bridge.org
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@@ -52,10 +52,10 @@ gives a maximum supported force of
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uconvert(u"N",3u"MPa"*2*75u"mm"*(50u"mm")^2/(3*725u"mm"))
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#+end_src
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-#+RESULTS:
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+
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#+begin_results
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517.2413793103449 N
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-#+end_example
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+#+end_results
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** with rebar, assuming cracking
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:PROPERTIES:
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@@ -75,19 +75,19 @@ Assume $n=8$ for the steel's modulus over the concrete
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y0v=cIcrc(y-y0)+cIcrs(y-y0) |> simplify |> (u->solve(u,y0)[1])
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#+end_src
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-#+RESULTS:
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-#+begin_example
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+
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+#+begin_results
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31.1520370152924
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-#+end_example
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+#+end_results
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#+begin_src julia
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Iv=cIcrc((y-y0)^2)+ cIcrs((y-y0)^2) |> subs(y0=>y0v)
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#+end_src
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-#+RESULTS:
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-#+begin_example
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+
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+#+begin_results
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342599.125813200
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-#+end_example
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+#+end_results
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for a 30MPa crush strength concrete,
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by [[id:0c49d881-25e0-4e93-b1f9-a8e8cc3ad365][elastic flexure formulas]]
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@@ -96,19 +96,20 @@ by [[id:0c49d881-25e0-4e93-b1f9-a8e8cc3ad365][elastic flexure formulas]]
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crushload=uconvert( u"N" , 30u"MPa"*(Iv*1u"mm^4")/((75-y0v)*1u"mm")*4/725u"mm")
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#+end_src
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-#+RESULTS:
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-#+begin_example
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+
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+#+begin_results
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1293.24279495813 N
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-#+end_example
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+#+end_results
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the stress in the steel is
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#+begin_src julia
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uconvert(u"MPa", (crushload*725u"mm"/4)*8*(y0v-18)*1u"mm"/(Iv*1u"mm^4"))
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#+end_src
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-#+begin_example
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+
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+#+begin_results
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71.9871270820728 MPa
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-#+end_example
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+#+end_results
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So we put in way more steel than required,
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since it has a yield strength >250MPa.