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Week 9 - Slab Forms.slides.html
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Week 9 - Slab Forms.slides.html
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<h1 id="Formwork-for-Slabs">Formwork for Slabs<a class="anchor-link" href="#Formwork-for-Slabs">¶</a></h1>
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<h2 id="Check-All-Audio"><strong style="color:green">Check All Audio</strong><a class="anchor-link" href="#Check-All-Audio">¶</a></h2>
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<h1 id="Slab-Forms">Slab Forms<a class="anchor-link" href="#Slab-Forms">¶</a></h1>
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<p><a href = "http://i.imgur.com/dsYZ9Pt.png"><img src="http://i.imgur.com/dsYZ9Pt.png" alt = "Slab Form Parts" title = "Slab Form Parts" style="max-width:300px; max-height:300px; border:1px solid blue; float:right; margin-left:10px;"/></a></p>
<p>A slab form, at its most basic, consists of four parts:</p>
<ul>
<li>Plywood, that supports the slab</li>
<li>Joists, that support the plywood</li>
<li>Stringers, that support the joists</li>
<li>Shores, that support the stringers</li>
</ul>
<p>In a real slab form there are at least two other parts, the braces, and the form work for the sides of the slab. You already know about the braces, and you can think of the <a href="http://i.imgur.com/kCu8aMV.png">side forms</a> as just really short walls that are supported with nails at the bottom, and compression braces at the top.</p>
<p><a href = "https://ellismanufacturing.com/collections/all/products/shore-clamps"><img src="http://i.imgur.com/OgBEziC.jpg" alt = "Slab Form and Reshores" title = "Slab Form and Reshores" style="max-width:300px; max-height:300px; border:1px solid blue; float:left; margin-right:25px;"/></a></p>
<p>In the image to the right, the shores are green due to being pressure treated. This is not necessary, but I've shown them this way because if you walk into a home center you are most likely to see 4x4s that are green due to being treated.</p>
<p>The image to the left (<a href="http://www.ellisok.net/gallery">source</a>) is of a third floor slab form, supported on <a href="http://www.ellisok.net/shore-clamps/ellis-4x4-shore-clamp">Ellis Jacks</a>, (note that there are addition eccentricities in the shores). The second floor is being supported by reshores, but that is another topic. Additionally, there are options for <a href="http://www.sontac-scaffold.com/images/Products/prop-001.gif">shoring$^1$</a>, and even <a href="http://www.peri.com/shared/siteimg/history/1992_01.jpg">forms$^2$</a>. But, again, if you can understand how to design a slab form out of timber, then you can design one using other systems.</p>
<ol>
<li><a href="http://www.sontac-scaffold.com/en/products/steel-prop.htm">Source</a></li>
<li><a href="http://www.peri.com/en/company/company/history.cfm">Source</a></li>
</ol>
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<h2 id="Design-Process">Design Process<a class="anchor-link" href="#Design-Process">¶</a></h2>
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<p>The design procedure is similar to wall forms.</p>
<ol>
<li>Determine the load on the plywood.</li>
<li>Determine the support spacing for the plywood, (joists are used for support instead of studs in this case).</li>
<li>Determine the support spacing for the joists, (stringers are used for support instead of wales).</li>
<li>Determine the support spacing for the stringers, (shores instead of ties).</li>
<li>Determine the bearing strength (one additional case in slab forms).<ol>
<li>Bearing between joists and stringers.</li>
<li>Bearing between stringers and shores.</li>
</ol>
</li>
<li>Determine the capacity of the shore, (we will use timber columns for our shores).</li>
</ol>
<p>Aside from the fact that there is one additional bearing check we need to make, there is one other difference. That difference is the constructible spacings. When we were looking are wall forms everything we looked at was based around getting the spacings to work out with the size of a sheet of plywood. We only need to design around a sheet of plywood when we are doing the plywood support spacings in slab forms, i.e. the joist spacings. Our joists are not limited to $48"$ and $96"$, instead joists will generally be a standard lumber length. Lumber is typically sold in either $8'$, $10'$, $12'$, $14'$, or $16'$ lengths. This variety means that we will have to decide how long we want the joists to be when we determine their support spacings. For instance if we find that the joists should be supported every $42"$, then instead of rounding down to $32"$ to use an $8'$ long member ($3 \times 32" = 96" = 8'$) we will just use $14'$ long joists ($4 \times 42" = 168" = 14'$). I'll cover an analytically approach of determining this later.</p>
