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<title>Indian Harbor Villas Unit 23 Ren</title>
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<p align="center"><a name="3rd_Floor_Beam_Load_Calculations">
<font size="5"><b><span style="font-family: Calibri">3rd Floor</span></b></font><span style="font-family: Calibri"><font size="5"><b>
Beam Load Calculations</b></font></span></a></p> </td>
</tr>
<tr>
<td bgcolor="#0000FF" height="36">
<span style="font-family: Calibri">
<a href="http://www.mesi.net/IHV23/index.html" style="text-decoration: none">
<font color="#FFFFFF">IHV23 Renovation</font></a><font color="#FFFFFF">
> Beam Analysis</font></span></td>
</tr>
<tr>
<td><u><b>Existing Third Floor Plan</b></u><p>
<img border="0" src="index.7.gif" width="994" height="621"><p>
</td>
</tr>
<tr>
<td height="198"><b>Proposed Plan with Bathroom and Bearing Wall
Modification</b><p>
<img border="0" src="index.5.gif" width="990" height="569"><p>
</td>
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<p class="MsoNormal" align="center"><b>Side View of House, and Point
Load Diagram</b></p>
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<p align="center">
<span style="font-family: Calibri,sans-serif; font-size: 11pt; font-weight: 700">
C-Channel Beam with Wood 2x4 Bolted Through Beam Web at Center Line</span></td>
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<td height="673">
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt" align="center">
<b><span style="font-family: Calibri; text-decoration: underline">
<font size="5">Analysis</font></span></b></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black"><b>
Situation</b>: </span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Existing structure</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
has a shed roof with a </span>
<span style="font-size: 12.0pt; font-family: Arial; color: black">
bearing wall located at mid point of the rafter span. We desire to
create an opening in the bearing wall and require a beam to span the
opening. The beam will be simply supported on each end and the roof load
is uniformly distributed. The building length</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
is 31 feet and the beam is located at the mid-point, or 15.5 feet.
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt"> </p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
<b>Given</b>:</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Snow Load W</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">S</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 20 psf (per IBC 2003 for Delaware)</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Roof Load W</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 15 psf (estimated for wood rafters, drywall ceiling, plywood sheathing
and asphalt shingles)</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Allowable deflection ratio: 1/240 for wood roof</span></p>
<p style="line-height: normal; text-indent: 0in; word-break: normal; punctuation-wrap: hanging; margin: 0pt 0in">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Allowable live load deflection ratio: 1/360 </span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Tributary length L is 31/2=15.5</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
feet</span><span style="font-size: 12.0pt; font-family: Arial; color: black">
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Required span for beam</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
segment </span>
<span style="font-size: 12.0pt; font-family: Arial; color: black">is 5
feet 6</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
inches</span><span style="font-size: 12.0pt; font-family: Arial; color: black">
or 66</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
inches</span><span style="font-size: 12.0pt; font-family: Arial; color: black">
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt"> </p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black"><b>
Solution</b>:</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Consider an A-36 C3" x 4.1# steel channel beam: d = 3 inches, </span>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
t</span><font face="Arial"><span style="font-size: 12.0pt; color: black; vertical-align: sub">W</span></font><font face="Arial"><span style="font-size: 12.0pt; color: black; vertical-align: sub">
</span>
</font>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 0.17 inch, I</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">xx</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 1.66 inch</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">4</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">,
Z</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">xx</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 1.10 inch</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">3</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">,
yield stress = 36,000 psi</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Modulus of elasticity for steel, E = 2.9x10</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">7</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
lb-inch</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt"> </p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Total</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
weight: W = 5.5' x 15.5' x (20 psf + 15 psf) = 2984 lbs</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Uniform weight on beam: p = W/L </span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 2984 lb/ 66 inches</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 45 lbs/inch</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Max moment: M = pL</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">2</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">/8
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= (45 lbs/inch) x (66 inches)</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">2</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
/ 8 </span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
=
24,616 lb-inch</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Max bending stress: f</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">b</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= pL/8Z</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">xx</span><span style="font-size: 12.0pt; font-family: Arial; color: black">
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
= (d/2)(M/</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">I</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">xx</span><span style="font-size: 12.0pt; font-family: Arial; color: black">)
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
= (3 inches/2)(24,616 lb-inch/1.66
</span>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
inch</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">4</span><span style="font-size: 12.0pt; font-family: Arial; color: black">)
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
= 22,243</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
psi</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Allowable bending stress: F</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">b</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 0.66 x yield stress </span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 0.66 x 36,000 </span>
</p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 24,000 psi</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<b>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
-> bending stress f</span><font face="Arial"><span style="font-size: 12.0pt; color: black; vertical-align: sub">b</span></font><font face="Arial"><span style="font-size: 12.0pt; color: black; vertical-align: sub">
</span>
</font>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 22,243 psi < allowable bending stress F</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">b</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 24,000 psi</span></b></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt"> </p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Max deflection
D
= (5 x p x L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">4)</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">/(384
x E x I</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">xx</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">)
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 5(45 lbs/inch)(66)</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">4</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
/ 384(2.9x10</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: super">7</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">)(1.66)
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
=
0.23 inches</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Deflection ratio:
D/L
= 0.23 inch / 66 inches</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 1/284</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<b>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
-> Deflection ratio D/L = 1/284 < allowable deflection ratio 1/240 </span>
</b></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt"> </p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Live load deflection
D</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
=
D
x W</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
/ (W</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
+ W</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">S</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
)</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
=
0.23 inches x 20/(20+15)</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 0.15 inches</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Live load deflection ratio:
D</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">/L
= 0.15 inches / 66 inches</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 1/498 </span>
</p>
<p style="line-height: normal; text-indent: 0in; word-break: normal; punctuation-wrap: hanging; margin: 0pt 0in">
<b>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
-> Live load deflection ratio
D</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">L</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">/L
= 1/498 < allowable live load deflection ratio 1/360</span></b></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt"> </p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
Shear force: V = W x L/2</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black">
=</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
(45 lbs/inch)(66 inches)/2</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
=
1485 lb</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Shear stress: f</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">V</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= V / (t</span><font face="Arial"><span style="font-size: 12.0pt; color: black; vertical-align: sub">W</span></font><font face="Arial"><span style="font-size: 12.0pt; color: black; vertical-align: sub">
</span>
</font>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
x d)</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= (1485 lbs) / (0.285 inch x 3 inches)</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
=
2925 psi </span></p>
<p style="line-height: normal; text-indent: 0in; word-break: normal; punctuation-wrap: hanging; margin: 0pt 0in">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
Allowable shear stress: F</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: sub">V</span><span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 0.4 x yield stress</span><span style="font-size: 12.0pt; font-family: Arial; color: black">
</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 0.4 x 36,000 psi</span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
= 14,400 psi </span></p>
<p style="text-indent: 0in; margin-left: 0in; margin-top: 0pt; margin-bottom: 0pt">
<b>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
-> shear stress = </span></b>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline; font-weight:700">
2925 </span><b>
<span style="font-size: 12.0pt; font-family: Arial; color: black; vertical-align: baseline">
psi < allowable shear stress = 14,400 psi</span><span style="font-size: 12.0pt; font-family: Arial; color: black">
</span></b></p>
</td>
</tr>
</table>
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