints on how to create a rough estimate for the following problem.

Given two steel gates with the same dimensions, same material - e.g. everything is the same. The only difference is that the middle parts have different structures.

When applying some force to the top, the gate will start to be more and more deformed, and at some force the gate will touch the ground at the place where the blue arrow points.

I'm looking for a rough estimate of how much more force is needed for the second gate - i.e. how much more "sturdy" is the second gate.

I really don't need any exact calculation, but probably will need some material data, so:

• common steel thin-walled beam (25mm x 25mm x 2mm wall thick)
• each joint point is welded, we can be simplify and assume that the welds are exactly as strong as the material itself
• the suspension points can hold infinite force
• and any other possible simplification - this problem isn't for any rocket-science but for solving an evening talk with a friend.

• This isn't the focus of your question but Gate F2 looks a lot easier to climb over that F1 - usually the main purpose of a gate is to keep people out. Aug 12 '15 at 21:40
• I'm just saying, the (diagonal) grid is probably more expensive to produce, because you have more wield points, and because diagonal joints are probably more complicated than rectangular joints. Not sure if you can save this extra cost by using less material. Aug 13 '15 at 18:18
• Also if you apply force from another direction, e.g. by smashing a car into the gate, the result might be not so different. On the other hand, if you apply force to only a single bar, e.g. by pulling with a wire, then I expect the reduced distance between bars will increase resistance. Aug 13 '15 at 18:21

As grfrazee said, you won't know for sure until you do a finite element analysis. I was intrigued by this question as a colleague and I got into a discussion about this. While we both agreed the diagonal bracing would be better at resisting deflection, we wondered by what factor it would be better.

We were really curious so we settled the debate and did a quick structural analysis on SkyCiv Structural 3D (can try for free for one month if anyone is wondering). It took around an hour to set up both gates and analyze them mainly because we had to generate the node positions from scratch. Anyways here are the results of the linear static analysis which take into account the assumptions and simplifications you made. We applied a 5 kN POINT LOAD at both F1 and F2 and made each support a pin support at the locations you specified. Note that in the 3D colored results the deflection is 12X greater than the actual deflection of the gate in both scenarios - it is exaggerated so you can see the deflected shape of the gates.

## Gate #1

$\text{y-deflection at the bottom-left of the gate} = 31.74\text{ mm}$

$\text{Max total deflection} = 32.10\text{ mm}$

## Gate #2

$\text{y-deflection at the bottom-left of the gate} = 7.84\text{ mm}$

$\text{Max total deflection} = 7.55\text{ mm}$

Diagonal bracing (Gate #2) is clearly the winner. So when both gates are subjected to the same load it looks like Gate #2 resists deflection better (i.e. is more stiff) by a factor of 4.25.

Some more interesting points:

• There's a pretty high bending stress at that top right support in both scenarios ~ 350 MPa.
• The analysis didn't take into account self-weight of the gates.

Also let me add that there looks to be a scaling issue with the diagonal grid you have drawn, because when I modeled it I found that there were far less points than what was suggested by your diagram. I ensured that the parallel spacing between each rhombus was 300mm. This means the diagonal of each rhombus is roughly 424mm. Your gate is 3300mm in length so that means around 8 rhombi should fit across your gate in the x-direction - but you've drawn around 12. Just thought I'd let you know.

• The 4x matches nicely with @alephzero's analysis above. And the diagram confirms that indeed the diagonal braced section bends very little and the 600 mm section is the next limiting factor.
– jpa
Aug 13 '15 at 5:16
• Yep i agree. alephzero did a great quick estimate! Aug 13 '15 at 5:22
• Guys, you're absolutely marvelous. You and @alephzero too. Thank you. Oct 18 '15 at 17:43

Assuming the joints are welded, for the top gate to deform as you draw it the vertical bars will have to bend into an "S" shape. The flexibility in bending will be proportional to the cube of the length, if everything else is the same.

The stiffness of the three sections of the top gate will be proportional to $1/1^3 = 1$, $1/0.6^3 = 4.6$, and $1/0.4^3 = 15.6$. The total flexibility is dominated by the longest (middle) section.

In the bottom gate, the diagonal bars would be (to a first approximation) infinitely stiffer than the vertical bars since they carry shear in diagonal tension and compression, not in bending. The overall stiffness would be of the order of 4 or 5 times greater (based on the 4.6 above).

You could probably get away with less material in the diagonal bars (either thinner bars or fewer bars) but, a more detailed analysis is too much work to do by hand and for free!

It doesn't matter if the spacing of the diagonal bars matches the verticals, so long as the horizontal bars are strong enough to redistribute the load between them.

If stiffness is the only criterion, you might as well just have an outer rectangular frame and diagonal bracing, with no sections of "vertical bars" at all.

• +1 for the rectangular frame with diagonal bracing. Aug 12 '15 at 20:36

While you've described your problem pretty well, I don't think you're going to find a satisfactory answer without having to run a fairly complex finite element analysis on both structures.

The first gate structure will behave similarly to a Vierendeel truss since you have all of the pieces essentially moment-connected.

The second gate structure will likely fall somewhere between the Vierendeel and a traditional truss, though it's still, for the most part, moment connected with no real alignment of working points.

Normally, trusses are detailed such that their working points (i.e., the center of action of the axial force in the members) coincide on roughly the same point. This is to reduce bending in any single member since the eccentricity is approximately zero.

The second gate has some truss action due to the diamond-shaped section in the middle. Unfortunately, since the working points of the diamond section don't meet up with the vertical/horizontal sections, you're losing some of the advantage of the truss action.

• So, if I understand right - if the diamond shaped section, exactly will meet every second vertical bar (at the uppper/bottom) section - it will be better and the best would be if the diamond section would be have the same "periodicity" as the uppper/bottom vertical bars.. +1 :) will wait a while for other answers. ;) Aug 12 '15 at 19:09
• Yes, if the vertices of your diamond lattice matched the vertical bars, that would help. Aug 12 '15 at 19:11