<p>Before we start working on an example problem, I should mention a couple of assumptions I will be making in all slab design problems. Firstly, all joists will be 4x4s. This isn't required in a professional setting, but they are used commonly enough that it isn't an unreasonable assumption. Secondly, all stringers will be 4x6s (oriented in the strong direction). Again, it isn't really required but it is relatively common.</p>
<p>The reason that 4x4s and 4x6s are <em>so</em> common that I can make these assumptions, is that the use such stout members eliminates the need for labor intensive, intermediate blocking. Such blocking <em>would</em> be needed to prevent rollover for taller and thinner members. Let's go ahead, and work through an example problem.</p>
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<h1 id="Slab-Form-Design-Example:">Slab Form Design Example:<a class="anchor-link" href="#Slab-Form-Design-Example:">¶</a></h1>
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<h3 id="Determine-the-Following:">Determine the Following:<a class="anchor-link" href="#Determine-the-Following:">¶</a></h3>
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<ul>
<li>Joist Spacing in inches</li>
<li>Stringer Spacing in inches</li>
<li>Shore Spacing in inches</li>
<li>Shore Axial Load in pounds</li>
<li>Allowable Stringer Bearing Stress in psi</li>
<li>Actual Stringer Bearing Stress in psi</li>
<li>Verify that a 4x6 shoring will work.</li>
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<p>Design formwork for a concrete floor slab based on the following information:</p>
<ul>
<li>Thickness of concrete slab = 10”</li>
<li>Unbraced length for shores = 14 ft</li>
<li>Concrete unit weight = 150 lb/ft$^3$</li>
<li>Deflection limited to L/360 but not greater than 1/16”</li>
<li>All form lumber will be S4S Select Structural Hem-Fir with no splits</li>
<li>Assume wet conditions for lumber and wet conditions for plywood</li>
<li>Decking for the slab will be 3/4” Group II Plywood (S-2)</li>
<li>Load duration factor of 7 days</li>
<li>Dead Load for formwork material = 5.5 psf and Live Load = 50 psf</li>
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<div class=" highlight hl-ipython3"><pre><span class="o">%</span><span class="k">run</span> Older_Classes/Temp_struc_v_3_beta.py
<span class="o">%</span><span class="k">run</span> Beams/Timber_beam_v_02.1.py
<span class="c"># %run Beams/Find_Beam_lib.py</span>
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<pre>In order to display plots inline in the IPython notebook you must include
the following magic command:
%matplotlib inline
If you need to display plot you will need to used the following commmand
%matplotlib inline
Note: The atribute 'pick_list' is now available_grades (added Jan, 6, 2014)
Now using 2015 Timber code by default
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<div class=" highlight hl-ipython3"><pre><span class="n">t_concrete</span> <span class="o">=</span> <span class="mi">10</span> <span class="c">#in</span>
<span class="n">DL_form_work</span> <span class="o">=</span> <span class="mf">5.5</span> <span class="c">#psf</span>
<span class="n">LL</span> <span class="o">=</span> <span class="mi">50</span> <span class="c">#psf</span>
<span class="n">Wet</span> <span class="o">=</span> <span class="k">True</span>
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<div class=" highlight hl-ipython3"><pre><span class="n">ply</span> <span class="o">=</span> <span class="n">panel</span><span class="p">()</span>
<span class="c">#setting the thickness sets the structural properties </span>
<span class="c">#of the plywood automatically</span>
<span class="n">ply</span><span class="o">.</span><span class="n">nom_thick</span><span class="o">=</span><span class="s">'3/4'</span>
<span class="n">ply</span><span class="o">.</span><span class="n">group</span><span class="o">=</span><span class="mi">2</span>
<span class="n">ply</span><span class="o">.</span><span class="n">grade</span><span class="o">=</span><span class="s">'S-2'</span>
<span class="n">ply</span><span class="o">.</span><span class="n">condition</span> <span class="o">=</span> <span class="s">"wet"</span>
