Cantilevers

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All cell formulas checked with XLC equations against calculation reference.

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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 Cantilever

Case 2) Point Load on Cantilever

Case 3) Applied Moment on Cantilever

Case 1) Uniformly Distributed Load on Simply Supported Beam