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My problem is a bridge with a horizontal cord of span 12 m between two piers of arbitrary height. It is required to use a pin-connected truss, consisting of steel members bolted together to steel gusset plates. Assume the end supports at the piers to be a pin and a roller.

A vertical loading of a concentrated force $F$ [19.5 kN] acting 4 m from the left-hand support, and linearly distributed load $q$ [1250 N/m] acting on the central 6 m of the span. This load can be applied in part to several joints on the top cord within the given region.

The force of the wind and the weight of all members are to be neglected.

Assume the maximum tensile force in each member cannot exceed 4.25 kN, and the maximum compressive force cannot exceed 3.5 kN regardless of the length of the member.

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I knew that I can reduce the concentrated force by adding a pin on that force and join the pin to multiple members, but doing that leaves me with too much unknowns.

And also, am I able to reduce the 19.5k N load by replacing the single pin, where the load acts and adding two pins between the load so the load will be 9.75 kN in each pin? This approach is used

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There is no restriction about how the bridge should look like, but I designed mine so to have in each member tension not more then 4.25KN and compression less than 3.5 KN.

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  • $\begingroup$ Welcome to Engineering! What do you mean by "minimize that load"? And how is the bridge supported (simply supported at both ends?)? And what do you mean by putting "two pins between the load"? Do you mean hinges between the load and the supports? if that's the case, your bridge will be hypostatic (unstable) if the supports are pinned, since three (or more) hinges in line is unstable. Please edit your question with a sketch of your original bridge and what you mean by those "added pins". $\endgroup$ – Wasabi Jan 10 at 21:08
  • $\begingroup$ The question is now much improved, but I still don't understand what you have to do. You mention needing to use a truss, but your sketch doesn't have a truss. Are you saying you need to replace this structure with a truss? Also notice the structure in that sketch is unstable. And I still don't understand what you mean by "adding a pin on that force and join the pin to multiple members", or by "replacing the single pin, where the load acts and adding two pins between the load so the load will be 9.75 kN in each pin". Also, was your last phrase cut short? It seems incomplete. $\endgroup$ – Wasabi Jan 11 at 2:06
  • $\begingroup$ As I said, the question is now much better, it just needs a bit more work. Could you edit your question again, adding sketches showing examples of what you mean by adding and replacing pins? And, if possible, show us an example of what the final structure might look like (ignoring the math). $\endgroup$ – Wasabi Jan 11 at 2:08
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    $\begingroup$ Looking at your most recent edit, I need to ask: is the question basically "draw a truss over a 12m span which resists a concentrated load of 19.5kN placed 4m from the left support and a distributed load of 1250kN/m over the central 6m, such that each bar handles less than 4.25kN (tension) or 3.5kN (compression)"? In your question you use distances $a$ and $b$ and call the distributed load $q$, but in your sketches you actually have values for these variables. Must your work be generic (works for any $a$, $b$, $q$) or can we just adopt those values you've used? $\endgroup$ – Wasabi Jan 11 at 20:06
  • $\begingroup$ we can use the value that I mentioned. $\endgroup$ – Mohd Albusaidi Jan 11 at 21:49

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