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<div class=" highlight hl-ipython3"><pre><span class="n">Species</span> <span class="o">=</span> <span class="s">"HEM-FIR"</span>
<span class="n">Grade</span> <span class="o">=</span> <span class="s">'Select Structural'</span>
<span class="n">Shore_length</span> <span class="o">=</span> <span class="mi">14</span> <span class="c">#ft</span>
<span class="n">Shore_section_b</span> <span class="o">=</span> <span class="mf">3.5</span> <span class="c">#in</span>
<span class="n">Shore_section_d</span> <span class="o">=</span> <span class="mf">5.5</span> <span class="c">#in</span>
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<h2 id="Span-calculations">Span calculations<a class="anchor-link" href="#Span-calculations">¶</a></h2>
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<p>For Bending, span, $L = 10.95 \sqrt{\frac{F_b' S}{w}}$</p>
<p>For Rolling shear in sheathing, span, $L = \frac{20 \times F_s'}{w}\times \frac{I b }{Q}$</p>
<p>For Shear in dimensional lumber, span, $L = 13.33 \times \frac{F_v' b d}{w} + 2 d$</p>
<p>For deflection where $\Delta = {}^L/_{360}$, span, $L = 1.69 \sqrt[3]{\frac{E' I}{w}}$</p>
<p>For deflection where $\Delta = {}^1/_{16}\text{"}$, span, $L = 3.23 \sqrt[4]{\frac{E' I}{w}}$</p>
<p>Stress = Load/Area</p>
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<h2 id="Pressure">Pressure<a class="anchor-link" href="#Pressure">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span class="n">DL_fw</span> <span class="o">=</span> <span class="n">DL_form_work</span>
<span class="n">LL</span> <span class="o">=</span> <span class="n">LL</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">t_concrete</span>
<span class="n">SlabLoad</span> <span class="o">=</span> <span class="n">slab_load</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">LL</span> <span class="o">=</span> <span class="n">LL</span><span class="p">,</span> <span class="n">DL_forms</span> <span class="o">=</span> <span class="n">DL_fw</span><span class="p">)</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">SlabLoad</span><span class="o">.</span><span class="n">value</span>
<span class="c"># p = DL_fw+DL_con+LL</span>
<span class="nb">print</span><span class="p">(</span><span class="s">"Uninform pressure = %.2f psf"</span><span class="o">%</span><span class="k">p</span>)
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<pre>Uninform pressure = 180.50 psf
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<p>The load on the slab formwok is made up of, the Concrete Dead Load, the Formwork Dead Load, and the worker Live Load. We need to find the Concrete Dead Load, then calculate the total pressure $(p)$ on the slab formwork.</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">SlabLoad</span><span class="o">.</span><span class="n">work</span>
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$$\text{Concrete Dead Load } = DL_{con} = \text{Slab Thickness} \times \text{Unit weight of Concrete}$$
${}$
$$\text{Unit weight of concrete} = \gamma_{con} = 150 pcf$$
${}$
$$\text{Slab thickness } = t_{slab} = 10"$$
${}$
$$DL_{con} = t_{slab} \times \gamma_{con}$$
${}$
$$DL_{con} = 10" \times 150 pcf \times \frac{1 ft}{12 in}$$
${}$
$$DL_{con} = 125 psf$$
${}$
$$\text{Formwork Dead Load } = DL_{forms} = 5.5 psf$$
${}$
$$\text{Slab Live Load } = LL = 50 psf$$
${}$
$$\text{Total Pressure Load on the Slab Form Work} = p$$
${}$
$$p = \text{Concrete Dead Load} + \text{Formwork Dead Load } + \text{Slab Live Load }$$
${}$
$$p = DL_{con} + DL_{forms} + LL$$
${}$
$$p = 125 psf + 5.5 psf + 50 psf$$
${}$
$$p = 180.5 psf$$
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<h2 id="Plywood">Plywood<a class="anchor-link" href="#Plywood">¶</a></h2>
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<source src="https://github.com/damontallen/Construction-Lectures-Fall-2014/raw/master/Lecture%20Audio/Week%209/Slab%20Form%20Design/Plywood.mp3"
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<div class=" highlight hl-ipython3"><pre><span class="nb">print</span><span class="p">(</span><span class="s">'Plywood thickness = %s"'</span><span class="o">%</span><span class="k">ply</span>.nom_thick)
<span class="nb">print</span><span class="p">(</span><span class="s">'Plywood group = %s'</span><span class="o">%</span><span class="k">ply</span>.group)
<span class="nb">print</span><span class="p">(</span><span class="s">'Plywood stress ratting = %s'</span><span class="o">%</span><span class="k">ply</span>.grade)
<span class="nb">print</span><span class="p">(</span><span class="s">'Plywood moisture condition = %s'</span><span class="o">%</span><span class="k">ply</span>.condition)
