Beams

Units: SI(mm) & US(in).

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<table><tbody><tr><td></td>	<td>Purpose of calculation: </td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Calculate bending moments, shear, slope and deflection of a built in beam under a point load.</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Calculation Reference</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Roark's Formulas for Stress and Strain (7th Edition)</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Table 8.1 case 1d - Left end fixed, right end fixed </td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Calculation Validation</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Independent check on deflection checked at www.xcalcs.com</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>l =</td>	<td>5000</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>E =</td>	<td>210000</td>	<td>N/mm²</td>	<td>lbf/in²</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>I =</td>	<td>1900000</td>	<td>mm⁴</td>	<td>in⁴</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>W =</td>	<td>5000</td>	<td>N</td>	<td>lbf</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>a =</td>	<td>4000</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Boundary Values</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Vertical reaction at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>RA =</td>	<td>=(E14*(E11-E15)^2*(E11+2*E15))/(E11^3)</td>	<td>N</td>	<td>lbf</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Moment reaction at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>MA =</td>	<td>=(-E14*E15*(E11-E15)^2)/(E11^2)</td>	<td>Nmm</td>	<td>lbfin</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>End slope at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>θA =</td>	<td>0</td>	<td>rads</td>	<td>rads</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Deflection at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>yA =</td>	<td>0</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Vertical reaction at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>RB =</td>	<td>=(E14*E15^2*(3*E11-2*E15))/(E11^3)</td>	<td>N</td>	<td>lbf</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Moment reaction at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>MB =</td>	<td>=(-E14*E15^2*(E11-E15))/(E11^2)</td>	<td>Nmm</td>	<td>lbfin</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>End slope at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>θB =</td>	<td>0</td>	<td>rads</td>	<td>rads</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Deflection at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>yB =</td>	<td>0</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Selected maximum values of moments and deformations</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Max + M = 2Wa²(l-a)²/l³ at x=a; max possible value = Wl/8 when a= l/2</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Max -M=MA if a < l/2; max possible value = -0.1481Wl when a=1/3</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Max y=-2W(l-a)²a³/3EI(l+2a)² at x=2al/(l+2a) when a > 1/2; </td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>max possible value = -Wl3/192EI when x=a=1/2</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Calculate values for any point along longitudinal axis of the beam</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>x =</td>	<td>3000</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>x =</td>	<td>0</td>	<td>=AF55+$E11/10</td>	<td>=AG55+$E11/10</td>	<td>=AH55+$E11/10</td>	<td>=AI55+$E11/10</td>	<td>=AJ55+$E11/10</td>	<td>=AK55+$E11/10</td>	<td>=AL55+$E11/10</td>	<td>=AM55+$E11/10</td>	<td>=AN55+$E11/10</td>	<td>=AO55+$E11/10</td></tr>
				<tr><td></td>	<td></td>	<td>Heavyside step function</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Heavyside step function</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Hx =</td>	<td>=IF(E55>$E15,E55-$E15,0)</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Hx =</td>	<td>=IF(AF55>$E15,AF55-$E15,0)</td>	<td>=IF(AG55>$E15,AG55-$E15,0)</td>	<td>=IF(AH55>$E15,AH55-$E15,0)</td>	<td>=IF(AI55>$E15,AI55-$E15,0)</td>	<td>=IF(AJ55>$E15,AJ55-$E15,0)</td>	<td>=IF(AK55>$E15,AK55-$E15,0)</td>	<td>=IF(AL55>$E15,AL55-$E15,0)</td>	<td>=IF(AM55>$E15,AM55-$E15,0)</td>	<td>=IF(AN55>$E15,AN55-$E15,0)</td>	<td>=IF(AO55>$E15,AO55-$E15,0)</td>	<td>=IF(AP55>$E15,AP55-$E15,0)</td></tr>
				<tr><td></td>	<td></td>	<td>Heavyside step function raised to the power 0</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Heavyside step function raised to the power 0</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Hx0 =</td>	<td>=IF(E55>$E15,1,0)</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Hx0 =</td>	<td>=IF(AF55>$E15,1,0)</td>	<td>=IF(AG55>$E15,1,0)</td>	<td>=IF(AH55>$E15,1,0)</td>	<td>=IF(AI55>$E15,1,0)</td>	<td>=IF(AJ55>$E15,1,0)</td>	<td>=IF(AK55>$E15,1,0)</td>	<td>=IF(AL55>$E15,1,0)</td>	<td>=IF(AM55>$E15,1,0)</td>	<td>=IF(AN55>$E15,1,0)</td>	<td>=IF(AO55>$E15,1,0)</td>	<td>=IF(AP55>$E15,1,0)</td></tr>
				<tr><td></td>	<td></td>	<td>Transverse Shear</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Transverse Shear</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>V =</td>	<td>=$E21-$E14*E59</td>	<td>N</td>	<td>lbf</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>V =</td>	<td>=$E21-$E14*AF59</td>	<td>=$E21-$E14*AG59</td>	<td>=$E21-$E14*AH59</td>	<td>=$E21-$E14*AI59</td>	<td>=$E21-$E14*AJ59</td>	<td>=$E21-$E14*AK59</td>	<td>=$E21-$E14*AL59</td>	<td>=$E21-$E14*AM59</td>	<td>=$E21-$E14*AN59</td>	<td>=$E21-$E14*AO59</td>	<td>=$E21-$E14*AP59</td></tr>
				<tr><td></td>	<td></td>	<td>Bending Moment</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Bending Moment</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>M =</td>	<td>=$E23+$E21*E55-$E14*E57</td>	<td>Nmm</td>	<td>lbfin</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>M =</td>	<td>=$E23+$E21*AF55-$E14*AF57</td>	<td>=$E23+$E21*AG55-$E14*AG57</td>	<td>=$E23+$E21*AH55-$E14*AH57</td>	<td>=$E23+$E21*AI55-$E14*AI57</td>	<td>=$E23+$E21*AJ55-$E14*AJ57</td>	<td>=$E23+$E21*AK55-$E14*AK57</td>	<td>=$E23+$E21*AL55-$E14*AL57</td>	<td>=$E23+$E21*AM55-$E14*AM57</td>	<td>=$E23+$E21*AN55-$E14*AN57</td>	<td>=$E23+$E21*AO55-$E14*AO57</td>	<td>=$E23+$E21*AP55-$E14*AP57</td></tr>
				<tr><td></td>	<td></td>	<td>Slope</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Slope</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>θ =</td>	<td>=$E25+($E23*E55)/($E12*$E13)+($E21*E55^2)/(2*$E12*$E13)-($E14*E57^2)/(2*$E12*$E13)</td>	<td>rads</td>	<td>rads</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>θ =</td>	<td>=$E25+($E23*AF55)/($E12*$E13)+($E21*AF55^2)/(2*$E12*$E13)-($E14*AF57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AG55)/($E12*$E13)+($E21*AG55^2)/(2*$E12*$E13)-($E14*AG57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AH55)/($E12*$E13)+($E21*AH55^2)/(2*$E12*$E13)-($E14*AH57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AI55)/($E12*$E13)+($E21*AI55^2)/(2*$E12*$E13)-($E14*AI57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AJ55)/($E12*$E13)+($E21*AJ55^2)/(2*$E12*$E13)-($E14*AJ57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AK55)/($E12*$E13)+($E21*AK55^2)/(2*$E12*$E13)-($E14*AK57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AL55)/($E12*$E13)+($E21*AL55^2)/(2*$E12*$E13)-($E14*AL57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AM55)/($E12*$E13)+($E21*AM55^2)/(2*$E12*$E13)-($E14*AM57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AN55)/($E12*$E13)+($E21*AN55^2)/(2*$E12*$E13)-($E14*AN57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AO55)/($E12*$E13)+($E21*AO55^2)/(2*$E12*$E13)-($E14*AO57^2)/(2*$E12*$E13)</td>	<td>=$E25+($E23*AP55)/($E12*$E13)+($E21*AP55^2)/(2*$E12*$E13)-($E14*AP57^2)/(2*$E12*$E13)</td></tr>
				<tr><td></td>	<td></td>	<td>Deflection</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Deflection</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>y=</td>	<td>=$E27+$E25*E55+($E23*E55^2)/(2*$E12*$E13)+($E21*E55^3)/(6*$E12*$E13)-($E14*E57^3)/(6*$E12*$E13)</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>y=</td>	<td>=$E27+$E25*AF55+($E23*AF55^2)/(2*$E12*$E13)+($E21*AF55^3)/(6*$E12*$E13)-($E14*AF57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AG55+($E23*AG55^2)/(2*$E12*$E13)+($E21*AG55^3)/(6*$E12*$E13)-($E14*AG57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AH55+($E23*AH55^2)/(2*$E12*$E13)+($E21*AH55^3)/(6*$E12*$E13)-($E14*AH57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AI55+($E23*AI55^2)/(2*$E12*$E13)+($E21*AI55^3)/(6*$E12*$E13)-($E14*AI57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AJ55+($E23*AJ55^2)/(2*$E12*$E13)+($E21*AJ55^3)/(6*$E12*$E13)-($E14*AJ57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AK55+($E23*AK55^2)/(2*$E12*$E13)+($E21*AK55^3)/(6*$E12*$E13)-($E14*AK57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AL55+($E23*AL55^2)/(2*$E12*$E13)+($E21*AL55^3)/(6*$E12*$E13)-($E14*AL57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AM55+($E23*AM55^2)/(2*$E12*$E13)+($E21*AM55^3)/(6*$E12*$E13)-($E14*AM57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AN55+($E23*AN55^2)/(2*$E12*$E13)+($E21*AN55^3)/(6*$E12*$E13)-($E14*AN57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AO55+($E23*AO55^2)/(2*$E12*$E13)+($E21*AO55^3)/(6*$E12*$E13)-($E14*AO57^3)/(6*$E12*$E13)</td>	<td>=$E27+$E25*AP55+($E23*AP55^2)/(2*$E12*$E13)+($E21*AP55^3)/(6*$E12*$E13)-($E14*AP57^3)/(6*$E12*$E13)</td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Plot Deflection for 10 Points along the Length of the Beam</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr></tbody></table>