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<pre>Plywood thickness = 3/4"
Plywood group = 2
Plywood stress ratting = S-2
Plywood moisture condition = wet
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<div class=" highlight hl-ipython3"><pre><span class="c"># OVERRIDE</span>
<span class="c"># ply.F_b = 820 #psi/ft</span>
<span class="c"># ply.F_s = 44 #psi/ft</span>
<span class="c"># ply.E = 1300000 #psi/ft</span>
<span class="c"># ply.C_D = 1.25</span>
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<p>Knowing that the plywood is oriented in the strong direction, and our $C_D = 1.25$, we can look up the properties of the plywood in the <a href="http://www.apawood.org/SearchResults.aspx?q=Y510&tid=1">Plywood Design Specification</a>.</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">ply</span><span class="o">.</span><span class="n">show_props</span><span class="o">.</span><span class="n">work</span>
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$$\text{From the Plywood Properties Tables:}$$
$$t_{nom} = 3/4"$$
$$A = 2.884 (in^2/ft)$$
$$I = 0.197 (in^4/ft)$$
$$S = 0.412 (in^3/ft)$$
$$Ib/Q = 6.762 (in^2/ft)$$
$$F_b = 820 psi$$
$$F_s = 44 psi$$
$$E = 1.300E+06 psi$$
$$C_D = 1.250$$
$$strong = True$$
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<p>This means that the allowable stresses for the plywood are,</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">ply</span><span class="o">.</span><span class="n">show_allowable_stress</span><span class="o">.</span><span class="n">work</span>
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$$F_b' = F_b \times C_D$$
$$F_b' = 820 psi \times 1.25$$
$$F_b' = 1025 psi$$
$${}$$
$$F_s' = F_s \times C_D$$
$$F_s' = 44 psi \times 1.25$$
$$F_s' = 55 psi$$
$${}$$
$$E' = E$$
$$E' = 1.30E+06 psi$$
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<div class=" highlight hl-ipython3"><pre><span class="n">w</span> <span class="o">=</span> <span class="n">p</span>
<span class="nb">print</span><span class="p">(</span><span class="s">"w = %.2f plf"</span><span class="o">%</span><span class="k">w</span>)
<span class="n">joist_spacing</span> <span class="o">=</span> <span class="n">board_test</span><span class="p">(</span><span class="n">ply</span><span class="p">,</span><span class="n">w</span><span class="p">,</span><span class="n">plywood</span><span class="o">=</span><span class="k">True</span><span class="p">,</span> <span class="n">slab</span><span class="o">=</span><span class="k">True</span><span class="p">)</span>
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<pre>w = 180.50 plf
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<h2 id="Plywood-Span-Limits-(Joist-Spacing)">Plywood Span Limits (Joist Spacing)<a class="anchor-link" href="#Plywood-Span-Limits-(Joist-Spacing)">¶</a></h2>
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<source src="https://github.com/damontallen/Construction-Lectures-Fall-2014/raw/master/Lecture%20Audio/Week%209/Slab%20Form%20Design/Plywood%20Span%20Limits%20(Joist%20Spacing).mp3"
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<p>Now that we know the properties of the plywood we can calculate the maximum spacing of the joists due to bending, rolling shear, and both deflection limits.</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">joist_spacing</span><span class="o">.</span><span class="n">work</span>
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$$\text{For a pressure of }180 psf \text{ the line load equals } 180 plf $$
${}$
$$L = 10.95 \sqrt{\frac{F_b' S}{w}} = 10.95 \sqrt{\frac{1025 psi \times 0.412 in^3 }{ 180 plf }} =16.75" \text{ (due to bending)}$$
${}$
$$L = \frac{20 \times F_s'}{w}\times \frac{I b }{Q} =\frac{20 \times 55 psi }{ 180 plf }\times 6.762 in^2 = 41.21" \text{ (due to rolling shear)}$$
${}$
$$L = 1.69 \sqrt[3]{\frac{E' I}{w}} =1.69 \sqrt[3]{\frac{1.30E+06 psi \times 0.197 in^4 }{ 180 plf }} =18.99" \text{ (for }\Delta = L/360 \text{)}$$
${}$
$$L = 3.23 \sqrt[4]{\frac{E' I}{w}} =3.23 \sqrt[4]{\frac{1.30E+06 psi \times 0.197 in^4 }{ 180 plf }} =19.82" \text{ (for }\Delta = 1/16" \text{)}$$
${}$
$$\text{After rounding the smallest spacing to the nearest 1/16" and determining the maximum allowed}$$ $$\text{spacing lower than that, for the joists, the best spacing is 16.0" = 1.333 feet.}$$
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<h2 id="Joist-Line-Load">Joist Line Load<a class="anchor-link" href="#Joist-Line-Load">¶</a></h2>
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