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<table><tbody><tr><td></td>	<td>Purpose of calculation: </td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Calculate bending moments, shear, slope and deflection of a built in beam under a point load.</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Calculation Reference</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Roark's Formulas for Stress and Strain (7th Edition)</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Table 8.1 case 1d - Left end fixed, right end fixed </td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Calculation Validation</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Independent check on deflection checked at www.xcalcs.com</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>l =</td>	<td>5000</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>E =</td>	<td>210000</td>	<td>N/mm²</td>	<td>lbf/in²</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>I =</td>	<td>1900000</td>	<td>mm⁴</td>	<td>in⁴</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>W =</td>	<td>5000</td>	<td>N</td>	<td>lbf</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>a =</td>	<td>4000</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Boundary Values</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Vertical reaction at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>RA =</td>	<td>=OVD(E14*(E11-E15)^2*(E11+2*E15))/UND(E11^3)</td>	<td>N</td>	<td>lbf</td>	<td>=EQS(E21,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$25_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Moment reaction at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>MA =</td>	<td>=OVD(-E14*E15*(E11-E15)^2)/UND(E11^2)</td>	<td>Nmm</td>	<td>lbfin</td>	<td>=EQS(E23,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$27_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>End slope at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>θA =</td>	<td>0</td>	<td>rads</td>	<td>rads</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Deflection at left end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>yA =</td>	<td>0</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Vertical reaction at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>RB =</td>	<td>=OVD(E14*E15^2*(3*E11-2*E15))/UND(E11^3)</td>	<td>N</td>	<td>lbf</td>	<td>=EQS(E30,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$34_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Moment reaction at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>MB =</td>	<td>=OVD(-E14*E15^2*(E11-E15))/UND(E11^2)</td>	<td>Nmm</td>	<td>lbfin</td>	<td>=EQS(E32,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$36_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>End slope at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>θB =</td>	<td>0</td>	<td>rads</td>	<td>rads</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Deflection at right end</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>yB =</td>	<td>0</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td>Selected maximum values of moments and deformations</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Max + M = 2Wa²(l-a)²/l³ at x=a; max possible value = Wl/8 when a= l/2</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Max -M=MA if a < l/2; max possible value = -0.1481Wl when a=1/3</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Max y=-2W(l-a)²a³/3EI(l+2a)² at x=2al/(l+2a) when a > 1/2; </td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>max possible value = -Wl3/192EI when x=a=1/2</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Calculate values for any point along longitudinal axis of the beam</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>x =</td>	<td>3000</td>	<td>mm</td>	<td>in</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>x =</td>	<td>0</td>	<td>=AF55+$E11/10</td>	<td>=AG55+$E11/10</td>	<td>=AH55+$E11/10</td>	<td>=AI55+$E11/10</td>	<td>=AJ55+$E11/10</td>	<td>=AK55+$E11/10</td>	<td>=AL55+$E11/10</td>	<td>=AM55+$E11/10</td>	<td>=AN55+$E11/10</td>	<td>=AO55+$E11/10</td></tr>
				<tr><td></td>	<td></td>	<td>Heavyside step function</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Heavyside step function</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Hx =</td>	<td>=IF(E55>$E15,E55-$E15,0)</td>	<td></td>	<td></td>	<td>=EQS(E57,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$61_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Hx =</td>	<td>=IF(AF55>$E15,AF55-$E15,0)</td>	<td>=IF(AG55>$E15,AG55-$E15,0)</td>	<td>=IF(AH55>$E15,AH55-$E15,0)</td>	<td>=IF(AI55>$E15,AI55-$E15,0)</td>	<td>=IF(AJ55>$E15,AJ55-$E15,0)</td>	<td>=IF(AK55>$E15,AK55-$E15,0)</td>	<td>=IF(AL55>$E15,AL55-$E15,0)</td>	<td>=IF(AM55>$E15,AM55-$E15,0)</td>	<td>=IF(AN55>$E15,AN55-$E15,0)</td>	<td>=IF(AO55>$E15,AO55-$E15,0)</td>	<td>=IF(AP55>$E15,AP55-$E15,0)</td></tr>
				<tr><td></td>	<td></td>	<td>Heavyside step function raised to the power 0</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Heavyside step function raised to the power 0</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>Hx0 =</td>	<td>=IF(E55>$E15,1,0)</td>	<td></td>	<td></td>	<td>=EQS(E59,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$63_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Hx0 =</td>	<td>=IF(AF55>$E15,1,0)</td>	<td>=IF(AG55>$E15,1,0)</td>	<td>=IF(AH55>$E15,1,0)</td>	<td>=IF(AI55>$E15,1,0)</td>	<td>=IF(AJ55>$E15,1,0)</td>	<td>=IF(AK55>$E15,1,0)</td>	<td>=IF(AL55>$E15,1,0)</td>	<td>=IF(AM55>$E15,1,0)</td>	<td>=IF(AN55>$E15,1,0)</td>	<td>=IF(AO55>$E15,1,0)</td>	<td>=IF(AP55>$E15,1,0)</td></tr>
				<tr><td></td>	<td></td>	<td>Transverse Shear</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Transverse Shear</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>V =</td>	<td>=$E21-$E14*E59</td>	<td>N</td>	<td>lbf</td>	<td>=EQS(E61,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$65_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>V =</td>	<td>=$E21-$E14*AF59</td>	<td>=$E21-$E14*AG59</td>	<td>=$E21-$E14*AH59</td>	<td>=$E21-$E14*AI59</td>	<td>=$E21-$E14*AJ59</td>	<td>=$E21-$E14*AK59</td>	<td>=$E21-$E14*AL59</td>	<td>=$E21-$E14*AM59</td>	<td>=$E21-$E14*AN59</td>	<td>=$E21-$E14*AO59</td>	<td>=$E21-$E14*AP59</td></tr>
				<tr><td></td>	<td></td>	<td>Bending Moment</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Bending Moment</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>M =</td>	<td>=$E23+$E21*E55-$E14*E57</td>	<td>Nmm</td>	<td>lbfin</td>	<td>=EQS(E63,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$67_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>M =</td>	<td>=$E23+$E21*AF55-$E14*AF57</td>	<td>=$E23+$E21*AG55-$E14*AG57</td>	<td>=$E23+$E21*AH55-$E14*AH57</td>	<td>=$E23+$E21*AI55-$E14*AI57</td>	<td>=$E23+$E21*AJ55-$E14*AJ57</td>	<td>=$E23+$E21*AK55-$E14*AK57</td>	<td>=$E23+$E21*AL55-$E14*AL57</td>	<td>=$E23+$E21*AM55-$E14*AM57</td>	<td>=$E23+$E21*AN55-$E14*AN57</td>	<td>=$E23+$E21*AO55-$E14*AO57</td>	<td>=$E23+$E21*AP55-$E14*AP57</td></tr>
				<tr><td></td>	<td></td>	<td>Slope</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Slope</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>θ =</td>	<td>=$E25+OVD($E23*E55)/UND($E12*$E13)+OVD($E21*E55^2)/UND(2*$E12*$E13)-OVD($E14*E57^2)/UND(2*$E12*$E13)</td>	<td>rads</td>	<td>rads</td>	<td>=EQS(E65,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$69_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>θ =</td>	<td>=$E25+OVD($E23*AF55)/UND($E12*$E13)+OVD($E21*AF55^2)/UND(2*$E12*$E13)-OVD($E14*AF57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AG55)/UND($E12*$E13)+OVD($E21*AG55^2)/UND(2*$E12*$E13)-OVD($E14*AG57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AH55)/UND($E12*$E13)+OVD($E21*AH55^2)/UND(2*$E12*$E13)-OVD($E14*AH57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AI55)/UND($E12*$E13)+OVD($E21*AI55^2)/UND(2*$E12*$E13)-OVD($E14*AI57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AJ55)/UND($E12*$E13)+OVD($E21*AJ55^2)/UND(2*$E12*$E13)-OVD($E14*AJ57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AK55)/UND($E12*$E13)+OVD($E21*AK55^2)/UND(2*$E12*$E13)-OVD($E14*AK57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AL55)/UND($E12*$E13)+OVD($E21*AL55^2)/UND(2*$E12*$E13)-OVD($E14*AL57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AM55)/UND($E12*$E13)+OVD($E21*AM55^2)/UND(2*$E12*$E13)-OVD($E14*AM57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AN55)/UND($E12*$E13)+OVD($E21*AN55^2)/UND(2*$E12*$E13)-OVD($E14*AN57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AO55)/UND($E12*$E13)+OVD($E21*AO55^2)/UND(2*$E12*$E13)-OVD($E14*AO57^2)/UND(2*$E12*$E13)</td>	<td>=$E25+OVD($E23*AP55)/UND($E12*$E13)+OVD($E21*AP55^2)/UND(2*$E12*$E13)-OVD($E14*AP57^2)/UND(2*$E12*$E13)</td></tr>
				<tr><td></td>	<td></td>	<td>Deflection</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>Deflection</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td>y=</td>	<td>=$E27+$E25*E55+OVD($E23*E55^2)/UND(2*$E12*$E13)+OVD($E21*E55^3)/UND(6*$E12*$E13)-OVD($E14*E57^3)/UND(6*$E12*$E13)</td>	<td>mm</td>	<td>in</td>	<td>=EQS(E67,"Units= ; EqnPrefix=Eqn.; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$71_0")</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td>y=</td>	<td>=$E27+$E25*AF55+OVD($E23*AF55^2)/UND(2*$E12*$E13)+OVD($E21*AF55^3)/UND(6*$E12*$E13)-OVD($E14*AF57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AG55+OVD($E23*AG55^2)/UND(2*$E12*$E13)+OVD($E21*AG55^3)/UND(6*$E12*$E13)-OVD($E14*AG57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AH55+OVD($E23*AH55^2)/UND(2*$E12*$E13)+OVD($E21*AH55^3)/UND(6*$E12*$E13)-OVD($E14*AH57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AI55+OVD($E23*AI55^2)/UND(2*$E12*$E13)+OVD($E21*AI55^3)/UND(6*$E12*$E13)-OVD($E14*AI57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AJ55+OVD($E23*AJ55^2)/UND(2*$E12*$E13)+OVD($E21*AJ55^3)/UND(6*$E12*$E13)-OVD($E14*AJ57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AK55+OVD($E23*AK55^2)/UND(2*$E12*$E13)+OVD($E21*AK55^3)/UND(6*$E12*$E13)-OVD($E14*AK57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AL55+OVD($E23*AL55^2)/UND(2*$E12*$E13)+OVD($E21*AL55^3)/UND(6*$E12*$E13)-OVD($E14*AL57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AM55+OVD($E23*AM55^2)/UND(2*$E12*$E13)+OVD($E21*AM55^3)/UND(6*$E12*$E13)-OVD($E14*AM57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AN55+OVD($E23*AN55^2)/UND(2*$E12*$E13)+OVD($E21*AN55^3)/UND(6*$E12*$E13)-OVD($E14*AN57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AO55+OVD($E23*AO55^2)/UND(2*$E12*$E13)+OVD($E21*AO55^3)/UND(6*$E12*$E13)-OVD($E14*AO57^3)/UND(6*$E12*$E13)</td>	<td>=$E27+$E25*AP55+OVD($E23*AP55^2)/UND(2*$E12*$E13)+OVD($E21*AP55^3)/UND(6*$E12*$E13)-OVD($E14*AP57^3)/UND(6*$E12*$E13)</td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td>Plot Deflection for 10 Points along the Length of the Beam</td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr>
				<tr><td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td>	<td></td></tr></tbody></table>

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Nomenclature
Young's Modulus = E
Beam 2nd moment of area = I
Applied distributed load = W
Applied point load = P
Moment = M
Reaction force = R
Deflection = δ

Case 1) Uniformly Distributed Load on Simply Supported Beam
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. <table><tbody><tr><td></td> <td>W =</td> <td>500</td> <td>N</td> <td>lbf</td></tr> <tr><td></td> <td>L =</td> <td>3000</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>a =</td> <td>2000</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td></tr> <tr><td></td> <td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td></tr> <tr><td></td> <td>b =</td> <td>500</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>c =</td> <td>=C2-C3-C6</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>RA =</td> <td>=(C1)/(C2)((C6)/(2)+C7)</td> <td>N</td> <td>lbf</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>RB =</td> <td>=(C1)/(C2)((C6)/(2)+C3)</td> <td>N</td> <td>lbf</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>x1 =</td> <td>=C3+(C8C6)/(C1)</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>Mmax =</td> <td>=(C1)/(C6)((C12-C3^2)/(2))</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td>When a = c</td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>δB =</td> <td>=(C1)/(364C4C5)(8C2^3-4C2C6^2+C6^3)</td> <td>mm</td> <td>in</td></tr></tbody></table> XLC Enhanced Excel: Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. <table><tbody><tr><td></td> <td>W =</td> <td>500</td> <td>N</td> <td>lbf</td> <td></td></tr> <tr><td></td> <td>L =</td> <td>3000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>a =</td> <td>2000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td> <td></td></tr> <tr><td></td> <td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td> <td></td></tr> <tr><td></td> <td>b =</td> <td>500</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>c =</td> <td>=C2-C3-C6</td> <td>mm</td> <td>in</td> <td>=EQS(C7,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$40_0")</td></tr> <tr><td></td> <td>RA =</td> <td>=OVD(C1)/UND(C2)(OVD(C6)/UND(2)+C7)</td> <td>N</td> <td>lbf</td> <td>=EQS(C8,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$41_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>RB =</td> <td>=OVD(C1)/UND(C2)(OVD(C6)/UND(2)+C3)</td> <td>N</td> <td>lbf</td> <td>=EQS(C10,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$43_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>x1 =</td> <td>=C3+OVD(C8C6)/UND(C1)</td> <td>mm</td> <td>in</td> <td>=EQS(C12,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$45_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>Mmax =</td> <td>=OVD(C1)/UND(C6)(OVD(C12-C3^2)/UND(2))</td> <td>Nmm</td> <td>lbfin</td> <td>=EQS(C14,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$47_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td>When a = c</td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>δB =</td> <td>=OVD(C1)/UND(364C4C5)(8C2^3-4C2C6^2+C6^3)</td> <td>mm</td> <td>in</td> <td>=EQS(C17,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$50_0")</td></tr></tbody></table> Note: Both include SI(mm) & US(in) units (delete as appropriate).
Case 2) Point Load on Simply Supported Beam
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. <table><tbody><tr><td></td> <td>P =</td> <td>500</td> <td>N</td> <td>lbf</td></tr> <tr><td></td> <td>L =</td> <td>3000</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>a =</td> <td>2000</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td></tr> <tr><td></td> <td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td></tr> <tr><td></td> <td>b =</td> <td>=C2-C3</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>RA =</td> <td>=C1C6/C2</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td></td> <td>RB =</td> <td>=C1C3/C2</td> <td>N</td> <td>lbf</td></tr> <tr><td>when a = c</td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>δC =</td> <td>=(C1C2^3)/(48C4C5)</td> <td>mm</td> <td>in</td></tr></tbody></table> XLC Enhanced Excel:* Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. <table><tbody><tr><td></td> <td>P =</td> <td>500</td> <td>N</td> <td>lbf</td> <td></td></tr> <tr><td></td> <td>L =</td> <td>3000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>a =</td> <td>2000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td> <td></td></tr> <tr><td></td> <td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td> <td></td></tr> <tr><td></td> <td>b =</td> <td>=C2-C3</td> <td>mm</td> <td>in</td> <td>=EQS(C6,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$63_0")</td></tr> <tr><td></td> <td>RA =</td> <td>=C1C6/C2</td> <td>Nmm</td> <td>lbfin</td> <td>=EQS(C7,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$64_0")</td></tr> <tr><td></td> <td>RB =</td> <td>=C1C3/C2</td> <td>N</td> <td>lbf</td> <td>=EQS(C8,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$65_0")</td></tr> <tr><td>when a = c</td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>δC =</td> <td>=OVD(C1C2^3)/UND(48C4*C5)</td> <td>mm</td> <td>in</td> <td>=EQS(C10,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$67_0")</td></tr></tbody></table> Note: Both include SI(mm) & US(in) units (delete as appropriate).
Case 3) Applied Moment on Simply Supported Beam
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. <table><tbody><tr><td></td> <td>M =</td> <td>500000</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td></td> <td>L =</td> <td>3000</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>a =</td> <td>2000</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td></tr> <tr><td></td> <td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td></tr> <tr><td></td> <td>b =</td> <td>=C2-C3</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td>RA =</td> <td>=-C1/C2</td> <td>N</td> <td>lbf</td></tr> <tr><td></td> <td>RB =</td> <td>=C1/C2</td> <td>N</td> <td>lbf</td></tr> <tr><td></td> <td>MA =</td> <td>=C1</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td>When a > b</td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>δC =</td> <td>=-(C1C3C6)/(3C4C5)((C3)/(C2)-(C6)/(C2))</td> <td>mm</td> <td>in</td></tr></tbody></table> XLC Enhanced Excel:* Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. <table><tbody><tr><td></td> <td>M =</td> <td>500000</td> <td>Nmm</td> <td>lbfin</td> <td></td></tr> <tr><td></td> <td>L =</td> <td>3000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>a =</td> <td>2000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td></td> <td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td> <td></td></tr> <tr><td></td> <td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td> <td></td></tr> <tr><td></td> <td>b =</td> <td>=C2-C3</td> <td>mm</td> <td>in</td> <td>=EQS(C6,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$79_0")</td></tr> <tr><td></td> <td>RA =</td> <td>=-C1/C2</td> <td>N</td> <td>lbf</td> <td>=EQS(C7,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$80_0")</td></tr> <tr><td></td> <td>RB =</td> <td>=C1/C2</td> <td>N</td> <td>lbf</td> <td>=EQS(C8,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$81_0")</td></tr> <tr><td></td> <td>MA =</td> <td>=C1</td> <td>Nmm</td> <td>lbfin</td> <td>=EQS(C9,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$82_0")</td></tr> <tr><td>When a > b</td> <td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td></td> <td>δC =</td> <td>=-OVD(C1C3C6)/UND(3C4C5)*(OVD(C3)/UND(C2)-OVD(C6)/UND(C2))</td> <td>mm</td> <td>in</td> <td>=EQS(C11,"Units= ; EqnPrefix=Eqn. ; EqnNo= 0; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$84_0")</td></tr></tbody></table> Note: Both include SI(mm) & US(in) units (delete as appropriate).

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Nomenclature
Young's Modulus = E
Beam 2nd moment of area = I
Applied distributed load = W
Applied point load = P
Moment = M
Reaction force = R
Deflection = δ

Case 1) Uniformly Distributed Load on Cantilever
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. <table><tbody><tr><td>W =</td> <td>500</td> <td>N</td> <td>lbf</td></tr> <tr><td>L =</td> <td>3000</td> <td>mm</td> <td>in</td></tr> <tr><td>a =</td> <td>2000</td> <td>mm</td> <td>in</td></tr> <tr><td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td></tr> <tr><td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td></tr> <tr><td>b =</td> <td>500</td> <td>mm</td> <td>in</td></tr> <tr><td>c =</td> <td>=B2-B3-B6</td> <td>mm</td> <td>in</td></tr> <tr><td>MA =</td> <td>=B1(B3+(B6)/(2))</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td></td> <td></td> <td></td> <td></td></tr> <tr><td>RA =</td> <td>=B1</td> <td>N</td> <td>lbf</td></tr> <tr><td>δB =</td> <td>=(B1)/(24B4B5)(8B3^3+18B3^2B6+12B3B6^2+3B6^3+12B3^2B7+12B3B6B7+4B6^2B7)</td> <td>mm</td> <td>in</td></tr></tbody></table> XLC Enhanced Excel:* Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. <table><tbody><tr><td>W =</td> <td>500</td> <td>N</td> <td>lbf</td> <td></td></tr> <tr><td>L =</td> <td>3000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>a =</td> <td>2000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td> <td></td></tr> <tr><td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td> <td></td></tr> <tr><td>b =</td> <td>500</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>c =</td> <td>=B2-B3-B6</td> <td>mm</td> <td>in</td> <td>=EQS(B7,"Units= ; EqnPrefix=Eqn. ; EqnNo= 9; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$69_0")</td></tr> <tr><td>MA =</td> <td>=B1(B3+OVD(B6)/UND(2))</td> <td>Nmm</td> <td>lbfin</td> <td>=EQS(B8,"Units= ; EqnPrefix=Eqn. ; EqnNo= 10; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$70_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td>RA =</td> <td>=B1</td> <td>N</td> <td>lbf</td> <td>=EQS(B10,"Units= ; EqnPrefix=Eqn. ; EqnNo= 11; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$72_0")</td></tr> <tr><td>δB =</td> <td>=OVD(B1)/UND(24B4B5)(8B3^3+18B3^2B6+12B3B6^2+3B6^3+12B3^2B7+12B3B6B7+4B6^2*B7)</td> <td>mm</td> <td>in</td> <td>=EQS(B11,"Units= ; EqnPrefix=Eqn. ; EqnNo= 12; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$73_0")</td></tr></tbody></table> Note: Both include SI(mm) & US(in) units (delete as appropriate).
Case 2) Point Load on Cantilever
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. <table><tbody><tr><td>P =</td> <td>500</td> <td>N</td> <td>lbf</td></tr> <tr><td>L =</td> <td>3000</td> <td>mm</td> <td>in</td></tr> <tr><td>a =</td> <td>2000</td> <td>mm</td> <td>in</td></tr> <tr><td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td></tr> <tr><td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td></tr> <tr><td>b =</td> <td>=B2-B3</td> <td>mm</td> <td>in</td></tr> <tr><td>MA =</td> <td>=B1B3</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td>RA =</td> <td>=B1</td> <td>N</td> <td>lbf</td></tr> <tr><td>δC =</td> <td>=(B1B3^3)/(3B4B5)</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td></td> <td></td> <td></td></tr> <tr><td>δB =</td> <td>=(B1B3^3)/(3B4B5)(1+(3B6)/(2B3))</td> <td>mm</td> <td>in</td></tr></tbody></table> XLC Enhanced Excel: Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. <table><tbody><tr><td>P =</td> <td>500</td> <td>N</td> <td>lbf</td> <td></td></tr> <tr><td>L =</td> <td>3000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>a =</td> <td>2000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td> <td></td></tr> <tr><td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td> <td></td></tr> <tr><td>b =</td> <td>=B2-B3</td> <td>mm</td> <td>in</td> <td>=EQS(B6,"Units= ; EqnPrefix=Eqn. ; EqnNo= 13; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$86_0")</td></tr> <tr><td>MA =</td> <td>=B1B3</td> <td>Nmm</td> <td>lbfin</td> <td>=EQS(B7,"Units= ; EqnPrefix=Eqn. ; EqnNo= 14; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$87_0")</td></tr> <tr><td>RA =</td> <td>=B1</td> <td>N</td> <td>lbf</td> <td>=EQS(B8,"Units= ; EqnPrefix=Eqn. ; EqnNo= 15; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$88_0")</td></tr> <tr><td>δC =</td> <td>=OVD(B1B3^3)/UND(3B4B5)</td> <td>mm</td> <td>in</td> <td>=EQS(B9,"Units= ; EqnPrefix=Eqn. ; EqnNo= 16; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$89_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td>δB =</td> <td>=OVD(B1B3^3)/UND(3B4B5)(1+OVD(3B6)/UND(2B3))</td> <td>mm</td> <td>in</td> <td>=EQS(B11,"Units= ; EqnPrefix=Eqn. ; EqnNo= 17; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$91_0")</td></tr></tbody></table> Note: Both include SI(mm) & US(in) units (delete as appropriate).
Case 3) Applied Moment on Cantilever
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. <table><tbody><tr><td>M =</td> <td>500000</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td>L =</td> <td>3000</td> <td>mm</td> <td>in</td></tr> <tr><td>a =</td> <td>2000</td> <td>mm</td> <td>in</td></tr> <tr><td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td></tr> <tr><td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td></tr> <tr><td>b =</td> <td>=B2-B3</td> <td>mm</td> <td>in</td></tr> <tr><td>MA =</td> <td>=B1</td> <td>Nmm</td> <td>lbfin</td></tr> <tr><td>RA =</td> <td>0</td> <td>N</td> <td>lbf</td></tr> <tr><td>δC =</td> <td>=(B1B3^2)/(2B4B5)</td> <td>mm</td> <td>in</td></tr> <tr><td></td> <td></td> <td></td> <td></td></tr> <tr><td>δB =</td> <td>=(B1B3^2)/(2B4B5)(1+(2B6)/(B3))</td> <td>mm</td> <td>in</td></tr></tbody></table> XLC Enhanced Excel: Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. <table><tbody><tr><td>M =</td> <td>500000</td> <td>Nmm</td> <td>lbfin</td> <td></td></tr> <tr><td>L =</td> <td>3000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>a =</td> <td>2000</td> <td>mm</td> <td>in</td> <td></td></tr> <tr><td>E =</td> <td>210000</td> <td>MPa</td> <td>psi</td> <td></td></tr> <tr><td>I =</td> <td>1000000</td> <td>mm⁴</td> <td>in⁴</td> <td></td></tr> <tr><td>b =</td> <td>=B2-B3</td> <td>mm</td> <td>in</td> <td>=EQS(B6,"Units= ; EqnPrefix=Eqn. ; EqnNo= 18; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$104_0")</td></tr> <tr><td>MA =</td> <td>=B1</td> <td>Nmm</td> <td>lbfin</td> <td>=EQS(B7,"Units= ; EqnPrefix=Eqn. ; EqnNo= 19; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$105_0")</td></tr> <tr><td>RA =</td> <td>0</td> <td>N</td> <td>lbf</td> <td></td></tr> <tr><td>δC =</td> <td>=OVD(B1B3^2)/UND(2B4B5)</td> <td>mm</td> <td>in</td> <td>=EQS(B9,"Units= ; EqnPrefix=Eqn. ; EqnNo= 20; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$107_0")</td></tr> <tr><td></td> <td></td> <td></td> <td></td> <td></td></tr> <tr><td>δB =</td> <td>=OVD(B1B3^2)/UND(2B4B5)(1+OVD(2B6)/UND(B3))</td> <td>mm</td> <td>in</td> <td>=EQS(B11,"Units= ; EqnPrefix=Eqn. ; EqnNo= 21; Multiplication= 0; ShowWorking= 0; EqnStyle= 0; Eqp$H$109_0")</td></tr></tbody></table> Note: Both include SI(mm) & US(in) units (delete as appropriate).
Case 1) Uniformly Distributed Load on Simply Supported Beam
	Native Excel: Click in the text area below and copy. Paste into cell A1 of a worksheet. XL_code XLC Enhanced Excel: Use XLC’s ‘Web Paste’ button to paste at any position in worksheet. Includes mathematical formatting and XLC equations. XLC_code Note: Both include SI(mm) & US(in) units (delete as appropriate).

Case 1) Uniformly Distributed Load on Simply Supported Beam

Case 2) Point Load on Simply Supported Beam

Case 3) Applied Moment on Simply Supported Beam

Case 1) Uniformly Distributed Load on Cantilever

Case 2) Point Load on Cantilever

Case 3) Applied Moment on Cantilever

Case 1) Uniformly Distributed Load on Simply Supported Beam

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Case 1) Uniformly Distributed Load on Simply Supported Beam

Case 2) Point Load on Simply Supported Beam

Case 3) Applied Moment on Simply Supported Beam

Case 1) Uniformly Distributed Load on Cantilever

Case 2) Point Load on Cantilever

Case 3) Applied Moment on Cantilever

Case 1) Uniformly Distributed Load on Simply Supported Beam

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